Our reality is a 3 + 1 pseudo-Riemannian spacetime manifold whose intrinsic curvature manifests itself as gravity, right? Well no, because descriptions are not reality, and math is not physics. Indeed, when taken at its most literal, face-value, what the \.
Category: mathematics – Page 22
Quantum-Prime Computing: How Prime Numbers Could Unlock New Paths for Brain, Mind, and Computation
Even so, many wonder: If the universe is at bottom deterministic (via stable laws of physics), how do these quantum-like phenomena arise, and could they show up in something as large and complex as the human brain?
Quantum-Prime Computing is a new theoretical framework offering a surprising twist: it posits that prime numbers — often celebrated as the “building blocks” of integers — can give rise to “quantum-like” behavior in a purely mathematical or classical environment. The kicker? This might not only shift how we view computation but also hint at new ways to understand the brain and the nature of consciousness.
Below, we explore why prime numbers are so special, how they can host quantum-like states, and what that might mean for free will, consciousness, and the future of computational science.
Exotic ‘Paraparticles’ That Defy Categorization May Exist in Many Dimensions
Theoretical physicists predict the existence of exotic “paraparticles” that defy classification and could have quantum computing applications.
By Davide Castelvecchi & Nature magazine
Theoretical physicists have proposed the existence of a new type of particle that doesn’t fit into the conventional classifications of fermions and bosons. Their ‘paraparticle’, described in Nature on January 8, is not the first to be suggested, but the detailed mathematical model characterizing it could lead to experiments in which it is created using a quantum computer. The research also suggests that undiscovered elementary paraparticles might exist in nature.
Mathematical insight into neuron readout drives significant improvements in neural net prediction accuracy
Reservoir computing (RC) is a powerful machine learning module designed to handle tasks involving time-based or sequential data, such as tracking patterns over time or analyzing sequences. It is widely used in areas such as finance, robotics, speech recognition, weather forecasting, natural language processing, and predicting complex nonlinear dynamical systems. What sets RC apart is its efficiency―it delivers powerful results with much lower training costs compared to other methods.
RC uses a fixed, randomly connected network layer, known as the reservoir, to turn input data into a more complex representation. A readout layer then analyzes this representation to find patterns and connections in the data. Unlike traditional neural networks, which require extensive training across multiple network layers, RC only trains the readout layer, typically through a simple linear regression process. This drastically reduces the amount of computation needed, making RC fast and computationally efficient.
Inspired by how the brain works, RC uses a fixed network structure but learns the outputs in an adaptable way. It is especially good at predicting complex systems and can even be used on physical devices (called physical RC) for energy-efficient, high-performance computing. Nevertheless, can it be optimized further?
Artificial imagination with the ‘exocortex:’ Researcher proposes software to aid scientific inspiration and imagination
Artificial intelligence (AI) once seemed like a fantastical construct of science fiction, enabling characters to deploy spacecraft to neighboring galaxies with a casual command. Humanoid AIs even served as companions to otherwise lonely characters. Now, in the very real 21st century, AI is becoming part of everyday life, with tools like chatbots available and useful for everyday tasks like answering questions, improving writing, and solving mathematical equations.
AI does, however, have the potential to revolutionize scientific research —in ways that can feel like science fiction but are within reach.
At the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory, scientists are already using AI to automate experiments and discover new materials. They’re even designing an AI scientific companion that communicates in ordinary language and helps conduct experiments. Kevin Yager, the Electronic Nanomaterials Group leader at the Center for Functional Nanomaterials (CFN), has articulated an overarching vision for the role of AI in scientific research.
Quantum Algorithms Could Prompt Faster Solutions For Complex Simulations
Quantum computers may soon dramatically enhance our ability to solve problems modeled by nonreversible Markov chains, according to a study published on the pre-print server arXiv.
The researchers from Qubit Pharmaceuticals and Sorbonne University, demonstrated that quantum algorithms could achieve exponential speedups in sampling from such chains, with the potential to surpass the capabilities of classical methods. These advances — if fully realized — have a range of implications for fields like drug discovery, machine learning and financial modeling.
Markov chains are mathematical frameworks used to model systems that transition between various states, such as stock prices or molecules in motion. Each transition is governed by a set of probabilities, which defines how likely the system is to move from one state to another. Reversible Markov chains — where the probability of moving from, let’s call them, state A to state B equals the probability of moving from B to A — have traditionally been the focus of computational techniques. However, many real-world systems are nonreversible, meaning their transitions are biased in one direction, as seen in certain biological and chemical processes.
Mathematical technique ‘opens the black box’ of AI decision-making
Western researchers have developed a novel technique using math to understand exactly how neural networks make decisions—a widely recognized but poorly understood process in the field of machine learning.
Many of today’s technologies, from digital assistants like Siri and ChatGPT to medical imaging and self-driving cars, are powered by machine learning. However, the neural networks —computer models inspired by the human brain —behind these machine learning systems have been difficult to understand, sometimes earning them the nickname “black boxes” among researchers.
“We create neural networks that can perform specific tasks, while also allowing us to solve the equations that govern the networks’ activity,” said Lyle Muller, mathematics professor and director of Western’s Fields Lab for Network Science, part of the newly created Fields-Western Collaboration Centre. “This mathematical solution lets us ‘open the black box’ to understand precisely how the network does what it does.”
Researchers STUNNED As A.I Improves ITSELF Towards Superintelligence (BEATS o1)
00:00 — Self-Improving Models.
00:23 — AllStar Math Overview.
01:34 — Monte-Carlo Tree.
02:59 — Framework Steps Explained.
04:46 — Iterative Model Training.
06:11 — Surpassing GPT-4
07:18 — Small Models Dominate.
08:01 — Training Feedback Loop.
10:09 — Math Benchmark Results.
13:19 — Emergent Capabilities Found.
16:09 — Recursive AI Concerns.
20:04 — Towards Superintelligence.
23:34 — Math as Foundation.
27:08 — Superintelligence Predictions.
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Physicists experimentally observe topological defects in glasses for the first time
The amorphous state of matter is the most abundant form of visible matter in the universe, and includes all structurally disordered systems, such as biological cells or essential materials like glass and polymers.
An amorphous material is a solid whose molecules and atoms form disordered structures, meaning that they do not occupy regular, well-defined positions in space.
This is the opposite of what happens in crystals, whose ordered structure facilitates their mathematical description, as well as the identification of those “defects,” which practically control the physical properties of crystals, such as their plastic yielding and melting, or the way an electric current propagates through them.