The surprisingly subtle geometry of a familiar game shows how quickly math gets complicated.
Category: mathematics – Page 42
The technology can reconstruct a hidden scene in just minutes using advanced mathematical algorithms.
Potential use case scenarios
Law enforcement agencies could use the technology to gather critical information about a crime scene without disturbing the evidence. This could be especially useful in cases where the scene is dangerous or difficult to access. For example, the technology could be used to reconstruct the scene of a shooting or a hostage situation from a safe distance.
The technology could also have applications in the entertainment industry. For instance, it could create immersive gaming experiences that allow players to explore virtual environments in 3D. It could also be used in the film industry to create more realistic special effects.
The universe, with its myriad mysteries, has long captivated our curiosity, and among its enigmatic phenomena, black holes have held a prominent place. These collapsed cores of dead stars, known for devouring everything in their vicinity, have a cosmic counterpart that challenges our understanding – the elusive ‘white holes.’
Imagine delving into the intricacies of space-time around a black hole, subtracting the collapsed star’s mass, and unveiling the mathematical description of a white hole – a massless singularity. Unlike their gravitational counterparts, black holes, where matter disappears into an event horizon, white holes defy entry. They expel matter at an astonishing rate, akin to hitting a cosmic ‘rewind’ button.
The critical role of the mammalian hippocampus in the formation, translation and retrieval of memory has been documented over many decades. There are many theories of how the hippocampus operates to encode events and a precise mechanism was recently identified in rats performing a short-term memory task which demonstrated that successful information encoding was promoted via specific patterns of activity generated within ensembles of hippocampal neurons. In the study presented here, these “representations” were extracted via a customized non-linear multi-input multi-output (MIMO) mathematical model which allowed prediction of successful performance on specific trials within the testing session. A unique feature of this characterization was demonstrated when successful information encoding patterns were derived online from well-trained “donor” animals during difficult long-delay trials and delivered via online electrical stimulation to synchronously tested naïve “recipient” animals never before exposed to the delay feature of the task. By transferring such model-derived trained (donor) animal hippocampal firing patterns via stimulation to coupled naïve recipient animals, their task performance was facilitated in a direct “donor–recipient” manner. This provides the basis for utilizing extracted appropriate neural information from one brain to induce, recover, or enhance memory related processing in the brain of another subject.
To understand the neural basis of memory, several features of the context in which the memories occur and are utilized, and the functional aspects of the brain areas involved, need to be identified and controlled (Hampson et al., 2008; Eichenbaum and Fortin, 2009). In prior studies we achieved both of these important contingencies as well as overcoming possible alternative interpretations of the relationship between recorded hippocampal ensemble activity and the behavioral task in which short-term memory formation is necessary (Deadwyler and Hampson, 2006; Deadwyler et al., 2007), and developing an effective mathematical/operational model for online prediction of CA1 hippocampal cell activity from simultaneously recorded input firing patterns from synaptically connected CA3 neurons (Song et al., 2009; Berger et al., 2011; Hampson et al., 2011).
Physicists found that the music of Johann Sebastian Bach contains mathematical patterns that help convey information.
By Elise Cutts
An innovative new chip uses light for fast, efficient AI computations, promising a leap in processing speeds and privacy.
Penn Engineers have developed a new chip that uses light waves, rather than electricity, to perform the complex math essential to training AI. The chip has the potential to radically accelerate the processing speed of computers while also reducing their energy consumption.
The silicon-photonic (SiPh) chip’s design is the first to bring together Benjamin Franklin Medal Laureate and H. Nedwill Ramsey Professor Nader Engheta’s pioneering research in manipulating materials at the nanoscale to perform mathematical computations using light — the fastest possible means of communication — with the SiPh platform, which uses silicon, the cheap, abundant element used to mass-produce computer chips.
This isn’t rocket science it’s neuroscience.
Ever since the dawn of antiquity, people have strived to improve their cognitive abilities. From the advent of the wheel to the development of artificial intelligence, technology has had a profound leverage on civilization. Cognitive enhancement or augmentation of brain functions has become a trending topic both in academic and public debates in improving physical and mental abilities. The last years have seen a plethora of suggestions for boosting cognitive functions and biochemical, physical, and behavioral strategies are being explored in the field of cognitive enhancement. Despite expansion of behavioral and biochemical approaches, various physical strategies are known to boost mental abilities in diseased and healthy individuals. Clinical applications of neuroscience technologies offer alternatives to pharmaceutical approaches and devices for diseases that have been fatal, so far. Importantly, the distinctive aspect of these technologies, which shapes their existing and anticipated participation in brain augmentations, is used to compare and contrast them. As a preview of the next two decades of progress in brain augmentation, this article presents a plausible estimation of the many neuroscience technologies, their virtues, demerits, and applications. The review also focuses on the ethical implications and challenges linked to modern neuroscientific technology. There are times when it looks as if ethics discussions are more concerned with the hypothetical than with the factual. We conclude by providing recommendations for potential future studies and development areas, taking into account future advancements in neuroscience innovation for brain enhancement, analyzing historical patterns, considering neuroethics and looking at other related forecasts.
Keywords: brain 2025, brain machine interface, deep brain stimulation, ethics, non-invasive and invasive brain stimulation.
Humans have striven to increase their mental capacities since ancient times. From symbolic language, writing and the printing press to mathematics, calculators and computers, mankind has devised and employed tools to record, store, and exchange thoughts and to enhance cognition. Revolutionary changes are occurring in the health care delivery system as a result of the accelerating speed of innovation and increased employment of technology to suit society’s evolving health care needs (Sullivan and Hagen, 2002). The aim of researchers working on cognitive enhancement is to understand the neurobiological and psychological mechanisms underlying cognitive capacities while theorists are rather interested in their social and ethical implications (Dresler et al., 2019; Oxley et al., 2021).
University of Pennsylvania engineers have developed a new chip that uses light waves, rather than electricity, to perform the complex math essential to training AI. The chip has the potential to radically accelerate the processing speed of computers while also reducing their energy consumption.
The silicon-photonic (SiPh) chip’s design is the first to bring together Benjamin Franklin Medal Laureate and H. Nedwill Ramsey Professor Nader Engheta’s pioneering research in manipulating materials at the nanoscale to perform mathematical computations using light—the fastest possible means of communication—with the SiPh platform, which uses silicon, the cheap, abundant element used to mass-produce computer chips.
The interaction of light waves with matter represents one possible avenue for developing computers that supersede the limitations of today’s chips, which are essentially based on the same principles as chips from the earliest days of the computing revolution in the 1960s.
After cracking an unsolvable mathematics problem last year, AI is back to tackle geometry.
Developed by Google DeepMind, a new algorithm, AlphaGeometry, can crush problems from past International Mathematical Olympiads—a top-level competition for high schoolers—and matches the performance of previous gold medalists.
When challenged with 30 difficult geometry problems, the AI successfully solved 25 within the standard allotted time, beating previous state-of-the-art algorithms by 15 answers.
Lee Smolin joins TOE to discuss his work in theoretical physics, the dynamic nature of the laws of physics and the concept of time.
TIMESTAMPS:
00:00:00 — Intro.
00:04:13 — Doubly Special Relativity and Violation of Lorentz Invariance.
00:09:15 — The Concept of Thick Time.
00:19:11 — Duality Between String Theory and Loop Quantum Gravity.
00:23:50 — Condensed Matter Theory.
00:28:35 — Approximating by a Continuum and Discrete Sets.
00:34:11 — Misapprehensions about Loop Quantum Gravity.
00:38:43 — Defining Complexity and the View of the Universe by One Observer.
00:43:52 — Causal Energetic: The Relationship Between Varieties and Kinetic Energy.
00:48:38 — Varying Parameters in the Universe.
00:53:35 — The Bomes Interpretation of Quantum Mechanics.
00:58:30 — Causality and Relativity.
01:03:15 — Different Styles in Mathematics and Chess.
01:07:55 — The Fundamental Questions in Biology.
01:12:49 — Marrying Outside Your Field.
01:18:04 — Discussion on Authors and Novels.
01:23:35 — Conversations with Fire Robin.
01:28:39 — Being Sincere and Ambitious.
01:33:39 — A Visit from BJ
01:38:34 — Outro.
NOTE: The perspectives expressed by guests don’t necessarily mirror my own. There’s a versicolored arrangement of people on TOE, each harboring distinct viewpoints, as part of my endeavor to understand the perspectives that exist.
THANK YOU: To Mike Duffey for your insight, help, and recommendations on this channel.
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