Tootfinder

PCHands: PCA-based Hand Pose Synergy Representation on Manipulators with N-DoF
En Yen Puang, Federico Ceola, Giulia Pasquale, Lorenzo Natale
https://arxiv.org/abs/2508.07945 htt…

PCHands: PCA-based Hand Pose Synergy Representation on Manipulators with N-DoF
We consider the problem of learning a common representation for dexterous manipulation across manipulators of different morphologies. To this end, we propose PCHands, a novel approach for extracting hand postural synergies from a large set of manipulators. We define a simplified and unified description format based on anchor positions for manipulators ranging from 2-finger grippers to 5-finger anthropomorphic hands. This enables learning a variable-length latent representation of the manipulato…

On the spectral theory in the Fock space with polynomial eigenfunctions
A. V. Turbiner (deceased), N. L. Vasilevski (deceased)
https://arxiv.org/abs/2508.05924 https://

On the spectral theory in the Fock space with polynomial eigenfunctions
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex representation of the 3-dimensional Heisenberg algebra, proposed by Turbiner-Vasilevski (2021) in Ref.7, this construction is reduced to the linear differential operators in $(\frac{\partial}{\partial \overline{z}}\,,\,\frac{\partial}{\partial z})$ acting on …

Irreducible restrictions of spin representations of symmetric and alternating groups
Alexander Kleshchev, Lucia Morotti, Pham Huu Tiep
https://arxiv.org/abs/2510.08223 https://

Irreducible restrictions of spin representations of symmetric and alternating groups
Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H

Learning Global Representation from Queries for Vectorized HD Map Construction
Shoumeng Qiu, Xinrun Li, Yang Long, Xiangyang Xue, Varun Ojha, Jian Pu
https://arxiv.org/abs/2510.06969

Learning Global Representation from Queries for Vectorized HD Map Construction
The online construction of vectorized high-definition (HD) maps is a cornerstone of modern autonomous driving systems. State-of-the-art approaches, particularly those based on the DETR framework, formulate this as an instance detection problem. However, their reliance on independent, learnable object queries results in a predominantly local query perspective, neglecting the inherent global representation within HD maps. In this work, we propose \textbf{MapGR} (\textbf{G}lobal \textbf{R}epresent…

Is it Gaussian? Testing bosonic quantum states
Filippo Girardi, Freek Witteveen, Francesco Anna Mele, Lennart Bittel, Salvatore F. E. Oliviero, David Gross, Michael Walter
https://arxiv.org/abs/2510.07305

Is it Gaussian? Testing bosonic quantum states
Gaussian states are widely regarded as one of the most relevant classes of continuous-variable (CV) quantum states, as they naturally arise in physical systems and play a key role in quantum technologies. This motivates a fundamental question: given copies of an unknown CV state, how can we efficiently test whether it is Gaussian? We address this problem from the perspective of representation theory and quantum learning theory, characterizing the sample complexity of Gaussianity testing as a fu…

Expected Signature Kernels for L\'evy Rough Paths
Peter K. Friz, Paul P. Hager
https://arxiv.org/abs/2509.07893 https://arxiv.org/pdf/2509.07893…

Expected Signature Kernels for Lévy Rough Paths
The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular, can help reduce computational costs. Building on the representation of the expected signature of (inhomogeneous) Lévy processes with absolutely continuous characteristics as the development of an absolutely continuous path in the extended tensor algebra [F.-H…

Time-Frequency Filtering Meets Graph Clustering
Marcelo A. Colominas, Stefan Steinerberger, Hau-Tieng Wu
https://arxiv.org/abs/2510.07503 https://arxiv.org…

Time-Frequency Filtering Meets Graph Clustering
We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are strongly connected and have relatively few connections between them. The graph clustering problem is well studied, we show how these ideas can suggest (many) new ways to identify signal components. Numerical experiments illustrate the ideas.

Universal Representation of Generalized Convex Functions and their Gradients
Moeen Nehzati
https://arxiv.org/abs/2509.04477 https://arxiv.org/pdf/2509.0447…

Universal Representation of Generalized Convex Functions and their Gradients
Solutions to a wide range of optimization problems, from optimal transport theory to mathematical economics, often take the form of generalized convex functions (GCFs). This characterization can be used to convert nested bilevel optimization problems into single-level optimization problems. Despite this, the characterization has not been fully exploited in numerical optimization. When the solution to an optimization problem is known to belong to a particular class of objects, this information…

Extensions of realizable Hamiltonian and complexity one GKM$_4$ graphs
Oliver Goertsches, Grigory Solomadin
https://arxiv.org/abs/2509.00392 https://arxiv.…

Extensions of realizable Hamiltonian and complexity one GKM$_4$ graphs
We prove that the GKM graphs of GKM$_4$ manifolds that are either Hamiltonian or of complexity one extend to torus graphs. The arguments are based on a reformulation of the extension problem in terms of a natural representation of the fundamental group of the GKM graph, using a coordinate-free version of the axial function group of Kuroki, as well as on covers of GKM graphs and acyclicity results for orbit spaces of GKM manifolds.

Structure Transfer: an Inference-Based Calculus for the Transformation of Representations
Daniel Raggi, Gem Stapleton, Mateja Jamnik, Aaron Stockdill, Grecia Garcia Garcia, Peter C-H. Cheng
https://arxiv.org/abs/2509.03249

Structure Transfer: an Inference-Based Calculus for the Transformation of Representations
Representation choice is of fundamental importance to our ability to communicate and reason effectively. A major unsolved problem, addressed in this paper, is how to devise \textit{representational-system (RS) agnostic} techniques that drive representation transformation and choice. We present a novel calculus, called \textit{structure transfer}, that enables representation transformation across diverse RSs. Specifically, given a \textit{source} representation drawn from a source RS, the rules …

A polynomial algorithm to compute the boxicity and threshold dimension of complements of block graphs
Marco Caoduro, Will Evans, Tao Gaede
https://arxiv.org/abs/2510.02199 https…

A polynomial algorithm to compute the boxicity and threshold dimension of complements of block graphs
The boxicity of a graph $G$ is the minimum dimension $d$ that admits a representation of $G$ as the intersection graph of a family of axis-parallel boxes in $\mathbb{R}^d$. Computing boxicity is an NP-hard problem, and there are few known graph classes for which it can be computed in polynomial time. One such class is the class of block graphs. A block graph is a graph in which every maximal $2$-connected component is a clique. Since block graphs are known to have boxicity at most two, computin…

XTRA: Cross-Lingual Topic Modeling with Topic and Representation Alignments
Tien Phat Nguyen, Vu Minh Ngo, Tung Nguyen, Linh Van Ngo, Duc Anh Nguyen, Sang Dinh, Trung Le
https://arxiv.org/abs/2510.02788

XTRA: Cross-Lingual Topic Modeling with Topic and Representation Alignments
Cross-lingual topic modeling aims to uncover shared semantic themes across languages. Several methods have been proposed to address this problem, leveraging both traditional and neural approaches. While previous methods have achieved some improvements in topic diversity, they often struggle to ensure high topic coherence and consistent alignment across languages. We propose XTRA (Cross-Lingual Topic Modeling with Topic and Representation Alignments), a novel framework that unifies Bag-of-Words …

Guaranteed Time Control using Linear Matrix Inequalities
V\'ictor Costa da Silva Campos, Mariella Maia Quadros, Luciano Frezzato, Leonardo Mozelli, Anh-Tu Nguyen
https://arxiv.org/abs/2510.02636

Guaranteed Time Control using Linear Matrix Inequalities
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state constraints. This approach is based on a harmonic transformation of the Lyapunov function and a novel piecewise quadratic representation of this transformed Lyapunov function over a simplicial partition of the state space. The problem is solved in a policy iteration…

Conformal four-point ladder integrals in diverse dimensions and polylogarithms
S. E. Derkachov, A. P. Isaev, L. A. Shumilov
https://arxiv.org/abs/2510.04235 https://

Conformal four-point ladder integrals in diverse dimensions and polylogarithms
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to study their properties, such as symmetries, loop and dimensional shift identities. In even integer dimensions, latter allows one to reduce the problem to two-dimensional case, where the notable factorization holds. Additionally, for a specific choice of propaga…

Computing moment polytopes - with a focus on tensors, entanglement and matrix multiplication
Maxim van den Berg, Matthias Christandl, Vladimir Lysikov, Harold Nieuwboer, Michael Walter, Jeroen Zuiddam
https://arxiv.org/abs/2510.08336

Computing moment polytopes - with a focus on tensors, entanglement and matrix multiplication
Tensors are fundamental in mathematics, computer science, and physics. Their study through algebraic geometry and representation theory has proved very fruitful in the context of algebraic complexity theory and quantum information. In particular, moment polytopes have been understood to play a key role. In quantum information, moment polytopes (also known as entanglement polytopes) provide a framework for the single-particle quantum marginal problem and offer a geometric characterization of ent…

LUIVITON: Learned Universal Interoperable VIrtual Try-ON
Cong Cao, Xianhang Cheng, Jingyuan Liu, Yujian Zheng, Zhenhui Lin, Meriem Chkir, Hao Li
https://arxiv.org/abs/2509.05030

LUIVITON: Learned Universal Interoperable VIrtual Try-ON
We present LUIVITON, an end-to-end system for fully automated virtual try-on, capable of draping complex, multi-layer clothing onto diverse and arbitrarily posed humanoid characters. To address the challenge of aligning complex garments with arbitrary and highly diverse body shapes, we use SMPL as a proxy representation and separate the clothing-to-body draping problem into two correspondence tasks: 1) clothing-to-SMPL and 2) body-to-SMPL correspondence, where each has its unique challenges. Wh…

Extremal polynomials for the Rogosinski--Szeg\H{o} estimates of the third coefficient of nonnegative sine polynomials
Dmitriy Dmitrishin, Alexander Stokolos, Walter Trebels
https://arxiv.org/abs/2509.22238

Extremal polynomials for the Rogosinski--Szegő estimates of the third coefficient of nonnegative sine polynomials
In the class of normalized sine-polynomials $S(t),$ non-negative on $[0,π],$ W.Rogosinski and G.Szegő 1950 considered a number of extremal problems and proved, among other things, sharp upper and lower estimates for the coefficient $a_3.$ Their proof is based on the Lukács representation of non-negative algebraic polynomials. This method does not lead to the construction of polynomials attaining the extreme values. We consider the corresponding problem in the framework of normalized typica…

ApproxJoin: Approximate Matching for Efficient Verification in Fuzzy Set Similarity Join
Michael Mandulak, S M Ferdous, Sayan Ghosh, Mahantesh Halappanavar, George Slota
https://arxiv.org/abs/2507.18891

ApproxJoin: Approximate Matching for Efficient Verification in Fuzzy Set Similarity Join
The set similarity join problem is a fundamental problem in data processing and discovery, relying on exact similarity measures between sets. In the presence of alterations, such as misspellings on string data, the fuzzy set similarity join problem instead approximately matches pairs of elements based on the maximum weighted matching of the bipartite graph representation of sets. State-of-the-art methods within this domain improve performance through efficient filtering methods within the filte…

DiffSDA: Unsupervised Diffusion Sequential Disentanglement Across Modalities
Hedi Zisling, Ilan Naiman, Nimrod Berman, Supasorn Suwajanakorn, Omri Azencot
https://arxiv.org/abs/2510.05717

DiffSDA: Unsupervised Diffusion Sequential Disentanglement Across Modalities
Unsupervised representation learning, particularly sequential disentanglement, aims to separate static and dynamic factors of variation in data without relying on labels. This remains a challenging problem, as existing approaches based on variational autoencoders and generative adversarial networks often rely on multiple loss terms, complicating the optimization process. Furthermore, sequential disentanglement methods face challenges when applied to real-world data, and there is currently no es…

Symbolic dynamics, shadowing and representation of real numbers with some countably piecewise linear Markov maps
Zolt\'an Kalocsai
https://arxiv.org/abs/2508.17159 https://

Symbolic dynamics, shadowing and representation of real numbers with some countably piecewise linear Markov maps
We study piecewise linear Markov maps, with countable Markov partitions, inspired by a problem of the Miklós Schweitzer competition of the János Bolyai Mathematical Society in 2022. We introduce $\ell$-Markov partitions and apply ideas of symbolic dynamics to our systems, relating them to Markov shifts. We prove the shadowing property for the system from the competition. We also investigate the possible orbits of rational numbers, for a class of piecewise linear Markov maps which generalize o…

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
Wolter Groenevelt, Carel Wagenaar
https://arxiv.org/abs/2507.13483

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
In this paper, we study rational functions of $q$-Racah type and a multivariate extension, using representation theory of $\mathcal U_q(\mathfrak{sl}_2)$. Eigenfunctions of twisted primitive elements in $\mathcal U_q(\mathfrak{su}_2)$ can be expressed in terms of $q^{-1}$-Krawtchouk polynomials. Using this, we show that overlap coefficients of solutions of a generalized eigenvalue problem (GEVP) and an eigenvalue problem (EVP) can be expressed in terms of a rational function of $_4φ_3$-type. W…

Preventing Singularity Problem in $f(R)$ Dark Energy Models
Romy Hanang Setya Budhi, Nehla Shobcha, Norma Sidik Risdianto
https://arxiv.org/abs/2508.20430 https://

Preventing Singularity Problem in $f(R)$ Dark Energy Models
The curvature singularity problem in $f(R)$ dark energy models poses a significant challenge to their viability as alternatives to the $Λ$CDM paradigm. In this work, we investigate the possibility of resolving this issue by incorporating higher-order corrections that are compatible with the inflationary phase. We analyze the effects of adding $R^2$, $R^{\frac{m+2}{m+1}}$ and $α$-attractor representation in $f(R)$ gravity terms to types of dark energy $f(R)$ models, focusing on their ability t…

Cubic incompleteness: Hilbert's tenth problem begins at degree three
Milan Rosko
https://arxiv.org/abs/2510.00759 https://arxiv.org/pdf/2510.00759

Cubic incompleteness: Hilbert's tenth problem begins at degree three
We present a preliminary result addressing a long-standing open question: Are cubic Diophantine equations undecidable?} We answer in the affirmative. By encoding Gödel's first incompleteness theorem via a Fibonacc-based Göodel numbering and the Zeckendorf representation, we reduce the arithmetic complexity sufficiently to construct an explicit \emph{cubic Diophantine equation} whose solvability is independent of a model provided by \emph{Peano axioms}. We present three results. First, a commo…

Lattice results for the equation of state in dense QCD-like theories
Etsuko Itou
https://arxiv.org/abs/2508.03090 https://arxiv.org/pdf/2508.03090

Lattice results for the equation of state in dense QCD-like theories
We review recent progress in Monte Carlo simulations of dense two-color QCD (QC$_2$D), focusing on the phase diagram, the equation of state, and the sound velocity in the low-temperature regime. In three-color QCD at finite density, especially at low temperatures, the notorious sign problem makes lattice Monte Carlo simulations intractable. In contrast, QC$_2$D is free from this issue due to the pseudoreality of the quark representation. Recent independent lattice studies have revealed unexpect…

Compact representation of maximal palindromes
Takuya Mieno
https://arxiv.org/abs/2508.14384 https://arxiv.org/pdf/2508.14384…

Compact representation of maximal palindromes
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and bioinformatics. Although the number of palindromic factors in a string of length $n$ can be quadratic, they can be implicitly represented in $O(n \log n)$ bits of space by storing the lengths of all maximal palindromes in an integer array, which can be compu…

Optimal Simulation Budget Allocation Under Unknown Sampling Variance
Jianzhong Du, Ilya O. Ryzhov, Siyang Gao
https://arxiv.org/abs/2509.02138 https://arxi…

Optimal Simulation Budget Allocation Under Unknown Sampling Variance
The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed with both its mean and variance being unknown. Using a Bayesian representation of the probability of correct selection, which allows us to explicitly model uncertainty about the variance, we provide a theoretical characterization of the optimal allocation of the…

Exact versus Approximate Representations of Boolean Functions in the De Morgan Basis
Arkadev Chattopadhyay, Yogesh Dahiya, Shachar Lovett
https://arxiv.org/abs/2507.13963

Exact versus Approximate Representations of Boolean Functions in the De Morgan Basis
A seminal result of Nisan and Szegedy (STOC, 1992) shows that for any total Boolean function, the degree of the real polynomial that computes the function, and the minimal degree of a real polynomial that point-wise approximates the function, are at most polynomially separated. Extending this result from degree to other complexity measures like sparsity of the polynomial representation, or total weight of the coefficients, remains poorly understood. In this work, we consider this problem in t…

On Distributionally Robust Lossy Source Coding
Giuseppe Serra, Photios A. Stavrou, Marios Kountouris
https://arxiv.org/abs/2507.17366 https://arxiv.org/pdf…

On Distributionally Robust Lossy Source Coding
In this paper, we investigate the problem of distributionally robust source coding, i.e., source coding under uncertainty in the source distribution, discussing both the coding and computational aspects of the problem. We propose two extensions of the so-called Strong Functional Representation Lemma (SFRL), considering the cases where, for a fixed conditional distribution, the marginal inducing the joint coupling belongs to either a finite set of distributions or a Kullback-Leibler divergence s…

Dyadic Neural Dynamics: Extending Representation Learning to Social Neuroscience
Maria Glushanina, Jeffrey Huang, Michelle McCleod, Brendan Ames, Evie Malaia
https://arxiv.org/abs/2509.23479

Dyadic Neural Dynamics: Extending Representation Learning to Social Neuroscience
Social communication fundamentally involves at least two interacting brains, creating a unique modeling problem. We present the first application of Contrastive Embedding for Behavioral and Neural Analysis (CEBRA) to dyadic EEG hyperscanning data, extending modeling paradigms to interpersonal neural dynamics. Using structured social interactions between participants, we demonstrate that CEBRA can learn meaningful representations of joint neural activity that captures individual roles (speaker-l…

Topology-Aware Graph Reinforcement Learning for Dynamic Routing in Cloud Networks
Yuxi Wang, Heyao Liu, Guanzi Yao, Nyutian Long, Yue Kang
https://arxiv.org/abs/2509.04973 https…

Topology-Aware Graph Reinforcement Learning for Dynamic Routing in Cloud Networks
This paper proposes a topology-aware graph reinforcement learning approach to address the routing policy optimization problem in cloud server environments. The method builds a unified framework for state representation and structural evolution by integrating a Structure-Aware State Encoding (SASE) module and a Policy-Adaptive Graph Update (PAGU) mechanism. It aims to tackle the challenges of decision instability and insufficient structural awareness under dynamic topologies. The SASE module mod…

Invariant Rings of $ \mathbb{G}_{a} $-Representations are not always Finitely Generated in Positive Characteristic
Stephen Maguire
https://arxiv.org/abs/2509.15431 https://

Invariant Rings of $ \mathbb{G}_{a} $-Representations are not always Finitely Generated in Positive Characteristic
Hilbert's 14th Problem asks the following question. Given a linear representation $ β: G \to \operatorname{GL}(\mathbf{V}) $ of a linear algebraic group over a field $ k $ is the ring $ S_{k}(\mathbf{V}^{\ast}) $ a finitely generated $ k $-algebra? For reductive groups the answer is yes. However, in general the answer is no. Nagata provided one of the earliest counterexamples to this claim and his counterexample was extended by Shigeru Mukai. However, if $ G $ is equal to $ \mathbb{G}_{a} $ an…

Configurational-force-driven adaptive refinement and coarsening in topology optimization
Gabriel Stankiewicz, Chaitanya Dev, Paul Steinmann
https://arxiv.org/abs/2507.15570 http…

Configurational-force-driven adaptive refinement and coarsening in topology optimization
The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of a fine mesh is essential to obtain geometrically well-defined structures and to accurately compute response quantities such as the von Mises stress. Therefore, the computational cost of solving a fine-mesh topology optimization problem quickly adds up. To ad…

Decomposition of the polynomials over the spherical subalgebra
Ibrahim Nonkane, Jean Kabor\'e
https://arxiv.org/abs/2509.00194 https://arxiv.org/pdf/25…

Decomposition of the polynomials over the spherical subalgebra
Given a finite subgroup $W \subset \GL(\fh)$ of the linear group of a finite-dimensional complex vector field $\fh$, it is a well-studied problem to describe the structure of the symmetric algebra $B= \sym(\fh^*)$ as a representation of $G$, and also as a module over the ring of invariant differential operators under $W$ in the ring $\D(\fh)$ of differential operators on $\fh$. Since the rational Cherednik algebra $H_c(W,\fh)$ and the spherical algebra $eH_ce$ are respectively universal deforma…

Geometry of effective field theory positivity cones
Quentin Bonnefoy, Vicente Cort\'es, Emanuele Gendy, Christophe Grojean, Karim Ritter von Merkl, Paula Naomi Pilatus
https://arxiv.org/abs/2508.18165

Geometry of effective field theory positivity cones
Positivity bounds are theoretical constraints on the Wilson coefficients of an effective field theory. These bounds emerge from the requirement that a given effective field theory must be the low-energy limit of a relativistic quantum theory that satisfies the fundamental principles of unitarity, locality, and causality. The task of deriving these bounds can be reformulated as the geometric problem of finding the extremal representation of a closed convex cone~$\mathcal C_W$. More precisely, in…

Efficient Optimal Path Planning in Dynamic Environments Using Koopman MPC
Mohammad Abtahi, Navid Mojahed, Shima Nazari
https://arxiv.org/abs/2510.02584 https://

Efficient Optimal Path Planning in Dynamic Environments Using Koopman MPC
This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization of system dynamics only, our work focuses on finding a global linear representation for the optimal path planning problem that includes both the nonlinear robot dynamics and collision-avoidance constraints. We deploy extended dynamic mode decomposition to ide…

Additive systems for $\mathbb{Z}$ are undecidable
Andrei Zabolotskii
https://arxiv.org/abs/2508.17285 https://arxiv.org/pdf/2508.17285

Additive systems for $\mathbb{Z}$ are undecidable
What are the collections of sets ${A}_i\subset\mathbb{Z}$ such that any $n\in\mathbb{Z}$ has exactly one representation as $n=a_0+a_1+\dotsb$ with $a_i\in{A}_i$? The answer for $\mathbb{N}_0$ instead of $\mathbb{Z}$ is given by a theorem of de Bruijn. We describe a family of natural candidate collections for $\mathbb{Z}$, which we call canonical collections. Translating the problem into the language of dynamical systems, we show that the question of whether the sumset of a canonical collection …

Diffusion is a code repair operator and generator
Mukul Singh, Gust Verbruggen, Vu Le, Sumit Gulwani
https://arxiv.org/abs/2508.11110 https://arxiv.org/pdf…

Diffusion is a code repair operator and generator
Code diffusion models generate code by iteratively removing noise from the latent representation of a code snippet. During later steps of the diffusion process, when the code snippet has almost converged, differences between discrete representations of these snippets look like last-mile repairs applied to broken or incomplete code. We evaluate the extent to which this resemblance can be exploited to leverage pre-trained code diffusion models for the problem of last-mile repair by considering tw…

Triadic Network Formation
Chris Muris, Cavit Pakel
https://arxiv.org/abs/2509.26420 https://arxiv.org/pdf/2509.26420

Triadic Network Formation
We study estimation and inference for triadic link formation with dyad-level fixed effects in a nonlinear binary choice logit framework. Dyad-level effects provide a richer and more realistic representation of heterogeneity across pairs of dimensions (e.g. importer--exporter, importer--product, exporter--product), yet their sheer number creates a severe incidental parameter problem. We propose a novel ``hexad logit'' estimator and establish its consistency and asymptotic normality. Identificati…

A Riemann-Hilbert Approach to Slavnov Overlaps in the Lieb-Liniger model
Eldad Bettelheim
https://arxiv.org/abs/2507.19025 https://arxiv.org/pdf/2507.19025…

A Riemann-Hilbert Approach to Slavnov Overlaps in the Lieb-Liniger model
We provide a method to compute Slavnov overlaps in the Lieb-Liniger model using the steepest descent method of the Riemann-Hilbert problem. To do so, we employ the Matsuo-Kostov Representation of the Slavnov overlaps to write an integral equation for the respective resolvent, and then represent this equation as a Riemann-Hilbert problem. To demonstrate the validity and applicability of the method by computing the Anderson orthogonality catastrophe in the $c\to\infty$ limit, corresponding to fre…

Factorization by extremal privacy mechanisms: new insights into efficiency
Chiara Amorino, Arnaud Gloter
https://arxiv.org/abs/2507.21769 https://arxiv.org…

Factorization by extremal privacy mechanisms: new insights into efficiency
We study the problem of efficiency under $α$ local differential privacy ($α$ LDP) in both discrete and continuous settings. Building on a factorization lemma, which shows that any privacy mechanism can be decomposed into an extremal mechanism followed by additional randomization, we reduce the Fisher information maximization problem to a search over extremal mechanisms. The representation of extremal mechanisms requires working in infinite dimensional spaces and invokes advanced tools from co…

CASPER: Concept-integrated Sparse Representation for Scientific Retrieval
Lam Thanh Do, Linh Van Nguyen, David Fu, Kevin Chen-Chuan Chang
https://arxiv.org/abs/2508.13394 https:…

CASPER: Concept-integrated Sparse Representation for Scientific Retrieval
The exponential growth of scientific literature has made it increasingly difficult for researchers to keep up with the literature. In an attempt to alleviate this problem, we propose CASPER, a sparse retrieval model for scientific search that utilizes tokens and keyphrases as representation units (i.e. dimensions in the sparse embedding space), enabling it to represent queries and documents with research concepts and match them at both granular and conceptual levels. To overcome the lack of sui…

Counting Answer Sets of Disjunctive Answer Set Programs
Mohimenul Kabir, Supratik Chakraborty, Kuldeep S Meel
https://arxiv.org/abs/2507.11655 https://

Counting Answer Sets of Disjunctive Answer Set Programs
Answer Set Programming (ASP) provides a powerful declarative paradigm for knowledge representation and reasoning. Recently, counting answer sets has emerged as an important computational problem with applications in probabilistic reasoning, network reliability analysis, and other domains. This has motivated significant research into designing efficient ASP counters. While substantial progress has been made for normal logic programs, the development of practical counters for disjunctive logic pr…

A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface
Harald Garcke, Robert N\"urnberg
https://arxiv.org/abs/2508.19198 …

A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell \geq 2$. In the semidiscrete continuous-in-time setting we are able to prove a stability estimate that mimics a corresponding result for the continuous problem. Some numerical results, including a convergence experiment, demonstrate the practicality and accuracy…

Simulation-based inference using splitting schemes for partially observed diffusions in chemical reaction networks
Petar Jovanovski, Andrew Golightly, Umberto Picchini, Massimiliano Tamborrino
https://arxiv.org/abs/2508.11438

Simulation-based inference using splitting schemes for partially observed diffusions in chemical reaction networks
We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This is challenging for two main reasons. First, the (multi-dimensional) SDEs cannot be explicitly solved and are driven by multiplicative and non-commutative noise, requiring the development of advanced numerical schemes for their approximation and simulation. Sec…

Joint space-time wind field data extrapolation and uncertainty quantification using nonparametric Bayesian dictionary learning
George D. Pasparakis, Ioannis A. Kougioumtzoglou, Michael D. Shields
https://arxiv.org/abs/2507.11385

Joint space-time wind field data extrapolation and uncertainty quantification using nonparametric Bayesian dictionary learning
A methodology is developed, based on nonparametric Bayesian dictionary learning, for joint space-time wind field data extrapolation and estimation of related statistics by relying on limited/incomplete measurements. Specifically, utilizing sparse/incomplete measured data, a time-dependent optimization problem is formulated for determining the expansion coefficients of an associated low-dimensional representation of the stochastic wind field. Compared to an alternative, standard, compressive sam…

Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise
Giorgio Ferrari, Anna Pajola
https://arxiv.org/abs/2507.19123 https://…

Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise
We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mean-field equilibrium exists, in which the mean-field interaction term is adapted to the common noise and the stopping time is randomized. Furthermore, under suitable monotonicity assumptions and for a…

Modularity from $q$-series
Ken Ono
https://arxiv.org/abs/2509.20316 https://arxiv.org/pdf/2509.20316

Modularity from $q$-series
In 1975, G. E. Andrews challenged the community to provide a proof that takes the summatory forms of the Rogers--Ramanujan $q$-series as input and directly establishes their modularity. This question is important because many different $q$-series appearing in combinatorics, representation theory, and physics often seem to be mysteriously modular, yet there is no general test to confirm this directly from the exotic $q$-series expressions. In this note, solve this general problem using $q$-serie…

Positive polynomials and the truncated moment problem on plane cubics
Mario Kummer, Alja\v{z} Zalar
https://arxiv.org/abs/2508.13850 https://arxiv.org/pdf/…

Positive polynomials and the truncated moment problem on plane cubics
The truncated moment problem supported on a given closed set $K$ in $\mathbb{R}^2$ ($K$-TMP) asks to characterize conditions for a given linear functional on bivariate polynomials of bounded degree to have an integral representation with respect to a Borel measure $μ$ with $\text{supp}μ\subseteq K$. The solutions to the $K$-TMP are known for $K$, which is a line, a quadratic curve, and for some cases of cubic curves. In this paper, we solve the $C$-TMP for every cubic curve $C$. Our first res…

Portfolio construction using a sampling-based variational quantum scheme
Gabriele Agliardi, Dimitris Alevras, Vaibhaw Kumar, Roberto Lo Nardo, Gabriele Compostella, Sumit Kumar, Manuel Proissl, Bimal Mehta
https://arxiv.org/abs/2508.13557

Portfolio construction using a sampling-based variational quantum scheme
The efficient and effective construction of portfolios that adhere to real-world constraints is a challenging optimization task in finance. We investigate a concrete representation of the problem with a focus on design proposals of an Exchange Traded Fund. We evaluate the sampling-based CVaR Variational Quantum Algorithm (VQA), combined with a local-search post-processing, for solving problem instances that beyond a certain size become classically hard. We also propose a problem formulation tha…

The Hadamard parametrix on half-Minkowski with Robin boundary conditions: Fundamental solutions and Hadamard states
B. Costeri, C. Dappiaggi, B. A. Ju\'arez-Aubry, R. D. Singh
https://arxiv.org/abs/2509.26035

The Hadamard parametrix on half-Minkowski with Robin boundary conditions: Fundamental solutions and Hadamard states
We address the problem of constructing fundamental solutions and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime with Robin boundary conditions in $d \geq 2$ spacetime dimensions. First, using a generalisation of the Robin-to-Dirichlet map exploited by Bondurant and Fulling [J. Phys. A: Math. Theor. {\bf 38} 7 (2005)] in dimension $2$, we obtain a representation for the advanced and retarded Green operators in terms of a convolution with the kernel of the inverse Robin-to-D…

Efficient Construction of Implicit Surface Models From a Single Image for Motion Generation
Wei-Teng Chu, Tianyi Zhang, Matthew Johnson-Roberson, Weiming Zhi
https://arxiv.org/abs/2509.20681

Efficient Construction of Implicit Surface Models From a Single Image for Motion Generation
Implicit representations have been widely applied in robotics for obstacle avoidance and path planning. In this paper, we explore the problem of constructing an implicit distance representation from a single image. Past methods for implicit surface reconstruction, such as \emph{NeuS} and its variants generally require a large set of multi-view images as input, and require long training times. In this work, we propose Fast Image-to-Neural Surface (FINS), a lightweight framework that can reconstr…

Unbiased Binning: Fairness-aware Attribute Representation
Abolfazl Asudeh (Mila), Zeinab (Mila), Asoodeh, Bita Asoodeh, Omid Asudeh
https://arxiv.org/abs/2509.21785 https://…

Unbiased Binning: Fairness-aware Attribute Representation
Discretizing raw features into bucketized attribute representations is a popular step before sharing a dataset. It is, however, evident that this step can cause significant bias in data and amplify unfairness in downstream tasks. In this paper, we address this issue by introducing the unbiased binning problem that, given an attribute to bucketize, finds its closest discretization to equal-size binning that satisfies group parity across different buckets. Defining a small set of boundary candi…

The Global Glimm Property for C*-algebras of topological dimension zero
Ping Wong Ng, Hannes Thiel, Eduard Vilalta
https://arxiv.org/abs/2507.16261 https:/…

The Global Glimm Property for C*-algebras of topological dimension zero
We show that a C*-algebra with topological dimension zero has the Global Glimm Property (every hereditary subalgebra contains an almost full nilpotent element) if and only if it is nowhere scattered (no hereditary subalgebra admits a finite-dimensional representation). This solves the Global Glimm Problem in this setting. It follows that nowhere scattered C*-algebras with finite nuclear dimension and topological dimension zero are pure.

Particle systems and the supercooled Stefan problem with non-integrable initial data
Thomas Blore, D. G. M Flynn, Ben Hambly
https://arxiv.org/abs/2507.16703

Particle systems and the supercooled Stefan problem with non-integrable initial data
We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing for the possibility of sequences of successive jumps to occur instantaneously. Under certain conditions, the scaling limit gives a representation for the supercooled Stefan problem and its free boundary. This allows us to give a precise asymptotic limit for the…

The Boiling-Frog Problem of Physics Education
Gerd Kortemeyer
https://arxiv.org/abs/2508.08842 https://arxiv.org/pdf/2508.08842

The Boiling-Frog Problem of Physics Education
It is astonishing how rapidly general-purpose AI has crossed familiar thresholds in introductory physics. Comparing outputs from successive models, GPT-5 Thinking moves far beyond the plug-and-chug tendencies seen earlier: on a classic elevator problem it works symbolically, notes when variables cancel, and verifies results; attempts to prompt novice-like behavior mainly affect tone, not method. On representation translation, the model scores 24/26 (92.3%) on TUG-Kv4.0. In a card-sorting proxy …

Parameterizing quasi-quintessence and quasi-phantom fields without the nearly flat potential approximation
Anna Chiara Alfano, Youri Carloni
https://arxiv.org/abs/2509.15146 htt…

Parameterizing quasi-quintessence and quasi-phantom fields without the nearly flat potential approximation
An alternative dark energy description based on a generalized K-essence scenario is here explored. In particular, we consider a \emph{quasi-quintessence} and/or \emph{quasi-phantom} field, whose pressure does not depend on the kinetic energy, firstly discussed in the context of the cosmological constant problem. In so doing, we fix the background evolution and investigate the main observational signatures of its corresponding fluid-like representation. The corresponding scalar field can be para…

Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
Fabian Mussnig, Jacopo Ulivelli
https://arxiv.org/abs/2508.11600 https://

Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting convex body is given by an explicit representation formula in terms of the measure. More generally, existence problems for mixed area measures are addressed. The approach relies on constructing explicit convex solutions to mixed Monge-Ampère equations on $\mathbb…

End-to-End Learning of Multi-Organ Implicit Surfaces from 3D Medical Imaging Data
Farahdiba Zarin, Nicolas Padoy, J\'er\'emy Dana, Vinkle Srivastav
https://arxiv.org/abs/2509.12068

End-to-End Learning of Multi-Organ Implicit Surfaces from 3D Medical Imaging Data
The fine-grained surface reconstruction of different organs from 3D medical imaging can provide advanced diagnostic support and improved surgical planning. However, the representation of the organs is often limited by the resolution, with a detailed higher resolution requiring more memory and computing footprint. Implicit representations of objects have been proposed to alleviate this problem in general computer vision by providing compact and differentiable functions to represent the 3D object…

Robot Learning with Sparsity and Scarcity
Jingxi Xu
https://arxiv.org/abs/2509.16834 https://arxiv.org/pdf/2509.16834…

Robot Learning with Sparsity and Scarcity
Unlike in language or vision, one of the fundamental challenges in robot learning is the lack of access to vast data resources. We can further break down the problem into (1) data sparsity from the angle of data representation and (2) data scarcity from the angle of data quantity. In this thesis, I will discuss selected works on two domains: (1) tactile sensing and (2) rehabilitation robots, which are exemplars of data sparsity and scarcity, respectively. Tactile sensing is an essential modalit…

Second Quantization for the Kepler Problem
John C. Baez
https://arxiv.org/abs/2507.11428 https://arxiv.org/pdf/2507.11428

Second Quantization for the Kepler Problem
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss the quantum Kepler problem for a spin-$\frac{1}{2}$ particle. We show that the Hilbert space $\mathcal{H}$ of bound states for this problem is unitarily equivalent, as a representation of $\text{SU}(2) \times \text{SU}(2)$, to the Hilbert space of solutions o…

Identifying Neural Connectivity using Bernoulli Autoregressive Partially Linear Additive Models
Carla Pinkney, Carolina Euan, Alex Gibberd
https://arxiv.org/abs/2507.18218 https…

Identifying Neural Connectivity using Bernoulli Autoregressive Partially Linear Additive Models
Characterising the interactions between spiking neurons is central to our understanding of cognitive processes such as memory, perception and decision making. In this work, we consider the problem of inferring connectivity in the brain network from non-stationary high-dimensional spike train data. Under a binned spike count representation of these data, we propose a Bernoulli autoregressive partially linear additive (BAPLA) model to identify the effective connectivity of a population of neurons…

Neighbor-Sampling Based Momentum Stochastic Methods for Training Graph Neural Networks
Molly Noel, Gabriel Mancino-Ball, Yangyang Xu
https://arxiv.org/abs/2508.00267 https://

Neighbor-Sampling Based Momentum Stochastic Methods for Training Graph Neural Networks
Graph convolutional networks (GCNs) are a powerful tool for graph representation learning. Due to the recursive neighborhood aggregations employed by GCNs, efficient training methods suffer from a lack of theoretical guarantees or are missing important practical elements from modern deep learning algorithms, such as adaptivity and momentum. In this paper, we present several neighbor-sampling (NS) based Adam-type stochastic methods for solving a nonconvex GCN training problem. We utilize the con…

Bailouts by Representation: A Minimal TLC Theory with Weighted Consent
Xinli Guo
https://arxiv.org/abs/2508.08693 https://arxiv.org/pdf/2508.08693

Bailouts by Representation: A Minimal TLC Theory with Weighted Consent
We develop a purely theoretical mechanism in which provincial bailouts are disciplined by two levers derived from Weighted Representative Democracy (WRD): a political shadow cost of public funds and a weighted-consent cap on any transfer. Bailouts are considered only when an externality threshold is met. With quadratic implementation costs, the static problem yields a simple ''threshold--linear--cap'' (TLC) policy: zero below a lower activation point, linear in the middle, and flat at an upper …

Representation Quantization for Collaborative Filtering Augmentation
Yunze Luo, Yinjie Jiang, Gaode Chen, Jingchi Wang, Shicheng Wang, Ruina Sun, Jiang Yuezihan, Jun Zhang, Jian Liang, Han Li, Kun Gai, Kaigui Bian
https://arxiv.org/abs/2508.11194

Representation Quantization for Collaborative Filtering Augmentation
As the core algorithm in recommendation systems, collaborative filtering (CF) algorithms inevitably face the problem of data sparsity. Since CF captures similar users and items for recommendations, it is effective to augment the lacking user-user and item-item homogeneous linkages. However, existing methods are typically limited to connecting through overlapping interacted neighbors or through similar attributes and contents. These approaches are constrained by coarse-grained, sparse attributes…

Coming up from $-\infty$ for KPZ via stochastic control
Nicolas Perkowski, Carlos Villanueva Mariz
https://arxiv.org/abs/2508.18140 https://arxiv.org/pdf/2…

Coming up from $-\infty$ for KPZ via stochastic control
We derive a lower bound, independent of the initial condition, for the solution of the KPZ equation on the torus through its representation as the value function of a (conditional) stochastic control problem. With the same techniques, we also prove a bound for its oscillation, again independent of initial conditions, from which a Harnack type inequality for the rough heat equation (on the torus) can be obtained.

Information-Theoretic Fairness with A Bounded Statistical Parity Constraint
Amirreza Zamani, Abolfazl Changizi, Ragnar Thobaben, Mikael Skoglund
https://arxiv.org/abs/2508.12847

Information-Theoretic Fairness with A Bounded Statistical Parity Constraint
In this paper, we study an information-theoretic problem of designing a fair representation that attains bounded statistical (demographic) parity. More specifically, an agent uses some useful data $X$ to solve a task $T$. Since both $X$ and $T$ are correlated with some sensitive attribute or secret $S$, the agent designs a representation $Y$ that satisfies a bounded statistical parity and/or privacy leakage constraint, that is, such that $I(Y;S) \leq ε$. Here, we relax the perfect demographic …

On sharpness in Local Converse Theorems for classical groups and $G_2$
Moshe Adrian, Shaun Stevens
https://arxiv.org/abs/2509.22390 https://arxiv.org/pdf/2…

On sharpness in Local Converse Theorems for classical groups and $G_2$
We prove various results about the Local Converse Problem for split reductive groups $G$ over a non-archimedean local field~$F$ of characteristic $0$ and residual characteristic $p$. In particular, we prove that when $G$ is a symplectic or special orthogonal group, or the exceptional group $G_2$, and $p$ is large enough, then the optimal standard Local Converse Theorem for $G(F)$ requires twisting by representations of $GL_r(F)$ with $r$ up to half the dimension of the standard representation o…

Reflected generalized BDSDEs driven by non-homogeneous L\'evy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions
Badr Elmansouri, Mohammed Elhachemy, Mohamed Marzougue, Mohamed El Jamali
https://arxiv.org/abs/2509.25912

Reflected generalized BDSDEs driven by non-homogeneous Lévy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions
We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous Lévy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution. Furthermore, we apply these results to obtain a probabilistic representation for the viscosity solutions of an obstacle problem governed by stochastic integro-partial differential equations with a nonlinear Neumann boundary condition.

Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles
Mathias Drton, Marina Garrote-L\'opez, Niko Nikov, Elina Robeva, Y. Samuel Wang
https://arxiv.org/abs/2507.10767

Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles
The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the presence of cycles entails difficulties such as the fact that models need no longer be characterized by conditional independence relations. As a result, learning cyclic causal structures remains a challenging problem. In this paper, we offer new insights on this p…

Triad Representation for the Anisotropic Tensor Renormalization Group in Four Dimensions
Yuto Sugimoto, Shoichi Sasaki
https://arxiv.org/abs/2507.21909 https://

Triad Representation for the Anisotropic Tensor Renormalization Group in Four Dimensions
The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice QCD calculations at finite density. One possible approach that enables faster computations in four-dimensional lattice theories is the anisotropic tensor renormalization group (ATRG). However, the computational cost remains substantial and requires significant computational resources. In this paper, …

Nonlinear filtering based on density approximation and deep BSDE prediction
Kasper B{\aa}gmark, Adam Andersson, Stig Larsson
https://arxiv.org/abs/2508.10630 https://

Nonlinear filtering based on density approximation and deep BSDE prediction
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using the well-known deep BSDE method and neural networks. The method is trained offline, which means that it can be applied online with new observations. A mixed a priori-a posteriori error bound is proved under an elliptic condition. The theoretical convergence …

Tightening the mixed integer linear formulation for the piecewise linear approximation in general dimensions
Quentin Ploussard, Xiang Li, Matija Pavi\v{c}evi\'c
https://arxiv.org/abs/2508.09395

Tightening the mixed integer linear formulation for the piecewise linear approximation in general dimensions
This paper addresses the problem of tightening the mixed-integer linear programming (MILP) formulation for continuous piecewise linear (CPWL) approximations of data sets in arbitrary dimensions. The MILP formulation leverages the difference-of-convex (DC) representation of CPWL functions. We introduce the concept of well-behaved CPWL interpolations and demonstrate that any CPWL interpolation of a data set has a well-behaved version. This result is critical to tighten the MILP problem. We presen…

Multimodal-enhanced Federated Recommendation: A Group-wise Fusion Approach
Chunxu Zhang, Weipeng Zhang, Guodong Long, Zhiheng Xue, Riting Xia, Bo Yang
https://arxiv.org/abs/2509.19955

Multimodal-enhanced Federated Recommendation: A Group-wise Fusion Approach
Federated Recommendation (FR) is a new learning paradigm to tackle the learn-to-rank problem in a privacy-preservation manner. How to integrate multi-modality features into federated recommendation is still an open challenge in terms of efficiency, distribution heterogeneity, and fine-grained alignment. To address these challenges, we propose a novel multimodal fusion mechanism in federated recommendation settings (GFMFR). Specifically, it offloads multimodal representation learning to the serv…

Quadratic BSDEs with double constraints driven by G-Brownian motion
Wei He, Qiangjun Tang
https://arxiv.org/abs/2508.18744 https://arxiv.org/pdf/2508.18744…

Quadratic BSDEs with double constraints driven by G-Brownian motion
In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via G-BMO martingale techniques, along with fixed point arguments, the Skorokhod problem, the backward Skorokhod problem, and the θ-method, we establish existence and uniqueness results for such G-BSDEs under both bounded and unbounded terminal conditions.