arXiv preprints from January 1, 2026 through September 22, 2026 — 08:20:54 EST
We introduce a new extrinsic discretization of tangent vector fields on triangle meshes that is continuous, with bounded derivatives that are continuous almost everywhere, supporting pointwise evaluation and integration of differential operators. We achieve this by building a continuous normal field over the mesh via Phong...
In this work, the massless-massive correspondence for the on-shell scattering amplitudes is constructed so the massive amplitudes could inherit advantageous techniques developed in the massless calculation. This correspondence is established by matching massless amplitudes to Minimal Helicity-Chirality (MHC) amplitudes, which arise...
We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal-insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled...
We introduce a universal Bochner formula for scalar curvature that contains, as special cases, the stability inequality for minimal slicings, a Schrödinger-Lichnerowicz-type formula, and a higher-dimensional version of Stern's level-set identity.
We prove Gromov's conjecture on the total mean curvature of fill-ins in various cases. Our methods are based on surgery to reduce the statement to fill-ins of spheres, which can be treated by instances of the positive mass theorem. For spin fill-ins, where we permit the mean curvature to take negative values, we build on a classical...
Coded computing has emerged as a key framework for addressing the impact of stragglers in distributed computation. While polynomial functions often admit exact recovery under existing coded computing schemes, non-polynomial functions require approximate reconstruction from a finite number of evaluations, posing significant challenges....
This study examines the application of Bayesian approach in the context of clinical trials, emphasizing their increasing importance in contemporary biomedical research. While conventional frequentist approach provides a foundational basis for analysis, it often lacks the flexibility to integrate prior knowledge, which can constrain...
The manuscript is concerned with the Rudin-Keisler order of ultrafilters on measurable cardinals. The main theorem proved read as follows: Given regular cardinals $λ\leq κ$, the following theories are equiconsistent modulo ZFC: (1) $κ$ is a measurable cardinal with $o(κ)=λ^+$ (resp. $o(κ)=κ$). (2) The Rudin-Keisler order restricted to...
In this paper, we study three classes of subvarieties inside the variety of left-symmetric algebras. We show that these subvarieties are naturally related to some well-known varieties, such as alternative, assosymmetric and Zinbiel algebras. For certain subvarieties of the varieties of alternative and assosymmetric algebras, we...
Observations of active galactic nuclei have revealed a correlation between millimeter luminosity, X-ray luminosity, and mass, suggesting the emission in each of these bands is powered by a common source. Starting with a set of five general relativistic magnetohydrodynamic simulations with dynamically important magnetic fields, we...
Today's strongest video-language models (VLMs) remain proprietary. The strongest open-weight models either rely on synthetic data from proprietary VLMs, effectively distilling from them, or do not disclose their training data or recipe. As a result, the open-source community lacks the foundations needed to improve on the...
This work builds upon the recent monograph [5] on self-similar Markov trees. A self-similar Markov tree is a random real tree equipped with a function from the tree to $[0,\infty)$ that we call the decoration. Here, we construct local time measures $L(x,dt)$ at every level $x>0$ of the decoration for a large class of self-similar...
Addressing itinerary modification is crucial for enhancing the travel experience as it is a frequent requirement during traveling. However, existing research mainly focuses on fixed itinerary planning, leaving modification underexplored due to the scarcity of need-to-modify itinerary data. To bridge this gap, we formally define the...
Snowflakes play a crucial role in weather and climate. A significant portion of precipitation that reaches the surface originates as ice, even when it ultimately falls as rain. Contrary to the popular image of symmetric, dendritic crystals, most large snowflakes are irregular aggregates formed through the collision of primary ice...
Adaptive video streaming has facilitated improved video streaming over the past years. A balance among coding performance objectives such as bitrate, video quality, and decoding complexity is required to achieve efficient, content- and codec-dependent, adaptive video streaming. This paper proposes a multi-objective Pareto-front (PF)...
Talking head generation is increasingly important in virtual reality (VR), especially for social scenarios involving multi-turn conversation. Existing approaches face notable limitations: mesh-based 3D methods can model dual-person dialogue but lack realistic textures, while large-model-based 2D methods produce natural appearances but...
Network slicing is an architectural enabling technology that logically decouples the current cellular networks into infrastructure providers (InPs) and Network Slice Tenants (NSTs). The network resources (e.g., radio access resources at each cell) are owned by the InP, and are shared by the NSTs to provide a service to their mobile...
We present a pseudocode algorithm for translating our (Elementary) Mathematical Data Model schemes into relational ones and associated sets of non-relational constraints, used by MatBase, our intelligent data and knowledge base management system prototype. We prove that this algorithm is very fast, solid, complete, and optimal. We...
This work establishes the fundamental limits of the classical problem of multi-user distributed computing of linearly separable functions. In particular, we consider a distributed computing setting involving $L$ users, each requesting a linearly separable function over $K$ basis subfunctions from a master node, who is assisted by $N$...
We establish a Schur--Horn type inequality for symmetric hyperbolic polynomials. As an immediate consequence, we resolve a conjecture of Nam Q. Le on Hadamard-type inequalities for hyperbolic polynomials. Our argument is based on the Schur--Horn theorem, the Birkhoff theorem, and Gårding's concavity theorem for hyperbolicity cones....
Soft current algebras capture the infrared structure of scattering in asymptotically flat spacetimes, but an analogous algebraic description of finite-energy dynamics has been missing. We uncover an infinite-dimensional hard current algebra that encodes finite-energy contributions to scattering and implies novel Ward identities. The...
In the context of multi-agent multi-armed bandits (MA-MAB), fairness is often reduced to outcomes: maximizing welfare, reducing inequality, or balancing utilities. However, evidence in psychology, economics, and Rawlsian theory suggests that fairness is also about process and who gets a say in the decisions being made. We introduce a...
As LLM-based systems increasingly operate as agents embedded within human social and technical systems, alignment can no longer be treated as a property of an isolated model, but must be understood in relation to the environments in which these agents act. Even the most sophisticated methods of alignment, such as Reinforcement...
The Galaxy's most common known planetary systems have several Earth-to-Neptune-size planets in compact orbits. At small orbital separations, larger planets are less common than their smaller counterparts by an order of magnitude. The young star V1298 Tau hosts one such compact planetary system, albeit with four planets that are...
Using (10087$\pm$44)$\times$10$^{6}$ $J/ψ$ events collected with the BESIII detector at the BEPCII collider at the center-of-mass energy of $\sqrt{s}=3.097~\rm{GeV}$, we report the first search for $η\toπ^0S\toπ^0χ\barχ$ with $S$ denotes an on-shell dark scalar boson and $χ$ an invisible dark matter particle. No significant signals...