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Category: mathematics

Quantum Neural Networks Face the Hardware Test

Artificial neural networks have become powerful tools for finding patterns in complex data, from classifying images to predicting protein structures and assisting mathematical discovery. Yet their success has so far relied almost entirely on classical hardware. Recent developments in quantum-computing technologies make it timely to ask whether trainable models can also make use of quantum effects such as superposition and the intrinsic uncertainty associated with quantum measurements. What’s more, running neural networks on real quantum processors could potentially turn these networks into probes, revealing how different hardware architectures shape networks’ behaviors.

Philosophy Of Physics (@PhilosophyOfPhy) on X

The continuity equation was not the work of a single physicist. Its development grew from early hydraulic studies and the work of Daniel and Johann Bernoulli. In the eighteenth century, Jean le Rond d’Alembert produced the first partial-differential expression of mass conservation in fluid motion, and Leonhard Euler soon placed it in the general mathematical framework that became the foundation of modern fluid mechanics. It should therefore not be attributed solely to Giovanni Battista Venturi, whose later work concerned flow through constricted tubes. Its general form is ∂ρ/∂t + ∇·(ρv) = 0 where ρ is fluid density and v is the velocity field. The equation says that mass cannot simply appear or disappear: any change in the amount of fluid inside a region must be explained by fluid entering or leaving it. For steady flow through a pipe, this becomes ρ₁A₁v₁ = ρ₂A₂v₂ If the fluid is effectively incompressible, its density remains constant, giving the familiar form: A₁v₁ = A₂v₂ The meaning is simple. The same volume of fluid must pass through every section of the pipe each second. When the pipe becomes narrower, the fluid must move faster; when it becomes wider, the fluid slows down. This equation is fundamental to the study of pipes, nozzles, rivers, aircraft flow, circulation systems and computational fluid dynamics. More broadly, continuity equations appear throughout physics wherever something locally conserved, such as mass or electric charge, moves through space. The equation is not merely about fluids; it is the mathematical language of the principle that what flows into a region must either flow out or remain inside.

Tiny memristor chip cuts brain modeling time to under 10 milliseconds

A research team has developed the world’s first chip that can match the speed at which the human brain functions. The study, titled “A sub–10-millisecond neural dynamical system based on phase-change memristors,” was published in Science and was led by Professor Yang Yuchao of Peking University, together with researchers from the Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences.

Neural dynamical systems combine neural networks with mathematical equations that describe how complex systems change over time. They are useful for physical modeling, medical imaging and three-dimensional brain reconstruction. However, these systems require repeated calculations, error checks and adjustments to the size of each calculation step. In conventional computers, data must also move frequently between memory and the processor, increasing processing time and energy use.

Fast and accurate brain modeling is important for technologies that must respond in real time, including brain–computer interfaces, surgical navigation and medical imaging. Existing hardware often requires too much time and power for these demanding calculations. By performing key operations directly in memory, the new chip reduces data movement and brings high-quality brain modeling closer to real-time use.

How physics and mathematical modeling help us make better clothes

A new paper in the journal Nature Physics offers insights into the physics of liquid droplets—and while many people may not appreciate the mathematical accomplishment, they will benefit from the athletic wear and raincoats it makes possible. The recent article, “Tricky Tension,” explores the intersection of physics and textiles and how wetting is influenced by the structure of tiny individual liquid droplets.

In physics, the cohesive force between two phases is called surface tension. This allows small insects to walk on water.

In a three-phase system—where gas, liquid and solid objects all interact—there is a less-understood phenomenon called the line tension of a liquid droplet. This refers to the force acting at the boundary where the liquid droplet, the air and the solid surface on which the droplet sits all meet. Learning more about the mechanics of droplets on solid surfaces, known as sessile droplets, is important for understanding the wetting and drying of textiles, especially for very small droplets.

A scheme to verify gates of a quantum computer without examining devices

Quantum computers, systems that process information using the principles of quantum mechanics, could solve some problems that cannot be tackled by the classical computers currently used worldwide. Despite their potential, verifying that these computers are working correctly and can reliably perform computations remains challenging.

Shubhayan Sarkar, a researcher at the University of Gdansk, recently introduced a new scheme for certifying that quantum chips (unitary gates) in a quantum computer are operating correctly without relying on assumptions about their internal components. This scheme, introduced in a paper published in Physical Review Letters, uses an approach referred to as almost device-independent (DI) certification.

“Consider the computer you are using right now,” Sarkar told Phys.org. “If it provides the answer to a mathematical problem, how do you know that the computation is correct? In practice, we rarely verify every calculation ourselves.

Astronomers spot an extremely rare galaxy mega-merger

Scale in the universe is hard to understand from a purely human perspective. Many times, the math just doesn’t sit well with our brains, which evolved to capture and process data about the world around us rather than grok the complexities of stellar dynamics and galaxy mergers. But every once in a while, astronomers find something that, if we can wrap our heads around the numbers, gives a sense of just how big the universe is.

That is precisely what a new paper, available on the arXiv preprint server from a group of astronomers led by Z.L. Wen of the Chinese Academy of Sciences, hopes to do when it describes a merger of not one, not two, but six supermassive galaxies and the active dynamics they are subject to.

Admittedly, this paper isn’t the one that originally found the cluster. That was done back in 2018 by several all-sky surveys, including the Two Micron All Sky Survey, WISE and SuperCOSMOS. But it was the first to identify that the cluster contained a group of six merging galaxies at its heart. That tidbit was hidden away in Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys data.

New topology-based biomarkers may improve breast cancer prediction

For decades, pathologists have diagnosed and graded breast cancer by looking at tissue samples under a microscope, searching for telltale signs of disorder in the structure of cells and tissues. Now, researchers at Columbia and their collaborators have developed a new computational approach that transforms those visual patterns into quantitative measurements, potentially improving how clinicians predict breast cancer outcomes and choose therapies.

In a recent study published in Cancer Research, researchers used mathematical tools known as topology to develop biomarkers quantifying the organizational structure of breast cancer tissue. The approach generated continuous numerical scores that predicted patient survival and treatment response more accurately than many traditional biomarkers, while also showing less variation across racial and ethnic groups.

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