Tootfinder

Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients
Andrey Piatnitski, Elena Zhizhina
https://arxiv.org/abs/2506.00872

Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients
We study homogenization problem for non-autonomous parabolic equations of the form $\partial_t u=L(t)u$ with an integral convolution type operator $L(t)$ that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.

Topologizability and Power Boundedness of Convolutions and Toeplitz Operators on Power Series Spaces
Nazl{\i} Do\u{g}an
https://arxiv.org/abs/2507.00897 ht…

Topologizability and Power Boundedness of Convolutions and Toeplitz Operators on Power Series Spaces
We completely characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on $Λ_{1}(n)$ and $Λ_{\infty}(n)$, and consequently on $H(\mathbb{C})$ and $H(\mathbb{D})$.

Research on Improving the High Precision and Lightweight Diabetic Retinopathy Detection of YOLOv8n
Fei Yuhuan, Sun Xufei, Zang Ran, Wang Gengchen, Su Meng, Liu Fenghao
https://arxiv.org/abs/2507.00780

Research on Improving the High Precision and Lightweight Diabetic Retinopathy Detection of YOLOv8n
Early detection and diagnosis of diabetic retinopathy is one of the current research focuses in ophthalmology. However, due to the subtle features of micro-lesions and their susceptibility to background interference, ex-isting detection methods still face many challenges in terms of accuracy and robustness. To address these issues, a lightweight and high-precision detection model based on the improved YOLOv8n, named YOLO-KFG, is proposed. Firstly, a new dynamic convolution KWConv and C2f-KW mod…

Inequalities in Fourier analysis on binary cubes
Ton\'ci Crmari\'c, Vjekoslav Kova\v{c}, Shobu Shiraki
https://arxiv.org/abs/2507.01359 https://

Inequalities in Fourier analysis on binary cubes
This paper studies two classical inequalities, namely the Hausdorff-Young inequality and equal-exponent Young's convolution inequality, for discrete functions supported in the binary cube $\{0,1\}^d\subset\mathbb{Z}^d$. We characterize the exact ranges of Lebesgue exponents in which sharp versions of these two inequalities hold, and present several immediate consequences. First, if the functions are specialized to be the indicator of some set $A\subseteq\{0,1\}^d$, then we obtain sharp upper bo…

Runge--Kutta generalized Convolution Quadrature for sectorial problems
Jing Guo, Maria Lopez-Fernandez
https://arxiv.org/abs/2506.21242 https://

Runge--Kutta generalized Convolution Quadrature for sectorial problems
We study the application of the generalized convolution quadrature (gCQ) based on Runge--Kutta methods to approximate the solution of an important class of sectorial problems. The gCQ generalizes Lubich's original convolution quadrature (CQ) to variable steps. High-order versions of the gCQ have been developed in the last decade, relying on certain Runge--Kutta methods. The Runge--Kutta based gCQ has been studied so far in a rather general setting, which includes applications to boundary integr…

Online Audio-Visual Autoregressive Speaker Extraction
Zexu Pan, Wupeng Wang, Shengkui Zhao, Chong Zhang, Kun Zhou, Yukun Ma, Bin Ma
https://arxiv.org/abs/2506.01270

Online Audio-Visual Autoregressive Speaker Extraction
This paper proposes a novel online audio-visual speaker extraction model. In the streaming regime, most studies optimize the audio network only, leaving the visual frontend less explored. We first propose a lightweight visual frontend based on depth-wise separable convolution. Then, we propose a lightweight autoregressive acoustic encoder to serve as the second cue, to actively explore the information in the separated speech signal from past steps. Scenario-wise, for the first time, we study ho…

This https://arxiv.org/abs/2312.16863 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Existence and spectrality of infinite convolutions generated by infinitely many admissible pairs
In this paper, we study the spectrality of infinite convolutions generated by infinitely many admissible pairs which may not be compactly supported, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. First, we prove that the infinite convolution exists and is a spectral measure if the sequence of admissible pairs satisfies the remainder bounded condition, and it has a subsequence consisting of genera…

Asymptotics of the spectra of the Dirichlet and Dirichlet-Neumann problems for the Sturm-Liouville equation with integral perturbation
A. A. Shkalikov, V. N. Sivkin
https://arxiv.org/abs/2506.24095

Asymptotics of the spectra of the Dirichlet and Dirichlet-Neumann problems for the Sturm-Liouville equation with integral perturbation
The article studies the Dirichlet and Dirichlet-Neumann problems for the Sturm-Liouville equation perturbed by an integral operator with a convolution kernel. Sharp asymptotic formulas for the eigenvalues of these problems are found. The formulas contain information about the Fourier coefficients of the potential and the kernel, and estimates are obtained for the remainder terms of the asymptotics, which take into account both the rate of decrease as the eigenvvalues tend to infinity and the ra…

Programmable electro-optic frequency comb empowers integrated parallel convolution processing
Jinze He, Junzhe Qiang, Yiying Dong, Jingyi Wang, Tian Dong, Gongcheng Yue, Rongjin Zhuang, Mingze Lv, Siyuan Yu, Zhongjin Lin, Xinlun Cai, Yuanmu Yang, Guanhao Wu, Yang Li
https://arxiv.org/abs/2506.18310…

Programmable electro-optic frequency comb empowers integrated parallel convolution processing
Integrated photonic convolution processors make optical neural networks (ONNs) a transformative solution for artificial intelligence applications such as machine vision. To enhance the parallelism, throughput, and energy efficiency of ONNs, wavelength multiplexing is widely applied. However, it often encounters the challenges of low compactness, limited scalability, and high weight reconstruction latency. Here, we proposed and demonstrated an integrated photonic processing unit with a parallel …

M3ANet: Multi-scale and Multi-Modal Alignment Network for Brain-Assisted Target Speaker Extraction
Cunhang Fan, Ying Chen, Jian Zhou, Zexu Pan, Jingjing Zhang, Youdian Gao, Xiaoke Yang, Zhengqi Wen, Zhao Lv
https://arxiv.org/abs/2506.00466

M3ANet: Multi-scale and Multi-Modal Alignment Network for Brain-Assisted Target Speaker Extraction
The brain-assisted target speaker extraction (TSE) aims to extract the attended speech from mixed speech by utilizing the brain neural activities, for example Electroencephalography (EEG). However, existing models overlook the issue of temporal misalignment between speech and EEG modalities, which hampers TSE performance. In addition, the speech encoder in current models typically uses basic temporal operations (e.g., one-dimensional convolution), which are unable to effectively extract target …

Hinich's model for Day convolution revisited
Christoph Winges
https://arxiv.org/abs/2506.06025 https://arxiv.org/pdf/2506.06025…

Hinich's model for Day convolution revisited
We prove that Hinich's construction of the Day convolution operad of two $\mathcal{O}$-monoidal $\infty$-categories is an exponential in the $\infty$-category of $\infty$-operads over $\mathcal{O}$, and use this to give an explicit description of the formation of algebras in the Day convolution operad as a bivariant functor.

Bi-Residual Neural Network based Synchronous Motor Electrical Faults Diagnosis: Intra-link Layer Design for High-frequency Features
Qianchao Wang, Leena Heistrene, Yoash Levron, Yuxuan Ding, Yaping Du
https://arxiv.org/abs/2505.23097

Bi-Residual Neural Network based Synchronous Motor Electrical Faults Diagnosis: Intra-link Layer Design for High-frequency Features
In practical resource-constrained environments, efficiently extracting the potential high-frequency fault-critical information is an inherent problem. To overcome this problem, this work suggests leveraging a bi-residual neural network named Bi-ResNet to extract the inner spatial-temporal high-frequency features using embedded spatial-temporal convolution blocks and intra-link layers. It can be considered as embedding a high-frequency extractor into networks without adding any parameters, helpi…

Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
Yingwen Guo, Yinnian He, Wenlin Qiu, Xiangcheng Zheng
https://arxiv.org/abs/2506.22782

Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power-law memory kernel. We prove regularity and long-time exponential decay of the solutions, as well as a long-time convolution-type Grönwall inequality to support numerical analysis. A Volterra-Stokes projection is developed and analyzed to facilitate the parabolic-type duality argument, leading to the long-time error …

EHCube4P: Learning Epistatic Patterns Through Hypercube Graph Convolution Neural Network for Protein Fitness Function Estimation
Muhammad Daud, Philippe Charton, Cedric Damour, Jingbo Wang, Frederic Cadet
https://arxiv.org/abs/2506.16921

EHCube4P: Learning Epistatic Patterns Through Hypercube Graph Convolution Neural Network for Protein Fitness Function Estimation
Understanding the relationship between protein sequences and their functions is fundamental to protein engineering, but this task is hindered by the combinatorially vast sequence space and the experimental noise inherent in fitness measurements. In this study, we present a novel framework that models the sequence landscape as a hypercube $H(k,2)$ and integrates wavelet-based signal denoising with a graph convolutional neural network (GCN) to predict protein fitness across rugged fitness landsca…

Variational formula for the logarithmic potential of free additive convolutions
Francesco Concetti, David Belius, Giuseppe Genovese
https://arxiv.org/abs/2506.19064

Variational formula for the logarithmic potential of free additive convolutions
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and the logarithmic potential of second measure. The result applies in particular to the additive convolution with the semicircle or Marchenko-Pastur laws, for which the formula simplifies. The logarithmic potential of additive convolutions appears for instance in…

TasVisAn and InsPy -- Python Packages for Triple-Axis Spectrometer Data Visualization, Analysis, Instrument Resolution Calculation, and Convolution
Guochu Deng
https://arxiv.org/abs/2506.18216

TasVisAn and InsPy -- Python Packages for Triple-Axis Spectrometer Data Visualization, Analysis, Instrument Resolution Calculation, and Convolution
Experimental data collected from a triple-axis spectrometer (TAS) are typically analysed by considering the instrument resolution, as the resolution of a TAS instrument is often complex and significantly influences the measured results. Two Python packages, TasVisAn and InsPy, have been developed to visualize and analyse data from TAS instruments - particularly from the cold-neutron TAS Sika and the thermal-neutron TAS Taipan at the Australian Centre for Neutron Scattering. TasVisAn offers a ra…

An isometry theorem induced by the Radon transform between the convolution and interleaving distances
Michiaki Takiwaki
https://arxiv.org/abs/2506.12046 ht…

An isometry theorem induced by the Radon transform between the convolution and interleaving distances
One-parameter persistence modules are applied to various subjects as tools in data analysis. On the other hand, since the theoretical study of multi-parameter persistence modules is not enough and in progress, they have few applications. The sheaf theory is expected to elucidate detailed properties of persistence modules and give features of multi-parameter ones for applications. However, the categories of sheaves on two or more dimensional Euclidean spaces have more complicated structures than…

All-optical convolution utilizing processing in memory based on a cold atomic ensemble
Ying-Hao Ye, Jia-Qi Jiang, En-Ze Li, Wei Zhang, Da-Chuang Li, Zhi-Han Zhu, Dong-Sheng Ding, Bao-Sen Shi
https://arxiv.org/abs/2506.14716

All-optical convolution utilizing processing in memory based on a cold atomic ensemble
Processing in memory (PIM) has received significant attention due to its high efficiency, low latency, and parallelism. In optical computation, coherent memory is a crucial infrastructure for PIM frameworks. This study presents an all-optical convolution experiment conducted within computational storage based on a cold atomic ensemble. By exploiting the light-atom phase transfer facilitated by the electromagnetically induced transparency, we demonstrated spiral phase contrast processing of phot…

Eulerian-type polynomials over Stirling permutations
Shi-Mei Ma, Jun-Ying Liu, Jean Yeh, Yeong-Nan Yeh
https://arxiv.org/abs/2506.16438 https://

Eulerian-type polynomials over Stirling permutations
It is well known that ascents, descents and plateaux are equidistributed over the set of classical Stirling permutations. Their common enumerative polynomials are the second-order Eulerian polynomials. In this paper, we first provide a convolution formula for the second-order Eulerian polynomials, which gives a variant of a result of Gessel (arXiv:2005.04133). As an application, a determinantal expression for the second-order Eulerian polynomials is obtained. Secondly, we investigate the convol…

Quantum Wasserstein distances for quantum permutation groups
Anshu, David Jekel, Therese Basa Landry
https://arxiv.org/abs/2505.19269 https://

Quantum Wasserstein distances for quantum permutation groups
We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra.

Convolutional method for data assimilation An improved method on neuronal electrophysiological data
Dawei Li, Henry D. I. Abarbanel
https://arxiv.org/abs/2506.11365

Convolutional method for data assimilation An improved method on neuronal electrophysiological data
We present a convolution-based data assimilation method tailored to neuronal electrophysiology, addressing the limitations of traditional value-based synchronization approaches. While conventional methods rely on nudging terms and pointwise deviation metrics, they often fail to account for spike timing precision, a key feature in neural signals. Our approach applies a Gaussian convolution to both measured data and model estimates, enabling a cost function that evaluates both amplitude and timin…

U-R-VEDA: Integrating UNET, Residual Links, Edge and Dual Attention, and Vision Transformer for Accurate Semantic Segmentation of CMRs
Racheal Mukisa, Arvind K. Bansal
https://arxiv.org/abs/2506.20689

U-R-VEDA: Integrating UNET, Residual Links, Edge and Dual Attention, and Vision Transformer for Accurate Semantic Segmentation of CMRs
Artificial intelligence, including deep learning models, will play a transformative role in automated medical image analysis for the diagnosis of cardiac disorders and their management. Automated accurate delineation of cardiac images is the first necessary initial step for the quantification and automated diagnosis of cardiac disorders. In this paper, we propose a deep learning based enhanced UNet model, U-R-Veda, which integrates convolution transformations, vision transformer, residual links…

Spectrally accurate and efficient convolution with the 3D free-space Laplace Green's function via the super-potential
Lukas Exl, Sebastian Schaffer
https://arxiv.org/abs/2506.04489

Spectrally accurate and efficient convolution with the 3D free-space Laplace Green's function via the super-potential
We present a high-accuracy spectral method for solving the unbounded three-dimensional Poisson equation with smooth, compactly supported sources. The approach is based on a super-potential formulation, where the solution is obtained by applying the Laplacian to a convolution with the biharmonic Green's function. A separable Gaussian-sum (GS) approximation enables efficient FFT-based computation with quasi-linear complexity. Owing to the improved regularity of the biharmonic kernel, the GS cutof…

Data Driven Approach to Input Shaping for Vibration Suppression in a Flexible Robot Arm
Jarkko Kotaniemi, Janne Saukkoriipi, Shuai Li, Markku Suomalainen
https://arxiv.org/abs/2506.14405

Data Driven Approach to Input Shaping for Vibration Suppression in a Flexible Robot Arm
This paper presents a simple and effective method for setting parameters for an input shaper to suppress the residual vibrations in flexible robot arms using a data-driven approach. The parameters are adaptively tuned in the workspace of the robot by interpolating previously measured data of the robot's residual vibrations. Input shaping is a simple and robust technique to generate vibration-reduced shaped commands by a convolution of an impulse sequence with the desired input command. The gene…

Combining social relations and interaction data in Recommender System with Graph Convolution Collaborative Filtering
Tin T. Tran, Vaclav Snasel, Loc Tan Nguyen
https://arxiv.org/abs/2506.02834

Combining social relations and interaction data in Recommender System with Graph Convolution Collaborative Filtering
A recommender system is an important subject in the field of data mining, where the item rating information from users is exploited and processed to make suitable recommendations with all other users. The recommender system creates convenience for e-commerce users and stimulates the consumption of items that are suitable for users. In addition to e-commerce, a recommender system is also used to provide recommendations on books to read, movies to watch, courses to take or websites to visit. Simi…

Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field
Zhonghua Li, Yutong Song, Qiyu Yang, Shengbo Zhao
https://arxiv.org/abs/2506.12342

Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field
In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convolution formula and combing special GCD sums, our result generalizes the work of Bondarenko et al. and Fonga in 2023. We also set a lower bound by the resonance method when the real part is near the critical line, both of the above results refine part of Yang's work in 2022.

Transformative or Conservative? Conservation laws for ResNets and Transformers
Sibylle Marcotte, R\'emi Gribonval, Gabriel Peyr\'e
https://arxiv.org/abs/2506.06194

Transformative or Conservative? Conservation laws for ResNets and Transformers
While conservation laws in gradient flow training dynamics are well understood for (mostly shallow) ReLU and linear networks, their study remains largely unexplored for more practical architectures. This paper bridges this gap by deriving and analyzing conservation laws for modern architectures, with a focus on convolutional ResNets and Transformer networks. For this, we first show that basic building blocks such as ReLU (or linear) shallow networks, with or without convolution, have easily exp…

Difference-differential fields of continuous functions
Seiji Nishioka
https://arxiv.org/abs/2506.13117 https://arxiv.org/pdf/2506.131…

Difference-differential fields of continuous functions
The set C of complex-valued continuous functions on [0,\infty) is a ring by the addition and the convolution. It has the quotient field Q(C), by which J. Mikusinski developed his operational calculus. In this paper, we revisit a derivation and a transforming operator for Q(C) written in his textbook, and define another transforming operator related to the q-shift operator, which gives structures of a q-difference field and a difference field of Mahler type to Q(C). Appropriate derivatives are a…

End-to-End Diarization utilizing Attractor Deep Clustering
David Palzer, Matthew Maciejewski, Eric Fosler-Lussier
https://arxiv.org/abs/2506.11090 https://…

End-to-End Diarization utilizing Attractor Deep Clustering
Speaker diarization remains challenging due to the need for structured speaker representations, efficient modeling, and robustness to varying conditions. We propose a performant, compact diarization framework that integrates conformer decoders, transformer-updated attractors, and a deep clustering style angle loss. Our approach refines speaker representations with an enhanced conformer structure, incorporating cross-attention to attractors and an additional convolution module. To enforce struct…

Maximal Counts in the Stopped Occupancy Problem
Alexander Gnedin, Svante Janson, Yaakov Malinovsky
https://arxiv.org/abs/2506.20411 https://

Maximal Counts in the Stopped Occupancy Problem
We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of boxes tends to infinity, the distribution of the maximal occupancy count does not converge, but can be approximated by a convolution of two Gumbel distributions, with the approximating distribution having oscillations close to periodic on a logarithmic scale. …

Permutation-Avoiding FFT-Based Convolution
Nicolas Venkovic, Hartwig Anzt
https://arxiv.org/abs/2506.12718 https://arxiv.org/pdf/2506…

Permutation-Avoiding FFT-Based Convolution
Fast Fourier Transform (FFT) libraries are widely used for evaluating discrete convolutions. Most FFT implementations follow some variant of the Cooley-Tukey framework, in which the transform is decomposed into butterfly operations and index-reversal permutations. While butterfly operations dominate the floating-point operation count, the memory access patterns induced by index-reversal permutations significantly degrade the FFT's arithmetic intensity. In practice, discrete convolutions are oft…

MAGNet: A Multi-Scale Attention-Guided Graph Fusion Network for DRC Violation Detection
Weihan Lu, Hong Cai Chen
https://arxiv.org/abs/2506.07126 https://

MAGNet: A Multi-Scale Attention-Guided Graph Fusion Network for DRC Violation Detection
Design rule checking (DRC) is of great significance for cost reduction and design efficiency improvement in integrated circuit (IC) designs. Machine-learning-based DRC has become an important approach in computer-aided design (CAD). In this paper, we propose MAGNet, a hybrid deep learning model that integrates an improved U-Net with a graph neural network for DRC violation prediction. The U-Net backbone is enhanced with a Dynamic Attention Module (DAM) and a Multi-Scale Convolution Module (MSCM…

Homogenization of non-symmetric convolution type operators
Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina, Elena Zhizhina
https://arxiv.org/abs/2506.07176

Homogenization of non-symmetric convolution type operators
The paper studies homogenization problem for a bounded in $L_2(\mathbb R^d)$ convolution type operator ${\mathbb A}_\eps$, $\eps >0$, of the form $$ ({\mathbb A}_\eps u) (\x) = \eps^{-d-2} \int_{\R^d} a((\x-\y)/\eps) μ(\x/\eps, \y/\eps) \left( u(\x) - u(\y) \right)\,d\y. $$ It is assumed that $a(\x)$ is a non-negative function from $L_1(\R^d)$, and $μ(\x,\y)$ is a periodic in $\x$ and $\y$ function such that $0< μ_- \leqslant μ(\x,\y) \leqslant μ_+< \infty$. No symmetry assumption on $a(\c…

Twisted Graded Categories
Shai Keidar, Shaul Ragimov
https://arxiv.org/abs/2506.11240 https://arxiv.org/pdf/2506.11240

Twisted Graded Categories
Given a presentably symmetric monoidal $\infty$-category $\mathcal{C}$ and an $\mathbb{E}_{\infty}$-monoid $M$, we introduce and classify twisted graded categories, which generalize the Day convolution structure on $\mathrm{Fun}(M, \mathcal{C})$. These are characterized by a braiding encoded in symmetric group actions on tensor powers, whose character we show depends only on the $\mathbb{T}$-equivariant monoidal dimension. We analyze the $\mathbb{T}$-action on the dimension of invertible object…

Replaced article(s) found for physics.med-ph. https://arxiv.org/list/physics.med-ph/new
[1/1]:
Practical Global Backprojection-Convolution in Transmission Cone-beam Computed Tomography

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
Delta-modular ILP Problems of Bounded Codimension, Discrepancy, and Convolution (new version)

Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings
Fu Houshan
https://arxiv.org/abs/2506.07071

Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings
We primarily investigate the properties of characteristic polynomials of semimatroids. In particular, we provide a combinatorial interpretation of their coefficients, generalizing the Whitney's Broken Circuit Theorem. We also prove that the unsigned coefficients of the characteristic polynomial form a unimodal and log-concave sequence, extending the Rota-Heron-Welsh Conjecture to semimatroids. Furthermore, we present convolution identities for the multiplicative characteristic and Tutte polynom…

Frequency Dynamic Convolutions for Sound Event Detection
Hyeonuk Nam
https://arxiv.org/abs/2506.12785 https://arxiv.org/pdf/2506.1278…

Frequency Dynamic Convolutions for Sound Event Detection
Recent research in deep learning-based Sound Event Detection (SED) has primarily focused on Convolutional Recurrent Neural Networks (CRNNs) and Transformer models. However, conventional 2D convolution-based models assume shift invariance along both the temporal and frequency axes, leadin to inconsistencies when dealing with frequency-dependent characteristics of acoustic signals. To address this issue, this study proposes Frequency Dynamic Convolution (FDY conv), which dynamically adjusts convo…

$L^p$-Theory and Noncommutative Geometry in Quantum Harmonic Analysis
Saeed Hashemi Sababe, Ismail Nikoufar
https://arxiv.org/abs/2506.18907 https://

$L^p$-Theory and Noncommutative Geometry in Quantum Harmonic Analysis
Quantum harmonic analysis extends classical harmonic analysis by integrating quantum mechanical observables, replacing functions with operators and classical convolution structures with their noncommutative counterparts. This paper explores four interrelated developments in this field: (i) a noncommutative $L^p$-theory tailored for quantum harmonic analysis, (ii) the extension of quantum harmonic analysis beyond Euclidean spaces to include Lie groups and homogeneous spaces, (iii) its deep conne…

Elementary discrete diffusion/redistancing schemes for the mean curvature flow
Antonin Chambolle, Daniele De Gennaro, Massimiliano Morini
https://arxiv.org/abs/2506.05946

Elementary discrete diffusion/redistancing schemes for the mean curvature flow
We consider here a fully discrete and explicit scheme for the mean curvature flow of boundaries, based on an elementary diffusion step and a precise redistancing operation. We give an elementary convergence proof for the scheme under the standard CFL condition $h\sim\varepsilon^2$, where $h$ is the time discretization step and $\varepsilon$ the space step. We discuss extensions to more general convolution/redistancing schemes.

This https://arxiv.org/abs/2505.14927 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Error-Free Demodulation of Pixelated Interferograms: Updated review and circumstantial evidence of plagiarism by 4D Technology Corporation
This paper examines the historical development that led to error-free phase demodulation of pixelated spatial-carrier interferograms between 2004 and 2010. It also evaluates evidence suggesting that 4D Technology Corporation (4DTC), in their SPIE 7790 publication [18], may have adopted key concepts from a manuscript submitted by Servin and collaborators, which at that time was still under peer review [17]. We analyze 4DTC algorithms based on 2x2 and 3x3 spatial convolution phase shifting method…

Invertible Complex Measures on Euclidean Spaces
David Berger, Alexander Lindner
https://arxiv.org/abs/2506.09012 https://arxiv.org/pd…

Invertible Complex Measures on Euclidean Spaces
In 1971 Taylor characterised all complex measures on $\mathbb{R}$ that are invertible with respect to convolution as those which can be written in the form $δ_γ\ast σ^{\ast m} \ast \exp(ν)$ for some $γ\in \mathbb{R}$, some complex measure $ν$, some $m\in \mathbb{Z}$ and a given fixed invertible finite signed measure $σ$ (which has characteristic function $\mathbb{R} \ni z \mapsto (1+i z)/(1-i z)$). We extend Taylor's result to complex measures on $\mathbb{R}^n$. Somewhat surprisingly, th…

Alzheimers Disease Classification in Functional MRI With 4D Joint Temporal-Spatial Kernels in Novel 4D CNN Model
Javier Salazar Cavazos, Scott Peltier
https://arxiv.org/abs/2506.02060

Alzheimers Disease Classification in Functional MRI With 4D Joint Temporal-Spatial Kernels in Novel 4D CNN Model
Previous works in the literature apply 3D spatial-only models on 4D functional MRI data leading to possible sub-par feature extraction to be used for downstream tasks like classification. In this work, we aim to develop a novel 4D convolution network to extract 4D joint temporal-spatial kernels that not only learn spatial information but in addition also capture temporal dynamics. Experimental results show promising performance in capturing spatial-temporal data in functional MRI compared to 3D…

This https://arxiv.org/abs/2504.07552 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Uniqueness of supercritical Gaussian multiplicative chaos
We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends on the choice of regularisation only through a multiplicative constant and can be characterised as an integrated atomic measure with a random intensity expressed in terms of the critical Gaussian multiplicative chaos.

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
Eduardo Abi Jaber, Aur\'elien Alfonsi, Guillaume Szulda
https://arxiv.org/abs/2506.04911

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
We establish new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an approximation scheme and showing its convergence. A particular emphasis is made on the stochastic invariance of the solution in a closed convex set. To do so, we extend the notion of kernels that preserve nonnegativity introduced in \cite{Alfonsi23} to non-convolut…