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A UNSW Sydney mathematician has discovered a new method to tackle algebra’s oldest challenge—solving higher polynomial equations.

Polynomials are equations involving a variable raised to powers, such as the degree two polynomial: 1 + 4x – 3x2 = 0.

The equations are fundamental to math as well as science, where they have broad applications, like helping describe the movement of planets or writing computer programs.

The quantum black hole with (almost) no equations by Professor Gerard ‘t Hooft.

How to reconcile Einstein’s theory of General Relativity with Quantum Mechanics is a notorious problem. Special relativity, on the other hand, was united completely with quantum mechanics when the Standard Model, including Higgs mechanism, was formulated as a relativistic quantum field theory.

Since Stephen Hawking shed new light on quantum mechanical effects in black holes, it was hoped that black holes may be used to obtain a more complete picture of Nature’s laws in that domain, but he arrived at claims that are difficult to use in this respect. Was he right? What happens with information sent into a black hole?

The discussion is not over; in this lecture it is shown that a mild conical singularity at the black hole horizon may be inevitable, while it doubles the temperature of quantum radiation emitted by a black hole, we illustrate the situation with only few equations.

About the Higgs Lecture.

The Faculty of Natural, Mathematical & Engineering Sciences is delighted to present the Annual Higgs Lecture. The inaugural Annual Higgs Lecture was delivered in December 2012 by its name bearer, Professor Peter Higgs, who returned to King’s after graduating in 1950 with a first-class honours degree in Physics, and who famously predicted the Higgs Boson particle.

A quantum computer can solve optimization problems faster than classical supercomputers, a process known as “quantum advantage” and demonstrated by a USC researcher in a paper recently published in Physical Review Letters.

The study shows how , a specialized form of quantum computing, outperforms the best current classical algorithms when searching for near-optimal solutions to complex problems.

“The way quantum annealing works is by finding low-energy states in , which correspond to optimal or near-optimal solutions to the problems being solved,” said Daniel Lidar, corresponding author of the study and professor of electrical and computer engineering, chemistry, and physics and astronomy at the USC Viterbi School of Engineering and the USC Dornsife College of Letters, Arts and Sciences.

In recent years, computer scientists have created various highly performing machine learning tools to generate texts, images, videos, songs and other content. Most of these computational models are designed to create content based on text-based instructions provided by users.

Researchers at the Hong Kong University of Science and Technology recently introduced AudioX, a model that can generate high quality audio and music tracks using texts, video footage, images, music and audio recordings as inputs. Their model, introduced in a paper published on the arXiv preprint server, relies on a diffusion transformer, an advanced machine learning algorithm that leverages the so-called transformer architecture to generate content by progressively de-noising the input data it receives.

“Our research stems from a fundamental question in artificial intelligence: how can intelligent systems achieve unified cross-modal understanding and generation?” Wei Xue, the corresponding author of the paper, told Tech Xplore. “Human creation is a seamlessly integrated process, where information from different sensory channels is naturally fused by the brain. Traditional systems have often relied on specialized models, failing to capture and fuse these intrinsic connections between modalities.”

In a network, pairs of individual elements, or nodes, connect to each other; those connections can represent a sprawling system with myriad individual links. A hypergraph goes deeper: It gives researchers a way to model complex, dynamical systems where interactions among three or more individuals—or even among groups of individuals—may play an important part.

Instead of edges that connect pairs of nodes, it is based on hyperedges that connect groups of nodes. Hypergraphs can represent higher-order interactions that represent collective behaviors like swarming in fish, birds, or bees, or processes in the brain.

Scientists usually use a hypergraph to predict dynamic behaviors. But the opposite problem is interesting, too. What if researchers can observe the dynamics but don’t have access to a reliable model? Yuanzhao Zhang, an SFI Complexity Postdoctoral Fellow, has an answer.

It would be difficult to understand the inner workings of a complex machine without ever opening it up, but this is the challenge scientists face when exploring quantum systems. Traditional methods of looking into these systems often require immense resources, making them impractical for large-scale applications.

Researchers at UC San Diego, in collaboration with colleagues from IBM Quantum, Harvard and UC Berkeley, have developed a novel approach to this problem called “robust shallow shadows.” This technique allows scientists to extract essential information from more efficiently and accurately, even in the presence of real-world noise and imperfections. The research is published in the journal Nature Communications.

Imagine casting shadows of an object from various angles and then using those shadows to reconstruct the object. By using algorithms, researchers can enhance sample efficiency and incorporate noise-mitigation techniques to produce clearer, more detailed “shadows” to characterize quantum states.

Researchers at Rice University have developed a new machine learning (ML) algorithm that excels at interpreting the “light signatures” (optical spectra) of molecules, materials and disease biomarkers, potentially enabling faster and more precise medical diagnoses and sample analysis.

“Imagine being able to detect early signs of diseases like Alzheimer’s or COVID-19 just by shining a light on a drop of fluid or a ,” said Ziyang Wang, an electrical and computer engineering doctoral student at Rice who is a first author on a study published in ACS Nano. “Our work makes this possible by teaching computers how to better ‘read’ the signal of light scattered from tiny molecules.”

Every material or molecule interacts with light in a unique way, producing a distinct pattern, like a fingerprint. Optical spectroscopy, which entails shining a laser on a material to observe how light interacts with it, is widely used in chemistry, materials science and medicine. However, interpreting spectral data can be difficult and time-consuming, especially when differences between samples are subtle. The new algorithm, called Peak-Sensitive Elastic-net Logistic Regression (PSE-LR), is specially designed to analyze light-based data.