Markets look like well-oiled machines on the surface: prices drift, risk is priced, and clever traders try to carve out a risk‑free profit by exploiting tiny mispricings. But behind the scenes the future is not a single weather forecast; it’s a landscape of many possible futures, each with its own probability. That kind of ambiguity…
The droplet perched on a surface is more than a pretty drop of water in a science fair. Its edge, the contact line where liquid meets solid and air, encodes a negotiation between molecules: a quiet vote about how much a surface wants to be kissed or ignored by a liquid. In industry, that tiny…
The Rise of the Self-Improving AI Imagine an AI so sophisticated it doesn’t just answer your questions; it also grades its own answers, identifying flaws and refining its responses based on its own self-assessment. This isn’t science fiction; it’s the core principle behind a groundbreaking new framework for aligning large language models (LLMs) with human…
Mathematicians often picture a dynamical system as a tiny machine that pushes every point along a path through space. The Point Escape Problem asks a deceptively simple question: if you start inside a closed region A and keep applying a rule f that reshapes the landscape, does your path ever leave A? The trap in…
The study of toric varieties has long inhabited the crosscurrents of geometry, combinatorics, and algebra. In this story, symmetry serves as a guide through the labyrinth of derived categories—the library of all coherent sheaves that encode geometric information. Xiaodong Yi’s new work builds on Bondal’s conjecture and adds a flexible twist: a generalized Thomsen collection…
The human nose is a tiny wind tunnel, a maze of curves and creases that shapes every breath we take. In the last couple of decades, scientists have started to treat that internal landscape like a living, breathing laboratory, using computational fluid dynamics (CFD) to predict how air flows through our nostrils, around turbinates, and…
Graphs are people’s stories drawn as networks: arrows and paths that hint at direction, speed, and influence. When researchers study these directed stories, they need a kind of reading tool that can cope with both structure and flow. That tool is directed treewidth, a way to measure how tangled a directed graph is and, crucially,…
Forecasting the future from data is a daily challenge. Real-world time series—prices, weather, traffic, energy demand—don’t stay put. They drift, surprise, and shift with seasons, events, and unseen quirks. When a model trained on one pattern meets a newer distribution, its accuracy can falter, like a compass spinning in fog. The problem isn’t just how…
In a quiet corner of the quantum world, a handful of ultracold polar molecules dance to an unusual tune. The trick is microwave shielding: a highly elliptic microwave field makes the long-range attraction between molecules behave as if they were bound in one dimension. The result is a surprisingly clean, almost architectural set of bound…
Hard X-rays on a Galactic Treasure Hunt Behind the glow of the night sky lies a hidden census of supermassive black holes. Some galaxies cradle actively feeding cores that spit out X‑rays so energetic they can cut through dust and gas like a cosmic X‑ray policy. The SRG mission, carrying two complementary eyes in space—the…
Symmetry isn’t just about pretty patterns in wallpaper or snowflakes. In mathematics, symmetry is a precise language that encodes how many ways you can shuffle a system without changing its essential shape. The objects behind this language are called finite groups, and they come with a catalog of elements that behave in specific, rule-bound ways….
The hunt for planets beyond our solar system rides on tiny, almost invisible nudges from starlight. Astronomers measure a star’s wobble—its radial velocity (RV)—to infer a planet’s presence, mass, and orbit. Over the past decades, template-based RV methods have become a central tool for turning a spectrum into a velocity signal, especially for cooler stars…
In a world where a handful of companies quietly collect and sell your personal signals, California’s data broker registry reads like a public ledger of a hidden economy. The registry promises transparency, but what happens when you actually try to see what a broker knows about you? That question sits at the heart of a…
In the data-driven world, researchers want to learn from sensitive information without exposing the individuals behind the numbers. Differential privacy, a formal way to guard each person’s imprint, has long traded a bit of accuracy for a large shield of confidentiality. Yet as data grow in dimension and messiness—think dozens or hundreds of variables per…
Intro Large language models have become the modern wild west of text: powerful, versatile, and increasingly hard to pin down. As their capabilities scale, so do the tricks people devise to coax them into saying or doing things their designers don’t intend. Among the cleverest strategies are obfuscation-based jailbreaks, where a malicious request is hidden…
The wave function is the beating heart of quantum mechanics, a mathematical swirl that encodes every possible future of a particle. Yet what we actually observe in the lab comes from real, tangible things: a spectrum, a scattering angle, a resonance peak. Those measurements are built from two pieces of the same story—the amplitude and…
Phase retrieval is the kind of puzzle you encounter when you try to reconstruct an image or a signal from brightness alone. In many real‑world imaging tasks—think X‑ray crystallography, coherent diffraction, or certain telescope observations—you don’t get to read the phase of a wave. You only see its intensity, the square of its amplitude. The…
In the quiet borders of math and physics, scientists chase whispers of information that arrive through noise. Some whispers come from faraway echoes of a signal we can’t see directly, and the challenge is to reconstruct what happened from the clues left in a handful of measurements. That task is what mathematicians call an inverse…
Meet the chunking breakthrough in urban knowledge Cities are built not just from concrete and cables but from pages of codes, standards, reports, and policy briefs. The way urban systems are managed depends on humans reading and connecting thousands of words across a sprawling landscape of documents. That heavy lift is exactly where a team…
Can a machine truly understand a joke? It’s a question that probes not just the limits of artificial intelligence, but also the very nature of human wit. Researchers at the University of Sheffield and the University of Manchester recently tackled this question, revealing some surprising limitations in even the most advanced language models’ ability to…