Tootfinder

This https://arxiv.org/abs/2402.12106 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The sign of linear periods
Let $G$ be a group with subgroup $H$, and let $(π,V)$ be a complex representation of $G$. The natural action of the normalizer $N$ of $H$ in $G$ on the space $\mathrm{Hom}_H(π,\mathbb{C})$ of $H$-invariant linear forms on $V$, provides a representation $χ_π$ of $N$ trivial on $H$, which is a character when $\mathrm{Hom}_H(π,\mathbb{C})$ is one dimensional. If moreover $G$ is a reductive group over a $p$-adic field, and $π$ is smooth irreducible, it is an interesting problem to express $χ…

Extensions of braid group representations to the monoid of singular braids
Valeriy G. Bardakov, Nafaa Chbili, Tatyana A. Kozlovskaya
https://arxiv.org/abs/2403.00516

Extensions of braid group representations to the monoid of singular braids
Given a representation $φ\colon B_n \to G_n$ of the braid group $B_n$, $n \geq 2$ into a group $G_n$, we are considering the problem of whether it is possible to extend this representation to a representation $Φ\colon SM_n \to A_n$, where $SM_n$ is the singular braid monoid and $A_n$ is an associative algebra, in which the group of units contains $G_n$. We also investigate the possibility of extending the representation $Φ\colon SM_n \to A_n$ to a representation $\widetildeΦ \colon SB_n \to…

This https://arxiv.org/abs/2402.18420 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

CafkNet: GNN-Empowered Forward Kinematic Modeling for Cable-Driven Parallel Robots
When deploying Cable-Driven Parallel Robots (CDPRs) in practice, one of the challenges is kinematic modeling. Unlike serial mechanisms, CDPRs have a simple inverse kinematics problem but a complex forward kinematics (FK) issue. Therefore, the development of accurate and efficient FK solvers has been a prominent research focus in CDPR applications. By observing the topology within CDPRs, in this letter, we propose a graph-based representation to model CDPRs and introduce CafkNet, a fast and gene…

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction
K. Aditya Mohan, Massimiliano Ferrucci, Chuck Divin, Garrett A. Stevenson, Hyojin Kim
https://arxiv.org/abs/2404.19075 https://arxiv.org/pdf/2404.19075
arXiv:2404.19075v1 Announce Type: new
Abstract: 4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an extremely ill-posed inverse problem. Existing approaches assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. We use a continuous time and space forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued object coordinates. Unlike existing state-of-the-art neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions even for extremely large CT data sizes. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

Generalized R\'enyi statistics
P\'eter Kevei, L\'aszl\'o Viharos
https://arxiv.org/abs/2404.03548 https://arxiv.org/p…

Generalized Rényi statistics
In Rényi's representation for exponential order statistics, we change the iid exponential sequence to any iid sequence, and call the resulting order statistic \emph{generalized Rényi statistic}. We prove that randomly reordering the variables in the generalized Rényi statistic, in the limit we obtain a sequence of iid exponentials. This result allows us to propose a new model for heavy-tailed data. We investigate the problem of estimation of the tail index in the new model.

This https://arxiv.org/abs/2402.14631 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Random Polynomials Associated with Non-orthonormal Bases
This article addresses an equidistribution problem concerning the zeros of random polynomials on $\mathbb{C}^{m},$ which are represented using a general basis that may not necessarily be orthonormal. We prove the equidistribution results which are more general than the previously acquired ones for non-discrete probability measures. More precisely, our result demonstrates that the equidistribution holds true even when the random coefficients in the basis representation are not independent and id…

This https://arxiv.org/abs/2402.07064 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Piecewise SOS-Convex Moment Optimization and Applications via Exact Semi-Definite Programs
This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets. These reformulations show that solving a single SDP finds the optimal value and an optimal probability measure of the original moment problem. This is done by establishing an SOS representation for the non-negativity of a piecewise SOS-convex function over a pr…

The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category
Arun S. Kannan
https://arxiv.org/abs/2404.02786 https://

The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category
The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $λ$ over such a group as the tensor product of Frobenius twists of simple modules with highest weights the weights appearing in a $p$-adic decomposition of $λ$, thereby reducing the character problem to a a finite collection of weights. In recent years this theorem has been extended to various quasi…

Bottoms Up for CHCs: Novel Transformation of Linear Constrained Horn Clauses to Software Verification
M\'ark Somorjai (Department of Measurement,Information Systems, Budapest University of Technology,Economics), Mih\'aly Dobos-Kov\'acs (Department of Measurement,Information Systems, Budapest University of Technology,Economics), Zs\'ofia \'Ad\'am (Department of Measurement,Information Systems, Budapest University of Technology,Economics), Levente Bajczi (Departme…

Bottoms Up for CHCs: Novel Transformation of Linear Constrained Horn Clauses to Software Verification
Constrained Horn Clauses (CHCs) have conventionally been used as a low-level representation in formal verification. Most existing solvers use a diverse set of specialized techniques, including direct state space traversal or under-approximating abstraction, necessitating purpose-built complex algorithms. Other solvers successfully simplified the verification workflow by translating the problem to inputs for other verification tasks, leveraging the strengths of existing algorithms. One such appr…

Computational Complexity of the Recoverable Robust Shortest Path Problem with Discrete Recourse
Marcel Jackiewicz, Adam Kasperski, Pawe{\l} Zieli\'nski
https://arxiv.org/abs/2403.20000

Computational Complexity of the Recoverable Robust Shortest Path Problem with Discrete Recourse
In this paper the recoverable robust shortest path problem is investigated. Discrete budgeted interval uncertainty representation is used to model uncertain second-stage arc costs. The known complexity results for this problem are strengthened. It is shown that it is Sigma_3^p-hard for the arc exclusion and the arc symmetric difference neighborhoods. Furthermore, it is also proven that the inner adversarial problem for these neighborhoods is Pi_2^p-hard.

Structure of Periodic Orbit Families in the Hill Restricted 4-Body Problem
Gavin M. Brown, Luke T. Peterson, Damennick B. Henry, Daniel J. Scheeres
https://arxiv.org/abs/2402.19181

Structure of Periodic Orbit Families in the Hill Restricted 4-Body Problem
The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family structures that exist in these types of systems. First, periodic orbits in the Circular Restricted 3-Body Problem (CR3BP) representation of the Earth-Moon (EM) system were identified. A Melnikov-type function was used to identify a set of candidate points on…

This https://arxiv.org/abs/2404.14399 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

MLQAOA: Graph Learning Accelerated Hybrid Quantum-Classical Multilevel QAOA
Learning the problem structure at multiple levels of coarseness to inform the decomposition-based hybrid quantum-classical combinatorial optimization solvers is a promising approach to scaling up variational approaches. We introduce a multilevel algorithm reinforced with the spectral graph representation learning-based accelerator to tackle large-scale graph maximum cut instances and fused with several versions of the quantum approximate optimization algorithm (QAOA) and QAOA-inspired algorithm…

Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps
Jakub Rydzewski
https://arxiv.org/abs/2404.02639 https://

Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often overlooked problem is what high-dimensional representation should be used to describe systems before dimensionality reduction. Here, we address this issue using a recently developed method called reweighted diffusion map [J. Chem. Theory Comput. 2022, 18, 7179-719…

Visualizing Progress in Broadening Participation in Computing: The Value of Context
Valerie Barr, Carla E. Brodley, Manuel A. P\'erez-Qui\~nones
https://arxiv.org/abs/2403.14708

Visualizing Progress in Broadening Participation in Computing: The Value of Context
Concerns about representation in computing within the U.S. have driven numerous activities to broaden participation. Assessment of the impact of these efforts and, indeed, a clear assessment of the actual "problem" being addressed are limited by the nature of the most common data analysis which looks at the representation of each population as a percentage of the number of students graduating with a degree in computing. This use of a single metric cannot adequately assess the impact of broadeni…

Dealing with Missing Modalities in Multimodal Recommendation: a Feature Propagation-based Approach
Daniele Malitesta, Emanuele Rossi, Claudio Pomo, Fragkiskos D. Malliaros, Tommaso Di Noia
https://arxiv.org/abs/2403.19841

Dealing with Missing Modalities in Multimodal Recommendation: a Feature Propagation-based Approach
Multimodal recommender systems work by augmenting the representation of the products in the catalogue through multimodal features extracted from images, textual descriptions, or audio tracks characterising such products. Nevertheless, in real-world applications, only a limited percentage of products come with multimodal content to extract meaningful features from, making it hard to provide accurate recommendations. To the best of our knowledge, very few attention has been put into the problem o…

This https://arxiv.org/abs/2308.07073 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Representation zeta functions of groups of type $A_2$ in positive characteristic
We prove two conjectures regarding the representation growth of groups of type $A_2$. The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representation zeta functions over local complete discrete valuation rings. The second is the Larsen--Lubotzky conjecture on the representation growth of irreducible lattices in groups of type $A_2$ in positive characteristic assuming Serre's conjecture on the congruence subgroup problem.

DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction
Chenhe Du, Xiyue Lin, Qing Wu, Xuanyu Tian, Ying Su, Zhe Luo, Hongjiang Wei, S. Kevin Zhou, Jingyi Yu, Yuyao Zhang
https://arxiv.org/abs/2404.17890 https://arxiv.org/pdf/2404.17890
arXiv:2404.17890v1 Announce Type: new
Abstract: Limited-angle and sparse-view computed tomography (LACT and SVCT) are crucial for expanding the scope of X-ray CT applications. However, they face challenges due to incomplete data acquisition, resulting in diverse artifacts in the reconstructed CT images. Emerging implicit neural representation (INR) techniques, such as NeRF, NeAT, and NeRP, have shown promise in under-determined CT imaging reconstruction tasks. However, the unsupervised nature of INR architecture imposes limited constraints on the solution space, particularly for the highly ill-posed reconstruction task posed by LACT and ultra-SVCT. In this study, we introduce the Diffusion Prior Driven Neural Representation (DPER), an advanced unsupervised framework designed to address the exceptionally ill-posed CT reconstruction inverse problems. DPER adopts the Half Quadratic Splitting (HQS) algorithm to decompose the inverse problem into data fidelity and distribution prior sub-problems. The two sub-problems are respectively addressed by INR reconstruction scheme and pre-trained score-based diffusion model. This combination initially preserves the implicit image local consistency prior from INR. Additionally, it effectively augments the feasibility of the solution space for the inverse problem through the generative diffusion model, resulting in increased stability and precision in the solutions. We conduct comprehensive experiments to evaluate the performance of DPER on LACT and ultra-SVCT reconstruction with two public datasets (AAPM and LIDC). The results show that our method outperforms the state-of-the-art reconstruction methods on in-domain datasets, while achieving significant performance improvements on out-of-domain datasets.

GraphMatcher: A Graph Representation Learning Approach for Ontology Matching
Sefika Efeoglu
https://arxiv.org/abs/2404.14450 https://…

GraphMatcher: A Graph Representation Learning Approach for Ontology Matching
Ontology matching is defined as finding a relationship or correspondence between two or more entities in two or more ontologies. To solve the interoperability problem of the domain ontologies, semantically similar entities in these ontologies must be found and aligned before merging them. GraphMatcher, developed in this study, is an ontology matching system using a graph attention approach to compute higher-level representation of a class together with its surrounding terms. The GraphMatcher ha…

This https://arxiv.org/abs/2308.07073 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Representation zeta functions of groups of type $A_2$ in positive characteristic
We prove two conjectures regarding the representation growth of groups of type $A_2$. The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representation zeta functions over local complete discrete valuation rings. The second is the Larsen--Lubotzky conjecture on the representation growth of irreducible lattices in groups of type $A_2$ in positive characteristic assuming Serre's conjecture on the congruence subgroup problem.

This https://arxiv.org/abs/2209.08768 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theory of functional principal component analysis for discretely observed data
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on eigen-decomposition plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely, the perturbation analysis of covariance operator for diverging number of eigencomponents obtained from noisy a…

This https://arxiv.org/abs/2401.05762 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Unlikely intersections problem for automorphisms of Markov surfaces
We study the problem of unlikely intersections for automorphisms of Markov surfaces of positive entropy. We show for certain parameters that two automorphisms with positive entropy share a Zariski dense set of periodic points if and only if they share a common iterate. Our proof uses arithmetic equidistribution for adelic line bundles over quasiprojective varieties, the theory of laminar currents and quasi-Fuchsian representation theory.

This https://arxiv.org/abs/2301.10550 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Structural insulators and promotors in networks under generic problem-solving dynamics
The collective coordination of distributed tasks in a complex system can be represented as decision dynamics on a graph. This abstract representation allows studying the performance of local decision heuristics as a function of task complexity and network architecture. Here we identify hard-to-solve and easy-to-solve networks in a social differentiation task within the basic model of small-world graphs. We show that, depending on the details of the decision heuristic as well as the length of th…

This https://arxiv.org/abs/2311.02695 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions
The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various assumptions that lead to identifiability of the underlying latent causal variables. A large corpus of these preceding approaches consider multi-environment data collected under different interventions on the causal model. What is common to virtually all of these wor…

A nonvariational form of the Neumann problem for H\"{o}lder continuous harmonic functions
M. Lanza de Cristoforis
https://arxiv.org/abs/2403.15057 htt…

A nonvariational form of the Neumann problem for Hölder continuous harmonic functions
We present a nonvariational setting for the Neumann problem for harmonic functions that are Hölder continuous and that may have infinite Dirichlet integral. Then we introduce a space of distributions on the boundary (a space of first order traces for Hölder continuous harmonic functions), we analyze the properties of the corresponding distributional single layer potential and we prove a representation theorem for harmonic Hölder continuous functions in terms of distributional single layer po…

CLAP: Learning Transferable Binary Code Representations with Natural Language Supervision
Hao Wang, Zeyu Gao, Chao Zhang, Zihan Sha, Mingyang Sun, Yuchen Zhou, Wenyu Zhu, Wenju Sun, Han Qiu, Xi Xiao
https://arxiv.org/abs/2402.16928

CLAP: Learning Transferable Binary Code Representations with Natural Language Supervision
Binary code representation learning has shown significant performance in binary analysis tasks. But existing solutions often have poor transferability, particularly in few-shot and zero-shot scenarios where few or no training samples are available for the tasks. To address this problem, we present CLAP (Contrastive Language-Assembly Pre-training), which employs natural language supervision to learn better representations of binary code (i.e., assembly code) and get better transferability. At th…

Square-free Word-representation of Word-representable Graphs
Biswajit Das, Ramesh Hariharasubramanian
https://arxiv.org/abs/2402.14426 https://

Square-free Word-representation of Word-representable Graphs
A graph $G = (V, E)$ is word-representable, if there exists a word w over the alphabet V such that for letters ${x, y} \in V$ , $x$ and $y$ alternate in $w$ if and only if $xy \in E$. In this paper, we prove that any non-empty word-representable graph can be represented by a word containing no non-trivial squares. This result provides a positive answer to the open problem present in the book Words and graphs written by Sergey Kitaev, and Vadim Lozin. Also, we prove that for a word-representable…

On the upper and lower covariances under multiple probabilities
Xinpeng Li, Jingxu Niu, Ke Zhou
https://arxiv.org/abs/2402.17462 https://

On the upper and lower covariances under multiple probabilities
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we propose a fast algorithm of calculation for upper and lower covariances under the finite number of probabilities. As an application, our algorithm can be used to solve a class of quadratic programming problem exactly, and we obtain a probabilistic representation …

Computational Complexity of Preferred Subset Repairs on Data-Graphs
Nina Pardal, Santiago Cifuentes, Edwin Pin, Maria Vanina Martinez, Sergio Abriola
https://arxiv.org/abs/2402.09265

Computational Complexity of Preferred Subset Repairs on Data-Graphs
The problem of repairing inconsistent knowledge bases has a long history within the communities of database theory and knowledge representation and reasoning, especially from the perspective of structured data. However, as the data available in real-world domains becomes more complex and interconnected, the need naturally arises for developing new types of repositories, representation languages, and semantics, to allow for more suitable ways to query and reason about it. Graph databases provide…

Aiming at the Target: Filter Collaborative Information for Cross-Domain Recommendation
Hanyu Li, Weizhi Ma, Peijie Sun, Jiayu Li, Cunxiang Yin, Yancheng He, Guoqiang Xu, Min Zhang, Shaoping Ma
https://arxiv.org/abs/2403.20296

Aiming at the Target: Filter Collaborative Information for Cross-Domain Recommendation
Cross-domain recommender (CDR) systems aim to enhance the performance of the target domain by utilizing data from other related domains. However, irrelevant information from the source domain may instead degrade target domain performance, which is known as the negative transfer problem. There have been some attempts to address this problem, mostly by designing adaptive representations for overlapped users. Whereas, representation adaptions solely rely on the expressive capacity of the CDR model…

2 2D Texture for Full Positive Parallax Effect
Alexandre Yip Gon\c{c}alves Dias, Marcelo Kn\"orich Zuffo
https://arxiv.org/abs/2402.16815 https://

2+2D Texture for Full Positive Parallax Effect
The representation of parallax on virtual environment is still a problem to be studied. Common algorithms, such as Bump Mapping, Parallax Mapping and Displacement Mapping, treats this problem for small disparity between a real object and a simplified model. This work will introduce a new texture structure and one possible render algorithm able to display parallax for large disparities, it is an approach based on the four-dimensional representation of the Light Field and was thought to positive …

Linear-Function Correcting Codes
Rohit Premlal, B. Sundar Rajan
https://arxiv.org/abs/2404.15135 https://arxiv.org/pdf/2404.15135

Linear-Function Correcting Codes
In this paper, we study linear-function correcting codes, a class of codes designed to protect linear function evaluations of a message against errors. The work "Function-Correcting Codes" by Lenz et al. 2023 provides a graphical representation for the problem of constructing function-correcting codes. We use this graph to get a lower bound the on redundancy required for function correction. By considering the function to be a bijection, such an approach also provides a lower bound on the redun…

Complexity function of the most significant digits of $2^N^D$
Mehdi Golafshan, Ivan Mitrofanov
https://arxiv.org/abs/2402.16210 https://

Complexity function of the most significant digits of $2^N^D$
We investigate unipotent dynamics on a torus and apply it to the following problem. Let $d$ be a positive integer. Consider the sequence of digits $(\textsc{\textbf{w}}_n)$, where $\textsc{\textbf{w}}_n$ is the most digit in the decimal representation of $2^{n^d}$. We prove that the complexity function of the sequence $(\textsc{\textbf{w}}_n)$ is, up to finitely many values, a polynomial.

This https://arxiv.org/abs/2309.05166 has been replaced.
initial toot: https://mastoxiv.page/@…

A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs
We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based on the recently introduced Permutation Matrix Representation Quantum Monte Carlo [Gupta, Albash and Hen, J. Stat. Mech. (2020) 073105], the problem of adapting the simulation to a given geometry amounts to generating a cycle basis for the graph on which the mo…

This https://arxiv.org/abs/2204.12469 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Image of the Gassner Representation of the Pure Braid Subgroup has Pairwise Free Generators
While much is known about the faithfulness of the Burau representation, the problem remains open for the Gassner representation for every $B_n$ with $n\geq 4$. We first find the definition of the Colored-Burau representation of Ainshel, Ainshel, Goldfeld, and Lemieux and we show that this is equivalent, when restricted to the pure braid subgroup, to the Gassner representation. The methods of Abdulrahim and Knudson require analysis within the lower central series of a free subgroup of the pure b…

This https://arxiv.org/abs/2402.06372 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral properties of the Dirichlet-to-Neumann operator for spheroids
We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix representation of this operator for both interior and exterior problems is derived. We show how the anisotropy of spheroids affects the eigenvalues and eigenfunctions of the operator. As examples of physical applications, we discuss diffusion-controlled reactions on spheroidal partially reactive targets and the statistics…

Uncertainty relation and the constrained quadratic programming
Lin Zhang, Dade Wu, Ming-Jing Zhao, Hua Nan
https://arxiv.org/abs/2404.18671 https://…

Uncertainty relation and the constrained quadratic programming
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance,by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in opt…

CafkNet: GNN-Empowered Forward Kinematic Modeling for Cable-Driven Parallel Robots
Zeqing Zhang, Linhan Yang, Cong Sun, Weiwei Shang, Jia Pan
https://arxiv.org/abs/2402.18420

CafkNet: GNN-Empowered Forward Kinematic Modeling for Cable-Driven Parallel Robots
When deploying Cable-Driven Parallel Robots (CDPRs) in practice, one of the challenges is kinematic modeling. Unlike serial mechanisms, CDPRs have a simple inverse kinematics problem but a complex forward kinematics (FK) issue. Therefore, the development of accurate and efficient FK solvers has been a prominent research focus in CDPR applications. By observing the topology within CDPRs, in this letter, we propose a graph-based representation to model CDPRs and introduce CafkNet, a fast and gene…

This https://arxiv.org/abs/2310.17660 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

An Invitation to Hypercomplex Phase Retrieval: Theory and Applications
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest. The hypercomplex PR (HPR) arises in many optical imaging and computational sensing applications that usually…

This https://arxiv.org/abs/2202.07090 has been replaced.
link: https://scholar.google.com/scholar?q=a

Representation varieties of twisted Hopf links
We study the representation theory of the fundamental group of the complement of a Hopf link with n twists. A general framework is described to analyze the $SL_r(C)$-representation varieties of these twisted Hopf links as byproduct of a combinatorial problem and equivariant Hodge theory. As application, close formulas of their E-polynomials are provided for ranks 2 and 3, both for the representation and character varieties.

This https://arxiv.org/abs/2309.11015 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

3D-U-SAM Network For Few-shot Tooth Segmentation in CBCT Images
Accurate representation of tooth position is extremely important in treatment. 3D dental image segmentation is a widely used method, however labelled 3D dental datasets are a scarce resource, leading to the problem of small samples that this task faces in many cases. To this end, we address this problem with a pretrained SAM and propose a novel 3D-U-SAM network for 3D dental image segmentation. Specifically, in order to solve the problem of using 2D pre-trained weights on 3D datasets, we adopte…

Faster algorithms on linear delta-matroids
Tomohiro Koana, Magnus Wahlstr\"om
https://arxiv.org/abs/2402.11596 https://arxiv.org…

Faster algorithms on linear delta-matroids
We show new algorithms and constructions over linear delta-matroids. We observe an alternative representation for linear delta-matroids, as a contraction representation over a skew-symmetric matrix. This is equivalent to the more standard "twist representation" up to $O(n^ω)$-time transformations, but is much more convenient for algorithmic tasks. For instance, the problem of finding a max-weight feasible set now reduces directly to the problem of finding a max-weight basis in a linear matroid…

Prove Symbolic Regression is NP-hard by Symbol Graph
Jinglu Song, Qiang Lu, Bozhou Tian, Jingwen Zhang, Jake Luo, Zhiguang Wang
https://arxiv.org/abs/2404.13820

Prove Symbolic Regression is NP-hard by Symbol Graph
Symbolic regression (SR) is the task of discovering a symbolic expression that fits a given data set from the space of mathematical expressions. Despite the abundance of research surrounding the SR problem, there's a scarcity of works that confirm its NP-hard nature. Therefore, this paper introduces the concept of a symbol graph as a comprehensive representation of the entire mathematical expression space, effectively illustrating the NP-hard characteristics of the SR problem. Leveraging the sy…

This https://arxiv.org/abs/2311.07187 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Solving Inverse Obstacle Scattering Problem with Latent Surface Representations
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse problem, we advocate the use of a trained latent representation of surfaces as the generative prior. This prior enjoys excellent expressivity within the given class of shapes, and meanwhile, the latent dimensionality is low, which greatly facilitates the comput…

This https://arxiv.org/abs/2210.00240 has been replaced.
link: https://scholar.google.com/scholar?q=a

Executable First-Order Queries in the Logic of Information Flows
The logic of information flows (LIF) has recently been proposed as a general framework in the field of knowledge representation. In this framework, tasks of procedural nature can still be modeled in a declarative, logic-based fashion. In this paper, we focus on the task of query processing under limited access patterns, a well-studied problem in the database literature. We show that LIF is well-suited for modeling this task. Toward this goal, we introduce a variant of LIF called "forward" LIF (…

This https://arxiv.org/abs/2402.01805 has been replaced.
link: https://scholar.google.com/scholar?q=a

Can LLMs perform structured graph reasoning?
Pretrained Large Language Models (LLMs) have demonstrated various reasoning capabilities through language-based prompts alone, particularly in unstructured task settings (tasks purely based on language semantics). However, LLMs often struggle with structured tasks, because of the inherent incompatibility of input representation. Reducing structured tasks to uni-dimensional language semantics often renders the problem trivial. Keeping the trade-off between LLM compatibility and structure complex…

The Simultaneous Interval Number: A New Width Parameter that Measures the Similarity to Interval Graphs
Jesse Beisegel, Nina Chiarelli, Ekkehard K\"ohler, Martin Milani\v{c}, Peter Mur\v{s}i\v{c}, Robert Scheffler
https://arxiv.org/abs/2404.10670

The Simultaneous Interval Number: A New Width Parameter that Measures the Similarity to Interval Graphs
We propose a novel way of generalizing the class of interval graphs, via a graph width parameter called the simultaneous interval number. This parameter is related to the simultaneous representation problem for interval graphs and defined as the smallest number $d$ of labels such that the graph admits a $d$-simultaneous interval representation, that is, an assignment of intervals and label sets to the vertices such that two vertices are adjacent if and only if the corresponding intervals, as we…

Spectral Map: Embedding Slow Kinetics in Collective Variables
Jakub Rydzewski
https://arxiv.org/abs/2404.01809 https://arxiv.org/pdf/…

Spectral Map: Embedding Slow Kinetics in Collective Variables
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a fundamental problem in physical chemistry. This problem is even more pronounced when CVs information about slow kinetics related to rare transitions between long-lived metastable states. To address this issue, we propose an unsupervised deep-learning method called sp…

Zeros of generalized hypergeometric polynomials via finite free convolution. Applications to multiple orthogonality
Andrei Martinez-Finkelshtein, Rafael Morales, Daniel Perales
https://arxiv.org/abs/2404.11479

Zeros of generalized hypergeometric polynomials via finite free convolution. Applications to multiple orthogonality
We address the problem of the weak asymptotic behavior of zeros of families of generalized hypergeometric polynomials as their degree tends to infinity. The main tool is the representation of such polynomials as a finite free convolution of simpler elements; this representation is preserved in the asymptotic regime, so we can formally write the limit zero distribution of these polynomials as a free convolution of explicitly computable measures. We derive a simple expression for the S-transform …

A nonvariational form of the Neumann problem for H\"{o}lder continuous harmonic functions
M. Lanza de Cristoforis
https://arxiv.org/abs/2403.15057 htt…

A nonvariational form of the Neumann problem for Hölder continuous harmonic functions
We present a nonvariational setting for the Neumann problem for harmonic functions that are Hölder continuous and that may have infinite Dirichlet integral. Then we introduce a space of distributions on the boundary (a space of first order traces for Hölder continuous harmonic functions), we analyze the properties of the corresponding distributional single layer potential and we prove a representation theorem for harmonic Hölder continuous functions in terms of distributional single layer po…

Happy and Immersive Clustering Segmentations of Biological Co-Expression Patterns
Richard Tj\"ornhammar
https://arxiv.org/abs/2402.06928 https://

Happy and Immersive Clustering Segmentations of Biological Co-Expression Patterns
In this work, we present an approach for evaluating segmentation strategies and solving the biological problem of creating robust interpretable maps of biological data by employing wards agglomerative hierarchical clustering applied to coexpression coordinates to deduce a faithful representation of the input. We adopt and quantify two analyte-centric metrics named happiness and immersiveness, one for describing the suitability of a single analyte concerning the segmentation as well as a secon…

Action Model Learning with Guarantees
Diego Aineto, Enrico Scala
https://arxiv.org/abs/2404.09631 https://arxiv.org/pdf/2404.09631

Action Model Learning with Guarantees
This paper studies the problem of action model learning with full observability. Following the learning by search paradigm by Mitchell, we develop a theory for action model learning based on version spaces that interprets the task as search for hypothesis that are consistent with the learning examples. Our theoretical findings are instantiated in an online algorithm that maintains a compact representation of all solutions of the problem. Among these range of solutions, we bring attention to act…

Scalable Robust Sparse Principal Component Analysis
Xiao Ling, Paul Brooks
https://arxiv.org/abs/2402.16712 https://arxiv.org/pdf/240…

Scalable Robust Sparse Principal Component Analysis
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the problem is NP-hard, we introduce a linear relaxation-based approach. Additionally, we present a novel fitting procedure, utilizing simple ratios and sorting techniques. The proposed algorithm demonstrates a worst-case time complexity of $O(n^2 m \log n)$ and, in ce…

Understanding Hybrid Spaces: Designing a Spacetime Model to Represent Dynamic Topologies of Hybrid Spaces
Wolfgang H\"ohl
https://arxiv.org/abs/2403.05221

Understanding Hybrid Spaces: Designing a Spacetime Model to Represent Dynamic Topologies of Hybrid Spaces
This paper develops a spatiotemporal model for the visualization of dynamic topologies of hybrid spaces. The visualization of spatiotemporal data is a well-known problem, for example in digital twins in urban planning. There is also a lack of a basic ontology for understanding hybrid spaces. The developed spatiotemporal model has three levels: a level of places and media types, a level of perception and a level of time and interaction. Existing concepts and types of representation of hybrid spa…

This https://arxiv.org/abs/2309.08630 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

PCN: A Deep Learning Approach to Jet Tagging Utilizing Novel Graph Construction Methods and Chebyshev Graph Convolutions
Jet tagging is a classification problem in high-energy physics experiments that aims to identify the collimated sprays of subatomic particles, jets, from particle collisions and tag them to their emitter particle. Advances in jet tagging present opportunities for searches of new physics beyond the Standard Model. Current approaches use deep learning to uncover hidden patterns in complex collision data. However, the representation of jets as inputs to a deep learning model have been varied, and …

Hook restriction coefficients
Sridhar P. Narayanan
https://arxiv.org/abs/2403.03443 https://arxiv.org/pdf/2403.03443

Hook restriction coefficients
Finding a combinatorial interpretation of the multiplicities of each irreducible representation of the symmetric group $S_n$ in the restriction of an irreducible polynomial representation of the general linear group $GL_n(\mathbb{C})$ remains an interesting open problem in algebraic combinatorics. In this paper we interpret the multiplicities of all irreducible representations of $S_n$ in the restriction of an irreducible polynomial representation of $GL_n(\mathbb{C})$ indexed by a hook partiti…

This https://arxiv.org/abs/2209.01808 has been replaced.
link: https://scholar.google.com/scholar?q=a

The evolution of turbulence theories and the need for continuous wavelets
In the first part of this article, I summarise two centuries of research on turbulence. I also critically discuss some of the interpretations that are still in use, as turbulence remains an inherently non-linear problem that is still unsolved to this day. In the second part, I tell the story of how Alex Grossmann introduced me to the continuous wavelet representation in 1983, and how he instantly convinced me that this is the tool I was looking for to study turbulence. In the third part, I pres…

The Boosted Difference of Convex Functions Algorithm for Value-at-Risk Constrained Portfolio Optimization
Marah-Lisanne Thormann, Phan Tu Vuong, Alain B. Zemkoho
https://arxiv.org/abs/2402.09194

The Boosted Difference of Convex Functions Algorithm for Value-at-Risk Constrained Portfolio Optimization
A highly relevant problem of modern finance is the design of Value-at-Risk (VaR) optimal portfolios. Due to contemporary financial regulations, banks and other financial institutions are tied to use the risk measure to control their credit, market and operational risks. For a portfolio with a discrete return distribution and finitely many scenarios, a Difference of Convex (DC) functions representation of the VaR can be derived. Wozabal (2012) showed that this yields a solution to a VaR constrai…

This https://arxiv.org/abs/2401.16100 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On simpliciality of function spaces not containing constants
We investigate simpliciality of function spaces without constants. We prove, in particular, that several properties characterizing simpliciality in the classical case differ in this new setting. We also show that it may happen that a given point is not represented by any measure pseudosupported by the Choquet boundary, illustrating so limits of possible generalizations of the representation theorem. Moreover, we address the abstract Dirichlet problem in the new setting and establish some common…

Spectral properties of the Dirichlet-to-Neumann operator for spheroids
Denis S. Grebenkov
https://arxiv.org/abs/2402.06372 https://ar…

Spectral properties of the Dirichlet-to-Neumann operator for spheroids
We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix representation of this operator for both interior and exterior problems is derived. We show how the anisotropy of spheroids affects the eigenvalues and eigenfunctions of the operator. As examples of physical applications, we discuss diffusion-controlled reactions on spheroidal partially reactive targets and the statistics…

Quaternion-Based Attitude Stabilization Using Synergistic Hybrid Feedback With Minimal Potential Functions
Xin Tong, Qingpeng Ding, Haiyang Fang, Shing Shin Cheng
https://arxiv.org/abs/2404.08326

Quaternion-Based Attitude Stabilization Using Synergistic Hybrid Feedback With Minimal Potential Functions
This paper investigates the robust global attitude stabilization problem for a rigid-body system using quaternion-based feedback. We propose a novel synergistic hybrid feedback with the following notable features: (1) It demonstrates central synergism by utilizing a minimal number of potential functions; (2) It ensures consistency with respect to the unit quaternion representation of rigid-body attitude; (3) Its state-feedback laws incorporate a shared action term that steers the system toward …

This https://arxiv.org/abs/2308.11823 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Revisiting Backflow Corrections by Tensor Representations: Benchmarks on Fermi-Hubbard-type Models
The quantum many-body problem is an important topic in condensed matter physics. To efficiently solve the problem, several methods have been developped to improve the representation ability of wave-functions.For the Fermi-Hubbard model, current state-of-the-art methods are neural network backflows and the hidden fermion Slater determinant. The backflow correction is an efficient way to improve the Slater determinant of free-particles. In this work we propose a tensor representation of the backf…

This https://arxiv.org/abs/2311.17406 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

LLM-State: Open World State Representation for Long-horizon Task Planning with Large Language Model
This work addresses the problem of long-horizon task planning with the Large Language Model (LLM) in an open-world household environment. Existing works fail to explicitly track key objects and attributes, leading to erroneous decisions in long-horizon tasks, or rely on highly engineered state features and feedback, which is not generalizable. We propose an open state representation that provides continuous expansion and updating of object attributes from the LLM's inherent capabilities for con…

Reading Rational Univariate Representations on lexicographic Groebner bases
Alexander Demin, Fabrice Rouillier, Joao Ruiz
https://arxiv.org/abs/2402.07141 …

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…

Hook restriction coefficients
Sridhar P. Narayanan
https://arxiv.org/abs/2403.03443 https://arxiv.org/pdf/2403.03443

Hook restriction coefficients
Finding a combinatorial interpretation of the multiplicities of each irreducible representation of the symmetric group $S_n$ in the restriction of an irreducible polynomial representation of the general linear group $GL_n(\mathbb{C})$ remains an interesting open problem in algebraic combinatorics. In this paper we interpret the multiplicities of all irreducible representations of $S_n$ in the restriction of an irreducible polynomial representation of $GL_n(\mathbb{C})$ indexed by a hook partiti…

Optimal Stopping of BSDEs with Constrained Jumps and Related Double Obstacle PDEs
Magnus Perninge
https://arxiv.org/abs/2402.17541 https://

Optimal Stopping of BSDEs with Constrained Jumps and Related Double Obstacle PDEs
We consider partial differential equations (PDEs) characterized by an upper barrier that depends on the solution itself and a fixed lower barrier, while accommodating a non-local driver. First, we show a Feynman-Kac representation for the PDE when the driver is local. Specifically, we relate the non-linear Snell envelope for an optimal stopping problem, where the underlying process is the first component in the solution to a stopped backward stochastic differential equation (BSDE) with jumps an…

This https://arxiv.org/abs/2208.03367 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sublinear Time Algorithm for Online Weighted Bipartite Matching
Online bipartite matching is a fundamental problem in online algorithms. The goal is to match two sets of vertices to maximize the sum of the edge weights, where for one set of vertices, each vertex and its corresponding edge weights appear in a sequence. Currently, in the practical recommendation system or search engine, the weights are decided by the inner product between the deep representation of a user and the deep representation of an item. The standard online matching needs to pay $nd$ t…

This https://arxiv.org/abs/2402.14631 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Random Polynomials Associated with Non-orthonormal Bases
This article addresses an equidistribution problem concerning the zeros of random polynomials on $\mathbb{C}^{m},$ which are represented using a general basis that may not necessarily be orthonormal. We prove the equidistribution results which are more general than the previously acquired ones for non-discrete probability measures. More precisely, our result demonstrates that the equidistribution holds true even when the random coefficients in the basis representation are not independent and id…

TIC: Translate-Infer-Compile for accurate 'text to plan' using LLMs and logical intermediate representations
Sudhir Agarwal, Anu Sreepathy
https://arxiv.org/abs/2402.06608

TIC: Translate-Infer-Compile for accurate 'text to plan' using LLMs and logical intermediate representations
We study the problem of generating plans for given natural language planning task requests. On one hand, LLMs excel at natural language processing but do not perform well on planning. On the other hand, classical planning tools excel at planning tasks but require input in a structured language such as the Planning Domain Definition Language (PDDL). We leverage the strengths of both the techniques by using an LLM for generating the PDDL representation (task PDDL) of planning task requests follow…

Local moment matching with Erlang mixtures under automatic roughness penalization
Oskar Laverny, Philippe Lambert
https://arxiv.org/abs/2402.15866 https://…

Local moment matching with Erlang mixtures under automatic roughness penalization
We consider the class of Erlang mixtures for the task of density estimation on the positive real line when the only available information is given as local moments, a histogram with potentially higher order moments in some bins. By construction, the obtained moment problem is ill-posed and requires regularization. Several penalties can be used for such a task, such as a lasso penalty for sparsity of the representation, but we focus here on a simplified roughness penalty from the P-splines liter…

The sign of linear periods
U. K. Anandavardhanan, Hengfei Lu, Nadir Matringe, Vincent S\'echerre, Chang Yang
https://arxiv.org/abs/2402.12106 https://<…

The sign of linear periods
Let $G$ be a group with subgroup $H$, and let $(π,V)$ be a complex representation of $G$. The natural action of the normalizer $N$ of $H$ in $G$ on the space $\mathrm{Hom}_H(π,\mathbb{C})$ of $H$-invariant linear forms on $V$, provides a representation $χ_π$ of $N$ trivial on $H$, which is a character when $\mathrm{Hom}_H(π,\mathbb{C})$ is one dimensional. If moreover $G$ is a reductive group over a $p$-adic field, and $π$ is smooth irreducible, it is an interesting problem to express $χ…

Curvature Augmented Manifold Embedding and Learning
Yongming Liu
https://arxiv.org/abs/2403.14813 https://arxiv.org/pdf/2403.14813

Curvature Augmented Manifold Embedding and Learning
A new dimensional reduction (DR) and data visualization method, Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed. The key novel contribution is to formulate the DR problem as a mechanistic/physics model, where the force field among nodes (data points) is used to find an n-dimensional manifold representation of the data sets. Compared with many existing attractive-repulsive force-based methods, one unique contribution of the proposed method is to include a non-pairwise fo…

Bridging 3D Gaussian and Mesh for Freeview Video Rendering
Yuting Xiao, Xuan Wang, Jiafei Li, Hongrui Cai, Yanbo Fan, Nan Xue, Minghui Yang, Yujun Shen, Shenghua Gao
https://arxiv.org/abs/2403.11453

Bridging 3D Gaussian and Mesh for Freeview Video Rendering
This is only a preview version of GauMesh. Recently, primitive-based rendering has been proven to achieve convincing results in solving the problem of modeling and rendering the 3D dynamic scene from 2D images. Despite this, in the context of novel view synthesis, each type of primitive has its inherent defects in terms of representation ability. It is difficult to exploit the mesh to depict the fuzzy geometry. Meanwhile, the point-based splatting (e.g. the 3D Gaussian Splatting) method usually…

This https://arxiv.org/abs/2403.08106 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

V-PRISM: Probabilistic Mapping of Unknown Tabletop Scenes
The ability to construct concise scene representations from sensor input is central to the field of robotics. This paper addresses the problem of robustly creating a 3D representation of a tabletop scene from a segmented RGB-D image. These representations are then critical for a range of downstream manipulation tasks. Many previous attempts to tackle this problem do not capture accurate uncertainty, which is required to subsequently produce safe motion plans. In this paper, we cast the represen…

This https://arxiv.org/abs/2403.12875 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Markovian lifting and optimal control for integral stochastic Volterra equations with completely monotone kernels
In this paper, we focus on solving the optimal control problem for integral stochastic Volterra equations in a finite dimensional setting. In our setting, the noise term is driven by a pure jump Lévy noise and the control acts on the intensity of the jumps. We use recent techniques proposed by Hamaguchi, where a crucial requirement is that the convolution kernel should be a completely monotone function. This allows us to use Bernstein's representation and the machinery of Laplace transform t…

Stability for a multi-frequency inverse random source problem
Tianjiao Wang, Xiang Xu, Yue Zhao
https://arxiv.org/abs/2403.13212 https://

Stability for a multi-frequency inverse random source problem
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized Gaussian random function. For the direct problem, by exploring the regularity of the Green function, we demonstrate that the direct problem admits a unique bounded solution with an explicit integral representation, which enhances the existing regularity result…

This https://arxiv.org/abs/2309.11015 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

3D-U-SAM Network For Few-shot Tooth Segmentation in CBCT Images
Accurate representation of tooth position is extremely important in treatment. 3D dental image segmentation is a widely used method, however labelled 3D dental datasets are a scarce resource, leading to the problem of small samples that this task faces in many cases. To this end, we address this problem with a pretrained SAM and propose a novel 3D-U-SAM network for 3D dental image segmentation. Specifically, in order to solve the problem of using 2D pre-trained weights on 3D datasets, we adopte…

Central Configurations with Dihedral Symmetry
Tingjie Zhou, Zhihong Xia
https://arxiv.org/abs/2404.08790 https://arxiv.org/pdf/2404.0…

Central Configurations with Dihedral Symmetry
As an application of the representation theory for the dihedral groups, we study the symmetric central configurations in the n-body problem where $n$ equal masses are placed at the vertices of a regular $n$-gon. Since the Hessian matrices at these configurations are typically very large, particularly when $n$ is large, computations of their eigenvalues present a challenging problem. However, by decomposing the action of the dihedral groups into irreducible representations, we show that the Hess…

This https://arxiv.org/abs/2208.03367 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sublinear Time Algorithm for Online Weighted Bipartite Matching
Online bipartite matching is a fundamental problem in online algorithms. The goal is to match two sets of vertices to maximize the sum of the edge weights, where for one set of vertices, each vertex and its corresponding edge weights appear in a sequence. Currently, in the practical recommendation system or search engine, the weights are decided by the inner product between the deep representation of a user and the deep representation of an item. The standard online matching needs to pay $nd$ t…

Isometric Representations of Calibrated Ordered Spaces on $C(X)$
Serdar Ay
https://arxiv.org/abs/2402.06417 https://arxiv.org/pdf/240…

Isometric Representations of Calibrated Ordered Spaces on $C(X)$
The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of $C(X)$, the space of all continuous functions on a compact Hausdorff space is a classical problem that has been considered by many authors. In this article we consider the more general case of calibrated ordered spaces, that is, ordered spaces with a specified family of seminorms generating its topology. For such spaces equivalent conditions on representabilit…

Curvature Augmented Manifold Embedding and Learning
Yongming Liu
https://arxiv.org/abs/2403.14813 https://arxiv.org/pdf/2403.14813

Curvature Augmented Manifold Embedding and Learning
A new dimensional reduction (DR) and data visualization method, Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed. The key novel contribution is to formulate the DR problem as a mechanistic/physics model, where the force field among nodes (data points) is used to find an n-dimensional manifold representation of the data sets. Compared with many existing attractive-repulsive force-based methods, one unique contribution of the proposed method is to include a non-pairwise fo…

Bridging 3D Gaussian and Mesh for Freeview Video Rendering
Yuting Xiao, Xuan Wang, Jiafei Li, Hongrui Cai, Yanbo Fan, Nan Xue, Minghui Yang, Yujun Shen, Shenghua Gao
https://arxiv.org/abs/2403.11453

Bridging 3D Gaussian and Mesh for Freeview Video Rendering
This is only a preview version of GauMesh. Recently, primitive-based rendering has been proven to achieve convincing results in solving the problem of modeling and rendering the 3D dynamic scene from 2D images. Despite this, in the context of novel view synthesis, each type of primitive has its inherent defects in terms of representation ability. It is difficult to exploit the mesh to depict the fuzzy geometry. Meanwhile, the point-based splatting (e.g. the 3D Gaussian Splatting) method usually…

This https://arxiv.org/abs/2402.02553 has been replaced.
link: https://scholar.google.com/scholar?q=a

Closed 4-braids and the Jones unknot conjecture
The Jones problem is a question whether there is a non-trivial knot with the trivial Jones polynomial in one variable $q$. The answer to this fundamental question is still unknown despite numerous attempts to explore it. In braid presentation the case of 4-strand braids is already open. S. Bigelow showed in 2000 that if the Burau representation for four-strand braids is unfaithful, then there is an infinite number of non-trivial knots with the trivial two-variable HOMFLY-PT polynomial and hence…

This https://arxiv.org/abs/2201.10539 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the intersection of local Arthur packets for classical groups and applications
In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on Mœglin's construction of local Arthur packets, we give a complete set of operators on the construction data, based on which, we provide algorithms and Sage codes to determine whether a given representation is of Arthur type. Furthermore, for any representation $π$ of Arthur type, we give a p…

This https://arxiv.org/abs/2403.15057 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A nonvariational form of the Neumann problem for Hölder continuous harmonic functions
We present a nonvariational setting for the Neumann problem for harmonic functions that are Hölder continuous and that may have infinite Dirichlet integral. Then we introduce a space of distributions on the boundary (a space of first order traces for Hölder continuous harmonic functions), we analyze the properties of the corresponding distributional single layer potential and we prove a representation theorem for harmonic Hölder continuous functions in terms of distributional single layer po…

This https://arxiv.org/abs/2206.01876 has been replaced.
link: https://scholar.google.com/scholar?q=a

A modularized algorithmic framework for interface related optimization problems using characteristic functions
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In particular, the problem focuses on interface related optimization problems where the interface is implicitly described by characteristic functions of the corresponding domains. Under such representation and discretization, the problem is then formulated into a di…

Random Polynomials Associated with Non-orthonormal Bases
Afrim Bojnik, Ozan G\"uny\"uz
https://arxiv.org/abs/2402.14631 https://

Random Polynomials Associated with Non-orthonormal Bases
This article addresses an equidistribution problem concerning the zeros of random polynomials on $\mathbb{C}^{m},$ which are represented using a general basis that may not necessarily be orthonormal. We prove the equidistribution results which are more general than the previously acquired ones for non-discrete probability measures. More precisely, our result demonstrates that the equidistribution holds true even when the random coefficients in the basis representation are not independent and id…

HybridFlow: Infusing Continuity into Masked Codebook for Extreme Low-Bitrate Image Compression
Lei Lu, Yanyue Xie, Wei Jiang, Wei Wang, Xue Lin, Yanzhi Wang
https://arxiv.org/abs/2404.13372

HybridFlow: Infusing Continuity into Masked Codebook for Extreme Low-Bitrate Image Compression
This paper investigates the challenging problem of learned image compression (LIC) with extreme low bitrates. Previous LIC methods based on transmitting quantized continuous features often yield blurry and noisy reconstruction due to the severe quantization loss. While previous LIC methods based on learned codebooks that discretize visual space usually give poor-fidelity reconstruction due to the insufficient representation power of limited codewords in capturing faithful details. We propose a …

Conformalized Credal Set Predictors
Alireza Javanmardi, David Stutz, Eyke H\"ullermeier
https://arxiv.org/abs/2402.10723 https://

Conformalized Credal Set Predictors
Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty representation, in particular due to their ability to represent both the aleatoric and epistemic uncertainty in a prediction. However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conforma…

This https://arxiv.org/abs/2403.15057 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A nonvariational form of the Neumann problem for Hölder continuous harmonic functions
We present a nonvariational setting for the Neumann problem for harmonic functions that are Hölder continuous and that may have infinite Dirichlet integral. Then we introduce a space of distributions on the boundary (a space of first order traces for Hölder continuous harmonic functions), we analyze the properties of the corresponding distributional single layer potential and we prove a representation theorem for harmonic Hölder continuous functions in terms of distributional single layer po…

Conformalized Credal Set Predictors
Alireza Javanmardi, David Stutz, Eyke H\"ullermeier
https://arxiv.org/abs/2402.10723 https://

Conformalized Credal Set Predictors
Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty representation, in particular due to their ability to represent both the aleatoric and epistemic uncertainty in a prediction. However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conforma…

Random Polynomials Associated with Non-orthonormal Bases
Afrim Bojnik, Ozan G\"uny\"uz
https://arxiv.org/abs/2402.14631 https://

Random Polynomials Associated with Non-orthonormal Bases
This article addresses an equidistribution problem concerning the zeros of random polynomials on $\mathbb{C}^{m},$ which are represented using a general basis that may not necessarily be orthonormal. We prove the equidistribution results which are more general than the previously acquired ones for non-discrete probability measures. More precisely, our result demonstrates that the equidistribution holds true even when the random coefficients in the basis representation are not independent and id…

This https://arxiv.org/abs/2201.10539 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the intersection of local Arthur packets for classical groups and applications
In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on Mœglin's construction of local Arthur packets, we give a complete set of operators on the construction data, based on which, we provide algorithms and Sage codes to determine whether a given representation is of Arthur type. Furthermore, for any representation $π$ of Arthur type, we give a p…

NeRF Solves Undersampled MRI Reconstruction
Tae Jun Jang, Chang Min Hyun
https://arxiv.org/abs/2402.13226 https://arxiv.org/pdf/2402.…

NeRF Solves Undersampled MRI Reconstruction
This article presents a novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF). With radial undersampling, the corresponding imaging problem can be reformulated into an image modeling task from sparse-view rendered data; therefore, a high dimensional MR image is obtainable from undersampled $k$-space data by taking advantage of implicit neural representation. A multi-layer perceptron, which is designed to output an image intensit…

Markovian lifting and optimal control for integral stochastic Volterra equations with completely monotone kernels
Stefano Bonaccorsi, Fulvia Confortola
https://arxiv.org/abs/2403.12875

Markovian lifting and optimal control for integral stochastic Volterra equations with completely monotone kernels
In this paper, we focus on solving the optimal control problem for integral stochastic Volterra equations in a finite dimensional setting. In our setting, the noise term is driven by a pure jump Lévy noise and the control acts on the intensity of the jumps. We use recent techniques proposed by Hamaguchi, where a crucial requirement is that the convolution kernel should be a completely monotone function. This allows us to use Bernstein's representation and the machinery of Laplace transform t…

What Is a Causal Graph?
Philip Dawid
https://arxiv.org/abs/2402.09429 https://arxiv.org/pdf/2402.09429…

What Is a Causal Graph?
This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality. For each of these we describe the relevant formal or informal semantics governing that representation. It is suggested that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.

This https://arxiv.org/abs/2104.03714 has been replaced.
link: https://scholar.google.com/scholar?q=a

The defocusing nonlinear Schrödinger equation with step-like oscillatory initial data
We study the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation under the assumption that the solution vanishes as $x \to + \infty$ and approaches an oscillatory plane wave as $x \to -\infty$. We first develop an inverse scattering transform formalism for solutions satisfying such step-like boundary conditions. Using this formalism, we prove that there exists a global solution of the corresponding Cauchy problem and establish a representation for this solution in terms of t…

This https://arxiv.org/abs/2104.03714 has been replaced.
link: https://scholar.google.com/scholar?q=a

The defocusing nonlinear Schrödinger equation with step-like oscillatory initial data
We study the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation under the assumption that the solution vanishes as $x \to + \infty$ and approaches an oscillatory plane wave as $x \to -\infty$. We first develop an inverse scattering transform formalism for solutions satisfying such step-like boundary conditions. Using this formalism, we prove that there exists a global solution of the corresponding Cauchy problem and establish a representation for this solution in terms of t…

Long-term Hydrothermal Bid-based Market Simulator
Joaquim Dias Garcia, Alexandre Street, Mario Veiga Pereira
https://arxiv.org/abs/2403.07270 https://

Long-term Hydrothermal Bid-based Market Simulator
Simulating long-term hydrothermal bid-based markets considering strategic agents is a challenging task. The representation of strategic agents considering inter-temporal constraints within a stochastic framework brings additional complexity to the already difficult single-period bilevel, thus, non-convex, optimal bidding problem. Thus, we propose a simulation methodology that effectively addresses these challenges for large-scale hydrothermal power systems. We demonstrate the effectiveness of t…

This https://arxiv.org/abs/2403.02182 has been replaced.
link: https://scholar.google.com/scholar?q=a

Ice-Tide: Implicit Cryo-ET Imaging and Deformation Estimation
We introduce ICE-TIDE, a method for cryogenic electron tomography (cryo-ET) that simultaneously aligns observations and reconstructs a high-resolution volume. The alignment of tilt series in cryo-ET is a major problem limiting the resolution of reconstructions. ICE-TIDE relies on an efficient coordinate-based implicit neural representation of the volume which enables it to directly parameterize deformations and align the projections. Furthermore, the implicit network acts as an effective regula…

Long-term Hydrothermal Bid-based Market Simulator
Joaquim Dias Garcia, Alexandre Street, Mario Veiga Pereira
https://arxiv.org/abs/2403.07270 https://

Long-term Hydrothermal Bid-based Market Simulator
Simulating long-term hydrothermal bid-based markets considering strategic agents is a challenging task. The representation of strategic agents considering inter-temporal constraints within a stochastic framework brings additional complexity to the already difficult single-period bilevel, thus, non-convex, optimal bidding problem. Thus, we propose a simulation methodology that effectively addresses these challenges for large-scale hydrothermal power systems. We demonstrate the effectiveness of t…