Japanese brand, master-piece is known for producing quality men’s bags with a high level of functionality since 1994. Every piece is constructed with the brand’s original materials, which are developed in their Osaka-based in-house factory, where they also craft their bags. For Fall/Winter 2022, master-piece presented the “sa-hou” bag model — merging the needs of tea enthusiasts with its line of functional bags. The concept focused on uniting the “tea-life” and “bag life” philosophies, when wearers can brew, carry and enjoy their favorite teas in style, wherever, whenever. The “sa-hou” bag comes with a draw-string fastening and is available in two sizes: nylon and waterproof leather. Priced at ¥17,050 JPY (approximately $115 USD), the nylon version comes in black, beige, or navy, while the leather version is retailed for ¥26,400 JPY (approximately $178 USD) and is only available in black or beige. Each bag comes with a special edition KINTO x master-piece transparent water bottle, available in black, brown, or clear colorway. The bottles are also sold separately in two capacities: ¥2,860 JPY (approximately $20 USD) for 300ml and ¥3,300 JPY (approximately $23 USD) for 500ml. To celebrate the launch, a special event will be held at master-piece’s Kyoto store and cafe on November 5. A selection of matcha and gyokuro tea will be available at the event, as well as a special menu featuring tea leaves from Ippodo Tea. All “sa-hou” bags purchased on the day will also come with Ippodo sencha tea bags. master-piece Kyoto / master-piece coffee Kyoto 26 Nakanocho Higashiiru Tominokoji Sanjo-dori Nakagyo Ward Kyoto 604-8083 Japan In other fashion news, check out ZEGNA’s new “Outdoor” collection for Fall/Winter 2022.
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Acclaimed indie-pop duo Tennis has shared “One Night With The Valet,” available now at all DSPs and streaming services. Produced and recorded by the husband and wife duo of Patrick Riley and Alaina Moore in their Denver, CO home studio, “One Night With The Valet” marks the first single from Tennis’s highly anticipated sixth studio album, POLLEN, arriving via their own Mutually Detrimental label on Friday, February 10, 2023. Pre-orders are available now HERE. “We wanted to write a big album,” says Tennis’ Alaina Moore. “something suited for radio, but our songs don’t follow conventional pop structures. Instead of choruses with universal themes, I write with a specificity that is new to me, narrowing in on the smallest details of our lives. The more we try to broaden our scope, the more we turn inward. “To keep ourselves from falling into old habits, we used instruments and gear that are new to us. We work alone and Patrick engineers. The sounds he creates are as foundational as any part he writes. We resist the urge to over edit or do too many takes. Unlike previous albums which have been more wall of sound, we make a point not to overpower my voice with a dense mix. “We named the album POLLEN. It is about small things with big consequences: a particle, a moment, a choice. It is me in a fragile state; sometimes inhabited freely, sometimes reacted against. It is striving to remain in a moment without slipping into dread. It is about the way I can be undone by a very small thing.” “One Night With The Valet” follows Tennis’ milestone fifth album, 2020’s acclaimed SWIMMER. Written during a four-month sailing excursion in the Sea of Cortez, Mexico and then produced and recorded by Riley and Moore in their Denver, CO home studio, the album saw the duo elevating their distinctive pop approach to heretofore unexplored new heights on such breakthrough singles as “Runner” and “Need Your Love,” both of which are joined by colorful companion videos directed by Luca Venter and streaming now at the official Tennis YouTube channel. Tennis followed SWIMMER with an original new single, “Borrowed Time,” penned exclusively for Adult Swim’s Rick and Morty and available now for streaming and download. The track was featured in the closing moments of S05 E09 “Forgetting Sarick Mortshall,” the penultimate episode of the animated series’ landmark fifth season. Last year also saw Tennis celebrate SWIMMER with their biggest North American live schedule to date, highlighted by sold out headline shows – including sold out two-night nights at both Los Angeles, CA’s Fonda Theatre and Brooklyn, NY’s Brooklyn Steel – as well as festival appearances across the country. A North American tour surrounding the arrival of POLLEN will be announced soon. For updates and additional information, please visit here. Listen to the new single here:
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When you’re taking on a character as iconic as Ebenezer Scrooge, should you try something different with the role?
No, says local actor Jim Reid, who’s playing the lead in Windsor Light Music Theatre’s production of A Christmas Carol — opening Friday night at the Chrysler Theatre. Sign up to receive daily headline news from the Windsor Star, a division of Postmedia Network Inc. A welcome email is on its way. If you don’t see it, please check your junk folder. The next issue of Windsor Star Headline News will soon be in your inbox. We encountered an issue signing you up. Please try again
“It’s such a classic character, and so many people already know the story, that if you start adding your own personal things — (audiences) might be put off by that,” Reid reasons. “I think I keep it pretty true to form.”
It’s telling that Reid’s favourite interpretations of Ebenezer Scrooge are classic performances: Alistair Sim in the 1951 black-and-white movie version of A Christmas Carol, and Albert Finney in the 1970 musical Scrooge.
As far as Reid is concerned, Charles Dickens’ familiar tale of redemption during the Christmas season speaks for itself.
Windsor Light Music Theatre’s portrayal of the story — directed by Michael Roy — makes sure to include Scrooge’s tragic past, which shaped him into literature’s most memorable miser.
“We try to give the backstory of why Ebenezer is the way he is,” Reid explains. “Our version talks about his father having to go to a debtor’s prison, and his mother dying shortly thereafter. He goes through a lot of trauma, as a boy.”
“It’s such a great part. Scrooge goes on such an emotional rollercoaster… It’s kind of the most extreme emotional journey that a character can go on.”
But does Reid believe in the book’s message of total positive character transformation being possible at any age?
“It’s somewhat of a fairytale. It’s possible. I think it’s unlikely,” Reid admits. “It’s a story of hope, really… That’s the magic of the story.”
Windsor Light Music Theatre presents A Christmas Carol at the Chrysler Theatre (201 Riverside Dr. West).
Performances take place this Friday and Saturday at 7:30 p.m., Sunday at 2 p.m., and next weekend (Nov. 25 and 26 at 7:30 p.m., Nov. 27 at 2 p.m.).
Ticket prices start at $35 for adults, $30 for youths and seniors.
For more information and to purchase tickets online, visit www.chryslertheatre.com or call 519-252-6579.
Learn more about Windsor Light Music Theatre productions at www.windsorlight.com.
Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. Advertisement Scientific Reportsvolume 12, Article number: 19859 (2022) Cite this article 63 Accesses 1 Altmetric Metrics details The paper analyzes a model of optical transmittance of ultra-diluted gas, considering gas particles’ non-locality and the quantum effect of their wave function spreading derived from solving the Schrödinger equation for a free particle. The analysis does not depend on a particular form of the wave function, but it assumes the reality of wave function. Among others, we show conserved mass gas clouds may become significantly more transparent than predicted by classic transmittance laws. This unexpected phenomenon is possible because mass conservation is governed by the sum of probabilities, while the Markov chain’s product of probabilities controls the transmittance. Furthermore, we analytically derive the upper limit the closed system transmittance may grow and demonstrate a boundless, open gas cloud transmittance may grow up to 100%. Finally, we show the impact on interpretations of quantum mechanics. The model is naturally applicable in deep space conditions, where the environment is sparse. Furthermore, the model responds to dark matter requirements. The Beer–Lambert exponential transmission law1,2 describing attenuation of monochromatic light by the homogeneous, the not very dense medium is well known for almost three centuries. Despite developing newer, more advanced transmittance models, it still applies to quantitative spectroscopy3, rarefied gases, and astrophysical measurements. All these models rely on an assumption of attenuating particle locality. However, an increasing number of experiments4,5 convince us that the underlying theory of Quantum mechanics is not a local realistic theory6,7. There is one more assumption in most “classic” transmittance models: a light detector is a macroscopic apparatus. Quantum mechanics is one of the most fundamental theories, so it is necessary to check whether these two assumptions limit the scope of applicability of classic transmittance models. Quantum spreading is an effect that involves spontaneous spatial smearing of the (Psi) wave function over time. It leads to the spreading of the (|Psi |^2) probability density of any reaction of a physical object described by such a function. It comes directly from the free particle Schrödinger equation solution8. Assuming wave function reality9,10 we apply this solution to each gas particle independently during its free time between successive collisions. We proposed a kind of “smeared gas” model. It leads, together with the assumption of non-locality, to a new model of electromagnetic transmittance of thin gases. One of the predictions of this model is that the measured optical transmittance depends, among others, i) on the size of the detector used and ii) on the duration of the particle mean free time. The classic “local” approach to transmittance, e.g., the Beer–Lambert law, does not predict such dependencies. This paper presents a deeper analysis of the smeared gas transmittance model11. We analyze open and closed systems. We show that transmittance may rise, thanks to spontaneous particle spread, even in the closed system but only up to some limit. We analytically derive this limit. We show that displacement of the measurement axis in relation to the cloud mass center may affect transmittance measurement. The G parameter11 of the smeared gas transmittance model is analyzed more thoroughly. In the end, we briefly address the possibility of distinguishing quantum mechanics interpretations using the outcome of the model. There are just a few assumptions for the model. Gas particles are independent of each other, and they are non-local wave functions (not necessary) of the same type. Gas is not relativistic, so the Schrödinger equation applies. Particle distribution is homogenous, and wave functions differ by position only. The light detector is of some finite size. The paper11 describes those assumptions in detail. In this paper, first we examine a gas cloud made of two-dimensional particles, see Fig. 1. We show later how the two-dimensional case upgrades to three dimensions, not affecting conclusions drawn. Most of the analysis considers a detector of some constant diameter equal to 2r. The detector radius r is used as a length unit (r=1) across the paper. In real-world cases, r may be from microns to meters. We assume 100% detector efficiency without loss of generality. We assume a simple measurement setup. Monochromatic light propagates perpendicularly to the detector from a source of precisely identical shape and size as the detector. The volume between them is called a “visibility tunnel”. This tunnel is the only area where photon absorption may affect the number of photons (not) counted by the detector. We assume the detector is big enough (macroscopic), so the visibility tunnel doesn’t get wider due to non-classic photon trajectories. Both the source and the detector are far from the cloud. See the “astronomical setup” considerations in Ref.11. We interpret each individual gas “particle” wave function realistically: “(Psi (x)) is a spatially extended field representing the probability amplitude to interact at x rather than an amplitude for finding, upon measurement, a particle”9. We don’t constrain the exact form of the wave function. The normal distribution is used later in the text. It fulfills the above requirement, and it is the free particle Schrödinger equation solution. Also, it provides a convenient spread measure, namely the standard deviation (stdev). For a free particle distribution derived from the Schrödinger equation, the standard deviation depends on particle free time (e.g. (4) in Ref.11). We assume low cloud density, thus a non-decohering environment to let particles evolve free for some time, so wave functions reach substantial spread spontaneously. For simplicity, the same spread for all particles in the cloud is considered: the same standard deviation for all probability distributions. However, combining multiple transmittance equations may relax the requirement for uniform distributions if necessary. Also, the presented model neither depends on the idea of wave function collapse nor applies directly to the quantum measurement problem. We are not analyzing what happens to a wave function after absorption. For text simplicity, we describe as “absorption” all types of events that may happen to a photon on its way to a detector, namely either scattering or absorption. A single particle cross-section ((sigma)) must be smaller than the detector area (sigma ll r^2), which is the case for any atomic or molecular gas and common macroscopic detectors. A sample diagram shows a gas cloud made of a few 2D particles. Their wavefunctions have the Gaussian distribution with uniform standard deviation stdev. Each particle is offset from the (x=0) axis by (o_n). The light direction, position of the light detector, and visibility tunnel (volume of integration) are marked red. The detector is centered and placed parallel to the X axis. Units are selected to have the detector diameter (r=1). This paper discusses a gas cloud optical transmittance model dependent on the size of a detector and gas particles’ wave function spread. However, to relate its predictions to actual physical environments, we also need to include properties such as the density of a gas cloud, cloud thickness, and (a single particle) attenuation cross-section. An appropriate inclusion will adjust the transmittance equation to a given setup, allowing quantitative, experimental predictions. In the proposed model, the G coefficient plays the role of a normalizing factor11. Its value depends on the physical properties of the scattering medium: wavelength-dependent particle cross-section, cloud thickness, and cloud density. To apply the G factor to the probabilistic model discussed in the paper, it must encode those properties as follows. G indicates how much ((0<Gle 1)) of the detector’s surface is “covered” by the obscuring cloud in the classical limit, i.e., gas particles wavefunctions are highly localized, and the detector is macroscopic: (r gg stdev). Such a definition is required to guarantee identical quantitative results of the classical model1 and our (in the classical limit, where (r gg stdev)). In other words, G is a probability that a photon (that would reach the detector in the absence of the cloud) is not absorbed/scattered somewhere in the cloud. And this is just a probabilistic complement of the classic transmittance (TR_{cl}) of a cloud: Let’s recall2(TR_{cl}=e^{-nlsigma }), where n is the particles number density, l is the cloud thickness in the measurement direction (light length) and (sigma) is particle attenuation cross-section. There are other popular ways of quantifying opacity, namely optical depth ((tau =nlsigma)) or absorbance (ABS). They are related to each other: (TR_{cl}=e^{-tau }=10^{-ABS}) so we can express G in terms of them: It is clear the G coefficient is limited: (0<Gle 1) as required. We see the G coefficient is yet another way of expressing a classical optical depth of a gas cloud. Moreover, it is directly related to optical depth or absorbance by the above simple arithmetic relation. We showed what is G for a homogenous cloud and monochromatic light. It is a simplification but still useful for many applications, e.g., spectroscopy and astrophysics. If necessary, one may extend the model presented here to heterogeneous clouds and many wavelengths the same way classic homogenous and monochromatic absorbance extends to more complicated cases. In the following examples and figures, we put (G=0.7). It is a case of a cloud with 30% transmittance (TR_{cl}=1{-}0.7) or optical depth (tau =-ln(TR_{cl})approx 1.20) or absorbance (ABS=-log_{10}(TR_{cl})approx 0.52). We chose this particular value because it corresponds to the typical transmittance in the conducted experiment12. This section shows how a single particle spread affects the absorption detection rate depending on the detector size and position. It is a kind of the simplest, single-particle gas cloud. We introduce probability distribution, detection rate and illustrate. We will be interested in finding a particle in a given volume of detectability tunnel perpendicular to the detector plane. To simplify calculations, we can project a 2D particle onto the detector plane thanks to distribution symmetry. This way, we get 1D normal distribution P: where stdev is particle standard deviation. The probability (P_v(o)) of finding a particle in a given volume of detectability tunnel ((o-r)<x<(o+r)) is the integral: where erf() denotes the Gauss error function, and o is the distance (offset) from the visibility tunnel axis to the particle. However, this probability is not equivalent to the probability of absorbing a photon by this particle in this volume. Absorption probability depends additionally on the physical properties of a cloud, as discussed in the previous section: particles’ cross-section, density, and thickness. This is what the G coefficient is responsible for. It encodes the probability of passing a photon from the source to the detector—in the presence of a classical cloud. Both events (i.e., the particle in the volume and absorbing a photon) must coincide to prevent a photon from reaching the detector. Therefore, we need to multiply both probabilities and take the complement to get the photon passing probability. This probability is, by definition, the cloud optical transmittance (TR): Applying Eq. (4) we find the transmittance: as measured by the r-radius detector, and the particle offset from the visibility tunnel axis by o. Sample graphs for (i) a single particle probability distribution, (ii) probability of finding a particle within a detectability tunnel, and (iii) transmittance as measured by a finite detector. The detector radius (r=1). Each column graphs for a different stdev value. (i) The first row shows particle distribution P(x) after Eq. (3). The solid red line is a sample detector position at (o=0). The dashed red lines show detectability tunnel (volume) boundaries. (ii) The middle row shows the probability (P_v(o)) of finding a particle within a detectability tunnel that is a volume constrained by the detector position o according to Eq. (4). (iii) The last row plots the transmittance (TR(o)=(1-G,P_v(o))) that would be measured by the 100% efficient detector set at o, see Eq. (6) with (G=0.7). The green dashed line shows classic transmittance (TR_{cl}). Figure 2 illustrates a single particle distribution and transmittance for a couple different standard deviations. The following columns present the relationships for ever wider standard deviations of the particle distribution. The first column corresponds to a well-located particle ((stdev ll r)), i.e., the classical situation of an ideal gas. With the increasing spread, we can see that (i) the transmittance for the detector in line with the particle is always the lowest, (ii) the transmittance for the detector offset further from the center increases. For an open, infinite system, the detector can be moved as far as possible. There will also be some probability of being obscured by the non-local particle. Let us study a system of many particles: odd number of 2D particles, lined up parallel to the detector, spaced every 2r. The detector is placed symmetrically in the middle. We will release those conditions later. An identical probability distribution gives the probability of locating each particle. Although we use the Gaussian distributions any probability distribution works, because (int _{-infty }^{infty }P(x)dx=1). This way, we do not get attached to any particular form of a wave packet. Again, to simplify calculations, we project 2D particles onto the detector plane to work with 1D distributions. Figure 3 shows such a configuration for (N=9) particles. The solid red line marks the detector, and the dashed red lines are the visibility tunnel boundaries. We define dilute gas cloud transmittance TR as proposed in Ref.11. Transmittance is the probability that a photon that the detector would have detected in the absence of a cloud passes not-absorbed the entire N-element cloud and is detected by the detector. Collisions with individual particles are independent, so we may consider this process as a Markov chain: where (G,P(o_n)) is the probability of photon being absorbed by n-th gas molecule, which is offset by (o_n) from the detector, see Eq. (5) in Ref.11. A sample configuration of 9 identical particles distributed evenly every 2r. The solid red line marks the detector, and the dashed red lines are visibility tunnel borders. Now we take advantage of the periodicity. Identical chunks (of the same shape and number) of the probability distribution both leak out and flow into the visibility tunnel. Thus, we can “unfold” a single distribution periodically instead of considering all distributions in one place. Next, we virtually “shift” the detector N times (by a period of 2r) and take the product of all its positions. This way we may substitute (o_n=r(2n-N-1)/2), and Eq. (7) turns into: The idea of dividing a probability distribution into many chunks, periodically every 2r as required by Eq. (8). Values of n, o, (P_v(o)), (G,P_v(o)) and (1-G,P_v(o)) are superimposed in red for every part for convenience. Figure 4 shows this idea. One distribution is divided into many chunks, periodically every 2r. Values of n, o, (P_v(o)), (G,P_v(o)) and (1-G,P_v(o)) are superimposed for every part for convenience. As expected, all probabilities (P_v(o)) sum up to 1, which means that the analyzed interval contains the entire particle. The probability is not “leaking” sideways. We interpret this as a conserved mass in the system. The following holds for (G=const): The transmittance is the product of (1-G,P_v(o_n)), see Eq. (7). The sum of its components is always constant (sum (1-G,P_v(o_n))=const) as shown above. However, the constant sum doesn’t guarantee the product is constant: It shows that even for closed systems with mass conserved, the transmittance may change because mass conservation depends on a sum (of some elements), but transmittance depends on a product (of the same elements). In general, the transmittance depends on how the distributions are divided. This division depends on (i) the shapes of the probability distributions and (ii) the width of the detector. The shape of the normal distribution depends only on its standard deviation. The detector size r significantly influences the individual product components values for either (r,sim ,stdev) or (r<stdev), influencing the product and, finally, the measured transmittance. In the classical case, for well-located (ideal gas) particles and macroscopic detector, we have (stdev,ll ,r). This way, all non-zero probability of a particle always gets to one chunk making all elements of the product of Eq. (7) equal to 1, except one element. The only element less than 1 determines the value of the entire product. The product doesn’t change upon changing r because there will always be only one such element. So, in this case, detector size can’t affect the transmittance measurement. It explains why we don’t observe transmittance dependence on detector size in classic systems. This analysis applies to any number of particles (N). For even N the (o_n) substitution leading to Eq. (8) should be just slightly different. Figure 5 shows the dependence of transmittance on the particle standard deviation for the measurement with a fixed size detector. The following section describes the chart details. The charts show the sample dependence of transmittance on the standard deviation for the measurement with a fixed size detector. The solid line is the measurement in the cloud axis, and the dashed line denotes some off-axis measurement. The length unit is equal to detector radius r. The detector width is 2 ((r=1)). A 1D cloud is (N=61) particles in total, and they are evenly spaced every 2r. The G coefficient is set to 0.7 (after (TR_{cl}=30%)). The particles have a 1D normal distribution where the standard deviation is denominated in detector radius units (r). The detector offset for off-axis detection is 20r from the cloud axis. The upper chart shows the magnification of the left part of the bottom diagram. If there are many more than one particle per detector area (like in any real-world setup), then we repeat the above reasoning many times in the following way. We divide the gas cloud into enough parts so that each of them contains statistically only one particle per “detector area”. We calculate the (partial) transmittance for each of these parts independently. From the property of independence of the probability of absorption by individual gas particles, we calculate the product of partial transmittances, obtaining the total transmittance of the entire cloud. The same approach works for analyzing inhomogeneous gas clouds. One should divide such a cloud into homogenous parts, calculate separately (partial) transmittances, and take their product to get total transmittance. Alternatively, we can do the trick of adjusting the constant G. We can set it equal to (1-TR_{cl}), where (TR_{cl}) is the classic transmittance of the cloud. Then we take a set of “artificial” particles distributed exactly every 2r as requested above. Such an artificial particle represents all real particles present in the visibility tunnel of a given chunk. Remember, however, the spread (e.g., the standard deviation) of this artificial particle is the same as any single cloud particle. I.e., we don’t sum individual particle masses to calculate spread speed. The latter method is very efficient for numerical computations. For a three-dimensional gas cloud, it first has to be cast onto the plane of the detector. For such a 2D model, we demand to distribute particles evenly: one particle per detector area. The straightforward way to analyze 2D is to consider normal distribution and a square detector with a side equal to 2r. For such a system: (i) an analytical solution is available, see (11) and (18) in Ref.11 and (ii) the square shape of the detector allows to cover the entire plane with adjacent detectors. Then, we can perform the same periodic reasoning as given above for the 1D model. An arbitrary shape of the detector makes reasoning more challenging and changes quantitative equations. Yet, it is still possible as it only requires a finite area of the detector. However, qualitatively the presented principle of the transmittance dependence on the detector area holds. The ideal gas is the classical limit of the model. Particles of such a gas have a negligible spread, and a detector is of macroscopic size ((r gg stdev))2. The upper chart of Fig. 5 shows this limit on the left, close to (stdev = 0). On the bottom chart of this figure, the area of the classical system applicability is practically invisible. An open system is a configuration where particle spread can reach a very high value, causing probability to leak out far from the cloud. We know, however, that in real physical systems, the maximum spread is limited. At least two factors limit stdev growth: (i) the age of the Universe and (ii) the cloud environment causing particle decoherence (collapse of wave functions). It seems, however, that there may be conditions in outer space where decoherence is negligible (darkness and high vacuum), so the age of the Universe is the only upper limit. Particles of atomic size can experience a very significant spread there. Spread (e.g., measured with stdev) may be many orders of magnitude greater than a detector size. As a result, a considerable transmittance increase may happen there. The upper limit of transmittance growth in the open system is 100% simply because probability (mass) leaks out of the system. When the gas cloud is vast and the particles’ spread is low, the probability doesn’t leak out beyond the cloud’s outline. Let us call it a closed system because it is, in fact, similar to closed systems with mass conserved. In such a setup, the probability of distant particles flows into the measurement region. For example, the gas may be closed in a sufficiently large chamber, i.e., its diameter (D_{chmb} gg stdev). Our experimental setup12, where (D_{chmb} sim {25}~textrm{cm}), (stdev sim {14},upmu textrm{m}) and (r sim {25},upmu textrm{m}) ((stdev approx 0.56r)) is such case. A closed system can also mean an open system (e.g., in outer space) but with a cloud diameter much larger than the spread: (D_{cloud} gg stdev). The cloud diameter is the diameter of the volume non-spread cloud occupies in a classical situation when (stdev rightarrow 0). An imaginary infinite system, i.e., particles placed infinitely far in all directions (perpendicular to the measurement axis), should also be considered a closed system. The classic ideal gas is a special case of a closed system. The green dashed line marked “Close system/Open system” on Fig. 5 indicates the approximate boundary between close and open systems. We found there is a limit of transmittance growth in a closed system. Generally, the increase is possible thanks to Eq. (8) product components factorization getting more uniform with increasing spread. All components tend to 1: ((1-G/K) rightarrow 1^{(-)}) because the probability distribution spreading does not change the area under the curve. K is a number of chunks that hold (P>0). K grows with the growth spread (stdev) so (G/K rightarrow 0^{(+)}), because (G=const). For large K we can rewrite Eq. (8) considering only chunks with (P>0) in the following way: We find there is upper limit of the last equation: because probability distribution gets divided into more and more (K) intervals. Reaching this limit is visible in Fig. 5 as a curve flattening in the middle of the chart. The dashed green line labeled (TR_{limit}) marks this limit. We conclude with an example. An almost entirely opaque (classically) cloud with (TR_{cl},=,0), (i.e., (G,=,1)) increases its transmittance (as a result of spontaneous spread but without mass escaping beyond the original cloud outline) up to a maximum of (TR_{limit}=e^{-1} approx 36.8%). The boundary between the closed and the open system is not clearly specified, especially when the cloud is in an unlimited (deep) space. Carrying out the transmittance measurement in such a closed system closer to one of the cloud edges (instead of centrally coaxial) affects results. Less probability flows into the visibility tunnel from either direction because there are fewer particles. Therefore, the measured transmittance may be higher (for a specific particle spread) than when measured centrally through the cloud. The dashed curve Fig. 5 shows such an off-axis measurement sample. It coincides with the solid line for the classic case (left-hand side). It is good. We don’t expect any deviations of this type for ideal gas. Also, both lines overlap on the right-hand side because the open system doesn’t have any specific axis. Only in the middle part of the chart, the dashed line is always above the solid line. It means that the transmittance measured closer to the edge of the cloud gets higher sooner (as stdev grows). This phenomenon may affect transmittance measurements of large deep space gas clouds. The above analysis allows, among others, to experimentally distinguish some interpretations of quantum mechanics. In particular, the pilot-wave interpretation13 assumes the existence of some localized objects that are only “controlled” by non-local functions. If it were so, if there were some kind of “balls” in the system with a certain probability (aka cross-section) of absorbing-or-not photons, then the dependence of transmittance on the spread would look different. In particular, the factorization of probabilities distributions would not affect the transmittance of a closed system. It would not lead to an increase in transmittance and reaching the (TR_{limit}=e^{-G}) limit. Instead, in a closed system, the transmittance would apply according to the classical law of transmittance (Beer-Lambert law). A probability leak could be a cause of the only possible change in transmittance. However, it happens only in an open system. Different QM interpretations lead to different smeared gas transmittance model predictions. The solid line indicates the transmittance predicted with the assumption of “non-locality reality”. The dashed line marks the transmittance assuming there are some small, ball-like objects absorbing-or-not photons, i.e., according to the pilot-wave interpretation. The pilot-wave interpretation does not reveal any difference from classic transmittance for systems with mass conserved (see “Closed system” range). Figure 6 shows this difference. The solid line indicates the transmittance predicted with the assumption of “non-locality reality”. It doesn’t expect any finite size, ball-like objects to exist. The dashed line marks the transmittance assuming some small, ball-like objects absorbing-or-not photons and that non-local wave functions just guide them. The dashed line shows the transmittance according to the pilot-wave interpretation. One can see the distance between the two graphs, which indicates the possibility of conducting experiments comparing the transmittances (such as Ref.12) and thus differentiating the interpretations. This analysis extends the transmittance analysis of ultra-diluted gases presented in Ref.11. It shows the non-obvious influence of particles’ quantum spread and detector area for optical transmittance measurement. It predicts that the optical transmittance of the smeared gas cloud may change (raise) even when the system’s mass is conserved, like in some laboratory experiments. We found the limit of such growth. The presented mathematical analysis does not depend on any specific form of the gas-particle wave function. The paper also presents a brief analysis of the possibilities of distinguishing between some interpretations of quantum mechanics. The model is falsifiable. We propose possible experiments in Ref.11 and report promising results of one of them in Ref.12. This model may help better understand phenomena occurring in deep space. A dark vacuum has natural conditions for the spontaneous formation of smeared gas out of ideal gas. Diluted gas is one of the most abundant forms of matter in the Universe. Observation of its transmittance, such as spectroscopy, is one of the essential tools for studying its properties: composition, density, changes, etc. This theory may be of some importance for the correct interpretation of astronomical observations and astrophysical models. In addition, the demonstrated tendency for a spontaneous increase in transmittance may be a part of the answer to the problem of the missing visible mass in the Universe, the so-called dark matter. All data generated or analysed during this study are included in this published article. Bouguer, P. Essai d’optique sur la gradation de la lumière (Optics Essay on the Attenuation of Light) 16 (Claude Jombert, 1729). Google Scholar McNaught, A. D. & Wilkinson, A. IUPAC. Compendium of Chemical Terminology, 2nd ed. (the Gold Book) (Blackwell Scientific Publications, 1997). Google Scholar Bernath, P. F. Spectra of Atoms and Molecules 465 (Oxford University Press, 2016). Google Scholar Handsteiner, J. et al. Cosmic Bell test: Measurement settings from milky way stars. Phys. Rev. Lett.118, 060401. https://doi.org/10.1103/PhysRevLett.118.060401 (2017). ArticleADSPubMed Google Scholar Rauch, D. et al. Cosmic Bell test using random measurement settings from high-redshift Quasars. Phys. Rev. Lett.121, 080403. https://doi.org/10.1103/PhysRevLett.121.080403 (2018). ArticleADSCASPubMed Google Scholar Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev.47, 777. https://doi.org/10.1103/PhysRev.47.777 (1935). ArticleADSCASMATH Google Scholar Musser, G. Spooky Action at a Distance 290 (Straus and Giroux, Scientific American/Farrar, 2016). Google Scholar Shankar, R. Principles of Quantum Mechanics 2nd edn. (Springer, 2011). MATH Google Scholar Hobson, A. There are no particles, there are only fields. Am. J. Phys.81, 211. https://doi.org/10.1119/1.4789885 (2013). ArticleADSCAS Google Scholar Long, G. L., Qin, W., Yang, Z. & Li, J. L. Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment. Sci. China Phys. Mech. Astron.61, 30311. https://doi.org/10.1007/s11433-017-9122-2 (2018). Article Google Scholar Ratajczak, J. M. The dark form of matter, on optical transmittance of ultra diluted gas. Results Phys.19, 103674. https://doi.org/10.1016/j.rinp.2020.103674 (2020). Article Google Scholar Ratajczak, J. M. Measurement of the dependence of ultra diluted gas transmittance on the size of the detector. Sci. Rep.11, 6221. https://doi.org/10.1038/s41598-021-85568-w (2021). ArticleCASPubMedPubMed Central Google Scholar Bohm, D. A suggested interpretation of the quantum theory in terms of hidden variables. Phys. Rev.85, 166. https://doi.org/10.1103/PhysRev.85.166 (1952). ArticleADSMathSciNetCASMATH Google Scholar Download references Author would like to thank Prof. Joanna Sułkowska for support and MooseFS for financial support of the work. Centre of New Technologies, University of Warsaw, Warsaw, Poland Jakub M. Ratajczak You can also search for this author in PubMedGoogle Scholar J.M.R. is the sole author of the manuscript. Correspondence to Jakub M. Ratajczak. The authors declare no competing interests. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. 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Warren native Matt Stawski went from filming local rock bands to directing a major feature film based on a classic children’s TV series. Stawski is the director behind Paramount Plus’s live-action animated film “Blue’s Big City Adventure,” released on the streaming service Friday. It’s based on the Nickelodeon series “Blue’s Clues & You!,” a revival of the 1990s show “Blue’s Clues,” featuring a courageous animated dog and its owner pursuing clues and solving problems. The film centers around the host of “Blue’s Clues & You!,” Josh, played by Joshua Dela Cruz, visiting New York for an audition. Tagging along is Blue and a few more familiar faces. Original “Blue’s Clues” host Steve Burns appears in the film for a nostalgic touch. This is Stawski’s first-ever feature film, which just so happens is also a musical. He has a thing for musicals. Q: Tell us how you got into the business of filmmaking. A: Oh, man, I actually went to Cousino High School in Warren, and they have a radio-TV station. My friends and I were able to borrow their gear all the time and we just started shooting local bands around Detroit. From there, I kept doing music videos and started building a reel. While I was going to Columbia College for directing, I started booking jobs for companies out here in California, doing hip-hop videos and motion graphics. Before I knew it, right when I graduated, I moved out to LA and had a job doing music videos. Sixteen years of music videos, and that took me straight into features, where I am now. Q: What’s been some of your best work or sets that you’ve been on? I hear you’ve done work for Train, CeeLo Green and worked on sets for Nickelodeon. A: One of the more well-known videos that I’m really proud of is the CeeLo Green, “Forget You” video. That was really fun because he wrote a sort of Motown song. Obviously, my whole life, I’ve been inspired by Motown. We went down to Hitsville USA, and we just went to all the spots on West Grand and really soaked in the history of Motown. I was able to sort of tap into some of that Motown doo-wop style in that CeeLo video. It’s been a balance of doing videos that I have to do to pay the bills and videos that I get to have creative freedom and make a really colorful, fun, exciting video. Q: I got a chance to watch Blue’s Big City Adventure and it definitely took me back to my own childhood. What was that process like for you in terms of directing? A: It was really fun. A lot of it was really new and a lot of it I had a lot of experience with. I have a lot of experience doing music videos and musicals. The musical element of it fell right in place, what was new for me was shooting in New York City out on the streets that was very new and incredible to see how that works. How you get film permits to shoot in some of these iconic locations, how you have to wait something out on the city street with pedestrians there, and how to do crowd control that was all new to me as well as shooting animated characters. That was a brand new learning experience for me as well, because on set with multiple animated characters in a scene with a live-action human, you have to make sure that you have all of the eyelines correct, you have to make sure that the live-action actors are interacting with the animated characters and holding their arms the right way and looking in the right directions. You have to make sure you capture with digital technology how the lighting is so when you’re animating the characters in post-production, the lighting looks natural on the animated characters. There was a lot of learning for me for sure, but we pulled it off, and it was really fun. I had a great crew to work with that’s what helped me achieve the film. Q: If you’ve been to New York before, you could easily say while watching the film: “That’s so New York-like.” For example, when Blue and Josh arrived in New York there were little scenes where we saw pizza boxes on top of the trash cans. How did you really capture the true New York? A: Before filming this, I’ve been there just on vacation. I shot one video there years ago with CeeLo. I did a lot of research and I asked a lot of the locals. We really spent a lot of time making sure that those iconic locations that we featured in the film were locations that we could build a musical out of and really interact with the architecture and the geography of New York City. We wanted to make sure that we captured some of the best locations and really did our research as to – where can we film in Central Park? What can we do around Bethesda Fountain? What fields can we shoot in for the big dance in the end? What are the best angles and even researched other films that shot in New York and how they shot some of the different locations and what lenses they used? What’s the most flattering way to make New York look because this is a kid’s movie? We wanted to make sure we presented a sort of candy-coated version of New York City, a very colorful representation of the city. Q: It was definitely interesting to see the previous Blue’s Clues characters in the movie. Why was that a decision to include them? A: Steve came around for a lot of the 25th anniversary promo stuff they were doing for Blue’s Clues. He really went viral, a year and a half ago when he came out and talked to the adults and told them why he left and that he was still their friend. It exploded, I think Nickelodeon really realized how important he was, as well as Donovan (Patton), who played Joe, how important they were to the younger generation and to the older generations, that grew up with Blue’s Clues. It was a no-brainer, to bring them in and have them reprise their roles in such a funny, sort of family-friendly adult way. Q: What do you want people to get most out of this film? Since it’s like multiple generations are watching it. A: I think the most important thing to me that I realized when we were going into it was this idea of inspiring kids to take chances, to follow their dreams, to sort of leave their little comfort zone, leave their bubble of safety, to chase their dreams. I think that the film does a good job showing Josh and Blue in storybook land and when they leave to go to New York City, the city’s very scary. But all they have to do is sort of close their eyes and listen to the music of the city, and find their little bits of wisdom from their friends around them that give them advice along the way. All the kids growing up on Blue’s Clues kind of have to realize that they might have to venture out of their comfort zone and go find their city or find their place where they want to live. And maybe if they want to stay in their own city that they grew up that’s great, but really embrace the culture and meet new people that you didn’t really grow up with, find people that make you learn new things. That’s really important and I want people to get that out of the film for sure. Q: What did you get out of making this film? And also, is this the first big title that you’ve directed? A: This is my first feature film. I’ve done some TV pilots in the past, and I’ve done some short films, but this is my first feature. I learned how important kids and family spaces are and how important it is to get the educational and inspirational aspects of the film right because little kids really look up to these characters. It’s really important, how you show them on screen and how you portray certain events. I really learned how to make a film in the kid space. That was probably my biggest learning experience because a lot of the music videos I’ve done have been more in the adult space. I was able to really play with that fantasy surrealist imagination, stuff that t kids are so great at. I was able to sort of become a kid again, making this movie. Q: Looking a little bit into the future what other projects do you have in store – I hear that recently you sold your musical horror films, to Universal Pictures. What’s up with that? A: We’re in development on the Monster Mash right now with Universal and we’re working on just getting the script in a good place so we can shoot it. I’m really excited for that because obviously, I am obsessed with Halloween. I grew up in Michigan, going out to the cider mills, going to Blake’s. Going up to Tilson Street in Romeo and seeing all the houses decorated. My girlfriend and I like to come home every year for Theatre Bizarre at the Masonic Temple. Detroit just goes off for Halloween. It’s one of the Halloween capitals of the country. More:Detroit’s Theatre Bizarre fills 8 floors, 350K square feet of Masonic Temple There’s a lot in the Monster Mash film, there’s a lot of good Easter eggs that really tie into Detroit and a lot of our Halloween culture. I’m really excited to film that, we’re still in the script phase, and we’re still in development. It might be a minute before we shoot that. But other than that, I’m trying to develop more musical concepts. At some point in my life, I would absolutely love to come back and make a true Motown musical. Q: I have to ask, are musicals like your thing? A: I’ve tried to watch almost every musical that’s ever existed. I’m not as big on actually going to the theater, it’s something I never really did. Just because it was always really pricey, so I always watch musical films. I love the fact that with musicals, you can break so many rules, one genre film where you can go full fantasy, and the audience accepts it and that’s a really fun space to play with. I absolutely adore musicals and I would love to make many, many more. More:Temptations’ ‘Ain’t Too Proud’ musical finally makes its way home as Detroit run begins Q: Before I let you go, can you give your best advice to aspiring filmmakers? A: Number one, is to create what you know. Don’t try to make a movie or take a job in an area that you’re not passionate about. If you grew up with a certain type of music if your grandma and grandpa played a certain type of music, and you’re obsessed with that music, make a movie about that music. If you grew up in a neighborhood that has something very specific to it, make a movie about that neighborhood. If you had a best friend, that was a character, if you could remember anything they said in their whole life and all the advice that they gave you, make a movie about that friend. Whatever interests you, whether it’s historical, whether it’s pop culture, make a movie about that because when you go and pitch a movie to Hollywood, you have to be the person in the room that knows the most about that topic. More:Tim Allen back in red suit for ‘The Santa Clauses’ series on Disney+ Q: One more thing when and where can the audience see Blue’s Big City Adventure? A: Blue’s Big City Adventure comes out on Paramount Plus on Nov. 18. You can get a free trial if you don’t already have it. I would advise everyone to make sure their volume is cranked up to 11, and watch it on the biggest screen possible. Because it’s a big fun movie, the kids are going to hopefully get up and dance and sing along to it.
WBOY.com Please enter a search term. Please enter a search term. by: Makayla Schindler Posted: Updated: by: Makayla Schindler Posted: Updated: MASONTOWN, W.Va. (WBOY) – West Virginia Sound Foundry celebrated its grand opening with a ribbon cutting on November 17 in its location at 416 South Main Street in Masontown. The idea for the business came about when a few friends came together and wanted to start up something to promote music and art in Preston County. Executive director Josh Salisbury said that kids were involved in sports and other activities, but there was a market missing for the arts for children who were interested in it locally. The new studio offers: “Music is such a huge part of my life and a huge part of my families’ lives, and you know, my son is a singer in one of the bands, and we just enjoy that life, we enjoy that lifestyle of being able to have music and we wanted to be able to share it with kids that maybe wouldn’t have the opportunity to do it otherwise,” said Salisbury. The WV Sound Foundry has already had a few public and fundraising performances. They will be having another performance on Dec. 17 in partnership with the Preston County Youth Center. This performance will include a mixture of Christmas and rock music. If interested in taking lessons or a class, the new studio’s hours are based on appointment through their website. Salisbury said that they are a little less expensive than some Morgantown groups so that people in the area will want to come out and give it a try. Copyright 2022 Nexstar Media Inc. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.
*Your language will be set using a browser cookie. Don’t have an account? Sign up Forgot your password? By Andrew J. Eisenberg The COVID-19 pandemic has presented enormous challenges, and a few opportunities, for music professionals around the world. The audio documentary Locking Down the Beat: Musical Livelihoods in Nairobi During at the Height of the COVID-19 Pandemic explores the impacts of the pandemic on the lives and livelihoods of four music professionals in Nairobi, Kenya, during the pandemic’s acute phase in 2020 and 2021. Produced by myself and a group of students and faculty at NYU Abu Dhabi, the work includes extended interviews woven together with music excerpts and location audio. Locking Down the Beat centres on interviews with four music professionals in Nairobi: Amin ‘Elchie’ Virani has been involved in Kenyan music production since the country’s youth music boom at the turn of the millennium, and now runs his own audio and video production firm. Janet Otieno is a popular gospel singer, who burst on the scene in 2013 after decades of singing in church. Makadem (Charles Ademsen) is a singer and multi-instrumentalist who performs in the Afro-fusion genre, while Timothy ‘Still Alive’ Boikwa is a multi-award winning music producer and the founder of Still Alive Records. We conducted our interviews over Zoom during March and April of 2021. It had been about a year since Kenya had seen its first COVID cases. Though a vaccination programme was getting underway, the country was experiencing a new wave of infections. A new partial lockdown of Nairobi was instituted while we were still in the midst of carrying out our interviews. Each interview lasted over an hour, and so a great deal has necessarily been left on the cutting room floor. In addition to chopping up and reordering the discussions, we also made surgical edits to remove long pauses, redundancies, and lengthy tangents. In a few cases, we even moved around an individual word or phrase for the sake of clarity and flow. But we endeavoured not to muddle any intended meanings, and the final product has been approved by all of our interviewees. Our overall aim was not to provide a comprehensive survey of the music industry in Nairobi during the COVID-19 pandemic, but rather an ethnographic portrait of the industry at an extraordinary moment, pieced together from a diverse set of voices and perspectives. Listen to the documentary below.
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Get the Latest Investment Ideas Delivered Straight to Your Inbox. Subscribe TICKERS: TLG; CHXMF; CM5R Source: Jacques Wortman (11/18/22) The owner of this Quebec project will include these exploration results in the upcoming definitive feasibility study, noted a Laurentian Bank Securities report.
Troilus Gold Corp. (TLG:TSX; CHXMF:OTC; CM5R:FRA) released additional drill results that “confirm the discovery of the new high-grade ‘Connector zone'” between the past-producing Z87 and J zones at its namesake Troilus project, reported Laurentian Bank Securities mining analyst Jacques Wortman in a November 8, 2022 research note. This new zone is outside of the pit shells outlined in previous preliminary economic assessments. “The intersection of a second high-grade structure (new X22 zone assays announced last month) further appears to validate Troilus Gold management’s decision to defer its economic study work to include the new structures in the definitive feasibility study by H2/23,” Wortman wrote. Regarding the new drill results, Troilus Gold reported five holes, all part of its recently completed 11,000-meter (11,000m) drill program aimed at expanding mineralization to the north and south of the Z87 pit. Wortman presented the results of the highlight holes. Hole 87-422 hit both J zone and Z87 mineralization, indicating the two areas connect. Intersection with the J zone was within 200m of surface, as indicated by the intercept, 1.75 grams per ton gold equivalent (1.75 g/t Au eq) over 138m, starting 157m downhole. Intersection with Z87 was deeper, as demonstrated through two intervals. They are 3.58 g/t Au eq over 38m, starting 200m downhole, and 5.19 g/t Au eq over 21m, starting 217m downhole. Wortman reported that the high-grade Connector zone structure looks to be subvertical. Drilling there appears to be perpendicular to and was likely not “down the throat of” the structure, given hole dip was 55 degrees. More work, however, is needed to delineate the structure’s actual orientation and thickness. As for stepout drilling from Z87, represented by four reported holes, it too was positive with mineralization encountered. Wortman relayed the results of three highlight holes, all of which were oriented to previously reported hole 87-421. The analyst also pointed out Laurentian’s target price on Troilus Gold, Buy rated, is CA$2.50 and the Canadian explorer’s current share price is about CA$0.56. The large difference between these prices implies a significant potential return for Troilus Gold investors.
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Streetwise Reports does not endorse or recommend the business, products, services or securities of any company mentioned on Streetwise Reports. 5) From time to time, Streetwise Reports LLC and its directors, officers, employees or members of their families, as well as persons interviewed for articles and interviews on the site, may have a long or short position in securities mentioned. Directors, officers, employees or members of their immediate families are prohibited from making purchases and/or sales of those securities in the open market or otherwise from the time of the decision to publish an article until three business days after the publication of the article. The foregoing prohibition does not apply to articles that in substance only restate previously published company releases. As of the date of this article, officers and/or employees of Streetwise Reports LLC (including members of their household) own securities of Troilus Gold Corp., a company mentioned in this article. Disclosures For Laurentian Bank Securities Equity Research, Troilus Gold Corp., November 8, 2022 “Laurentian Bank Securities Equity Research” is a trade name used by the Equity Research sector of Laurentian Bank Securities Inc. To access Laurentian Bank Securities’ regulatory disclosures, please click or press on the hyperlink – http://www.vmbl.ca/portal/disclosure The information contained in this document is based on what we deem to be reliable sources, but no guarantee or promise, explicit or implicit, is given as to the accuracy and exhaustiveness of these sources. This report shall under no circumstances be considered an offer to buy or sell, or a request to buy and/or sell the stocks mentioned. Laurentian Bank Securities Inc. and its employees may not be held liable for any monetary losses stemming from the implementation of the recommendations contained in this document. 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Member of the Investment Industry Regulatory Organization of Canada and of the Canadian Investor Protection Fund. The regulation of the securities market establishes requirements that annalysts must follow when issuing research reports or making recommendations. These guidelines are included in the research dissemination policy of Laurentian Bank Securities, available at http://www.vmbl.ca/portal/researchdissemination-policy. New Drill Results From Idaho Point to Gold Resource Growth Source: Geordie Mark (11/18/2022) The explorer’s ongoing exploration results at this project continue to be encouraging ahead of a mineral resource update expected next year, noted a Haywood Securities report. read more > The Narcotic Effect of the Reflexive Rebound Source: Michael Ballanger (11/14/2022) Expert Michael Ballanger of GGM Advisory Inc. reviews the newest dubbed “investment guru,” the outlook of the precious metals sector, and the current state of the stock market to tell you where he believes we are all headed. read more > Firm to Gain Mining Royalty on Project in Ecuador for $50M Source: Kerry Smith (11/14/2022) The acquisition is a 0.6% net smelter return royalty on production that is estimated to start at this copper-gold property in late 2029, noted a Haywood Securities report. read more > New Drill Results Expand Deposit, Leading to Buy Rating Source: Dr. Geordie Mark (11/14/2022) These early results of 2022 drilling at this Golden Triangle property highlight the presence of high silver grades and potential for future resource growth, noted a Haywood Securities report. read more > Copper Project Returns ‘Very Good’ Drill Results Source: Adam Schatzker (11/14/2022) This data set “highlights the potential of the southern starter pit and its ability to provide higher grade material for longer in the early years of the mine,” noted a Research Capital Corp. report. read more > New Drill Results From Idaho Point to Gold Resource Growth Source: Geordie Mark (11/18/2022) read more > The Narcotic Effect of the Reflexive Rebound Source: Michael Ballanger (11/14/2022) read more > Firm to Gain Mining Royalty on Project in Ecuador for $50M Source: Kerry Smith (11/14/2022) read more > New Drill Results Expand Deposit, Leading to Buy Rating Source: Dr. Geordie Mark (11/14/2022) read more > Copper Project Returns ‘Very Good’ Drill Results Source: Adam Schatzker (11/14/2022) read more >
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Sixty-eight per cent of master’s students who participated in Nature’s latest graduate-student survey say that they are satisfied with their current programmes, a level of contentment that puts them ahead of PhD-student colleagues (60%). And 79% say that they are also satisfied with their decision to pursue a graduate degree, compared with 74% for PhD students. This is the first Nature graduate-student survey to include master’s students, and they had much to say about their training and futures. The survey drew responses from 756 self-selected master’s students, who made up 23% of the total sample (see ‘Nature’s graduate student survey’). Forty-one per cent of the master’s degree respondents are studying in Asia, 30% are in Europe and 14% are in North or Central America, with a few responses coming from Australasia, Africa and South America. Fifty-two per cent of the master’s student respondents identify as female, and 46% as male. This article is the fifth of six linked to Nature’s global survey of graduate students. The last article in the series will examine respondents’ experiences of racism. Previous articles looked at finances, mobility, career progression and other aspects of graduate-student life. The questionnaire was created with Shift Learning, a market-research company in London, and was advertised on nature.com, in Springer Nature digital products and through e-mail campaigns. It was offered in English, Mandarin Chinese, Spanish, French and Portuguese. The full survey data sets are available at go.nature.com/3dyefwg. All face their own challenges and uncertainties, but many find that the higher degree they are pursuing is a valuable and rewarding part of their training — whether or not they intend to go on to a doctorate, says Elizabeth Friedman, who reviewed the survey results for Nature. She is a researcher in science, technology, engineering and mathematics (STEM) education at the University of Illinois Chicago. “There’s an entire world of successful master’s students, especially in STEM, who are on exciting career paths,” says Friedman, who is also the co-founder of the National Professional Science Master’s Association, an advocacy group based in Salt Lake City, Utah. “The master’s students I’ve interacted with are far more satisfied than the PhD students.” Master’s students are generally happy with their programmes, and many are already looking ahead to the next step (see ‘The master’s student experience’). Fifty-nine per cent of respondents say that they are planning to pursue a PhD eventually, whereas more than one-quarter aren’t sure whether they’ll do so. Friedman says that, in her experience, students who complete a master’s degree in a STEM field have plenty of job options if they decide not to continue their education. “Master’s students learn transferable skills,” she says. “Their career path can offer them more choices than a PhD student who has been hyper-focused on a particular research topic.”
Survey respondent Ethan Solomon, a second-year master’s student in microbiology at the University of Toronto in Canada, says that he has no plans to pursue a PhD after finishing his programme. This is mostly because he doesn’t want to commit another four or five years to education. “I was reluctant to spend so many years before you can get started building a life,” he says. “A PhD just isn’t valuable enough.” Solomon is not exactly sure what type of job he’d like to pursue — an entry-level position at a scientific-supply company is one option — but he believes that he’ll be prepared for the next step. He already has a work-like schedule that has him checking into the laboratory around 8.30 a.m. and leaving around 5 p.m.. “I like the structured work hours,” he says. In the survey, PhD students were more likely than master’s students to say that they worked more than 50 hours a week, with 43% and 35% reporting those hours, respectively. When asked what they appreciate about their programme, many master’s students said the element they enjoy most is working with interesting and bright people (54%); the second most-popular response was the intellectual challenge (47%).
Nature special: Young scientists Joshua Caley, a second-year master’s student in biochemistry at the University of New South Wales in Sydney, Australia, appreciates the rigour of his studies. He’s pursuing his programme on a part-time basis while he works as a product developer at a medical-device company. The job helps to pay the bills in an ultra-pricey city, but Caley says that he’s more engaged with his master’s programme than with his paid employment. “The stuff I’m doing at work is interesting, but it’s not really my kind of target,” he says. Caley says that he plans to pursue a PhD eventually, because it’s the only way he can continue doing research on his topic, which involves investigating the underpinnings of age-related disease. “I’m really interested in this particular field of research, and getting a PhD is the way that I can stay in it,” he says. Elizabeth Friedman is co-founder of the National Professional Science Master’s Association, a US advocacy group.Credit: Alon Friedman In the survey, 43% of master’s students say that they wouldn’t do anything different if they were starting their programme again, but there were some misgivings. One-third say that they would change their institution, and one-fifth would change their area of study. A biotechnology master’s student in India wrote in the comment section: “After this degree, there is a scarcity of jobs with a decent pay scale. I wish that I would have opted [for] software designing instead.” Another, studying biology in the United States, commented that she would change several things about her programme, starting with the stipend, which at the time of the survey was less than US$23,000 a year (see also Nature611, 189–191; 2022). Graduate students at her institution are prohibited from taking outside jobs, she says, which makes it almost impossible to live comfortably. She adds that she is happy with her adviser and with their relationship, but would like her programme to start formally evaluating advisers and maintain a standard for working in that role. “I have a wonderful adviser, but I know many peers who struggle with their advising relationship,” the student says. Career advice is clearly an area of concern among respondents (see ‘Degree of difficulty’). Less than one-quarter (22%) strongly agree that their supervisor “makes time for frank conversations about my career”. Twenty per cent strongly agree that their adviser “has encouraged me to attend career training and events”.
The survey suggests that master’s students have different career aspirations from doctoral students. Fewer than one-fifth say that they would prefer to land a job in industry ultimately, a noteworthy contrast to the 32% of PhD students with that goal. A slight majority (51%) say they are more likely to pursue a research career now than when they started their programme. Only 32% of PhD students say the same. Friedman says that master’s programmes in STEM often manage to promote and maintain an interest in research by giving students a chance to work in the lab or field while building other skills on the side. “If they’re in geology, for example, they’re out there doing the fieldwork,” she says. “They are also taught things like public speaking, written communication and project management.” Experiences can differ depending on the department, the university and the field, Friedman adds. She applauds any effort to improve understanding about this sector of trainees. That sentiment is shared by a master’s student in Canada, who finished her survey responses with this comment: “Thank you for including master’s students in this edition of the survey! We are an often-overlooked part of the graduate community.” doi: https://doi.org/10.1038/d41586-022-03758-6 PhDs: the tortuous truth ‘Not even enough money for food’: graduate students face cash crunch Stress and uncertainty drag down graduate students’ satisfaction Decolonizing the biosciences: Turning lip service into action Career Feature Why women aren’t from Venus, and men aren’t from Mars Career Q&A How to protect research ideas as a junior scientist Career Column Linked research hubs train students to tackle societal challenges Correspondence Obstacle race: the barriers facing graduates who study abroad Career Feature Are divisive US politics repelling international early-career scientists? Career Feature ‘Labour advantage’ drives greater productivity at elite universities News Iran: a biochemist on torment and hope Correspondence Quiet quitting in science: share your views Career News Francis Crick Institute London, United Kingdom Luxembourg Institute of Health (LIH) Strassen, Luxembourg The University of British Columbia (UBC) Vancouver, Canada German Aerospace Center (DLR) Ulm, Germany You have full access to this article via your institution.
Nearly half a million monthly listeners on Spotify love producer Sander W.’s chill house music. At the time of our interview, he’d amassed over 95 million Spotify streams in total. Sander’s self-disciplined dedication to creating music is the embodiment of the independent spirit we love to see from RouteNote artists. He also takes delight in lifting up other artists, running up-and-coming label Toneville Records with an aim to give producers a bump up to the next level of the music industry. Right now Sander and long-time collaborator Sönnefelt are celebrating their new release, “My Mind (Ft. Samuel Miller)”. The song secured a position on RouteNote’s Catalyst playlist, alongside other chill house tracks curated by our team – browse them all here. A big element of the dance track, out now on Toneville Records via RouteNote, is the skillful contrast between high and low throughout. Deep pulsing bass contrasts with melodic guitar harmonics, whilst octave mirroring in the simple vocals supplies a sweeter element. Give “My Mind” a spin, and see if you’re dancing even before the beat picks up! So, what inspires Sander, how did he get started on his production journey, and how do we fit in here at RouteNote? Read on to find out. Introduce yourself! Hi, I’m Sander Wolfs. I’m a chill house music producer under the name Sander W. and I run my own independent music label called Toneville Records. I’m operating from Brussels, Belgium. When I’m not in my studio, I love to clear my mind with sports like padel and soccer. Name the last two songs you listened to. “Summertime Sadness” by Y.V.E. 48, and “Medicine” by Lucas Estrada. Are you a self-taught producer? How did you get started making music? I started eight years ago, discovering Ableton by creating edits and mash ups for my previous DJ alias. That’s when my interest started to develop more. I checked out YouTube videos and tried to recreate existing songs. I removed all my games from my laptop, keeping only Ableton as a program in order to push myself to become very familiar with the tool.
Tell us about Toneville Records. What are the best and the most challenging things about running a label? The best thing about having an own imprint as a producer is that you have no filter on distributing new tracks. I can fully decide which tracks I release and from this I was able to create my catalogue and artist profile. These days it’s challenging to compete with other labels, and nowadays all labels have huge playlists and trade with other playlists. That’s the reason why I decided to work together with only a small amount of artists – but building a long-term collaboration, instead of doing single releases from different small artists, since that’s less profitable. Getting a track playlisted on streaming services guarantees streams and introduces the song to countless new music lovers. Do you have any top tips for securing adds on editorial playlists? I noticed that by releasing on a monthly basis and being consistent for some years will keep your monthly listeners high. In this way you also stay top-of-mind with your audience on Spotify.
Keep your Spotify profile up-to-date, and of course the most important tip is to create music that is unique and qualitative. DIY digital music distribution means that artists and producers no longer need to rely on major record label deals to be successful. How has RouteNote made releasing tracks easier? It’s very easy to upload tracks on RouteNote, and if you have any problems you have a reply within one day from the RouteNote team to help you. For me the best thing about RouteNote is that you also can split your profile with other artists and you don’t have to do that manually on your own. We’re in the last quarter of 2022 already! What’s been your proudest achievement so far this year – big or small? For me it’s always a great satisfaction if I see my track is booming on my own independent label. For example, “Sneaking Out” and “Happy Ever After” are two tracks that were picked up by Spotify this year. “Happy Ever After” was picked up by two editorial playlists, Tropical Houseand Feeling Good, Feeling Great. Where do you want to be in five years? I hope to be happy and healthy and I hope I can push my label to new boundaries. I love producing music, and as long as I can continue to do so I will be very grateful. Setting up your own independent record label has never been easier with RouteNote. Upload your own and other artists’ tracks to all the major streaming platforms like Spotify and Apple Music, for free. Check out RouteNote’s award-winning unlimited music distribution here! Your email address will not be published. Required fields are marked *
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Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. Advertisement Scientific Reportsvolume 12, Article number: 19843 (2022) Cite this article 108 Accesses Metrics details Many processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach’s results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime. Complexity often emerges from systems composed of many interacting subsystems. Under suitable conditions, such systems produce interesting coherent collective behavior, some of which even evidence universal features. Examples range from classical physics spin systems at criticality1, to environmentally relevant biological systems2,3 at criticality, and neuronal systems that may or may not be at criticality4. All have in common that their dynamics projects down to much lower-dimensional spaces, and that usually periods of fierce activity interchange with calmer periods. Corporate dynamics emerge from economic agents that exchange signals based on prices5, which puts it into the class described. The typical interchange between activity and calmer periods that we find in these systems is, in particular, found in biological neuronal activity. This is one of the reasons why in a recent work6, stock market indices developments were predicted by a deterministic low-dimensional neuroinformatics-borrowed Rulkov-type map7, and compared to the standard stochastic approach. This comparison yielded slightly superior modeling results of the deterministic over the stochastic one. The crucial observation, however, is that while the generally used stochastic approach fails to offer a convenient understanding of the modeling system’s build-up and of the involved parameters, the Rulkov map approach, due to its simplicity and explicitness, promised to open a door for a deeper understanding of the drivers of the market dynamics—in particular, if a mapping of the real-world data to model parameters could be established6. In the present work, we substantiate these observations and expectations. Here, to emphasize the broad system class embraced by our modeling methodology, we focus on a more general system level and use distinct real-world data. Using data from the market competition between companies as our example, we provide the existence of a convenient handle for guiding such apparently stochastic systems. Competition is an ubiquitous feature of physical and biological systems. For modeling, more specifically, activity developments of firms and the diffusion of innovations in business, Bass-type models8 were used (and later extended with behavioural assumptions on forecasting, e.g., Refs.9,10). Recently, agent communication and interaction structures have made these processes increasingly neuronal-like11. Since also the collective behavior of neuronal ensembles can collectively be modeled by suitably chosen individual neurons12, we model the specific real-world data from corporate dynamics by generalizing the Rulkov maps originally designed to reflect the behavior of individual neurons. The results of this modeling are then compared to those obtained from a stochastic ARIMA-EGARCH model (an approach specifically optimized for dealing with autoregressive, moving average, heteroscedastic asymmetric volatility processes). The comparison will evidence that the two approaches are toe-to-toe. The main aim of the present work is, however, to explicitly demonstrate that the simplicity and explanatory power inherent in deterministic models hosts salient advantages over the stochastic approach and to present a perspective of the insight and opportunities available by capitalizing on this. The present work is made self-sufficient by first repeating the main elements of our deterministic modeling approach. Analytical investigations of our model will reveal in “Stationary states and their stability” section an asymptotic stable stationary state. The precise nature of this stationary state and non-local properties are analyzed in “Numerical investigations of the theoretical model” section using numerical investigations. In the “Android’s market position” section, we will give a wrap-up of how the Android computer operating system achieved a leading position in the market, and what properties the current business state has, according to our analysis. In the conclusion section, we will emphasize the generic nature of the analyzed system type and of the obtained insights. At any level of abstraction of multicomponent systems, increased ’activity’, ’advantage’, or ’profit’ of a subsystem compared to a concurrent subsystem, are the consequences of several factors, such as skills, strategic positioning, etc., and it generally holds that above or below norm profits, respectively, may persist for prolonged periods of time13,14,15,16,17, but must converge to zero under perfect competition conditions, in the long run. For the following, we assume that all of these determining factors are combined in a variable that we shall call ’effort’ e, a quantity that would not be directly measurable, but manifest itself by consequences: The effort of a system at time (t+1), (e_{t+1}), is assumed to depend on a variable x characterizing ”profits” according to a bounded functional form which expresses that at (x_{t}=0), the effort (e_{t+1}) would be equal to a/b, but tend to ((a+1)/b) for (x_{t} rightarrow infty) and to ((a-1)/b) for (x_{t} rightarrow -infty). To obtain an effort bounded between 0 and 1, it is sufficient to set the parameters equal to (a=1) and (b=2). These assumptions entrain a number of consequences. A drop in profit at time t puts pressure on the system, forcing it to increase effort. The latter cannot always be maximal, because efforts imply a rise in costs; if profits are high, the firm has to throttle back. As a consequence, we may expect a differential relationship between effort and change in profits of the form As an illustration, in the business context, a strong link between demand, hours worked, and the profits can be expected. Whereas econometric analysis has not yet revealed the precise form of this link, previous work18 suggests that profits are mainly correlated with average working hours, i.e., is expressed by the concept of effort by Eq. (1), and that the function (f_n(x)) defined defined in (2) has the following properties For n even (f_n) is bounded: (0<f_n(x)le 1(=f_n(0))), (f_n(x)) vanishes for (x rightarrow pm infty), the first derivative of (f_n(x)) is bounded. More specifically, (max _{xin {mathbb {R}}}|f’_n(x)|< frac{n}{2}). (i), (ii) are obvious. (iii) Observe that (f’_{n}(x)=-frac{n x^{n-1}}{(1+x^n)^2}) and set (g(x): =-frac{f’_n(x)}{n}), from where we obtain (g'(x)=frac{x^{n-2}}{(1+x^n)^3}[(n-1)-(n+1)x^n]). Moreover, (g'(x)ge 0 iff -root n of {frac{n-1}{n+1}} le x le root n of {frac{n-1}{n+1}}), so that g(x) assumes its global maximum at (x=root n of {frac{n-1}{n+1}}) and its global minimum at (x=-root n of {frac{n-1}{n+1}}). Since g(x) is an odd function, it is easy to see that (max _{xin {mathbb {R}}} |g(x)|= g left( root n of {frac{n-1}{n+1}} right) = frac{n^2-1}{4n^2} root n of {frac{n+1}{n-1}}<frac{1}{4} root n of {frac{n+1}{n-1}}). The sequence (bigl ( frac{n+1}{n-1}bigr )_{nge 2}) is decreasing; hence, for all (nge 2) one has (frac{n+1}{n-1} le frac{2+1}{2-1} =3) and therefore (root n of {frac{n+1}{n-1}}le root n of {3}le sqrt{3}<2). This proves that (max _{xin {mathbb {R}}}|g(x)|<frac{2}{4}=frac{1}{2};; text {and} max _{xin {mathbb {R}}} |f’_{n}(x)|=ncdot max _{xin {mathbb {R}}}|g(x)|<frac{n}{2}). (square) Chosen in this way, n monitors the reactivity of profit (x_t), where lower values provide higher variability. To model company market competition, we will use a generalized version of Rulkov’s map approach developed for describing neuronal dynamics7 that takes care of the ”dragging” effect of economic variables that in classical stochastic models is implemented via autoregression19: While the change in profit (x_{t+1}) is the consequence of the previous value (x_t) and that of a long-trend value (y_{t}), the value of (y_{t+1}) depends on its previous value (y_{t}) and the short-term change (x_{t}). This can be to first order be implemented by where (beta) represents the sensitivity on the previous value and (-mu) is the ’mean reversion’ parameter. Low changes in profit will require high effort, and high efforts predict the recovery of profit. We may schematically depict this dependence by to a high value of (x_t), a low value of (x_{t+1}) follows, etc. To smoothen this process, the long-term trend y is added Under ’normal’ company performance, the effort will be intermediate, with (x_{t+1}approx 0). By combining Eq. (4) with Eq. (3), we obtain In the case of (gamma) and (delta) equal to zero, the maximum of (f_n(x_t)) determines the maximum effort. (x_{t+1}) will reach its peak value at (x_{t}=0); a small deviation from zero even will cause a dramatic change in the company’s effort. Proposition 2.1 shows that, in the case of (gamma) and (delta) equal to zero, the maximum of x will be (alpha). For assessing the influence of n in (f_{n}(x_t)) regarding the stability of Eq. (5), we use some classical results of two-dimensional discrete dynamical systems where F, G on ({mathbb {R}}^2mapsto {mathbb {R}}) are any nonlinear functions. A stationary point ((x^*,y^*)) of Eq. (6) satisfies Consider the quadratic equation (lambda ^2-blambda +c=0), with (b,cin {mathbb {R}}). Assume that then one has (|lambda _{1,2}|<1), where (lambda _{1,2}) denotes the roots of the quadratic equation. Let ((x^*,y^*)) be a stationary point of system (6) and let J be the Jacobian matrix at ((x^*,y^*)), i.e., Then ((x^*,y^*)) is stable if the solutions (lambda _{1,2}) of the characteristic equation of J have modulus smaller than 1, i.e. by Lemma 3.1, if For deeper insights see, e.g., [27, Chapter V]. For (beta not =1), system (5) admits for any even n the stationary points where (x^*) is any solution of the equation where Moreover, any stationary point of system (5) is stable if Stationary points of (5) satisfy which yields (10,11) as a solution. It remains to check the stability of the stationary points, i.e. that the Jacobian matrix of system (5) satisfies the conditions (9). From (13) and Proposition 2.1 (iii), we have (|alpha f’_n(x^*)|<frac{alpha n}{2}< 1, ;text {i.e.,} ; -1< alpha f’_n(x^*)<1.) With (13), it follows that: (det ,J=alpha beta f’_n(x^*)+gamma mu<beta +gamma mu <1,) (1-Tr,J+det ,J=(1-beta )bigl ( 1- alpha f’_n(x^*) bigr )+gamma mu >0,) (1+Tr,J+det ,J=(1+beta )bigl ( 1+ alpha f’_n(x^*) bigr )+gamma mu >0,) which concludes the proof. (square) These results predict the existence and properties of stationary points of the market competition process as follows. We will start with two explicit examples based on simplifying parameters and finite even n, before we turn to the asymptotic case (n rightarrow infty). Let (n=2) and (beta not =1). In this case, Eq. (11) reduces to where a, b, d are given by Eq. (12). The (complex) roots of such an equation can be given explicitly by means of Cardano’s formula: where It is well known that such a formula gives one, two or three real solutions, according to whether In particular, if one has (p>0), i.e., (3a^2-b^2>0), (17) yields a unique real solution. If, however, it follows that (a=gamma mu +1-beta >0), (b=(beta -1)delta -gamma eta >0), (d=(beta -1)(alpha +delta )-gamma eta >0), (a-b=(1-beta )(1+delta )+gamma (eta +mu )>0) and therefore (3a^2-b^2>a^2-b^2=(a-b)(a+b)>0). Hence, under assumption (19) Theorem 3.3 predicts system (5) to have a unique stable stationary point ((x^*,y^*)), with (y^*=frac{mu x^*-eta }{beta -1}) and (x^*) given by Eq. (17). Moreover (by the positivity of the coefficients a, b, d), one has that (x^*<0). For (n>2) even and (beta =1), system (5) has, however, a unique stationary point ((x^*,y^*)) given by which is stable if (0<alpha <frac{2}{n}) and (0<gamma mu <1-frac{alpha n}{2}). In fact, by Proposition 2.1 (iii), one has (-frac{n}{2}<f’_n(x^*)<frac{n}{2}). As a consequence, the Jacobian has the properties (det (J)=alpha f’_n(x^*)+gamma mu<frac{alpha n}{2}+gamma mu <1), (1- Tr(J)+det (J)=gamma mu >0), (1+ Tr(J)+det (J)=2(1+alpha f’_n(x))+gamma mu>2bigl ( 1-frac{alpha n}{2}bigr )+gamma mu >0), which, according to Theorem 3.3, proves the stability of ((x^*,y^*)). In this limiting case, we have i.e., (f_{infty }(x) = Pi bigl (frac{x}{2}bigr )), where (Pi) represents the rectangle function. If (alpha >0, ;; 0<beta<1, ;; 0<gamma mu <1), for stationary points, using (y=frac{mu x-eta }{beta -1}) (see Eq. 10), we have (x=frac{gamma eta +(1-beta )(delta +alpha f_{infty }(x))}{gamma mu +1-beta }=:Lambda +nu f_{infty }(x)), where Since (f_{infty }in {0,frac{1}{2},1 }), the stationary points of system (5) satisfy one of the expressions ((x^*_1,y^*_1)) is therefore stationary if and only if (’iff’) (f_infty (x^*_1)=0), i.e. iff (|x^*_1|=|Lambda | >1); ((x^*_2,y^*_2)) is stationary iff (f_infty (x^*_2) = 1), i.e. iff (|x^*_2|=|Lambda + nu | <1); ((x^*_3,y^*_3)) is stationary iff (f_infty (x^*_3) = 1/2), i.e. iff (|x^*_3|=|Lambda + nu /2| =1). Using ((Lambda , nu )) as the pair of parameters, ((x^*_1, y^*_1)) is stationary iff ((Lambda , nu )) satisfies (Lambda < -1) or (Lambda >1) (half-planes); ((x^*_2, y^*_2)) is stationary iff ((Lambda , nu )) satisfies (-1< Lambda + nu < 1) (stripe); ((x^*_3, y^*_3)) is stationary iff ((Lambda , nu )) lays on the lines (lambda + nu /2=-1) or (Lambda + nu /2 =1) (line). Thus, depending on the values of ((Lambda , nu )), we obtain 0, 1, 2, 3 stationary points. By stability properties, the half plane (nu >0) divides into regions (A, B, ldots , G) (see the central rectangle of Fig. 1). The stationary points ((x^*_1, y^*_1)) and ((x^*_2, y^*_2)) will always be stable: The Jacobian matrix satisfies Eq. (9), since one has (det (J) = gamma mu <1 text{ and } 1 pm Tr(J) + det (J) = 1pm beta + gamma mu >0). The stability of the point ((x^*_3,y^*_3)) can, however, not be determined by linearization, since in its neighbourhood the dynamics are discontinuous. Using numerical simulations we found that the stationary points at (x^*_3= pm 1) are unstable. We thus have one stable stationary point ((x^*_1, y^*_1)) if (Lambda < -1) and (nu le -1-Lambda), or if (Lambda <-1) , (nu ge 1-Lambda) and (Lambda + nu /2 ne pm 1), or when (Lambda >1) and (Lambda + nu /2 ne pm 1); one stable stationary point ((x^{*}_{2}, y^{*}_{2})) if (-1le Lambda le 1) and (-1-Lambda<nu <1-Lambda); two stable stationary points, ((x^*_1, y^*_1)) and ((x^*_2, y^*_2)), if (Lambda < -1), (-1-Lambda< nu < 1-Lambda) and (Lambda + nu /2 ne – 1); no stationary point if (-1le Lambda le 1), (1-Lambda le nu) and (Lambda + nu /2 ne pm 1); one unstable stationary point ((x^*_3, y^*_3)) if (-1le Lambda le 1), and (Lambda + nu /2 = pm 1); two stationary points, ((x^*_1, y^*_1)) (stable) and ((x^*_3, y^*_3)) (unstable), if (Lambda < -1), or (Lambda >1) and (Lambda + nu /2 = pm 1); three stationary points, ((x^*_1, y^*_1)) (stable), ((x^*_2, y^*_2)) (stable) and ((x^*_3,y^*_3)) (unstable), if (Lambda < -1), (-1-Lambda< nu < 1-Lambda) and (Lambda + nu /2 = – 1). For (nrightarrow infty), we therefore observe seven possible scenarios, depending on the number of stationary points obtained. Theoretical results are generally valid only locally around the stationary state and therefore provide little information regarding basins of attraction involved. Moreover, they fail to reveal what happens if stationary states become unstable. “Stationary states and their stability” section provides sufficient, but not necessary, conditions that yield only conservative predictions of the dynamics to be expected, and also leave the dependence on the order n of the response function f unresolved. To remedy this weakness, we complement our theoretical study with a numerical analysis, where the state space is explored starting from random initial conditions by means of (10^3) simulated paths of 1200 iteration steps each, using different choices of n. The numerical tests suggest that the partition into seven areas obtained from asymptotic n is still valid for n non-asymptotic. Together with the central asymptotic ((Lambda ,nu )) plane partition of Fig. 1, vector-field sub-panels illustrate this finding, where our specifically chosen parameter values were A: (beta =0.8, alpha =0.2, delta =0.1, gamma =1, eta =-1, mu =0.6); B: (beta =0.8, alpha =0.1, delta =0.1, gamma =0.4, eta =-1, mu =2); C: (beta =0.8, alpha =2, delta =0.1, gamma =1, eta =-1, mu =0.5); D: (beta =0.8, alpha =4, delta =0.1, gamma =0.4, eta =1, mu =2); E: (beta =0.8, alpha =5.8, delta =0.1, gamma =0.4, eta =1, mu =2); F: (beta =0.8, alpha =1.8, delta =0.1, gamma =0.4, eta =-3, mu =2); G: (beta =0.8, alpha =1.8, delta =0.1, gamma =1, eta =-1, mu =0.6). Center panel: Stationary states of system (5) in the ((Lambda ,nu )) plane. Small figures: Exemplary illustrations using vector fields on the ({x,y}) state-space with locations of stable fixed-points (green) and unstable fixed-points (red) indicated. More detailed numerical results are presented in the following subsections. Figure 2a exhibits the behavior obtained for variable (alpha), where for (alpha < 1/3) the assumptions of Theorem 3.3 are satisfied. The simulations confirm that when (beta =1) there is always a stationary state with (x^* = eta / mu), and that for all explored values of (alpha), this stationary state is stable. This does not contradict Theorem 3.3 and Example 3.5, since the latter represents a sufficient, but not a necessary, condition. For small (alpha), the stationary state (20) is the only attractor for (nrightarrow infty); at (alpha = 1.39) the system becomes multistable, by saddle-node bifurcation giving birth to a stable period-6 cycle. Depending on the specificity of parameter (alpha), the system either tends to the stationary state (20) or is attracted by another periodic, or chaotic, orbit. Upon increasing (alpha), a Feigenbaum cascade20, 21 emerges, leading from periodic to chaotic behavior. Asymptotic behaviour of system (5) (a) for (n=4, beta =1, delta =0, gamma =1, eta =-0.05, mu =0.9) and (b) for (n=2, beta =0.99, delta =-0.05, gamma =1, eta =-0.0011, mu =0.0025), for different values of (alpha). Last 200 steps from 1200 iterations from (10^3) initial conditions are shown. Figure 2b collects the results obtained for (alpha ne – 0.05) (thus either satisfying or violating the assumptions of Theorem 3.3 and Example 3.4, respectively). The simulations confirm the theoretical result that for small (alpha), the stationary point (17) is stable. As a sufficient condition, the theoretical threshold of (alpha) is, however, very conservative; in reality, the stationary state loses stability for (alpha = 2.2), due to a supercritical flip (or ’period-doubling’) bifurcation. At that level of (alpha), the stable stationary state is replaced by a stable cycle of period 2 that at (alpha = 2.6) loses its stability and is replaced by a stable cycle of period 4. These are the first steps of a flip-type or period doubling bifurcation cascade20, 21 that generally leads to a chaotic attractor dense of unstable periodic orbits. For (alpha in [3.55,4.13]) the only attractor of the system is a period 3 limit cycle. Figure 3 reports the last 200 iterations (out of 1200 simulation steps) of (10^3) simulated paths with (nrightarrow infty), illustrating that the process always approaches a stable state. This not only confirms the arguments of “Case (n=+infty)” section; additionally, it exemplifies that the stationary state of this system does not need to be a simple period one: As (alpha) increases to (alpha = 2.45), a period-11 arises through to a saddle-node bifurcation and disappears through the same mechanism at (alpha = 3.75), whereas at (alpha ge 3.68) a period-7 emerges from a saddle-node bifurcation of the loop, persisting up to (alpha =6.1) where stability is lost due to a supercritical period doubling bifurcation (bifurcation parameters and types were identified using the MatContM22 software). Asymptotic behavior of (5) for (nrightarrow infty , beta =0.9, delta =0, gamma =1, eta =-0.05, mu =0.9) and different values of (alpha). Last 200 of 1200 iterations of (10^3) simulation runs. This is the rough overview of the landscape in which the process when modeled by our approach will take place. It will emerge from our numerical investigations involving real-world data, that, as approaches with different orders n yield results of similar quality, the order n of function f cannot be fixed in a decisive manner (cf. Table 4 below). We demonstrate in the following that our deterministic modeling captures Android’s market competition data. Over the last decade from January 2009 to July 2021, Android’s market percentage rose from 0 to 40.96%, cf. Fig. 4 (based on monthly retrieved StatCounter23 data). Table 1 exhibits the main statistical properties of this data, where skewness and excess kurtosis account for a heavily asymmetric dynamics with extreme deviations. Evolution of Android’s market percentage P, top panel, and corresponding logarithmic changes Log(P), bottom panel, from January 2009 to July 2021 (monthly data). Such properties pose problems for modelling and forecasting. While outliers are generally seen as inconsistent observations24, in economics and finance, skewness and kurtosis are inherent characteristics, and extreme observations are common25,26. In univariate financial time series, innovations are assumed to be symmetric, so that outliers are more difficult to detect than in independent data, since a single outlier may affect subsequent observations27. When it comes to modelling and forecasting, the computational challenge is kurtosis maximisation. To solve that problem, a recent suggestion was to convert projections with maximal kurtosis in univariate financial time series, into an easier to solve eigenvalue problem28. However, kurtosis-based projection pursuit, aimed at removing excess kurtosis, suffers from a crucial drawback: Kurtosis may not be defined for relevant distributions (e.g., the Student-t distribution with 4 or less degrees of freedom; for non-normal multivariate distributions, the fourth cumulant may be a null matrix), so that kurtosis might not be an appropriate projection index29 (for the situation in emerging stock markets, see Ref.30). Our low-dimensional deterministic approach masters the computational challenge posed by the highly skewed time series with extreme kurtosis in a computationally cheap manner. The empirical time series we use captures the monthly percentual change of Android’s market share. We first present modeling results, where we compare our low-dimensional deterministic approach based on Rulkov maps with an elaborate stochastic approach. We first demonstrate that the proposed deterministic approach is as good as the traditional stochastic one. The parameters yielding the optimal results permit us then to determine the location of the real-world data within our theoretical system landscape. The first step in our analysis consists in calibrating the Rulkov approach. Calibration involves a nonlinear regression, performing a robust estimation via an iteratively re-weighted least squares algorithm31. At each iteration, based on the residuals from the previous iteration, the weights are recalculated, until they converge. To compare the results with those of the stochastic approach, the ARIMA-EGARCH approach was taken, with degrees, (p, d, q) and (a, b), respectively, chosen using the Bayesian information criterion (BIC) and the Akaike information criterion (AIC). In the following, we will denote the achieved ’optimal’ stochastic model by ARIMA-EGARCH*. To arrive at a two-dimensional representation, a slow component y is associated with the market dynamics data x, by means of performing an exponentially weighted moving average32,33,34 on x. Evaluations of the dynamic time warping distances confirm that the differences between the stochastic and the Rulkov approaches are at the level of white noise effects (see our Appendix for details). For a first strong demonstration of the strength of our deterministic approach, we consider forecasting. For this, we take the values (x_s, ; y_s) known at time s, from which, with the help of (5), the values at times (t>s) are calculated. Model parameters are calibrated over the rolling window ([s-m+1,s]), where (m=12) is chosen due to the monthly frequency of the data (in contrast to a calibration across the whole data set shown later). Using the mean absolute percentage error (MAPE)35 and the absolute prediction error as measures, the obtained forecasts are compared to those from the ARIMA-EGARCH* model (the latter based on a mean of (10^3) iterations), see Table 2 and Fig. 5. The two approaches evidence similar fits both for the process and its trend, confirming that the deterministic model performs at least as well as the stochastic one. Absolute percentage forecast error E: deterministic versus stochastic approach, components x and y (Android market share data). As an even stronger second argument for the strength of our approach are the results obtained by calibrating Rulkov and ARIMA-EGARCH*, respectively, over the whole time series, cf. Table 3. This setting poses a major modeling challenge when volatility is high, or if the system changes from one regime of behavior to another. The quality of the modeling results reported in Fig. 6, is corroborated in Table 4 ((n=2)-panel) by the ratio between the relative mean absolute error RMAE and the normalized root-mean square error (NRMSE). From visual inspection and error data, it is evident that both approaches capture the market dynamics equally well. Modeling comparison: (a) Android time series variable x (blue), versus Rulkov state variable ({hat{x}}) (red); (b) Android time series variable y (blue), versus Rulkov state variable ({hat{y}}) (red). (c) Android time series variable x (blue), vs. ARIMA-EGARCH* state variable ({hat{y}}) (red); (d) Android time series variable y (blue), versus Rulkov state variable ({hat{y}}) (red). Table 3 reports the parameters that we have obtained from the analysis of the in-sample calibrated time series. Albeit the particular case of a negative value of (alpha) was neither included in the presented model discussion nor in our numerical investigations, numerical investigations reveal that the parameters of the empirical state satisfy the conditions (19) of Example 3.4, so that the motion around the equilibrium state ((-0.0246,0.0005)) should be globally stable. Across the time scales embraced by our empirical data, indeed a deterministic convergence to the mentioned fixed-point is observed on intermediate time scales, on which over shorter time scales a stochastic component seems to act as a ’disturber’. Table 4 confirms our earlier made observation that the order n of the reactivity plays a minor role in the modeling. To date, whether financial data should preferentially be seen as deterministic or as stochastic processes is still unsettled. Some of the available data appear, however, to exhibit a substantial chaotic component36,37,38. Measures that indicate such a property are a positive maximal Lyapunov exponent39,40,41,42,43 (leaving open potential randomness); similarly, large values of the approximate entropies indicate that fluctuations over a time series are unpredictable44,45 (e.g., a regular alternation of 1 and 0 yields the value 0.0022 compared to around 0.63 for a random sequence of 0 and 1). As additional means, correlation dimensions measure the fractal dimension D of the space occupied by the data points43,46,47. For one-dimensional time series, D is directly related to the Hurst exponent48 H by (D= 2 – H)49,50 (for stock markets, H has been shown to be around 0.5-0.651,52). Finally, the normalized ’spectral entropy’ variant SE53 of Shannon’s entropy54 measures the average level of ”information” in a random variable55,56,57. Table 5 exhibits the values of the above-mentioned descriptors of the real-time series of Android market share, demonstrating consistency with the results from the Rulkov approach. While these results, indeed, seem to suggest a chaotic component in the data, most of the numerical methods used are, unfortunately, hampered by the lack of reaching a reliable saturation regime upon using variable embedding dimensions, and thus should not be used to umpire between deterministic chaotic vs. stochastic market data. Figure 7a compares the entropy for the log-changes of Android’s market share versus the entropy of a random white noise process, confirming that the information content of both signals is high, which can be taken as an indication of either chaos or randomness being present in the data. Figure 7b compares the spectral entropy SE of the ARIMA-EGARCH* with that of the Rulkov approach, showing an almost complete overlap of results. Spectral entropy SE (a) of the log-changes of Android’s market share (black) versus that of a white noise signal (magenta) exhibiting similar entropy levels; (b) of the stochastic (blue, continuous line) vs. the deterministic (orange, dashed line) calibrated approaches, for x– (top) and for y-variable (bottom). The almost perfect overlap of the two aligns well with the real-world data shown in (a). The temporal evolution of the Hurst exponent shown in Fig. 8 confirms the possibility of a low-dimensional chaotic component in the data. Evolution of the Hurst exponent H of the logarithmic Android market share changes (rolling windows). We explored the advantages that a low-dimensional deterministic approach may have when applied to traditionally considered stochastic data. Comparisons of in-sample calibration, forecasting and stability analysis of the two deterministic with the stochastic approach, have revealed an example of a commonly exclusively stochastic considered data that hosts a substantial ingredient of deterministic features. For our real-world computer operating systems market share data, our findings indicate stochasticity prevails on the shortest scale and determinism on the intermediate scale. On larger time scales (above one year) the dynamics appear to change again (details not included). Given a desired time-scale, excess entropies, a recently developed tool for comparing models with data58 will provide more details on the accurateness of the modeling of the data. We suspect that beyond the specific data investigated, such a characterization may be a generic feature of a large class of real-world complex multicomponent systems, where our advocated deterministic approach offers insight into otherwise hidden structures that underlie the production of individually stochastic events. Our detailed analysis focused on the model’s dependence on the parameter (alpha) expressing the system’s responsiveness on short time scales. Upon a change of this parameter, stationary states may lose their stability, give way to a Feigenbaum cascade and to other bifurcation phenomena. In this way, our deterministic modeling reveals a strongly multistable nature underlying the generation of individual events, where the identified equilibria may be targets or avoided, by taking appropriate control measures59,60. Thus, in addition to providing short-term predictions of reliability comparable to that obtained from the stochastic view, the deterministic approach offers an overview of the landscape of potential behaviours, that upon a change of externally accessible parameters may be monitored from outside by means of external guidance. From a more global perspective, our investigations reveal strong similarities between local scale market behavior (as pursued here) with that at the more global level (such as the financial stress index), and neuronal firing behavior from various contexts. The embracing system category may, independently of the application specificity, bear substantial importance as a class of theoretical study. The data that support the findings of this study are available from the corresponding author upon reasonable request. Stoop, R. et al. Criticality favours neuronal information representation but not computation. Entropy6, 66 (2022). 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Introduction to dynamic systems; theory, models, and applications, tech. rep. (1979). Download references The authors wish to express their gratitude towards Prof. Michele Mininni, University of Bari, for valuable and constructive suggestions. Neuroinformatics and Physics Departments, University and ETH of Zürich, Winterthurerstr. 390, 8057, Zürich, Switzerland Ruedi Stoop Department of Economics and Finance, Università degli Studi di Bari Aldo Moro, Via C. Rosalba 53, Bari, 70124, Italy Giuseppe Orlando Department of Methods and Models for Economics, Territory and Finance, Università degli Studi di Roma ”La Sapienza”, Via del Castro Laurenziano 9, Rome, 00185, Italy Michele Bufalo Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan, 20133, Italy Fabio Della Rossa You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar Concept: R.S. and G.O., writing: R.S. and G.O., Computations: G.O., M.B. and F.D.R. All authors reviewed the manuscript. Correspondence to Ruedi Stoop. The authors declare no competing interests. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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