arXiv preprints from January 1, 2026 through July 28, 2026 — 01:30:46 EST
We show that powersets over structures with a bounded counting sequence can be sampled efficiently without evaluating the generating function. An algorithm is provided, implemented, and tested. Runtimes are comparable to existing Boltzmann samplers reported in the literature.
Photonic molecules can mimic interactions of atomic energy levels, offering new ways to manipulate cavity eigenstates. Current methods using evanescent coupling of multiple cavities face challenges in scalability, flexibility, and coupling control, especially for complex systems. Here we introduce a new method that uses a single...
Two graphs are isomorphic exactly when they admit the same number of homomorphisms from every graph. Hence, a graph is recognized up to isomorphism by homomorphism counts over the class of all graphs. Restricting to a specific graph class yields some natural isomorphism relaxations and modulates recognition to particular graph...
We introduce a new model structure on the category of dendroidal spaces, designed to provide a further model for the homotopy theory of $\infty$-operads. This model is directly analogous to a recent construction on the category of simplicial spaces by Moser and Nuiten, and can be seen as its dendroidal counterpart. In our new model...
Scientific surveys require not only summarizing large bodies of literature, but also organizing them into clear and coherent conceptual structures. However, existing automatic survey generation methods typically focus on linear text generation and struggle to explicitly model hierarchical relations among research topics and structured...
Large language model (LLM) agents have demonstrated remarkable capabilities in complex decision-making and tool-use tasks, yet their ability to generalize across varying environments remains a under-examined concern. Current evaluation paradigms predominantly rely on trajectory-based metrics that measure task success, while failing to...
We study the anisotropic linear Maxwell system on a bounded domain $Ω$ with perfectly conducting boundary conditions. It is damped via a conductivity $σ$ which is strictly positive on a collar at the boundary. We prove that solutions decay exponentially to 0, if the fields have no magnetic charges on $Ω$ and no electric charges off...
Bi$_2$O$_2$Se is an emerging high-performance layered semiconductor with excellent stability. While experimental studies have explored carrier transport across various doping levels for both $n$-type and $p$-type conduction, a comprehensive theoretical understanding remains incomplete. In this work, we present parameter-free...
We say a hypergraph $\mathcal{H}$ contains a graph $G$ as trace if there exists a vertex subset $S \subseteq V(\mathcal{H})$ such that $|S| = V(G)$ and $\{e \cap S \mid e \in E(\mathcal{H})\}$ contains $G$ as a subgraph. We use $\mathrm{ex}(n, Tr_r(G))$ to denote the maximum number of edges in an $r$-uniform hypergraph on $n$...
We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition recovers local differential privacy (LDP) for $c\to 0$. We derive achievable bounds on...
Powerful 3D representations such as DUSt3R invariant point maps, which encode 3D shape and camera parameters, have significantly advanced feed forward 3D reconstruction. While point maps assume static scenes, Dynamic Point Maps (DPMs) extend this concept to dynamic 3D content by additionally representing scene motion. However,...
Object detectors often perform well in-distribution, yet degrade sharply on a different benchmark. We study cross-dataset object detection (CD-OD) through a lens of setting specificity. We group benchmarks into setting-agnostic datasets with diverse everyday scenes and setting-specific datasets tied to a narrow environment, and...
Search and recommendation (S&R) are core to online platforms, addressing explicit intent through queries and modeling implicit intent from behaviors, respectively. Their complementary roles motivate a unified modeling paradigm. Early studies to unify S&R adopt shared encoders with task-specific heads, while recent efforts reframe item...
With the emergence of massively parallel processing units, parallelization has become a desirable property for new sequence models. The ability to parallelize the processing of sequences with respect to the sequence length during training is one of the main factors behind the uprising of the Transformer architecture. However,...
Many-body localization (MBL) appears to be a robust example of ergodicity breaking in many-body interacting systems. Here, we review different aspects of MBL, concentrating on various ways the disorder may be introduced into the system studied. In particular, we consider both the random and quasiperiodic diagonal (i.e., on-site)...
This paper presents an innovative framework that boosts computing power by utilizing ubiquitous computing power distribution and enabling higher computing node accessibility via adaptive UAV positioning, establishing a UAV-enabled Computing Power Network (UAV-CPN). In a UAV-CPN, a UAV functions as a dynamic relay, outsourcing...
Understanding the demographics of close-in planets is crucial for insights into exoplanet formation and evolution. We present a detailed analysis of occurrence rates for close-in (0.5-16 day) planets with radii between 2 and 20$\,R_{\oplus}$ around FGK main-sequence stars. Our study uses a comprehensive sample from four years of TESS...
Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In particular, DeepONets offer a natural formulation for PDE solving, since the solution of a partial...
We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a nontrapping condition. Our approach relies on a new trace estimate for the corresponding...
This paper addresses the Counting Long Aggregated Visits problem, which is defined as follows. We are given $n$ users and $m$ regions, where each user spends some time visiting some regions. For a parameter $k$ and a query consisting of a subset of $r$ regions, the task is to count the number of distinct users whose aggregate time...
We consider a critical problem in a bounded domain involving the $p$-Grushin operator $Δ_α^p$. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of García Azorero and Peral Alonso to the $p$-Grushin operator. A central part of our analysis is the...
The rapid evolution of Large Language Models (LLMs) has fostered diverse paradigms for automated slide generation, ranging from code-driven layouts to image-centric synthesis. However, evaluating these heterogeneous systems remains challenging, as existing protocols often struggle to provide comparable scores across architectures or...
In this paper, we study two semilinear systems describing a monotubular and a two-stream heat exchanger. Neither system is exactly controllable; however, for each we specify a subspace of the state space with respect to which the system is exactly controllable, thus establishing partial exact controllability.
Let $n,k$ be positive integers such that $n\geq k$, and let $H$ be a hypergeometric random variable counting the number of black marbles in a sample without replacement of size $k$ from an urn that contains $i\in \{1,\ldots, n\}$ black and $n - i$ white marbles. It is shown that \[ \mathbb{P}(H \ge \mathbb{E}(H)) \ge k/n\, , \,...
This paper presents an echo-side modulation framework for integrated sensing and communication (ISAC) systems. A space-time reconfigurable intelligent surface (ST-RIS) impresses a continuous-phase modulation onto the radar echo, enabling uplink data transmission with a phase modulation of the transmitted radar-like waveform. The...