Whether you follow Master P’s music, his philanthropic efforts, or his straightforward approach to educating people about the game, there is no doubt you have picked up a few tips from the brilliant hip hop mogul. During the “Assets over Liabilities Live” panel during the 2022 REVOLT Summit x AT&T on Saturday, Sept. 24, Master P revealed one of his most valuable tips: How to get any car you want for free. Co-panelist Rashad Bilal pointed out to the attendees buying cars and jewelry as a business owner is a liability. “Cars are a liability. Jewelry — a lot of the time — is a liability. It may make you feel good [and] it has street credibility, but it doesn’t have any real value in the real world,” he said. “So when we start to change our mindset, it becomes extremely difficult to spend money on liabilities. Once you’ve [become] educated on assets, you look at everything as an opportunity. So instead of spending that $1,000, [you start to think], ‘I could have invested that $1,000.’” The 52-year-old mogul replied to Bilal: “Well, I am going to tell y’all something that might make a lot of sense that they don’t teach us — credit is so important. I want to show y’all that you might want that nice car, but let’s buy that car if it’s over 6,000 pounds, and let’s put that car in a company’s name or an LLC, so we can write it off and get that car for free.” Master P continued, “You can get whatever car you want. Say, for instance, it’s a [Mercedes] Benz [or] it’s a Cadillac — it [doesn’t] matter. You can write these cars off. And guess what? We can lease it. We don’t have to own nothing. We can’t take it with us.” He further explained to the audience that the tips he shared comes from communities outside the Black culture, and we need to start thinking intelligently. “The most important thing that I realize [is] I am keeping and saving my money while I am out here leasing these cars. I can get a new one every year,” Master P expressed. “And so we have to start thinking like that. They [have] been programming [their] cultures like that for years. We don’t understand that. And so [when] I go to a dealership and look for a car over 6,000 pounds, I am writing it off.” "Baywatch" actress Donna D'Errico shared a sexy lingerie photo on Instagram Monday, days after she revealed she feels "lonely" and "unloved" in a vulnerable post to her fans. Donna D'Errico just dropped another lingerie photo on Instagram where her abs and legs are super sculpted. Donna has a vegan diet and works out with a trainer. Shania Twain opened up about aging and posing nude to TalkShopLive, a livestreaming online network, Monday. The country superstar also dished on her upcoming album, “Queen of Me." The royal's son-in-law, a former rugby player, was wearing some very NSFW boxers at the time. Hilarie Burton, JoJo Siwa and Holly Robinson Peete criticized Cameron Bure's comments that the Great American Family network will "keep traditional marriage at the core" of its storytelling Anything for Mugler. Things have been a little rocky lately for the legendary R&B group Xscape, and there has been some miscommunication that has member LaTocha Scott in the spotlight. Lily-Rose Depp, the 23-year-old daughter of Vanessa Paridis and Johnny Depp, is ready to open up. Talking to Elle as their new cover star, the otherwise ultra-private rising actress gave her two cents about having famous parents, growing up in the industry, and even shared some thoughts about her father’s recent defamation trial against ex-wife […] It's kind of wild that Pete only dated Ariana for five months, because I felt that relationship ruled our lives for years.View Entire Post › Actress and her husband Aaron Phypers were shot at by an irate driver on the way to set. Shania Twain is back with new music and a racy photo shoot for her album, Queen of Me, but she has a good reason for deciding to pose in the nude this time around. It wasn’t to get a reaction from her fans, it was about doing something empowering for herself. At 57, she decided […] Marisa Tomei is one of those stars who you can’t help but get so excited when they post on social media, because you know it’s going to be a stunning snapshot. And her latest photo of herself may be one of our favorites yet! On Nov 16, the Spider-Man: Homecoming star shared a rare snapshot […] The Brady Bunch never revealed what happened to Carol Brady's first husband. While the show's creator said that Carol and her husband were divorced, he was hesitant to portray this on the show, as divorce was seen as taboo at the time. Florence Henderson, who played Carol, decided to devise her own backstory, and told the press that she believed her character killed her husband.View Entire Post › Taylor Swift has toned legs and a peek of her butt in a bodysuit and chainmail dress in new photos from the EMAs. She's all about baked goods and white wine. Without looking much into it, it’s safe to assume that all the Kardashian-Jenners have graced the cover of Vogue at least once. Their unprecedented fame and their status as an ever-so-fashionable family certainly gives that impression. For ultimate momager Kris Jenner, however, that wasn’t the case – until today. Revealed on Nov 15, Jenner is seen […] The Queen Ramonda actor reacted to the shocking twist in "Wakanda Forever," saying she feared how fans would react. Kate Moss is a model who rose to fame in the 1990s. In her decades-long career, she's worn sheer dresses, mesh tops, and see-through skirts. Hilary Swank—who is expecting with her husband Philip Schneider—gave fans a glimpse into her Colorado home which boasts sweeping mountain views, or as the actress calls it, their "artwork." Kylie Jenner was a standout at the opening of the Thierry Mugler: Couturissime exhibit on Tuesday Hacks star Hannah Einbinder is the latest to weigh in on Dave Chappelle’s now-infamous monologue from Saturday’s installment of Saturday Night Live. While NBC remains mum on the fallout from the comedian’s appearance, Einbinder took to social media to acknowledge that “yeah, the Chappelle monologue was littered with antisemitism” and added he “did it masterfully.” […]
With 2018’s “God of War,” a reinvention of the long-running mythical action series for Sony’s PlayStation consoles, the hero, Kratos, was transformed. While Kratos was once a man of more fury than words, Sony’s Santa Monica Studio’s’ “God of War” turned him into one of the video game medium’s most famous dads. In a game of fabled, larger-than-life beings, it was inner conflict that ruled, specifically Kratos’ impossible struggle to shield his son Atreus from the physical and emotional dangers of a confused world. “God of War” became a hit, winning top honors at the yearly Game Awards and selling 23 million copies worldwide. Its parenting themes were celebrated, held up as a further example of mainstream gaming’s continued maturation and ability to handle complex themes. Now, Kratos and Atreus have returned this month in “God of War Ragnarök,” a massive adventure in which the younger deity tries to come to terms with his fate and Kratos struggles with Norse legends that constantly aim to needle him into fits of rage, all while coming to grips with his own foreshadowed death. “God of War Ragnarök” is shaping up to be the biggest video game release of the holiday season. Just days after its release, “God of War Ragnarök” led the 2022 Game Awards nominations with 10. Kratos, prior to the release of the 2018 title, was described in a documentary by “God of War” director Cory Barlog as being a character who is all-argh, all the time, a masculine protagonist who could expertly rip your head off but do little else. Yet “God of War Ragnarök” director Eric Williams has been subtly trying to flesh out Kratos beyond those toxic-masculinity impulses since the first game in the series, 2005’s “God of War.” Williams was adamant, for instance, that a hugging mechanic be placed amid a climactic battle of the 2005 title, where Kratos would have to lend his wife and child health to keep them protected during the fight. It was meant to play out as a manifestation of Kratos’ dreams and nightmares, as players already knew the ultimate tragic fate of his family. It also planted a seed that Kratos could eventually evolve, though that would be more than a decade in the making. “It was so metaphorical,” Williams said recently in the offices of Santa Monica Studio. “He was fighting the demons within himself, but he was giving his life to his family. That always stuck with me. That could be a thesis for a change in the character, which we took and ran with.”
While life-giving hugs amid a frantic battle may be a long way removed from walk-and-talk scenes in “Ragnarök” or extended fights as breathless in their action as in their dialogue, it was a scene, says Barlog, that began to shift the thinking at Santa Monica Studio. “God of War” (2018) and, even more so, “Ragnarök” are examples of games that challenge the player to never set down the controller. Even plot expository moments that explain, for example, Kratos’ fraught relationship with the goddess Freya are delivered with forward momentum. Barlog says that was the argument he used to persuade David Jaffe, director of the first “God of War,” not to cut the midbattle hugs. “We were really excited about what we could do in the game,” Barlog says. “We make games. And it’s really neat and fun to do cinematic things, but how can you actually feel like the player has agency?” Tender moments typically occur in narrative, nonplayable scenes, but games over the last decade and a half have been experimenting with how to better meld the two.
“We’ve grown slowly, over a decade or two, to that point,” Barlog says, citing Naughty Dog’s “The Last of Us” (2013) as proof that big budget video games can equally balance violence and emotion. “But I think 2018 was possible to me because of so many other games. “‘The Last of Us’ is defining. You can challenge people on more than killing things, and they’ll want it. It proved to the executives that this is viable. Prior, it was maybe too niche. For the longest time, it was always about the back of the box. You had to have a gimmicky thing to sell it, as opposed to saying that doing something good and engaging people on all emotional levels — not just anger, frustration and fear — is viable.” But that scene was also emblematic of what has become another staple of “God of War” and now “Ragnarök”: finding small, personal moments in a game with gods, goddesses, beasts and dragons.
“So much of Norse mythology is built around the prophecy of Ragnarök. It’s the only mythology where the gods not only know when they’re going to die, they know who is going to kill them,” says narrative director Matt Sophos. “But the more we started to focus on that, the more we kept going, ‘We’re off the path.’ … As you’re developing a story, especially one as big as this one, and you know you’re going to have deal with Ragnarök, we could see every time that we were starting to veer off into too much of the prophecy and mythology lane and needed to bring it back to the personal.” That tension is present at the start of the game, with Kratos and Atreus returning home to their relatively humble cottage for a moment of introspective disagreement. Seconds later, however, they’re disrupted by a visit from Thor and Odin. A large-scale battle ensues between Kratos and Thor, with Thor leading Kratos to a far-away battle arena. As the fight drags on, Kratos becomes increasingly concerned over Atreus’ whereabouts and what Odin may be up to with his son.
“We take liberties with Norse mythology,” says Meghan Morgan Juinio, the studio’s director of product development. “We are not a reality-based game, but our settings are based on things that happen to real people. I think that’s where the emotional connection with our fans comes from. Sure, there’s fantasy elements and enemies you wouldn’t see in the real world, but the experiences and the relationships between the characters are very much like things you would see in real life.” First-time game director Williams says he wanted “Ragnarök” to pick up where “God of War” left off. His goal wasn’t to reinvent the franchise but to have it feel as if it were a new chapter in a continuing saga. “The best compliment I can possibly get, in my opinion, would be that I feel invisible as a director and [that] it feels like a true continuation,” says Williams. “To me, they’re siblings, and they need to co-exist. I don’t want it to be [Barlog’s] game and my game. To me, that would be sad. I want you to jump in and say, ‘This feels like we just dropped off.’ There are differences, but I don’t think they’re so drastic that it would feel strange or awkward now.” Barlog says he can play “Ragnarök” and notice where Williams deviated from his own choices. Nothing large-scale, however. Just little details here and there. Williams maps out each scene with Excel spreadsheets, for instance, a step Barlog skips. “Eric’s like the Wes Anderson of game directors,” Barlog says. “Wes will establish exactly what’s on the set. All the set dressing. A certain figurine that’s on the shelf for one of the characters is fundamentally just as important as the hero prop that exists in the foreground. Its placement means something, not only to Wes but to the characters. He’s fastidious in his planning.”
Out of necessity. Williams says he learned early in the directorial process that he lives with aphantasia, an inability to visualize mental images in one’s mind. To conquer it, Williams said he would overcompensate, sometimes giving artists dozens of visual references or heavily detailed documentation. “I am very rigid,” he says. “I like planning a lot of stuff out. I’ll write everything out in detail. A lot of people find that restrictive. ‘What am I supposed to do?’ You’re supposed to make it. But I wouldn’t take that well, either. I had to leave a little bit of wiggle room. It was a learning process.”
Barlog says Santa Monica Studio is currently “spread out on a lot of different things,” although he declined to offer specifics. The studio has in the past published a diverse slate of independent games, including Thatgamecompany’s thoughtful collaborative work “Journey,” and has occasionally spoken of a canceled project that was believed to have had a sci-fi focus.
But Williams is quick to add that if the company dedicates itself full-time to the “God of War” franchise, there’s no shame in that. “I remember talking to someone from another game company, where they were trying to get me to leave. The said, ‘Do you just want to be known as the “God of War” guy for the rest of your life?’ That was your big pitch to dissuade me? Because yes, I kind of do.” Entertainment & Arts Ron Gilbert once said he would never return to the ‘Monkey Island’ franchise unless he owned the brand. Things changed.
Entertainment & Arts After a 20-plus-year absence, Roberta and Ken Williams, the wife and husband behind the breakthrough video game ‘King’s Quest,’ make an unlikely comeback.
It's a date Get our L.A. Goes Out newsletter, with the week's best events, to help you explore and experience our city. You may occasionally receive promotional content from the Los Angeles Times. Follow Us Todd Martens joined the Los Angeles Times in 2007 and covers a mix of interactive entertainment (video games) and pop music. Previously, Martens reported on the music business for Billboard Magazine. He has contributed to numerous books, including “The Big Lebowski: An Illustrated, Annotated History of the Greatest Cult Film of All Time.” He continues to torture himself by rooting for the Chicago Cubs and, while he likes dogs, he is more of a cat person. Entertainment & Arts
The latest breaking updates, delivered straight to your email inbox. The Loggerhead Marinelife Center in Juno Beach saw its third-highest nesting year on record, for all species combined. While the center is encouraged by the success they have seen this season, they’d like to see more years with consistent highs before they can say population recovery has occurred. Director of Research Justin Perrault stopped by the studio to give us an update. For more information, click here. Hearst Television participates in various affiliate marketing programs, which means we may get paid commissions on editorially chosen products purchased through our links to retailer sites.
By SVG Staff Tuesday, November 15, 2022 – 5:12 pm Print This Story | Subscribe Standards and interoperability have always been a key part of Riedel Communications’ culture, which is why Firehouse Productions — a designer, installer, and operator of sound reinforcement systems for tours, broadcasts, and corporate events — chose Riedel to change up show dynamics at the 10th annual Global Citizen Festival in New York City. Firehouse deployed Riedel’s state-of-the-art Artist digital matrix intercom network with Bolero wireless intercom system as a plug-and-play solution to seamlessly integrate and extend the reach of an OB Truck using a legacy communication system. Riedel’s Artist and Bolero systems provided clear, reliable communications across Central Park’s Great Lawn, including communications with drones and helicopters via Riedel’s RiFace.
Skip to main content Although he has lived in Toronto for the past 20 years, Lavie Lujah has never forgotten his roots in St Elizabeth. He is even prouder being the first person from his home town to release an album of songs. “I feel excited and fulfilled to know that a dream once deemed lost has come true, and an idea long ago conceived has become a product to be consumed. I also feel humbled to be the first from my little bush [community named] Kinowl in St Elizabeth to produce a music album,” he said. That album, I am Lavie Lujah, was released in October. It contains 21 songs including Certified Yardie, which won the inaugural Jamaica International Independence Festival Song Competition in 2021. Jamaica Rise And Shine, which placed second in that contest in July, is also on the album, which is co-produced by Small Axe Music Production, Fyahbeats.com, and SFRbeats.com. A behaviour specialist by profession, Lavie Lujah finally pursued his passion for music two years ago by recording I Can’t Breathe, which was inspired by the racially charged George Floyd incident of May 2020 in the US. Other singles on his album include the humorous Joe Grind and sensuous You’re Beautiful. “I am hoping to reach a cross-section of music lovers all over the world and definitely lovers of reggae music,” he said.
Sign in The holiday season means advice columnist Carolyn Hax’s annual celebration of holiday horror stories is around the corner. Since 2000, readers have shared their favorite holiday memories, whether they be the most ridiculous or touching, to the special live chat, also known as the Holiday Hootenanny. In December 2000, Carolyn wrote an article, “Great Expectations,” about the highs and irrational lows the anticipation of the holidays brings. In a live chat discussing the piece, readers shared how their own expectations of the holidays were let down in all kinds of hilarious ways — and the hootenanny was born. In the years since, many have brought big laughs recounting their stories of holiday celebrations gone haywire. Before this year’s hootenanny, read through past years’ live chats that have made this tradition special. These stories have become often referenced lore in Carolyn’s reader community. If you think we missed an essential hootenanny moment, let us know here. If you’re new to the live chat or the column, this glossary of terms might be helpful. From the very first Hootenanny comes the Death Chair story about one family’s cursed seat at the head of the holiday dining table. You can probably guess what happened to a couple of the reader’s relatives who sat there. The original poster even gave readers an update 18 years later! Bonus: This chat also, separately, features the Reindeer Poop Award. The first holiday chat (2000) A turkey, a tequila sauce, a ball of fire. What more do you need? (See also the exploding Bacardi ham of 2016.) The 2010 Holiday Hootenanny of Horrors The absence of stuffing at Thanksgiving causes one reader to have an epic meltdown that is fondly remembered by many live chat participants. If you thought this would be the end of the original poster’s stuffing woes, their update one year later will prove you wrong. Hootenanny of Holiday Horrors 2015 The Naked Susan story begins with an innocent enough family game of charades but has an ending for the hootenanny ages that includes a significant cliffhanger. Don’t worry — the original poster came back with a much-asked about update the next year. Hootenanny of Holiday Horrors 2018 The 2020 Holiday Hootenanny came in hot with a decaying, 20-something-year-old gag centerpiece made of food scraps. Celery Man has leafy jazz hands, three toothpick legs and a place of honor every holiday season. The original poster sent over a photo of the celery man, seen here in a reply to Carolyn’s greeting in the next week’s live chat. Hootenanny of Holiday Horrors 2020 Carolyn shares a remixed version of Clement C. Moore’s poem, “A Visit From St. Nicholas,” by her dad, John Hax, in many of the hootenannies. What began as a holiday tradition from the Hax household became a hootenanny mainstay. The poems are mini time capsules with their references to the political climate or popular celebrities of the moment — like the 2012 version with the lines, “On Newt and Michelle. On Rick, Ron and Mitt.” Hootenanny of Holiday Horrors 2012
Spatial audio has been on a slow rise in popularity over the past few years, and more and more clubs, venues, and corners of the industry are starting to notice. Yet the number of producers and audio engineers willing to learn how to mix in this new medium hasn't kept pace with how fast the technology has grown. This means there is no better time than now for producers and engineers looking to break into the pro audio world to strike while the iron is hot. And if you're looking for a place to start learning how to work with spatial audio, CRAS (Conservatory for Recording Arts & Sciences) and Spatial is the place to do it. They are an award-winning immersive audio technology and software set to unveil a groundbreaking new curriculum designed to train engineers and producers for new job opportunities in experiential, immersive audio. We sat down with Monica Bolles of Spatial to dive deep into why right now is the best time to use this powerful immerging technology. Monica Bolles is a digital artist, audio engineer, and composer from Boulder, CO, with a B.S. in Music Production from CU Denver and an M.S. in Creative Technology and Design from CU Boulder. She has created and produced works exhibited in the 140-channel speaker array at the Cube at Virginia Tech, the IMERSA Fulldome Summit, NIME (New Interfaces for Musical Expression), and the Conference of World Affairs, among others. There is a massive uptick in interest currently for spatial audio. When Oculus first announced its Kickstarter and launched the hype around VR, you suddenly saw all of these big audio companies beginning to pay attention to spatial audio. Before that, I’d say it existed in the fringes of academia and European research institutes like IRCAM. Now the industry is paying attention to the rise of VR/AR/XR, immersive experiences, and the metaverse… suddenly ‘immersive’ is the new hot thing, and everyone wants to be involved. That means that there are a lot of opportunities. It’s still early days, too, so I think there’s a lot of room for new faces. There are also many new toolsets on the market that make it much easier to be creative. Companies like Spatial are creating studio suites for non-linear spatial audio design specifically valuable for creating large-scale immersive installations and experiences. Other companies are actively pushing into applications for live music and in-home listening… With all the support behind new formats and toolsets, it is easier to create efficient workflows and focus on the creativity of the projects without worrying as much about technical complexities. There is a lot of educational noise right now, and it can be hard for someone interested in learning to work with spatial audio to find good information about what ‘spatial audio’ is. Many studio engineers I talk to that are just getting into spatial audio think it refers to Dolby Atmos. In truth, people use various algorithmic approaches to solve ‘spatialization,’ and each algorithm can offer them something different. While Dolby has created a particular set of standards and tools that work within those standards, there are so many other tools and standards being developed by other companies (like Spatial, which I mentioned above) that can be used to create a spatial audio mix. Every approach has a ‘sound,’ and choosing a spatial audio algorithm is like selecting an eq. Choosing the tool, you are using, or the standard depends on the application of your mix and what part of the industry you are trying to work in. In reality, the tools, workflows, and standards are still developing; there are still a lot of limitations, so you have to be willing to do the research, innovate, and think outside of your ‘traditional’ training. When creating a spatial mix, most of the tools available at this point focus on the ability to virtualize the positioning of sounds. However, due to the way these algorithms work, many tools we use as studio engineers, such as FXs, eq, and compression, won’t work. You could use regular plugins on a mono sound that is a ‘source’ in your audio space, but after that, you are limited as to what other ways you can affect the sound of the overall mix. Any tool you use after the spatial virtualization will affect the spatialization. I’m not sure Mastering has been figured out yet. You will also have to get good at routing and understanding how to do complex bussing. While DAWs have come a long way in making it easier to interface with different spatial audio formats, there will still be a certain amount of complexity to how you will need to route and set up your IO and configurations. Space. As a mix engineer, you constantly try to find space for your sounds. In stereo, we use eq and compression to help us find space. With spatial mixing, you don’t need to use those tools as much because you create space through virtualized space. You can help give your sounds space to breathe by just positioning them in different locations of your virtualized ‘space.’ Being in a ‘niche’ field has helped me in life. If you know something nobody else knows, you will set yourself up for being valuable. Are there more job prospects with this skill set? I think that’s hard to say. The industry is growing rampant, but many people are also trying to break into this space. As a mix engineer, you are competing against some of the top mix engineers in the industry that are hopping on the spatial audio hype train. If you are someone just coming out of school as an audio engineer, I think to break into spatial audio; you have to be passionate about it and find a way to approach it from a unique angle. Because it’s such a new industry, there’s still room for a lot of innovation; the rules are still being written so take advantage of that. Spatial audio is currently being used in many different audio industries, so this will vary based on what part of the industry you want to go into. The tools and processes you are going to use are going to be different too. Spatial audio is a massive component of the VR/AR/XR space. Most creators in this space use ambisonics-based toolsets and spatial audio plugins that allow 6 degrees of freedom. We are seeing spatial audio introduced to the live performance space. There is a lot of exciting work around designing spatial audio installations for theme parks, event spaces, museums, and health facilities. The Spatial, Inc. toolset is paving the way for non-linear content creation most applicable to building sound worlds for installations. More and more music is being mixed for spatial audio. Car manufacturers are starting to include spatial audio. Sennheiser Ambeo Mobility is taking the lead on this. Almost every part of the industry is being influenced by spatial audio. Some tremendous online communities have a lot of knowledge to share and can be good to join and learn from if you are starting. I help host a virtual Spatial Audio Meetup through NOTAM and also help co-host the Immersive Audio Podcast, both great resources for learning about many of the tools and projects people are working on. There is also the Spatial Audio in VR/AR/MR group on Facebook, which I highly recommend anyone in the industry to join. AES has conferences specifically oriented toward spatial audio; sometimes, they host online events. Anyone with the correct initiative can quickly learn how to mix binaural audio with free or near-free toolsets. Still, if you want to start working with multichannel systems, you have to find a place to let you come in and start playing with their system. For that, I would recommend finding a university with facilities that you can use and programs oriented toward spatial audio. Some places host residencies or more short-term programs as well. Managing Editor at Magnetic Magazine – Former Marketing Manager at the Hyperbits Masterclass – Writer, Content Strategist, Music Producer, and Record Label Manager
Our council-manager form of government combines the civic leadership of elected officials with the managerial experience of an appointed city manager. Beyond all else, we are a service organization, and we are here to serve our community. Roseville is the largest city in Placer County and called home by 135,000 people. Find the resources you need here. We are a place where businesses small and large find success. Ideally located, Roseville provides first-rate services, competitive costs, solid long-range planning and an educated, growing population.
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 Communications Biologyvolume 5, Article number: 1244 (2022) Cite this article 88 Accesses 1 Altmetric Metrics details Many neuroscience theories assume that tuning modulation of individual neurons underlies changes in human cognition. However, non-invasive fMRI lacks sufficient resolution to visualize this modulation. To address this limitation, we developed an analysis framework called Inferring Neural Tuning Modulation (INTM) for “peering inside” voxels. Precise specification of neural tuning from the BOLD signal is not possible. Instead, INTM compares theoretical alternatives for the form of neural tuning modulation that might underlie changes in BOLD across experimental conditions. The most likely form is identified via formal model comparison, with assumed parametric Normal tuning functions, followed by a non-parametric check of conclusions. We validated the framework by successfully identifying a well-established form of modulation: visual contrast-induced multiplicative gain for orientation tuned neurons. INTM can be applied to any experimental paradigm testing several points along a continuous feature dimension (e.g., direction of motion, isoluminant hue) across two conditions (e.g., with/without attention, before/after learning). Neurons in mammalian sensory cortex often exhibit tuning functions, responding selectively to a narrow range of values of a stimulus feature such as line orientation1. Moreover, experimental manipulations of perceptual or cognitive state can modulate these tuning functions, providing crucial insights into the neural mechanisms of perception and cognition. For example, spatial attention achieves performance gains by multiplicative rescaling of orientation tuning functions in macaque V42, rather than through a bias shift (additive shift) or increased selectivity (sharpening). As another example, Fig. 1a shows a neuron in mouse primary visual cortex3, tuned to motion direction, that appears to undergo multiplicative rescaling as spatial frequency is manipulated (Fig. 1a). However, single-cell electrophysiology is rarely feasible in humans, and non-invasive techniques such as functional magnetic resonance imaging (fMRI) reflect the activity of many cells: a patch of striate cortex the size of a typical fMRI voxel (2 mm3) reflects the activity of approximately 300,000–500,000 neurons4. Nonetheless, fMRI studies reveal feature-selective tuning in voxels (e.g., in which a voxel’s BOLD response varies systematically as a function of a well-defined feature such as stimulus orientation)5,6, which is assumed to arise from a non-uniform distribution of tuning preferences across the neurons contributing to a voxel7. a Modulation of neural tuning. In this neuron (mouse primary visual cortex)3, direction tuning interacts multiplicatively with spatial frequency (cpd: cycles per degree; (Delta F/F): average change in fluorescence). b Convolution ((*)) of neural tuning functions with a weight distribution leads to voxel tuning functions. The modeling procedure of INTM assumes that the observed voxel tuning functions reflect the shape of the neural tuning functions as applied across the distribution of preferred orientations (the weight distribution) within each voxel. Compare with Eq. 3. c An additive shift in the neural tuning function causes an additive shift in the voxel tuning function. d Multiplicative gain in the neural tuning function causes multiplicative gain in the voxel tuning function. Compare c and d with Equation 4. Like neural tuning functions, voxel tuning functions are modulated by manipulations of perceptual state8,9,10,11, and so it is tempting to infer the form of neural-level tuning modulation directly from observed changes in voxel tuning. But, as many have acknowledged, directly inferring neural behavior from voxel behavior might be misleading10,12,13,14. The relationship between voxel and neural tuning functions presents a many-to-one inverse problem: the same voxel tuning function can arise from many different combinations of the shape of the underlying neural tuning functions and the distribution of neurons across different preferred stimulus values (e.g., the number of neurons preferring vertical, horizontal, or oblique orientations). Thus, fMRI tuning does not uniquely specify tuning at the neural level14. Rather than quantitatively solving this inverse problem, which is probably not possible, we developed a framework that allows drawing qualitative conclusions about changes in neural level tuning from the Blood Oxygen Level Dependent (BOLD) signal. We term the framework Inferring Neural Tuning Modulation (INTM). Building on encoding models15,16,17, INTM assumes that voxel tuning emerges from the combined activity of feature-tuned neurons. Unlike many existing encoding models, which assume that voxel activity is driven by a discrete number of neural “subpopulations”, INTM conceptualizes the underlying neural preferences as existing along a continuum (Fig. 1b). This continuous distribution resembles population receptive field mapping, but whereas population receptive field mapping is generally concerned with uncovering the quantitative parameters of tuning (e.g., the size of receptive neural fields, or the population’s preferred location in the visual field)18, INTM is designed to uncover the modulation of tuning. To do this, INTM leverages the observation that some forms of modulation produce patterns of BOLD data that are distinct from other forms (Fig. 1c, d), and so the BOLD data provide information about which form of tuning modulation is most likely. This framework encompasses many kinds of analyses, but, in short, INTM prescribes building multiple encoding models of voxel data that are parameterized by continuous distributions at the neural level, followed by comparison between the models in light of the observed BOLD data to uncover the most likely form of tuning modulation. We validated INTM by applying it to a new dataset for which the “ground truth” modulation of tuning was known from single-cell recordings: changes in visual contrast induce multiplicative scaling in orientation-tuned neurons19,20,21. This simple test-case demonstrates the advantages of INTM, considering that existing methods, if interpreted as indicating the underlying neural tuning functions, can easily reach the wrong conclusion about the form of neural tuning modulation when applied to changes in visual contrast c.f.,14,22. We used INTM to design two complementary analyses that differ in the assumptions required for the statistical models underlying the analyses. The first analysis uses Bayesian estimation and quantitative model comparison by making parametric assumptions for the shape of neural tuning (a circular Normal distribution). The second makes no assumptions about the shape of neural tuning (i.e., a non-parametric analysis), providing a qualitative check of whether similar conclusions are reached. Critically, both techniques are needed, with the parametric model not only providing statistical model comparison, but also indicating the expected qualitative data patterns for the non-parametric check. As applied to BOLD data collected from the primary visual cortex of human participants viewing oriented gratings at high versus low contrast, the techniques correctly implicated multiplicative scaling, despite working with only voxel-level data. We first use INTM to build a parametric model of voxel tuning for inferring how changes in stimulus contrast modulate neural tuning. The resulting model provides a concrete demonstration of the ways in which different kinds of neural tuning modulation should produce different behaviors at the level of the voxel. The parametric modeling approach involves assuming specific forms of the neural tuning functions, and further specifying the contribution of these tuning functions to a voxel’s activity with a continuous distribution. For application to orientation preferences, which lie on a circular measurement scale, the contributions are assumed to follow a circular Normal distribution (Fig. 2). The circular Normal distribution resembles a typical Normal distribution but is periodic, thereby accommodating the circular nature of orientations. The distribution’s density function has a period of (2pi), but orientations have a period of (pi), so the values of the orientations used in an experimental design are doubled when applying the model. For an orientation, (r), the density function is where ({kappa }_{1}) is a concentration parameter, (phi) is the orientation of the peak value of the function, and ({I}_{0}(cdot )) is the modified Bessel function of the first kind, of order 0. The numerator of Eq. 1 produces a periodic bell shape peaking at (phi), with the concentration parameter determining its “sharpness”. Left: A Kohonen network was used to simulate orientation preference maps. Each panel represents a separate voxel. Right: Weight distribution for each voxel. The histograms represent the tallies of each preferred orientation in the left panels. The black line is the best fitting (maximum likelihood estimation) circular Normal density function (Eq. 1). The horizontal gray (shaded) ribbons give the 99% confidence interval for a flat distribution (i.e., the range of heights that we would expect when a simulated voxel contains an equal number of neurons tuned to all orientations). Given the amount of cortex sampled by each stimulated voxel, most weight distributions tend to be flat, but the fitted von Mises density function can capture individual modes. In the parametric model, there are two uses of the circular Normal distribution. First, Eq. 1 describes the relative contribution to a voxel’s activity of different subpopulations of neurons that prefer different orientations, and so we refer to it as a “weight distribution”. With a flat weight distribution (low ({kappa }_{1})), the neurons within a voxel are in equal proportion (resulting in a complete absence of voxel tuning even if the contributing neurons are well-tuned). With a peaked weight distribution (high ({kappa }_{1})), most of a voxel’s activity is driven by neurons tuned to orientations around (phi) (resulting in sharp voxel tuning if the contributing neurons are also well-tuned). A circular Normal density function fits single cell orientation tuning functions adequately23 and so, in INTM, a second circular Normal distribution function is used to specify the individual neural tuning functions (Eq. 2). Although this equation relies on the distribution function, the interpretation is not a probability density but instead a description of neurons’ responses to orientations. In this equation, the concentration parameter indicates the sharpness of a single cell’s tuning. To account for a neuron’s baseline activity and responsiveness, we included additional parameters. The baseline activity parameter reflects the activity of a neuron in the absence of stimulation and is implemented as an additive offset, (alpha). The parameter for responsiveness models how well a neuron responds to stimulation and is implemented as a gain parameter, (gamma). With the addition of these baseline activity and responsiveness parameters, Eq. 2 specifies the neural tuning function, ({NTF}(cdot )) for orientation of a presented stimulus relative to that neuron’s preferred orientation. Within each voxel (but not across voxels), all neural tuning functions are assumed to take on the same circular Normal parameter values. The voxel tuning function is obtained by convolving Eqs. 1 and 2 (Fig. 1b). This results in Eq. 3, the voxel tuning function, ({VTF}(cdot )), in a baseline condition (e.g., low-contrast stimuli). It is critical to note that the choice of baseline condition is arbitrary (e.g., the high-contrast condition could be labeled as the baseline) considering that the model is applied to both conditions conjointly. The only difference in terms of which condition is labeled as baseline is whether the modulation parameters are increases or decreases. The subscript (v) indicates parameters that are estimated separately for each voxel. The concentration parameter, ({kappa }_{v}), is equal to neither ({kappa }_{1}) nor ({kappa }_{2}), but is a function of both24. Thus, the model does not distinguish between voxels containing a concentrated distribution of orientation-tuned neurons each of which has diffuse tuning (high ({kappa }_{1}) and low ({kappa }_{2})), and voxels containing a diffuse distribution of orientation-tuned neurons each with concentrated tuning (low ({kappa }_{1}) and high ({kappa }_{2})). The key insight behind INTM is the realization that there is no need to differentiate between such possibilities, if the measurement goal is identification of the qualitative form of neural tuning modulation rather than precise specification of neural tuning functions. Within the INTM framework, each form of tuning modulation is instantiated by incorporating additional parameters that modulate one or more parameters in the baseline voxel tuning function (Eq. 3, Fig. 1c, d). In this validation test case as applied to visual contrast manipulations, we considered two forms of tuning modulation that are capable of producing an average increase in neural activity: multiplicative gain and additive shift. Other forms of neural tuning modulation, such as bandwidth changes and tuning preference shifts, could be implemented within the INTM framework, but these forms were not included in the candidate set of models for this test case because they do not change average neural activity (i.e., they are not viable models for the neural modulation that underlies changes in visual contrast). In this test case, multiplicative gain is known to be “ground truth”—that is, changes in visual contrast induce multiplicative gain in single-neuron tuning functions19,20,21. However, in seeming contradiction to multiplicative modulation, an examination of raw voxel tuning functions suggests an additive increase with increases in visual contrast (Fig. 4a, b). Nevertheless, averages can be misleading, and a formal model comparison between additive shift and multiplicative gain is required that considers each voxel separately, particularly when considering that many of the voxels contributing to the average exhibit poor tuning. For completely untuned voxels, additive shift and multiplicative gain are indistinguishable and so the average will necessarily look additive. If INTM works, it should leverage differences between voxels (i.e., capitalize on the small proportion of well-tuned voxels), to reach the conclusion that multiplicative gain is the more likely form of tuning modulation despite what the average BOLD signal appears to show. To model a change in multiplicative gain, we included a voxel-specific gain multiplier parameter, ({g}_{v}) (Eq. 4a). To model an additive shift change, we included another, voxel-specific additive shift parameter, ({a}_{v}) (Eq. 4b). In summary, Eq. 3 captures the situation for low contrast in both models, whereas either Eq. 4a or 4b captures the situation for high contrast. For other applications, shifts in orientation preferences could be modeled by allowing ({phi }_{v}) to change across conditions, and a change in concentration could be modeled by allowing ({kappa }_{v}) to change across conditions. In the current dataset, these forms were not pursued because neither allows contrast to alter the average activity of a voxel across orientations—an effect that was clearly present in the empirical data (Fig. 4a)—and so these forms could be rejected without explicit modeling. Equations 3, 4a, and 4b model voxel activity at each tested orientation, at each level of contrast. However, there is variability in voxel activation across runs, and this variability varies across voxels (some voxels are noisier than others, Supplementary Fig. 2). These sources of variability were included in the model, and all voxel-specific parameters were estimated hierarchically (Supplementary Methods). Hierarchical estimation of voxel tuning functions combines information across voxels, allowing model comparison to automatically down-weight the noisier voxels and magnify the well-tuned voxels25. The parametric model assumes that all neurons within a voxel share a common shape for their tuning function (homogeneity of tuning shape), which is unlikely to hold strictly true. However, some degree of tuning shape heterogeneity should not invalidate inferences drawn about the form of tuning modulation, provided that tuning function shape does not differ systematically as a function of the orientation preference of the neurons. That is, there could exist a range of tuning function shapes, but if that heterogeneity occurs to the same extent for neurons centered on all preferred orientations, then it should not lead to scenarios where one form of modulation mimics another at the voxel level. Nevertheless, to assess whether such heterogeneity posed a problem when adjudicating between the forms of tuning modulation, we also developed a non-parametric check that does not make this assumption. If the non-parametric check supports the same qualitative conclusion as the parametric model, this suggests that the homogeneity of tuning shape assumption was adequate. INTM judges the relative plausibility of each form of neural tuning modulation (e.g., Eq. 4a versus 4b) with model comparison based on empirical data. But under what circumstances should model comparison be trusted? To assess the extent to which inherent properties of the models (e.g., their flexibility) allow reliable model comparison, we assessed model recovery via two kinds of simulation: data-informed and data-uninformed26. Model recovery entails producing simulated data from each model, asking whether the model that produced the simulated data is better able to capture its own data than competitor models. If a model is overly flexible, then it might provide a better explanation of data generated by other models than do the generating models themselves. Data-uninformed model recovery asks whether the model comparison technique is well-calibrated to the relative flexibility of each model in general. First, synthetic data were generated with each model using “weakly informative” priors (Supplementary Methods). These priors were not designed to reflect precise experimental knowledge but instead simply provide a rough scale for each parameter individually. Next, the models were applied to these synthetic data, keeping in mind the “ground truth”, data-generating model. The model comparison technique has built-in adjustments for flexibility by approximating the ability of each model to predict held-out data (i.e., cross-validation). However, this approximation might be inadequate, providing too much or too little penalty for model flexibility. Data-uninformed recovery asks whether this model comparison is operating as it should in general. There is no guarantee that a specific real dataset will be diagnostic regarding a particular model comparison. For instance, if none of the voxels is sufficiently well-tuned, then the two forms of tuning modulation will make the same prediction. Similarly, if the manipulation of visual contrast is too weak, it would not be possible to reach a reliable conclusion. Whether the real dataset is sufficient for differentiating between the candidate models is assessed using data-informed model recovery by repeating the recovery process using what has been learned about the parameters of the models from the empirical data. Whereas data-uninformed model recovery assesses the fairness of model comparison across a wide range of individual parameters that are plausible given the prior distribution, data-informed recovery generates synthetic data by sampling from the posterior distribution obtained by estimating the models with empirical data. Generating synthetic data that are consistent with real data constrains the parameters (e.g., tuning width and modulation) to a much narrower and more realistic range of values. Indeed, the behavior from the posterior parameter values closely matches the weak tuning effects seen in the real data at the level of separate voxels (e.g., Supplementary Fig. 5). Because the data-uninformed model recovery has priors that are only weakly informative, it can allow extreme parameter values for estimated beta-weights, and hence implausibly sharp tuning functions; this increases the chance that each generating model will produce a unique signature pattern in the data, making model recovery likely to succeed. By contrast, the more constrained data-informed model recovery presents more of a challenge to model recovery, providing greater reassurance in the case that it succeeds. The parametric model assumed normal functions for the NTFs and weight distributions and additionally assumed homogeneity of NTF shape within a voxel. These assumptions will often be violated, but such violations might not pose a problem for model comparison, particularly if the violations of these assumptions are uniformly applied across the stimulus dimension of interest. Nevertheless, as a complement to parametric model comparison, we developed a more qualitative non-parametric check of the empirical data. If this check supports the same conclusion as the parametric model, this suggests that any violations of parametric assumptions were insufficient to alter the theoretical conclusions. The parametric model is crucial to the development of the non-parametric check and the specific parametric models under consideration should first be used to generate predictions for the check. The consequences of parametric assumptions are then considered in light of these predictions. In the case of a comparison between multiplicative gain versus additive shift, these two forms of tuning modulation can be distinguished using voxel-wise regression; if the modulation is multiplicative, a within-voxel plot comparing high- versus low-contrast should have a slope greater than 1, whereas if the tuning modulation is additive, this plot should reveal a slope equal to 1. Furthermore, these predictions do not rely on parametric assumptions. For instance, if a voxel is multimodal, preferring more than one orientation, this would serve only to rearrange the order of the orientations in the regression plot, but the qualitative distinction between a slope of 1 versus a slope greater than 1 would still map onto additive shift versus multiplicative gain. The generality of the slope test across all shapes of tuning function and all shapes of weight distribution is mathematically proved in Supplementary Methods Eqs. 1–4. The key difference between these two forms of tuning modulations is that the multiplicative model allows the effect of contrast to vary by orientation whereas the additive model does not. Additive modulation corresponds to an increase in neural activity at all orientations. Thus, regardless of the weight distribution and regardless of the shape of the neural tuning functions, additive tuning modulation causes the low-contrast tuning function to shift upwards uniformly across orientations (Fig. 3, top left). Hence, a scatterplot of the voxel’s response to high-contrast stimuli against its response to low-contrast stimuli has a slope of 1 (Fig. 3, top right). In contrast, multiplicative tuning modulation corresponds to a greater increase in neural activity at the most preferred orientations (Fig. 3, bottom left), and a scatterplot of a voxel’s response to high versus low-contrast stimuli has a slope larger than 1 (Fig. 3, bottom right). Therefore, the models can be differentiated by plotting high-contrast activity against low-contrast activity and calculating the slope of the best fitting line (Fig. 3, right). A slope of one implies additive shift, but a slope greater than one implies multiplicative gain (see also Supplementary Methods). The only assumption made in this analysis is that the magnitude of the additive shift or multiplicative gain is the same for all neurons contributing to a particular voxel or, more specifically, that if the magnitude of modulation does vary across neurons, it does not vary systematically with neurons’ preferred orientation (see Supplementary Information). a Average voxel tuning at low and high contrast using binning to average (see Methods). Error bars give 95% confidence interval for the mean of the 1010 V1 voxels across seven participants. b Examples of individual voxel BOLD data in comparison to posterior predictions of the multiplicative gain model. The panels show the 16 voxels with the largest average difference in activity across levels of contrast. Vertical error bars span 95% confidence intervals (within-subjects), and the width of the lines indicate the 95% highest density interval of the posterior predictive distribution for the multiplicative model (additive model looks similar). c Overall comparison between each model ((hat{beta })) and observed data ((beta)). Each point corresponds to a single voxel’s average activity at a given orientation at a given level of contrast. Panels show the average of the posterior for predictions from either the additive or multiplicative model. Analyzing the slope is not necessarily straightforward. First, the slope between high- and low-contrast cannot be determined using standard linear regression (i.e., estimating the line that minimizes the ordinary least squares error—the squared vertical distance between the line and the data). Standard linear regression estimates a relation between two sets of observations, such as the activity at low and high contrast. But when both of those observations are corrupted by noise, the estimated relationship is “diluted” and biased to zero27. To mitigate this dilution, the slope was estimated using orthogonal regression27, by finding the line that minimizes the squared Euclidean distances from the data (Methods, Supplementary Methods). Second, the slope analysis cannot be done across voxels because there may be covariance between a voxel’s low contrast (baseline) activation and the effect of contrast on the voxel’s activity (e.g., voxels with a larger response in the low-contrast condition may receive a larger contrast effect, and this tendency would bias an across-voxel analysis toward a slope greater than 1). To mitigate this confound, slopes were determined separately for every voxel, followed by an analysis of the distribution of slopes. Finally, even a within-voxel slope analysis produces results that are difficult to interpret because most voxels are only weakly tuned, responding to all orientations almost equivalently. For those voxels, the data for the slope analysis will be an uncorrelated cloud of points, and an orthogonal regression for a cloud of points can take on nearly any slope value, including positive or negative infinity for the case of vertical slopes. Therefore, we report, not the slope of the line, but instead the angle of the slope. In using INTM, we recommend first developing and comparing parametric models of how stimuli give rise to voxel activity during manipulations of cognitive or perceptual state, and then, in addition, to consider ways of relaxing those parametric assumptions to provide a non-parametric check of the model comparison results, as with the slope test for comparisons of multiplicative versus additive changes. Voxel tuning functions were first analyzed with a standard approach of “averaging” across circularly aligned voxels (Fig. 4)10, which is an appropriate technique if all voxels have similarly shaped tuning functions. This “binning” alignment technique appears to reveal an additive shift with contrast, in contrast to what is known from electrophysiology. This apparent additive shift is caused by the inclusion of many voxels with poor orientation tuning. When the BOLD response is aggregated across a many such “undiagnostic” voxels, the true form of tuning modulation is obscured (i.e., it appears additive rather than multiplicative). One approach to mitigating this variability would be to adopt experiment-specific thresholds, excluding some subset of “relatively” untuned or unresponsive voxels. However, it would be difficult to justify such thresholding for each experiment, and more importantly excluding voxels throws away information (e.g., about the average noise in voxels’ responses). The two techniques of INTM avoid thresholding, even while using the well-tuned “diagnostic” voxels to identify the most likely form of tuning modulation. Left: Simulated voxel tuning functions in which higher levels of contrast induce either an additive (top) or multiplicative (bottom) tuning modulation. The eight vertical lines are eight hypothetical orientations at which these voxel tuning functions might be probed, which would produce eight responses per level of contrast, High vs. Low. Note that, whereas the parametric model assumes that the weight distribution and neural tuning function follow specific shapes (e.g., unimodal distributions), the slope test does not (e.g., the voxel tuning function can be bimodal, as displayed). Right: The two kinds of neural tuning modulation reveal different signatures when the responses to high contrast stimuli are plotted against the responses to low-contrast stimuli. The diagonal line corresponds to no effect of contrast. A line drawn through the points produced by the additive model necessarily has a slope equal to 1 (top); under this form of modulation, the effect of contrast does not depend on the orientation. A line drawn through the points produced by the multiplicative model necessarily has a slope greater than 1 (bottom); under this form of modulation, the effect of contrast is largest at those orientations that are closest to the voxel’s preferred orientation. To evaluate the ability of the INTM parametric model to recover both kinds of modulation, we conducted model recovery by simulating datasets from the prior distribution for each candidate model, applying both models to both sets of generated data, and comparing the results using an approximation to cross-validation26,28 (see Methods). The models did not exhibit mimicry: model comparison picked the true data-generating model in every simulated dataset, providing strong evidence that the technique recovers the appropriate class of modulation. We next asked whether the parametric INTM analysis recovers the correct form of tuning modulation when applied to the observed fMRI data. Specifically, it is known from electrophysiology that the tuning functions of orientation-sensitive neurons undergo multiplicative tuning modulation with an increase in stimulus contrast19,20,21. Given this knowledge, model comparison on the collected BOLD data ought to favor the multiplicative model. Visual comparison of the posterior predictive distribution from both models revealed that both models largely captured individual voxel tuning functions adequately (Fig. 4b, c). The models were then compared to each other with cross-validation28. The multiplicative model provided the best account of the data: a difference of 14.5 standard errors, in units of expected log pointwise-predictive density28. A significance threshold (e.g., (alpha =0.05) or 1.65 standard errors) would suggest that this difference in predictive ability is poorly accounted for by a null model in which the two forms of tuning modulation are equally predictive. Exploiting what was learned about the plausible parameter values by observing the data, we further probed the validity of model comparison through data-informed model recovery26,28. Synthetic datasets were generated from the posterior distributions of the multiplicative and additive models. Next, the multiplicative and additive models were applied to each of these simulated datasets. All datasets were best accounted for by the model whose posterior was used to generate the data even though, as seen in Fig. 4, the differences between the models were very subtle. The parametric model correctly indicated that an increase in visual contrast caused an increase in multiplicative gain, but this result relied on assumptions of circular Normal distributions for the neural tuning function and distribution of weights for each voxel, as well as homogeneity of tuning shape for each voxel. However, we determined that the two candidate forms of tuning modulation should be distinguishable based on what they predict for the slope of a plot of high-contrast activity against low-contrast activity (Fig. 3, Introduction, Supplementary Methods), without relying on these parametric assumptions and the assumed homogeneity of tuning shape. As predicted by multiplicative tuning modulation, this non-parametric orthogonal regression slope analysis revealed slopes larger than 1, corresponding to slope angles greater than 45 degrees (Fig. 5). Figure 5b shows the distribution of within-voxel slopes, as estimated with orthogonal regression of the high- on the low-contrast activity (Introduction, Methods). The median slope had an angle greater than 45° (i.e., slope of 1). This tendency for slopes to be larger than 1, as predicted by the multiplicative model, was further supported by a hierarchical Bayesian estimation of the slopes (Supplementary Methods). a Orthogonal regression on data and model predictions. Each line corresponds to a single voxel. Most voxels are weakly responsive at each level of contrast and are only weakly influenced by the experimental manipulation (i.e., lines cluster in the lower left corner, close to the diagonal). Across voxels (i.e., comparing separate lines), both models capture larger visual contrast effects for more responsive voxels: predictions lying further rightward along the x-axis are located further away from the diagonal. However, only the multiplicative model captures the observed interaction between orientation and contrast within voxels. Compare to Fig. 3. b Distribution of within-voxel slopes. As allowed by multiplicative but not additive modulation, the distribution of slopes is shifted above 45° (i.e., slope of 1). Many theories of cognition predict specific kinds of neural tuning modulation with different manipulations e.g.,29,30. For instance, attention researchers do not only consider neural responses when people are in a state of high attention; this state is compared and contrasted to one of low attention, and theories of attention are informed by this comparison e.g.,31,32. However, these predictions for tuning modulation ‒ the manner in which neural tuning functions change ‒ are rarely tested in humans because there are no non-invasive techniques for recording from individual neurons. Tuning functions, and modulation of tuning functions, can be measured non-invasively using fMRI, but the response of a voxel reflects hundreds of thousands of neurons. Thus, voxel tuning functions have been interpreted as population-level properties of stimulus representations in the brain, population-level responses that cannot be used to infer properties of the underlying, individual neurons10,12,13,14. Rather than attempting a quantitative measurement of neural-level tuning from fMRI data, we developed a framework, INTM, for identifying the functional form of neural-level tuning modulation. A key component underlying the INTM framework is a modeled link between the neural and voxel tuning functions (Fig. 1b–d). This link justifies inferences of neural tuning modulation from voxel tuning modulation; even though the BOLD signal reflects the aggregated activity of many neurons, different forms of modulation can produce identifiable signatures in activity of the voxels (i.e., Eq. 4a vs 4b, Fig. 3), thereby allowing identification of the most likely form of modulation by applying each model to the BOLD data. We tested that link and validated INTM with a test case in which the neural-level “ground truth” modulation was known to be multiplicative gain19,20,21. This test case was particularly challenging because the average voxel results appeared to indicate a clear additive shift rather than multiplicative gain. We used INTM to design two techniques: 1) parametric assumptions of tuning function shapes and hierarchical Bayesian estimation of the models followed by formal model comparison; and 2) a qualitative, non-parametric check using orthogonal regression, without relying on parametric shape assumptions. Both techniques of the INTM framework correctly implicated multiplicative gain of neural tuning by leveraging subtle effects that were more apparent in some voxels than others. Several techniques have previously been developed to peer inside the voxel, but none of them statistically compares alternative theories of tuning modulation using a model that explicitly links neural tuning with voxel tuning. For example, biophysical models specify how the BOLD signal arises from the often nonlinear coupling between neural activity and vasculature33,34. But, despite this biological realism, these models have not yet been used to examine changes in neural tuning functions. In contrast to biophysical models, encoding models of fMRI data delve inside the voxel by modeling how components comprising a voxel (e.g., sub-voxel “channels”) transform stimuli into voxels’ activity5,15,16,17, and, promisingly, enable researchers to use the BOLD signal to uncover features of neural tuning18. Encoding models can be applied to multiple conditions ‒ for example through simulation35, or through fitting to data and inverting36 ‒ thereby estimating how the channels are modulated by an experimental manipulation. Inverting an encoding model uses it as a decoder, estimating channel responses for other stimuli15,16,37 or estimating how channels are modulated in other conditions38. But this use of inverted encoding models requires hard-wired (and arbitrary) assumptions about the shape of the channel responses in baseline conditions39,40. These assumptions are even more restrictive than those made by the parametric model in INTM considering that they not only assume a specific class of shape (e.g., a circular Normal), but they require adopting a specific, user-selected parameter value for that shape (e.g., a particular value for the width of the circular Normal). These assumptions mean that the inferred channel modulation cannot be taken to reflect the modulations in underlying neural functions that would be measured with electrophysiology, as users of such models readily acknowledge14,39. As a result, inverted encoding models have been used to pursue very different goals than the aim of the present study14 (i.e., understanding population- rather than neural-level representations). Beyond inverted encoding models, other researchers have compared the qualitative predictions of different forms of tuning modulation35,41,42, analogous to the logic underlying INTM’s non-parametric check. However, these techniques neither fit the alternative encoding models to empirical data, nor account for model flexibility. These previous attempts to peer inside voxels are combined in INTM. Like biophysical models, INTM connects the latent neural activity to the observed BOLD. It does so by assuming a linear coupling that is justified given our experimental design and the goals of our modeling procedure (we discuss potential violations of this assumption in more detail below)43,44,45,46. But unlike these biophysical models, INTM uses an encoding model (Fig. 1b–d, Eqs. 3, 4a, 4b). Like inverted encoding models, the parametric analysis in INTM assumes a specific class of neural tuning shape (circular Normal). But unlike inverted encoding models, it avoids the need to assume specific parameter values for the shape (e.g., tuning width). The non-parametric slope analysis in INTM takes things a step further by avoiding the need to assume a specific class of neural tuning shape. In applying the framework to data, we used a quantitative measure of the predictive abilities of each model (a form of cross-validation), a measure that is sensitive to both the flexibility of each model and the signal-to-noise ratio of the data. INTM is a general framework for inferring neural tuning modulation, but the two techniques developed in this report have a crucial feature that ought to be retained in further applications of the framework: analyses were within-voxel. As previously reported for voxel-wise orientation tuning6, most of the voxels in our study were poorly tuned, and they were additionally only weakly affected by stimulus contrast. Although we restricted the analyses to only those voxels whose population receptive fields overlapped with the stimulus (see Methods), most voxels were only weakly responsive (e.g., falling near the origin in Fig. 5a) and were minimally affected by visual contrast (e.g., lying near the diagonal in Fig. 5a). These voxel differences and other sources of voxel variation—including partial voluming47, proximity of each voxel to blood vessels48, the responsiveness of neurons within each voxel, etc. –are present in any fMRI experiment. Analyses that are insensitive to weak signals risk conflating different forms of tuning modulation, particularly when the noise differs across conditions (Supplementary Methods—Non-Parametric Check)22. In the current case, because most voxels exhibited nearly flat tuning, this altered the appearance of the average voxel tuning function (Fig. 4a), incorrectly suggesting that changing visual contrast causes an additive shift. This was because an additive shift is equivalent to multiplicative gain for a voxel with poor tuning. Both INTM techniques avoided this problem by assessing the voxels individually, identifying (and exploiting) the voxels that exhibited the unique combination of being well-tuned and possessing a strong visual contrast effect. Voxels with this combination of behaviors were more diagnostic for the comparison between different forms of tuning modulation. The techniques developed here were tailored to uncover changes in orientation tuning caused by stimulus contrast, relying on assumptions that will not be appropriate in all studies. We highlight these assumptions here and use them to clarify the distinction between the framework more generally versus specific applications of the framework. First, the models assumed that voxel tuning functions are a linear combination of the activity of the underlying neural tuning functions. This assumption is reasonable in some experiments43,44, but the relationship between neural firing rate and BOLD signal is not perfectly linear46,49. Second, the techniques implicitly assumed, through the general linear model used to estimate voxel activity, a hemodynamic response function that is shared across all voxels in all participants. Although canonical, that assumption is erroneous e.g.,50. Next, the parametric analysis approximated the distribution of neurons tuned to orientations within each voxel with a circular Normal distribution, which is unimodal and periodic. This approximation provided a convenient formula for deriving the voxel tuning function, and the resulting function matched the data (e.g., individual voxel tuning functions in Fig. 4b appear unimodal). However, this assumption may not hold for other types of stimuli, other brain regions, or for other scan parameters (e.g., an aperiodic stimulus like pitch would require an aperiodic tuning function). Violations of these assumptions may bias model comparison in some cases but, fortunately, none of the assumptions is intrinsic to the framework, and there are several ways of relaxing each of them. For example, more complex weight distributions such as multimodal functions could be used in the parametric model. Alternatively, we have shown that assumptions about the weight distributions can be bypassed by a technique like the non-parametric slope analysis. As an another example, although nonlinear relationships between the neural firing rate and the BOLD signal have been documented, multiple mathematical accounts have been proposed to explain these nonlinearities49,51,52, and these relationships could be incorporated into INTM. Despite its generality, INTM has two limitations that must be plainly acknowledged. The first is that INTM requires that the models under consideration make distinct predictions at the level of the voxel. For instance, the parametric and non-parametric INTM techniques both assume that the magnitude of tuning modulation is the same for all neurons that contribute to the voxel response. These techniques may be robust to relaxing this assumption if modulation magnitude differences apply uniformly across the weight distribution that maps neural preferences onto voxel preferences. But if the magnitude of modulation varies systematically, the models might no longer make distinct predictions at the level of the voxel. For example, if the magnitude of the additive shift is larger for neurons that prefer the same orientation as the voxel, this unlikely circumstance could produce a change in the voxel tuning function that is indistinguishable from a constant magnitude of multiplicative gain. The inability to discriminate these two scenarios exemplifies the fundamental inverse problem that INTM cannot solve: INTM cannot determine the parameters of tuning functions for individual neurons (indeed, it is not designed to). Instead, INTM operates upon distributions of neurons (grouped by, e.g., region-of-interest, voxel, feature preferences), and so it can compare only models whose distributions of tuning functions change in ways that are distinct. With the example of an additive shift whose magnitude happens to covary with the weight distribution, this might occur for some voxels, but is unlikely to occur with most voxels, demonstrating the need to use all of the voxels in the model comparison. The second key limitation is that INTM can differentiate only between models that are formally included in the model comparison process. If the “true” form of tuning modulation is not included in the set of possibilities, the results may mislead researchers into conflating the winning form of modulation with the true form. For instance, in the present study, the technique contrasted tuning modulation models in which just one form of modulation occurred but did not consider more complex situations in which multiple forms of tuning modulation could have occurred. For example, it is known from electrophysiology that with extended adaptation, orientation tuning functions can both widen and shift their preferred orientation53. Since that more complex model, in which tuning widened and shifted within every trial, was not included in model comparison, INTM is silent about whether that effect occurred. Note that such combinations of tuning modulation could be included in the model comparison process, but when attempting to adjudicate between complex models it would be critical to use model recovery simulations, specifically data-informed recovery, to determine if the collected data were sufficiently constraining. In summary, using a simple test case—modulation of orientation tuning by stimulus contrast—we presented and validated the INTM method for identifying the form of neural tuning modulation from a BOLD dataset. The method is applicable to a broad range of domains and manipulations. The main insight of the framework is that there are reasonable assumptions, which can be made in many neuroimaging studies, that enable inference about neural tuning modulation. The main requirement for using the technique is an experimental paradigm that: (1) produces measurable voxel tuning by testing the BOLD response at different levels of a single stimulus dimension (e.g., direction of motion, color, pitch), and (2) includes some cognitive manipulation of interest (e.g., with and without attention, before and after perceptual learning, complex versus simple stimuli) that modulates the voxel tuning from one condition to another. Now that INTM has been validated, it can be used to study modulations of neural tuning where electrophysiology has not yet provided an answer (e.g., studies of tuning modulation underlying tasks that cannot be taught to animals). Seven participants (22–31 years old; 3 female, 2 did not report) completed three sessions for monetary compensation ($50 per 2 h session). All participants had normal or corrected-to-normal vision. One additional participant completed a single session but exhibited substantial motion; their data were excluded. The procedure was approved by the University of Massachusetts Institutional Review Board. Stimuli were presented to participants with a gamma corrected 32” LCD monitor at 120 Hz refresh rate (Cambridge Research Systems). The experiment was designed using the Psychophysics toolbox (Version 3.0.14)54 and custom MATLAB code (2018b, MathWorks). Behavioral responses were collected with a button box (Current Design). Eye-tracking data were recorded at a rate of 1000 Hz with the Eyelink 1000 Plus system on a long range mount (SR Research), controlled using the Eyelink Toolbox extension to Psychtoolbox55. Due to a technical error, the button presses of one participant were not recorded. For the main experiment, participants completed 18 functional runs across three sessions. During each run, oriented grayscale gratings were presented twice at each of two levels of contrast (eight orientations at 50% or 100% Michelson contrast in all runs for six out of seven participants, eight orientations at 20% or 80% Michelson contrast in 12 runs for one participant, and seven orientations at 20% or 80% Michelson contrast in that participant’s remaining 6 runs). Grating parameters replicated those of Rademaker et al.56. Gratings (spatial frequency of 2 cycles per degree) were masked with annuli (1.2° inner and 7° outer radii). The annulus edges were smoothed with an isotropic 2D Gaussian kernel (1° kernel, 0.5° standard deviation). Throughout each run, a magenta fixation dot was presented in the center of the screen (0.2°, RGB: 0.7843, 0, 0.8886). In each trial, a counterphasing (5 Hz) grating was presented for five seconds. In the middle three seconds of each trial, the spatial frequency of the grating either increased or decreased (1 cycle per degree) for 200 ms. Participants were instructed to indicate via button press the direction of change as soon as they noticed it. Per run, gratings were presented at multiple orientations, twice at each combination of orientation and contrast. In most runs, there were eight orientations, but in one session of one participant (totaling six runs), only seven orientations were presented. Inter-stimulus intervals ranged from 8000 to 12000 ms in steps of 200 ms. A five-second fixation period preceded the first trial, and a fifteen-second fixation period succeeded the final trial. Each run lasted 490 s. We mapped a circular area of the visual field, of radius 8° centered on a central fixation point. pRF mapping scans followed the protocol of Benson et al.57. Briefly, natural images58 were overlaid on pink noise and viewed through a series of circular apertures (8° radius). Within one run per session, the apertures enabled view of either moving bars (2°) or rotating wedges (1/4 aperture) and rings that expanded and contracted (see stimulus software for details). In bar runs, a bar traversed the central region in cycles. During each cycle, the bar was visible for 28 s, followed by a 4 s blank period. The bar moved in one of eight directions (east, north, west, south, northeast, northwest, southwest, or southeast, in that order). A 16 s blank period preceded the first cycle, a 12 s blank period followed the fourth cycle, and there was a 16 s blank period at the end of all cycles (300 s in total). In the second pRF scan, the apertures were either wedges that rotated clockwise or counterclockwise, or they were rings that expanded or contracted. These runs started with a 16 s blank period, followed by two, 32 s cycles of a counterclockwise rotating wedge, two 28 s of expanding rings (each followed by a 4 s blank period), two 32 s clockwise wedge rotations, and two 28 s cycles of contracting rings (followed by 4 and 26 s of blank, respectively). The total run time was 300 s. Throughout the pRF scans, the color of a central fixation dot (0.3°) changed between black, white, and red. Participants were instructed to monitor the color of the fixation dot and press a button when the dot turned red. To help participants maintain fixation, a circular fixation grid was presented throughout. MRI data were collected on a 3T Siemens Skyra scanner with a 64-channel head coil. In each of the three sessions we collected field-mapping scans, functional scans, and a T1-weighted anatomical scan (MPRAGE, FOV 256 × 256, 1 mm isotropic, TE 2.13 ms, Flip Angle 9°). The anatomical scan was used to align field-mapping and functional images parallel to the calcarine sulcus. Gradient recall echo scans estimated the magnetic field. The pRF and primary functional data were collected with the same scan parameters (TR 1000 ms, TE 31 ms, flip angle 64°, FOV 94 × 94, 2.2 mm isotropic, interleaved acquisition, no slice gap, Multiband Acceleration Factor 4). To aid alignment of functional and anatomical images, single-band reference images were collected before each functional run for all but three participants (TR 8000 ms, TE 65.4 ms, flip angle 90°, FOV 94 × 94, 2.2 mm isotropic, interleaved acquisition, no slice gap). Preprocessing of images was performed with fMRIPrep 1.4.0, which relies on Nipype 1.2.0 and Nilearn 0.5.2 (RRID:SCR 001362). The T1-weighted (T1w) images were corrected for intensity non-uniformity (INU) with N4BiasFieldCorrection, distributed with ANTs 2.2.0. The T1w images were then skull-stripped with a Nipype implementation of the antsBrainExtraction.sh workflow (from ANTs), using OASIS30ANTs as target template. A T1w-reference map was computed after registration of the individual T1w images (after INU-correction) using mri_robust_template (FreeSurfer 6.0.1; RRID: SCR 001847). Brain surfaces were reconstructed using recon-all, and the brain mask estimated previously was refined with a custom variation of the method to reconcile ANTs- derived and FreeSurfer-derived segmentations of the cortical gray-matter of Mindboggle (RRID: SCR 002438). Brain tissue segmentation of cerebrospinal fluid (CSF), white-matter (WM) and gray-matter (GM) was performed on the brain-extracted T1w using fast (FSL 5.0.9, RRID:SCR 002823). For each of the functional runs, the following preprocessing was performed. First, a reference volume and its skull-stripped version were generated using a custom methodology of fMRIPrep. A deformation field to correct for susceptibility distortions was estimated based on a field map that was co-registered to the BOLD reference, using a custom workflow of fMRIPrep derived from D. Greve’s epidewarp.fsl script (www.nmr.mgh.harvard.edu/~greve/fbirn/b0/epidewarp.fsl) and further improvements of Human Connectome Project Pipelines. Based on the estimated susceptibility distortion, an unwarped BOLD reference was calculated for a more accurate co-registration with the anatomical reference. The BOLD reference was then co-registered to the T1w reference using bbregister (FreeSurfer) which implements boundary-based registration. Co-registration was configured with nine degrees of freedom to account for distortions remaining in the BOLD reference. Head-motion parameters with respect to the BOLD reference (transformation matrices, and six corresponding rotation and translation parameters) were estimated before any spatiotemporal filtering using mcflirt (FSL 5.0.9). The BOLD time-series were resampled to surfaces on the following spaces: fsaverage and fsnative (FreeSufer). The BOLD time-series were resampled onto their original, native space by applying a single, composite transform to correct for head-motion and susceptibility distortions. These resampled BOLD time-series will be referred to as “preprocessed BOLD”. A reference volume and its skull-stripped version were generated using a custom methodology of fMRIPrep. A set of physiological regressors were extracted to allow for component-based noise correction59. Principal components are estimated after high-pass filtering the pre-processed BOLD time-series (using a discrete cosine filter with 128 s cut-off) for the anatomical CompCor (aCompCor). The time-series entering the CompCor analyses are derived from a mask at the intersection of subcortical regions with the union of CSF and WM masks calculated in T1w space, after their projection to the native space of each functional run (using the inverse BOLD-to-T1w transformation). Gridded (volumetric) resamplings were performed using antsApplyTransforms (ANTs), configured with Lanczos interpolation to minimize the smoothing effects of other kernels. Non-gridded (surface) resamplings were performed using mri_vol2surf (FreeSurfer). To estimate voxel-wise responses to each orientation, a general linear model (GLM) was fit using SPM12 (version 7487, RRID:SCR 007037) to the time-series of each voxel during each orientation run. Fitting the GLM can be viewed as a preprocessing step to reduce the dimensionality of the data; the method presented here could be configured to run on the raw timeseries, but working with beta weights of a GLM rather than the raw timeseries drastically reduced the computational requirements of the Bayesian estimation. Prior to fitting the GLM, each voxel’s timeseries was converted into a percent signal change, relative to the average signal within a run (across voxels). Design matrices were convolved with the canonical hemodynamic response function, parameterized with the SPM12 defaults, and additionally contained both six motion (three translation and three rotation) and multiple aCompCor regressors. For each run, the number of components was determined by the broken-stick method. To mitigate the effects of stimulus vignetting—whereby orientation information differs between the edge and central portions of a grating60,61—we restricted the analyses to only striate voxels whose population receptive fields (pRFs) did not overlap with the stimulus edges. We estimated the pRFs of each voxel with standard methods. First, the preprocessed functional data for the pRF scans were converted into percent mean signal change within a run (across voxels). The compressive spatial summation model was fit to each voxel using analyzePRF HCP7TRET52,57. Following Benson et al., the compressive exponent of this model was set to 0.05. The resulting pRF parameters were combined with an anatomical prior for a Bayesian estimation of the parameters (neuropythy 0.94)62. Only the parameters of voxels for which the pRF explained more than 10% of the variance of the run were used as empirical parameters for Bayesian estimation; the remaining voxels’ posterior pRF parameters were determined entirely by the prior. The resulting pRF parameters determined whether a voxel would be retained for analyses. The pRF resembles an isotropic, bivariate Gaussian. The three pRF sessions were analyzed separately, resulting in three sets of three pRF parameters per voxel. Within a set of parameters, two indicate the center location of the pRF, and the third determines its size—the standard deviation of the Gaussian. A voxel was retained only if a circle centered on its pRF with radius equal to two standard deviations was entirely contained by the grating stimulus in each of the three sessions. The voxel tuning function (Fig. 4) was estimated according to a “binning” method10. First, each voxel’s activity was z-scored, separately for each voxel. Then, one run was held out and the voxel’s preferred orientation was calculated with the remaining runs. The preferred orientation was estimated as the orientation that produced the largest activity, averaged across runs and levels of contrast. Next, the activity in the held-out run was plotted against stimulus orientation translated into a function of distance from the voxel’s preferred orientation. This procedure was repeated once for each available run, holding out a different run on each repetition. Averages and repeated-measures confidence intervals, across voxels and ignoring participants, were then calculated63, treating contrast and distance from preferred orientation as within-voxel factors. In Fig. 4, one session of one participant was excluded; the figure shows only sessions in which the participant was shown eight orientations. Each of the voxel-specific parameters (baseline tuning function, tuning modulation, and variability in the output of the tuning function) were estimated with a hierarchical Bayesian model. All models were estimated with R (R Core Team) and its interface (RStan, 2.18.2) to the Stan language64. The Stan language provides a robust variation of Hamiltonian Monte Carlo65,66, which efficiently and accurately approximates Bayesian posterior distributions. Two diagnostics were used to assess the accuracy of the estimation. First, we calculated the split-(hat{R}) for each parameter in the model67. This value is analogous to an F-score in an analysis of variance, and values close to 1 give no evidence that the different Markov chains are sampling from different distributions. The split-(hat{R}) was below 1.1 for all parameters25. Second, chains were monitored for divergences, whose presence would indicate that the samples, even if they are from a common distribution, likely misrepresent the true posterior distribution. There were no divergences when applying the multiplicative and additive models to real data. In all applications of models to data, four chains were initialized with random values for the parameters (RStan defaults), and the sampling algorithm was given 1000 draws to adapt. After adaptation, each chain was used to draw 2000 samples from the posterior distribution. All model comparison was done with Pareto-smooth importance sampling, leave-one-out cross-validation plus, a technique for approximating cross-validation28. We refer readers to the original report for details of this technique. For data-uninformed model recovery, 100 datasets were simulated from the priors of both models. The datasets contained one participant contributing 100 voxels measured in 18 runs at 8 levels of orientation. Both the additive and multiplicative models were applied to each simulated dataset, resulting in 200 simulated datasets and 400 model applications. Data informed model recovery was implemented analogously to the data-uninformed model recovery. One hundred datasets were generated from the posterior of the multiplicative and additive models. The datasets contained six participants, each contributing 200 voxels measured in 18 runs at 8 levels of orientation. The multiplicative and additive models were applied to these simulated datasets and model comparison was conducted as above. A derivation of the slope for orthogonal regression can be found in Casella and Berger, chapter 1227. Here, we report the result. Let ({x}_{i}) be the activity of a voxel at low contrast on trial (i), out of (n) trials; let ({y}_{i}) be the activity of a voxel at high contrast on an analogous trial (i.e., the beta weight for the same orientation in the same run); let (bar{x}) be the voxel’s average activity at low-contrast; and let (bar{y}) be the voxel’s average activity at high-contrast. The following are the sums of squares and the cross-product. The slope, (g), that solves the total least squares problem is given by As stated in the main text, a separate slope was estimated for each voxel. In one session, one participant was shown seven rather than eight orientations. When calculating the slopes for this participant, the activity from those sessions were excluded. To show that there are circumstances in which a von Mises density function is a reasonable weight distribution, we simulated cortical orientation preference maps (Fig. 2). Each voxel was constructed with a Kohonen network. We tailored the network parameters so that, following self-organization, each voxel would contain a roughly accurate number of pinwheels for a voxel of size 2.2 mm3—the voxel sized used in this study—approximately two pinwheels per millimeter68. However, this simulation is meant as a “proof of concept”, rather than a demonstration that the von Mises distribution is an ideal weight distribution. That is, it does not consider many factors that likely influence how neuronal activity will be reflected in voxel activity48. For example, it does not consider the variability in pinwheel density across V1, vasculature, nor how cortical folding would allow disparate parts of cortex to be sampled by the same voxel. Nevertheless, it shows why we might expect weight distributions in most voxels to be relatively flat, with the deviations from uniformity being captured adequately by the single mode of the von Mises distribution. Each network was simulated as follows. First, a grid of 67 × 67 “neurons” was initialized to have a random orientation preference. Then, for 20000 iterations, the grid was presented with a random orientation stimulus. The neuron that preferred an orientation closest to the stimulus was selected, and the weights were updated. Weights were updated based on the proximity of a neuron in the grid to the winning neuron. Specifically, on iteration (i+1), the weight, (w), of neuron (j) was given by the following. In Eq. 6, (psi (x,sigma )) is the density of (x) as assigned by the density function of a normal distribution with mean 0 and standard deviation (sigma). The variable ({d}_{j}) is the distance on the grid between neuron (j) and the winning neuron (Euclidean distance, as calculated after setting a city-block distance of 0.03 between adjacent neurons). The learning rate ({delta }_{i}) is the difference between the neuron’s preferred orientation and the presented stimulus. 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Cowell & David E. Huber 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 Conceptualization: R.A.C. and D.E.H. Data curation: P.S. Formal analysis: P.S., R.A.C., and D.E.H. Funding acquisition: R.A.C. and D.E.H. Investigation: P.S., R.A.C., and D.E.H. Methodology: P.S., R.A.C., and D.E.H. Project administration: P.S., R.A.C., and D.E.H. Software: P.S., R.A.C., and D.E.H. Supervision: R.A.C. and D.E.H. Validation: P.S., R.A.C., and D.E.H. Visualization: P.S., R.A.C., and D.E.H. Writing—original draft: P.S., R.A.C., and D.E.H. Writing—review & editing: P.S., R.A.C., and D.E.H. Correspondence to Patrick Sadil. The authors declare no competing interests Communications Biology thanks Richard Henson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Jeanette Mumford, Anam Akhtar and Christina Karlsson Rosenthal. Peer reviewer reports are available. Publisher’s note 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/. Reprints and Permissions Sadil, P., Cowell, R.A. & Huber, D.E. A modeling framework for determining modulation of neural-level tuning from non-invasive human fMRI data. Commun Biol5, 1244 (2022). https://doi.org/10.1038/s42003-022-04000-9 Download citation Received: Accepted: Published: DOI: https://doi.org/10.1038/s42003-022-04000-9 Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article.
The song features the slick vocals of Twenty9xx and highlights Zaandr’s musical journey. It shows his true talent with a solid production that will get any dance floor jumping. With the addition of the vocal chorus, huge bass lines and intense sound design, this song truly shows Zaandr’s mission to propel his already energetic sound. Starting out as a drummer in a band at the age of 11, Zaandr has always had a keen interest in music from a very young age. After hearing electronic dance music for the first time a few years later, he knew that music production and DJing would be his destiny. Zaandr has already shown his range producing multiple genres such as Bass House, Future Bass and even Dubstep gaining support from industry leaders such as Jauz, Sikdope, Birthdayy Partyy, Corrupt, Slushii, DMVU, Noizu and more. He has also opened for headliners such as Rezz, Grabbitz, Figure, DJ Pauly D, UZ, DMVU, Kennedy Jones, Shipwrek, Victor Niglio and has played major festivals such as Breakaway Music Festival and Electric Forest. 1. Tell us about the first track that put you on the map in the electronic scene and the journey since. How did you get started? The story of me getting started is pretty interesting. I was not into electronic music whatsoever. That all changed when I heard deadmau5’s hit “ moar ghosts and stuff”. As soon as I heard that piece of music I knew my journey would start with making electronic music. So I acquired an old Dell laptop and really started just messing around with DAW’s and seeing what I could create and the journey just kept on going year after year. The first track that really gained some big traction was my solo release “Red Dress”. After creating that track I was really inspired to continue to make groundbreaking new sounds in my production as much as I possibly could. 2. Tell us about your latest project ‘All on me ft Twenty9xx’ All on me is an energetic bass house track that covers many genres in the span of one track. It is a true expression of ZAANDR’s ability to conquer any track he is making at the time. Listen on Spotify
STREAM / DOWNLOAD 3. Tell us something we wouldn’t normally find out about you? I’m a huge fan of the ocean and ocean life. I’m truly fascinated by it. Anytime I’m watching something at home alone it always turns out to be something about the earth and the ocean. My favorite animal is the octopus. 4. What single night out has been most memorable for you as a DJ and producer? When it comes to the most memorable night as a producer I would have to say there has been a couple nights that come to mind but 2 specifically. The first memory would have to be the first time I ever went to see an electronic music show which was deadmau5 in Chicago, and that was the first time I knew I wanted to make electronic music. The 2nd memory would have to be the first time I ever got to play live in front of a sold out show. Getting the feedback from an audience the first time knowing you can provide a fun experience live is truly exciting. 5. Give us the name of one track that never gets old for you no matter how many times you listen to it? Deadmau5 – Slip. 6. Dream collaboration and why? Skrillex without a doubt. 7. If you could play any festival, which would it be? Ultra music festival. 8. How do you get a track started? tell us about your production process – I would say it varies for each individual track. It usually has something to do with building my drums first and getting them sounding where they need to be. And then it can go into either the drop, the intro, a melody. It all just depends. 9. Upcoming projects? What are you currently working on? I have many projects I’m working on and many different types of genres within those projects between a few different artists. I’m excited to bring them all to light very soon. 10. The relationship between a DJ and the audience is crucial, and yet it seems to be a fragile one – how do you see the balance between giving the crowd what they want and treating them to something new? It’s all depending on the crowd. I think it’s important to be booked with artists that all bring a similar quality to the table when performing with each other. I think another aspect to that is having a vast playlist of music and always interacting with the crowd to see where their energy is. Always being ready to be able to change up the energy with where the crowd is growing. And when you have them in your grasp for a while and you can feel where their energy level is. That’s when you can really experiment with new ideas and try different things. Listen Zaandr – ‘All On Me’ (ft. Twenty9xx) on YouTube
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