arXiv preprints from January 1, 2026 through September 23, 2026 — 21:36:31 EST
In this paper, we prove finiteness results for K-trivial varieties in all dimensions. In dimension 2, these results are corollaries of the Global Torelli Theorem for polarized K3 surfaces. In particular, we establish a sufficient condition when two fibers of a projective family of K-trivial varieties are isomorphic via the Hodge...
The physics of information scrambling in quantum many-body systems is intimately related to thermalisation and emergence of chaos. However, its standard characterisation through bipartite entanglement or operator growth remains inherently coarse-grained, obscuring the spatiotemporal anatomy of how quantum information flows between...
LLM-based agents are increasingly deployed in product-level execution harnesses, where jailbreaks can trigger harmful tool use and persistent state changes, creating greater risks than unsafe text generation alone. Existing automatic red-teaming methods often rely on fixed attacks, while recent agentic attackers coordinate multiple...
We prove that the $q$-Ehrhart series of a hyperplane slice of a cube is a rational function with an explicit denominator that satisfies $q$-reciprocity, confirming a conjecture of Reiner and Rhoades for these polytopes. To do this, we find a generating set for the orbit harmonics ideal, which also yields the Hilbert series and graded...
Debris disks, composed of rocks, boulders, planetesimals, and the dust produced in their collisions, present the most readily observable components of mature planetary systems. They also serve as valuable diagnostic tools, enabling studies of planetary dynamical interactions and mineral compositions. Observed from optical to radio...
Low-dimensional reduction theories such as the Ott-Antonsen ansatz have played a crucial role in the study of populations of coupled oscillators. Their application, however, has largely been restricted to systems with frequency distributions of rational-function form, such as the Cauchy distribution. For such distributions, the...
Let $A$ be a commutative-associative algebra with an invertible derivation $D$, and put $R=D^{-1}$. We study the operations \begin{equation*} x\succ y=R(x)y,\qquad x\prec y=xD(y), \end{equation*} which define a Novikov-Zinbiel algebra. Using a simple graded model, we represent multilinear $\prec,\succ$-monomials by rational functions...
This paper addresses centroids, which are fundamental invariants of tensors. Our main results are as follows: (i) The construction of explicit tensors with very large centroids, whereas previously it had been conjectured that none such exist. (ii) An upper bound on the dimension of the centroid that is essentially attained by our...
Large-scale, standardized datasets have driven many advances in AI-based scientific modeling, from protein structure prediction to natural language processing. Infectious disease epidemiology is increasingly adopting AI methods for forecasting, surveillance, and outbreak analytics, but the time-series data available to train them...
Ordinary differential equations are commonly used throughout the sciences to build mechanistic models of time-dependent processes. Often, such models are Markov models describing the time-evolution of different interconnected "states". When these models have no "sources" or "sinks", they naturally conserve the total population of the...
This paper establishes that the system of ordinary differential equations arising from the sequential and distributive dual futile cycle has the structural capacity for Hopf bifurcations, whenever it is endowed with general parameter-rich kinetics, but it loses such capacity if it is endowed with mass action kinetics. The proof of the...
Parcellations distributed in Connectivity Informatics Technology Initiative (CIFTI) format cannot be used directly in many analysis programs that require volume input. Existing conversion options may leave voxels in cortical gray matter unlabeled or assign labels outside gray matter, depending on the mapping parameters. We present...
Reproducible biomarkers that monitor motor and cognitive dysfunction in amyotrophic lateral sclerosis (ALS) are needed. Previous work reported reduced beta-band event-related desynchronization (ERD) and attenuated post-movement event-related synchronization (ERS) in frontal and parietal channels during the sustained attention to...
Objective: Choosing between noninvasive respiratory support (NIRS) and invasive mechanical ventilation (IMV) for patients with acute respiratory failure is a complex, time-sensitive decision with heterogeneous treatment effects across patient subgroups. Although clinical trials and guidelines provide population-level guidance, it...
Protein language models organize sequence and structure at scale, but a global representation of how proteins respond to mutation remains lacking. We present RegimeFormer, a large protein perturbation model coupled to RegimeAtlas, constructed by harmonizing and indexing 202,556,313 non-redundant protein sequences across the tree of...
High-throughput drug screening relies on low-cost primary assays to prioritize compounds for more expensive dose-response profiling, where potency is ultimately quantified. Current screening strategies largely focus on identifying compounds that will confirm biological activity on follow-up, implicitly assuming that confirmed activity...
Spreading processes on networks often interact with other dynamics on the same nodes. Neurodegenerative disease provides one example: pathological proteins spread through anatomical connections, while neuronal activity influences and is altered by their spread, forming a spreading-activity feedback loop. However, models coupling...
Updating a graph by inserting or replacing nodes while preserving semantics and reusing existing structure is a recurring computational problem. In population genetics, this problem arises in the genotype representation graph (GRG), a directed acyclic graph that losslessly encodes phased genetic variation across hundreds of thousands...
Protein language models (pLMs) encode information about protein sequences which enable downstream tasks such as structure prediction, but their internal representations are not well understood. Sparse autoencoders (SAEs) provide a promising tool to disentangle latent pLM representations into interpretable features, but existing...
Mentalization - the ability to infer others' beliefs and intentions to guide one's own choices - is a key cognitive function underlying human social interactions. Large language models (LLMs) demonstrate behaviour consistent with humans on theory-of-mind tasks, yet whether these models can guide adaptive behaviour through...
With activity against multidrug-resistant pathogens and mechanisms distinct from conventional antibiotics, antimicrobial peptides (AMPs) offer a promising approach to combating antibiotic-resistant infections. However, their potency varies substantially across pathogen species, making accurate prediction of the minimum inhibitory...
Dementia comprises biologically heterogeneous disorders, yet current risk assessment provides limited insight into how subtype-specific risk emerges and diverges before clinical diagnosis. We developed NetMoint, a multimodal framework integrating partially observed plasma proteomic, structural magnetic resonance imaging and cerebral...
We develop $L^1$ bounds for the difference between a test function of a random sum and a standard normal random variable, where the summands are assumed to be independent but not necessarily identically distributed. The bounds are obtained through a new version of the approximate zero bias transformation specifically developed for...
Recursive application of the law of total variance decomposes the marginal variance of an outcome into components attributed to explanatory variables and a residual component. The resulting decomposition depends on the chosen conditioning order, and its components do not in general have causal interpretations. We develop a graph-based...
Reliable prediction of time-varying channel state information (CSI) is essential for efficient wireless communication. Each CSI frame is a matrix-valued representation of the wireless channel response, and a sequence of CSI frames forms a temporal channel trajectory. Modern deep learning-based CSI predictors, however, often provide...