Blog
The Dirac operator for the Ruelle-Koopman pair on L^p-spaces: an interplay between Connes distance and symbolic dynamics
Denote by $\bm{\mu}$ the maximal entropy measure for the shift \(\sigma\) acting on $\Omega = \{0, 1\}^\mathbb{N}$, by $\ruelle$ the associated Ruelle operator and by $\koopman = \ruelle^{\dagger}$ the Koopman operator, both acting on $\lp{2}(\bm{\mu})$. Using a diagonal representation $\pi$, the Ruelle-Koopman...
Applied Antifragility in Natural Systems: Evolutionary Antifragility
This chapter introduces evolutionary antifragility as the time-scale interaction characteristics of a natural dynamic system. It describes the benefit derived from input distribution unevenness, based on the emergent system dynamics and its uncertain and volatile interactions with the operating environment described by...
The case of the missing gallium vacancy in gallium arsenide: A multiscale explanation
Irradiation of gallium arsenide (GaAs) produces immobile vacancies and mobile interstitials. However, after decades of experimental investigation, the immobile Ga vacancy eludes observation, raising the question: Where is the Ga vacancy? Static first-principles calculations predict a Ga vacancy should be readily observed....
Birational properties of word varieties
We prove that the subvariety of $SL(2)\times SL(2)$ given by the matrix equation $w(X,Y)=\alpha$, where $w$ is a word in two letters, is closely related to an explicit smooth conic bundle over the associated `trace surface’ in the 3-dimensional affine space. When...
Ultra-sensitive radon assay using an electrostatic chamber in a recirculating system
Rare event searches such as neutrinoless double beta decay and Weakly Interacting Massive Particle detection require ultra-low background detectors. Radon contamination is a significant challenge for these experiments, which employ highly sensitive radon assay techniques to identify and select low-emission materials. This...
Learning Adaptive Parallel Reasoning with Language Models
Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs, leading to increased latency and exhausted context windows, while parallel methods such as self-consistency suffer from insufficient...
Long-lived entanglement of a spin-qubit register in silicon photonics
Color centers provide an optical interface to quantum registers based on electron and nuclear spin qubits in solids. The T center in silicon is an emerging spin-photon interface that combines telecom O-band optical transitions and a long-lived electron spin in a scalable...
Generating Dark Matter Subhalo Populations Using Normalizing Flows
Strong gravitational lensing is a powerful tool for probing the nature of dark matter, as lensing signals are sensitive to the dark matter substructure within the lensing galaxy. We present a comparative analysis of strong gravitational lensing signatures generated by dark matter...
Trends in Frontier AI Model Count: A Forecast to 2028
Governments are starting to impose requirements on AI models based on how much compute was used to train them. For example, the EU AI Act imposes requirements on providers of general-purpose AI with systemic risk, which includes systems trained using greater than...
Manifold Induced Biases for Zero-shot and Few-shot Detection of Generated Images
Distinguishing between real and AI-generated images, commonly referred to as ‘image detection’, presents a timely and significant challenge. Despite extensive research in the (semi-)supervised regime, zero-shot and few-shot solutions have only recently emerged as promising alternatives. Their main advantage is in alleviating...