Tootfinder

This https://arxiv.org/abs/2410.09425 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Computational complexity of the recoverable robust shortest path problem in acyclic digraphs
In this paper, the recoverable robust shortest path problem in acyclic digraphs is considered. The interval budgeted uncertainty representation is used to model the uncertain second-stage costs. The computational complexity of this problem has been open to date. In this paper, we prove that the problem is strongly NP-hard even for the case of layered acyclic digraphs. We also show that for the discrete budgeted uncertainty, the problem is not approximable unless P=NP.

On the Conjecture of the Representation Number of Bipartite Graphs
Khyodeno Mozhui, K. V. Krishna
https://arxiv.org/abs/2506.01057 https://

On the Conjecture of the Representation Number of Bipartite Graphs
While the problem of determining the representation number of an arbitrary word-representable graph is NP-hard, this problem is open even for bipartite graphs. The representation numbers are known for certain bipartite graphs including all the graphs with at most nine vertices. For bipartite graphs with partite sets of sizes $m$ and $n$, Glen et al. conjectured that the representation number is at most $\lceil \frac{m+n}{4}\rceil$, where $m+n \ge 9$. In this paper, we show that every bipartit…

Occlusion-Aware Ground Target Tracking by a Dubins Vehicle Using Visibility Volumes
Collin Hague, Artur Wolek
https://arxiv.org/abs/2506.03400 https://

Occlusion-Aware Ground Target Tracking by a Dubins Vehicle Using Visibility Volumes
This paper considers the problem of tracking a point of interest (POI) moving along a known trajectory on the ground with an uncrewed aerial vehicle (UAV) modeled as a Dubins vehicle using a line-of-sight (LOS) sensor through an urban environment that may occlude the POI. A visibility volume (VV) encodes a time-varying, three-dimensional representation of the sensing constraints for a particular POI position. A constant-altitude, translating, and radially time-varying circular standoff orbit is…

Scaling LLM Planning: NL2FLOW for Parametric Problem Generation and Rigorous Evaluation
Jungkoo Kang
https://arxiv.org/abs/2507.02253 https://

Scaling LLM Planning: NL2FLOW for Parametric Problem Generation and Rigorous Evaluation
Progress in enhancing large language model (LLM) planning and reasoning capabilities is significantly hampered by the bottleneck of scalable, reliable data generation and evaluation. To overcome this, I introduce NL2FLOW, a fully automated system for parametrically generating planning problems - expressed in natural language, a structured intermediate representation, and formal PDDL - and rigorously evaluating the quality of generated plans. I demonstrate NL2FLOW's capabilities by generating a …

This https://arxiv.org/abs/2506.03947 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Block Alpha-Circulant Preconditioners for All-at-Once Diffusion-Based Covariance Operators
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix operator in order to exploit inherent parallellism in the underlying problem. In this paper, we provide practical methods to apply block $α$-circulant preconditioners to the all-at-once system for the case where the main diffusion operation matrix cannot be readil…

This https://arxiv.org/abs/2409.01198 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages
This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree of freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for…

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…

Indexing Tries within Entropy-Bounded Space
Lorenzo Carfagna, Carlo Tosoni
https://arxiv.org/abs/2507.02728 https://arxiv.org/pdf/250…

Indexing Tries within Entropy-Bounded Space
We study the problem of indexing and compressing tries using a BWT-based approach. Specifically, we consider a succinct and compressed representation of the XBWT of Ferragina et al.\ [FOCS '05, JACM '09] corresponding to the analogous of the FM-index [FOCS '00, JACM '05] for tries. This representation allows to efficiently count the number of nodes reached by a given string pattern. To analyze the space complexity of the above trie index, we propose a proof for the combinatorial problem of coun…

This https://arxiv.org/abs/2505.11582 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

Comparing Lexical and Semantic Vector Search Methods When Classifying Medical Documents
Classification is a common AI problem, and vector search is a typical solution. This transforms a given body of text into a numerical representation, known as an embedding, and modern improvements to vector search focus on optimising speed and predictive accuracy. This is often achieved through neural methods that aim to learn language semantics. However, our results suggest that these are not always the best solution. Our task was to classify rigidly-structured medical documents according to t…

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…

High-Dimensional Regularized Additive Matrix Autoregressive Model
Debika Ghosh, Samrat Roy, Nilanjana Chakraborty
https://arxiv.org/abs/2506.01403 https://…

High-Dimensional Regularized Additive Matrix Autoregressive Model
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based representation in case of tensor time series. A bilinear or Tucker-decomposition based temporal effect is difficult to interpret on many occasions, along with its computational complexity due to the non-convex nature of the underlying optimization problem. Moreover, the…

Some geometric and spectral aspects of restriction problems
Hajer Bahouri, Veronique Fischer
https://arxiv.org/abs/2507.00204 https://

Some geometric and spectral aspects of restriction problems
This texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions to various domains related to this problem, including harmonic analysis, partial differential equations, spectral theory, representation theory, number theory, and many others.

This https://arxiv.org/abs/2504.01163 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Minimal pole representation for spectral functions
Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum transport simulations to the simulation of strongly correlated electron systems. This paper introduces a method for obtaining a compact, approximate representation of these functions, based on their parameterization on the real axis and a given approximate preci…

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…

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…

A Flavor of SO(10) Unification with a Spinor Higgs
Juanca Carrasco-Martinez, Lawrence J. Hall, Keisuke Harigaya, Kevin Langhoff
https://arxiv.org/abs/2506.20708

A Flavor of SO(10) Unification with a Spinor Higgs
We investigate Higgs Parity Unification-a realization of $SO(10)$ grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right symmetric stage where the $SU(2)_R$ symmetry breaking scale is fixed by the vanishing of the SM Higgs quartic coupling. The strong $CP$ problem is solved by parity. Gauge coupling unification successfully predicts $α_s(M_Z)$ to within 1%. The spinor Higgs natur…

A remarkable dynamical symmetry of the Landau problem
Tekin Dereli, Philippe Nounahon, Todor Popov
https://arxiv.org/abs/2506.11642 https://

A remarkable dynamical symmetry of the Landau problem
We show that the dynamical group of an electron in a constant magnetic field is the group of symplectomorphisms $Sp(4,\mathbb{R})$. It is generated by the spinorial realization of the conformal algebra $\mathfrak{so}(2,3)$ considered in Dirac's seminal paper "A Remarkable Representation of the 3 + 2 de Sitter Group". The symplectic group $Sp(4,\mathbb{R})$ is the double covering of the conformal group $SO(2,3)$ of 2+1 dimensional Minkowski spacetime which is in turn the dynamical group of a hyd…

Modeling the position and velocity distribution of space objects by maximizing entropy with energy constraint
Partha Chowdhury, Sanat K Biswas
https://arxiv.org/abs/2506.16606

Modeling the position and velocity distribution of space objects by maximizing entropy with energy constraint
In this work, we have developed a 6-dimensional joint probability density function for the 3-dimensional position and 3-dimensional velocity vectors of space objects in the Low Earth Orbit (LEO) based on the Principle of Maximum Entropy (MaxEnt), adhering to the principle of energy conservation. For the problem under consideration, maximizing entropy subject to energy conservation ensures that the derived probability density function (PDF) is the best representation of the uncertainty of a spac…

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…

Reminder: public protest is about visibility, not hiding. The power comes from people being willing to be visible, put their time on the line, and if needed, their bodies.
If you're going to start shit, maybe just ... don't. Direct action of the illegal sort requires careful planning and a tactical and strategic plan for why it will win. It happens sometimes, but it's not the mode, it's not the mode of the No Kings protests. This is a popular, public demonstration of outrage. It's legal (for now, and I hope, ever).
Yes, the police may try to kettle protesters and then trap them into curfew violations in places that have curfews. Masks won't save us from that where it happens. Just running the system with competent representation (and enough bodies to make it A Problem for the system) will.
We don't all need to be masked vigilantes at protests, and in a lot of cases, we need to be worried about the people masking up and starting shit. Remember that this is our opponents current tactic: masked, violent attacks. Don't look like them.

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…

Universal inverse Radon transforms: Complexity of Radon transforms and the hybrid functions
I. V. Anikin
https://arxiv.org/abs/2506.18911 https://

Universal inverse Radon transforms: Complexity of Radon transforms and the hybrid functions
For the reconstruction problem, the universal representation of inverse Radon transforms may imply the needed complexity of the direct Radon transforms which leads to the additional contributions. Meanwhile, in the standard theory of generalized functions, if the origin function which generates the Radon image is a pure-real function, as a rule the complexity of Radon transform becomes in question. In the letter, we demonstrate that the Fourier method together with the hybrid (Wigner-like) func…

Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic
Karthik Ganapathy
https://arxiv.org/abs/2506.15134 https://

Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic
A long-standing open problem in representation stability is whether every finitely generated commutative algebra in the category of strict polynomial functors satisfies the noetherian property. In this paper, we resolve this problem negatively over fields of positive characteristic using ideas from invariant theory. Specifically, we consider the algebra $P$ of polarizations of elementary symmetric polynomials inside the ring of all multisymmetric polynomials in $p \times \infty$ variables. We s…

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…

On nth Level Fractional Derivatives: An Equivalent Representation and Applications to Inverse Problem
Asim Ilyas, Salman A. Malik, Kamran Suhaib
https://arxiv.org/abs/2506.12614

On nth Level Fractional Derivatives: An Equivalent Representation and Applications to Inverse Problem
This work contributes to the theory of nth level fractional derivative, where $n$ is a positive integer. An equivalent representation of 2nd level fractional derivative in terms of Riemann-Liouville fractional derivative is presented. We generalized our result and provide representation of nth level fractional derivative. As an application, we solve an inverse problem defined for a diffusion equation involving 2nd level fractional derivative.

RaRa Clipper: A Clipper for Gaussian Splatting Based on Ray Tracer and Rasterizer
Da Li, Donggang Jia, Yousef Rajeh, Dominik Engel, Ivan Viola
https://arxiv.org/abs/2506.20202

RaRa Clipper: A Clipper for Gaussian Splatting Based on Ray Tracer and Rasterizer
With the advancement of Gaussian Splatting techniques, a growing number of datasets based on this representation have been developed. However, performing accurate and efficient clipping for Gaussian Splatting remains a challenging and unresolved problem, primarily due to the volumetric nature of Gaussian primitives, which makes hard clipping incapable of precisely localizing their pixel-level contributions. In this paper, we propose a hybrid rendering framework that combines rasterization and r…

Finding Some Impossibility of Flat-Folding of Given Origami Crease Pattern by Graphical Representation
Chihiro Nakajima
https://arxiv.org/abs/2506.12659 ht…

Finding Some Impossibility of Flat-Folding of Given Origami Crease Pattern by Graphical Representation
Flat-foldability problem of origami is the problem to determine whether a given crease pattern drawn on a piece of paper is possible to fold without any penetration or intrusion of a polygon into any connections among them. It is known from the results of Bern and Hayes and following studies that determining whether an origami diagram which constitute of polygons in general shapes can be flat-folded is an NP-hard problem. In this manuscript, on determining the flat foldability of unsigned creas…

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…

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…

Wanting to Be Understood Explains the Meta-Problem of Consciousness
Chrisantha Fernando, Dylan Banarse, Simon Osindero
https://arxiv.org/abs/2506.12086 htt…

Wanting to Be Understood Explains the Meta-Problem of Consciousness
Because we are highly motivated to be understood, we created public external representations -- mime, language, art -- to externalise our inner states. We argue that such external representations are a pre-condition for access consciousness, the global availability of information for reasoning. Yet the bandwidth of access consciousness is tiny compared with the richness of `raw experience', so no external representation can reproduce that richness in full. Ordinarily an explanation of experienc…

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…

This https://arxiv.org/abs/2312.10290 has been replaced.
link: https://scholar.google.com/scholar?q=a

Runtime Analysis of the SMS-EMOA for Many-Objective Optimization
This paper conducts the first rigorous runtime analysis of the SMS-EMOA for many-objective optimization. To this aim, we first propose a many-objective counterpart of the bi-objective OJZJ benchmark. We prove that SMS-EMOA computes the full Pareto front of this benchmark in an expected number of $O(μM n^k)$ iterations, where $n$ denotes the problem size (length of the bit-string representation), $k$ the gap size (a difficulty parameter of the problem), $M=(2n/m-2k+3)^{m/2}$ the size of the Par…

Optimizing Optimizations: Case Study on Detecting Specific Types of Mathematical Optimization Constraints with E-Graphs in JijModeling
Hiromi Ishii (Jij, Inc), Taro Shimizu (Jij, Inc), Toshiki Teramura (Jij, Inc)
https://arxiv.org/abs/2506.06495

Optimizing Optimizations: Case Study on Detecting Specific Types of Mathematical Optimization Constraints with E-Graphs in JijModeling
In solving mathematical optimization problems efficiently, it is crucial to make use of information about specific types of constraints, such as the one-hot or Special-Ordered Set (SOS) constraints. In many cases, exploiting such information gives asymptotically better execution time. JijModeling, an industrial-strength mathematical optimization modeller, achieves this by separating the symbolic representation of an optimization problem from the input data. In this paper, we will report a real-…

This https://arxiv.org/abs/2402.07141 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSC_…

Reading Rational Univariate Representations on lexicographic Groebner bases
In this contribution, we consider a zero-dimensional polynomial system in $n$ variables defined over a field $\mathbb{K}$. In the context of computing a Rational Univariate Representation (RUR) of its solutions, we address the problem of certifying a separating linear form and, once certified, calculating the RUR that comes from it, without any condition on the ideal else than being zero-dimensional. Our key result is that the RUR can be read (closed formula) from lexicographic Groebner bases o…

Effective open image theorem and a Linnik type problem for elliptic curves
Tian Wang, Zhining Wei
https://arxiv.org/abs/2507.06913 https://

Effective open image theorem and a Linnik type problem for elliptic curves
We study an effective open image theorem for families of elliptic curves and products of elliptic curves ordered by conductor. Unconditionally, we prove that for $100\%$ of pairs of elliptic curves, the largest prime $\ell$, for which the associated mod $\ell$ Galois representation fails to be surjective, is small. Additionally, for semistable families, our bound on $\ell$ is comparable to the result obtained under the Generalized Riemann Hypothesis. We reduce the problem to a Linnik type probl…

Dominating Set Knapsack: Profit Optimization on Dominating Sets
Sipra Singh
https://arxiv.org/abs/2506.24032 https://arxiv.org/pdf/25…

Dominating Set Knapsack: Profit Optimization on Dominating Sets
In a large-scale network, we want to choose some influential nodes to make a profit by paying some cost within a limited budget so that we do not have to spend more budget on some nodes adjacent to the chosen nodes; our problem is the graph-theoretic representation of it. We define our problem Dominating Set Knapsack by attaching Knapsack Problem with Dominating Set on graphs. Each vertex is associated with a cost factor and a profit amount. We aim to choose some vertices within a fixed budget …

On Riedtmann's well-behaved functors and applications to composites of irreducible morphisms
Viktor Chust, Fl\'avio U. Coelho
https://arxiv.org/abs/2507.03121

On Riedtmann's well-behaved functors and applications to composites of irreducible morphisms
In this survey, we summarize some results in the literature involving the mesh category, which is a combinatorial representation of the category of modules over a finite-dimensional associative algebra. We discuss Riedtmann's well-behaved functors, which compare the mesh category with the module category, and discuss how the properties of these functors can be applied to study the problem of composing irreducible morphisms, which is the problem of deciding when the composition of n irreducible …

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…

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…

Design of A* based heuristic algorithm for efficient interdiction in multi-Layer networks
Sukanya Samanta
https://arxiv.org/abs/2506.10017 https://

Design of A* based heuristic algorithm for efficient interdiction in multi-Layer networks
Intercepting a criminal using limited police resources presents a significant challenge in dynamic crime environments, where the criminal's location continuously changes over time. The complexity is further heightened by the vastness of the transportation network. To tackle this problem, we propose a layered graph representation, in which each time step is associated with a duplicate of the transportation network. For any given set of attacker strategies, a near-optimal defender strategy is com…

Identification of Impulse Response Functions for Nonlinear Dynamic Models
Christian Gourieroux, Quinlan Lee
https://arxiv.org/abs/2506.13531 https://

Identification of Impulse Response Functions for Nonlinear Dynamic Models
We explore the issues of identification for nonlinear Impulse Response Functions in nonlinear dynamic models and discuss the settings in which the problem can be mitigated. In particular, we introduce the nonlinear autoregressive representation with Gaussian innovations and characterize the identified set. This set arises from the multiplicity of nonlinear innovations and transformations which leave invariant the standard normal density. We then discuss possible identifying restrictions, such a…

Communication-Aware Map Compression for Online Path-Planning: A Rate-Distortion Approach
Ali Reza Pedram, Evangelos Psomiadis, Dipankar Maity, Panagiotis Tsiotras
https://arxiv.org/abs/2506.20579

Communication-Aware Map Compression for Online Path-Planning: A Rate-Distortion Approach
This paper addresses the problem of collaborative navigation in an unknown environment, where two robots, referred to in the sequel as the Seeker and the Supporter, traverse the space simultaneously. The Supporter assists the Seeker by transmitting a compressed representation of its local map under bandwidth constraints to support the Seeker's path-planning task. We introduce a bit-rate metric based on the expected binary codeword length to quantify communication cost. Using this metric, we for…

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…

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.

Implicit Neural Representation-Based MRI Reconstruction Method with Sensitivity Map Constraints
Lixuan Rao, Xinlin Zhang, Yiman Huang, Tao Tan, Tong Tong
https://arxiv.org/abs/2506.06043

Implicit Neural Representation-Based MRI Reconstruction Method with Sensitivity Map Constraints
Magnetic Resonance Imaging (MRI) is a widely utilized diagnostic tool in clinical settings, but its application is limited by the relatively long acquisition time. As a result, fast MRI reconstruction has become a significant area of research. In recent years, Implicit Neural Representation (INR), as a scan-specific method, has demonstrated outstanding performance in fast MRI reconstruction without fully-sampled images for training. High acceleration reconstruction poses a challenging problem, …

Semantic-enhanced Modality-asymmetric Retrieval for Online E-commerce Search
Zhigong Zhou, Ning Ding, Xiaochuan Fan, Yue Shang, Yiming Qiu, Jingwei Zhuo, Zhiwei Ge, Songlin Wang, Lin Liu, Sulong Xu, Han Zhang
https://arxiv.org/abs/2506.20330

Semantic-enhanced Modality-asymmetric Retrieval for Online E-commerce Search
Semantic retrieval, which retrieves semantically matched items given a textual query, has been an essential component to enhance system effectiveness in e-commerce search. In this paper, we study the multimodal retrieval problem, where the visual information (e.g, image) of item is leveraged as supplementary of textual information to enrich item representation and further improve retrieval performance. Though learning from cross-modality data has been studied extensively in tasks such as visual…

The invariant subspace problem and Rosenblum operators I
Junsheng Fang, Bingzhe Hou, Chunlan Jiang, Yuanhang Zhang
https://arxiv.org/abs/2506.15270 https:/…

The invariant subspace problem and Rosenblum operators I
Let $T\in B(\mathcal{H})$ be an invertible operator. From the 1940's, Gelfand, Hille and Wermer investigated the invariant subspaces of $T$ by analyzing the growth of $\|T^n\|$, where $n\in \mathbb{Z}$. In this paper, we study the invariant subspaces of $T$ by estimating the growth of $\|T^n+λT^{-n}\|$, where $n\in \mathbb{N}$ and $λ$ is a nonzero complex constant. The key ingredient of our approach is introducing the notion of shift representation operators, which is base…

Synthetic Turbulence via an Instanton Gas Approximation
Timo Schorlepp, Katharina Kormann, Jeremiah L\"ubke, Tobias Sch\"afer, Rainer Grauer
https://arxiv.org/abs/2507.05945

Synthetic Turbulence via an Instanton Gas Approximation
Sampling synthetic turbulent fields as a computationally tractable surrogate for direct numerical simulations (DNS) is an important practical problem in various applications, and allows to test our physical understanding of the main features of real turbulent flows. Reproducing higher-order Eulerian correlation functions, as well as Lagrangian particle statistics, requires an accurate representation of coherent structures of the flow in the synthetic turbulent fields. To this end, we propose in…

A Synthetic Pseudo-Autoencoder Invites Examination of Tacit Assumptions in Neural Network Design
Assaf Marron
https://arxiv.org/abs/2506.12076 https://

A Synthetic Pseudo-Autoencoder Invites Examination of Tacit Assumptions in Neural Network Design
We present a handcrafted neural network that, without training, solves the seemingly difficult problem of encoding an arbitrary set of integers into a single numerical variable, and then recovering the original elements. While using only standard neural network operations -- weighted sums with biases and identity activation -- we make design choices that challenge common notions in this area around representation, continuity of domains, computation, learnability and more. For example, our const…

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…

The setting sun diagram with complex external momenta
David Dudal, Duifje Maria van Egmond, Gastao Krein
https://arxiv.org/abs/2507.05921 https://

The setting sun diagram with complex external momenta
We revisit the issue of analytically continuing Feynman integrals from Euclidean to Minkowski signature, allowing for generic complex momenta. Although this is well-known in terms of the Källén-Lehmann representation, we consider potential alternative takes on the same problem and discuss how these are not necessarily equivalent to the Källén-Lehmann integral outcome. We present our analysis for a simple enough case -- the setting sun diagram in $d=2$ with a real mass -- but already with an…

Communication Complexity of Exact Sampling under R\'enyi Information
Spencer Hill, Fady Alajaji, Tam\'as Linder
https://arxiv.org/abs/2506.12219 ht…

Communication Complexity of Exact Sampling under Rényi Information
We study the problem of communicating a sample from a probability distribution $P$ given shared access to a sequence distributed according to another probability distribution $Q$. Li and El Gamal used the Poisson functional representation to show that the minimum expected message length to communicate a sample from $P$ can be upper bounded by $D(P||Q) + \log (D(P||Q) + 1) + 4$, where $D(\, \cdot \, || \, \cdot\, )$ is the Kullback-Leibler divergence. We generalize …

Absolutely Continuous Curves of Stochastic Processes
Beatrice Acciaio, Daniel Kr\v{s}ek, Gudmund Pammer, Marco Rodrigues
https://arxiv.org/abs/2506.13634 h…

Absolutely Continuous Curves of Stochastic Processes
We study absolutely continuous curves in the adapted Wasserstein space of filtered processes. We provide a probabilistic representation of such curves as flows of adapted processes on a common filtered probability space, extending classical results to the adapted setting. Moreover, we characterize geodesics in this space and derive an adapted Benamou--Brenier-type formula by reformulating adapted optimal transport as an energy minimization problem. As an application, we obtain a Skorokhod-type …

GSDNet: Revisiting Incomplete Multimodal-Diffusion from Graph Spectrum Perspective for Conversation Emotion Recognition
Yuntao Shou, Jun Yao, Tao Meng, Wei Ai, Cen Chen, Keqin Li
https://arxiv.org/abs/2506.12325

GSDNet: Revisiting Incomplete Multimodal-Diffusion from Graph Spectrum Perspective for Conversation Emotion Recognition
Multimodal emotion recognition in conversations (MERC) aims to infer the speaker's emotional state by analyzing utterance information from multiple sources (i.e., video, audio, and text). Compared with unimodality, a more robust utterance representation can be obtained by fusing complementary semantic information from different modalities. However, the modality missing problem severely limits the performance of MERC in practical scenarios. Recent work has achieved impressive performance on moda…

Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
Trong D. Dang, Chanh V. Le, Khoa D. Luu, Loc H Nguyen
https://arxiv.org/abs/2506.13000

Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave propagation. The key idea is to employ a novel spectral representation in time, using an orthonormal basis composed of Legendre polynomials weighted by exponential functions. This Legendre polynomial-exponential basis enables a stable and accurate decomposition in the…

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Reading Rational Univariate Representations on lexicographic Groebner bases
In this contribution, we consider a zero-dimensional polynomial system in $n$ variables defined over a field $\mathbb{K}$. In the context of computing a Rational Univariate Representation (RUR) of its solutions, we address the problem of certifying a separating linear form and, once certified, calculating the RUR that comes from it, without any condition on the ideal else than being zero-dimensional. Our key result is that the RUR can be read (closed formula) from lexicographic Groebner bases o…

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, …

MDR-DeePC: Model-Inspired Distributionally Robust Data-Enabled Predictive Control
Shihao Li, Jiachen Li, Christopher Martin, Soovadeep Bakshi, Dongmei Chen
https://arxiv.org/abs/2506.19744

MDR-DeePC: Model-Inspired Distributionally Robust Data-Enabled Predictive Control
This paper presents a Model-Inspired Distributionally Robust Data-enabled Predictive Control (MDR-DeePC) framework for systems with partially known and uncertain dynamics. The proposed method integrates model-based equality constraints for known dynamics with a Hankel matrix-based representation of unknown dynamics. A distributionally robust optimization problem is formulated to account for parametric uncertainty and stochastic disturbances. Simulation results on a triple-mass-spring-damper sys…

Robin problem with measure data and singular nonlinearities on the boundary
Andrzej Rozkosz
https://arxiv.org/abs/2507.07821 https://…

Robin problem with measure data and singular nonlinearities on the boundary
We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive renormalized solution and provide it stochastic representation, which can be viwed as a generalized nonlinear Feynman-Kac formula. From this representation we derive some additional regularity results for the solution and some uniqueness results.

From i-boxes to signed words
Alessandro Contu, Fan Qin, Qiaoling Wei
https://arxiv.org/abs/2507.06182 https://arxiv.org/pdf/2507.0618…

From i-boxes to signed words
The combinatorics of i-boxes has recently been introduced by Kashiwara--Kim--Oh--Park in the study of cluster algebras arising from the representation theory of quantum affine algebras. In this article, we associate to each chain of i-boxes a signed word, which canonically determines a cluster seed following Berenstein--Fomin--Zelevinsky. By bridging these two different languages, we are able to provide a quick solution to the problem of explicit determining the exchange matrices associated wit…

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…

Denoising radio pulses from air showers using machine-learning methods
Aur\'elien Benoit-L\'evy (for the GRAND Collaboration), Zhisen Lai (for the GRAND Collaboration), Oscar Macias (for the GRAND Collaboration), Ars\`ene Ferri\`ere (for the GRAND Collaboration)
https://arxiv.org/abs/2507.06688

Denoising radio pulses from air showers using machine-learning methods
The Giant Radio Array for Neutrino Detection (GRAND) aims to detect radio signals from extensive air showers (EAS) caused by ultra-high-energy (UHE) cosmic particles. Galactic, hardware-like, and anthropogenic noise are expected to contaminate these signals. To address this problem, we propose training a supervised convolutional network known as an encoder-decoder. This network is used to learn a coded representation of the data and remove specific features from it. This denoiser is trained usi…

Photometric Stereo using Gaussian Splatting and inverse rendering
Mat\'eo Ducastel (GREYC), David Tschumperl\'e, Yvain Qu\'eau
https://arxiv.org/abs/2507.06684

Photometric Stereo using Gaussian Splatting and inverse rendering
Recent state-of-the-art algorithms in photometric stereo rely on neural networks and operate either through prior learning or inverse rendering optimization. Here, we revisit the problem of calibrated photometric stereo by leveraging recent advances in 3D inverse rendering using the Gaussian Splatting formalism. This allows us to parameterize the 3D scene to be reconstructed and optimize it in a more interpretable manner. Our approach incorporates a simplified model for light representation and…

S-shaped Utility Maximization with VaR Constraint and Partial Information
Dongmei Zhu, Ashley Davey, Harry Zheng
https://arxiv.org/abs/2506.10103 https://

S-shaped Utility Maximization with VaR Constraint and Partial Information
We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the constrained problem admits a unique optimal solution and Lagrange multiplier or is infeasible. We also propose three algorithms (Lagrange, simulation, deep neural network) to solve the prob…

On the motion of a point charge in a plate capacitor considering influence effects
Heinz-J\"urgen Schmidt, Thomas Br\"ocker
https://arxiv.org/abs/2506.06132

On the motion of a point charge in a plate capacitor considering influence effects
A point charge between the plates of a capacitor generates an influence charge distribution on the plates that modify the electric field acting upon the point charge. This effect is described by the well-known Dirichlet Green's function for the two parallel conducting plate problem for which we derive an infinite mirror charge series representation. At the line perpendicular to the plates and passing through the point charge this Green's function and hence the total force can be explicitly eval…

Particle Swarm Optimization for Quantum Circuit Synthesis: Performance Analysis and Insights
Mirza Hizriyan Nubli Hidayat, Tan Chye Cheah
https://arxiv.org/abs/2507.02898

Particle Swarm Optimization for Quantum Circuit Synthesis: Performance Analysis and Insights
This paper discusses how particle swarm optimization (PSO) can be used to generate quantum circuits to solve an instance of the MaxOne problem. It then analyzes previous studies on evolutionary algorithms for circuit synthesis. With a brief introduction to PSO, including its parameters and algorithm flow, the paper focuses on a method of quantum circuit encoding and representation as PSO parameters. The fitness evaluation used in this paper is the MaxOne problem. The paper presents experimental…