Tootfinder

Further analysis of Peeling Sequences
D\'aniel G\'abor Simon
https://arxiv.org/abs/2510.03832 https://arxiv.org/pdf/2510.03832

Further analysis of Peeling Sequences
Let $P\subset \mathbf{R}^2$ be a set of $n$ points in general position. A peeling sequence of $P$ is a list of its points, such that if we remove the points from $P$ in that order, we always remove the next point from the convex hull of the remainder of $P$. Using the methodology of Dumitrescu and Tóth \cite{Dumitrescu}, with more careful analysis, we improve the upper bound on the minimum number of peeling sequences for an $n$ point set in the plane from $\frac{12.29^n}{100}$ to $\frac{9.78^n…

Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions
Endrit Dosti, Sergiy A. Vorobyov, Themistoklis Charalambous
https://arxiv.org/abs/2510.02965

Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce a new class of generalized composite estimating sequences, devised by exploiting the information embedded in the iterates generated during the minimization process. Building on these sequences, we propose a novel accelerated first-order method tailored for su…

Improving Tactile Gesture Recognition with Optical Flow
Shaohong Zhong, Alessandro Albini, Giammarco Caroleo, Giorgio Cannata, Perla Maiolino
https://arxiv.org/abs/2508.04338 ht…

Improving Tactile Gesture Recognition with Optical Flow
Tactile gesture recognition systems play a crucial role in Human-Robot Interaction (HRI) by enabling intuitive communication between humans and robots. The literature mainly addresses this problem by applying machine learning techniques to classify sequences of tactile images encoding the pressure distribution generated when executing the gestures. However, some gestures can be hard to differentiate based on the information provided by tactile images alone. In this paper, we present a simple ye…

GramTrans: A Better Code Representation Approach in Code Generation
Zhao Zhang, Qingyuan Liang, Zeyu Sun, Yizhou Chen, Guoqing Wang, Yican Sun, Lu Zhang, Ge Li, Yingfei Xiong
https://arxiv.org/abs/2510.02887

GramTrans: A Better Code Representation Approach in Code Generation
Code generation has shown great promise in assisting software development. A fundamental yet underexplored question is how the choice of code representation affects model performance. While existing studies employ various representations, such as treating code as plain text, grammar rule sequences, or syntax tree sequences, they lack a principled understanding of the relationship between parsing difficulty and model effectiveness. This paper proposes a conjecture: the easier a representation is…

Linear Recurrent Sequences, Markov Chains and Their Applications in Graph Theory
Rebecca Carter, M. Ram Murty
https://arxiv.org/abs/2510.03537 https://arxi…

Linear Recurrent Sequences, Markov Chains and Their Applications in Graph Theory
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of Markov chains. Finally, we apply these results to give estimates for the diameters of directed graphs.

Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes
Paul M. Riechers, Thomas J. Elliott
https://arxiv.org/abs/2509.03004 h…

Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes
To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic processes, we tackle the question of determining whether or not two different models produce the same observable behavior. This is the problem of identifiability. Curiously, the physics of the model need not correspond to the physics of the observations; rece…

Large Deviations Principle for Isoperimetry and Its Equivalence to Nonlinear Log-Sobolev Inequalities
Lei Yu
https://arxiv.org/abs/2510.04030 https://arxiv…

Large Deviations Principle for Isoperimetry and Its Equivalence to Nonlinear Log-Sobolev Inequalities
We investigate the large deviations principle (which concerns sequences of exponentially small sets) for the isoperimetric problem on product Riemannian manifolds $M^{n}$ equipped with product probability measures $ν^{\otimes n}$, where $M$ is a Riemannian manifold satisfying curvature-dimension bound $\mathrm{CD}(0,\infty)$. When the probability measure $ν$ satisfies a specific light-tail condition, we establish an exact characterization of the large deviations asymptotics for the isoperimet…

Linear RNNs for autoregressive generation of long music samples
Konrad Szewczyk, Daniel Gallo Fern\'andez, James Townsend
https://arxiv.org/abs/2510.02401 https://

Linear RNNs for autoregressive generation of long music samples
Directly learning to generate audio waveforms in an autoregressive manner is a challenging task, due to the length of the raw sequences and the existence of important structure on many different timescales. Traditional approaches based on recurrent neural networks, as well as causal convolutions and self-attention, have only had limited success on this task. However, recent work has shown that deep state space models, also referred to as linear RNNs, can be highly efficient in this context. In …

Managing Data for Scalable and Interactive Event Sequence Visualization
Sayef Azad Sakin, Katherine E. Isaacs
https://arxiv.org/abs/2508.03974 https://arxi…

Managing Data for Scalable and Interactive Event Sequence Visualization
Parallel event sequences, such as those collected in program execution traces and automated manufacturing pipelines, are typically visualized as interactive parallel timelines. As the dataset size grows, these charts frequently experience lag during common interactions such as zooming, panning, and filtering. Summarization approaches can improve interaction performance, but at the cost of accuracy in representation. To address this challenge, we introduce ESeMan (Event Sequence Manager), an eve…

The distribution of intersections in $\mathrm{SL}(3, \mathbb{Z}) \backslash \mathrm{SL}(3, \mathbb{R})$ and lattices related to roots of cubic congruences
Matthew Welsh
https://arxiv.org/abs/2509.00898

The distribution of intersections in $\mathrm{SL}(3, \mathbb{Z}) \backslash \mathrm{SL}(3, \mathbb{R})$ and lattices related to roots of cubic congruences
In this note we study the distribution of the intersections between certain translates of closed orbits of the positive diagonal subgroup in $\mathrm{SL}(3, \mathbb{Z}) \backslash \mathrm{SL}(3, \mathbb{R})$ with a maximal parabolic subgroup. These intersections are closely connected to roots of congruences for certain monic, irreducible cubic polynomials $F(X) \in \mathbb{Z}[X]$. The the main result is that the intersections, considered as a sequences in the diagonal subgroup and the parabolic…

Numerical solutions of the complete two-body system in QUMOND
J. Pflamm-Altenburg
https://arxiv.org/abs/2509.01493 https://arxiv.org/pdf/2509.01493

Numerical solutions of the complete two-body system in QUMOND
Due to the non-linearity of the QUMOND field equations, in the modelling of binaries so far the two-body system is replaced by an effective one-body system, where the central particle contains the total mass of both binary components and is orbited by a massless test particle. In this work, the discrepancy between the effective one-body treatment and the complete two-body solution in QUMOND is quantified. Particles are treated as limits of Dirac sequences. Then, the QUMOND contribution to the t…

Dimensionally-Efficient Transmission and Storage of Unitary Matrices
Juan Vidal Alegr\'ia
https://arxiv.org/abs/2510.04734 https://arxiv.org/pdf/2510.0…

Dimensionally-Efficient Transmission and Storage of Unitary Matrices
Unitary matrices are the basis of a large number of signal processing applications. In many of these applications, finding ways to efficiently store, and even transmit these matrices, can significantly reduce memory and throughput requirements. In this work, we study the problem of efficient transmission and storage of unitary matrices. Specifically, we explicitly derive a dimensionally-efficient parametrization (DEP) for unitary matrices that allows identifying them with sequences of real numb…

Decision Procedure for A Theory of String Sequences
Denghang Hu, Taolue Chen, Philipp R\"ummer, Fu Song, Zhilin Wu
https://arxiv.org/abs/2509.00948 https://

Decision Procedure for A Theory of String Sequences
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation, forming sub-sequences and updating elements. Strings and sequences are intimately related; many operations, e.g., matching a string according to a regular expression, splitting strings, or joining strings in a sequence, are frequently used in string-manipulat…

Cache-to-Cache: Direct Semantic Communication Between Large Language Models
Tianyu Fu, Zihan Min, Hanling Zhang, Jichao Yan, Guohao Dai, Wanli Ouyang, Yu Wang
https://arxiv.org/abs/2510.03215

Cache-to-Cache: Direct Semantic Communication Between Large Language Models
Multi-LLM systems harness the complementary strengths of diverse Large Language Models, achieving performance and efficiency gains unattainable by a single model. In existing designs, LLMs communicate through text, forcing internal representations to be transformed into output token sequences. This process both loses rich semantic information and incurs token-by-token generation latency. Motivated by these limitations, we ask: Can LLMs communicate beyond text? Oracle experiments show that enric…

APEX: Automatic Event Sequence Generation for Android Applications
Wenhao Chen, Morris Chang, Witawas Srisa-an, Yong Guan
https://arxiv.org/abs/2509.02412 https://

APEX: Automatic Event Sequence Generation for Android Applications
Due to the event driven nature and the versatility of GUI designs in Android programs, it is challenging to generate event sequences with adequate code coverage within a reasonable time. A common approach to handle this issue is to rely on GUI models to generate event sequences. These sequences can be effective in covering GUI states, but inconsistent in exposing program behaviors that require specific inputs. A major obstacle to generate such specific inputs is the lack of a systematic GUI exp…

On the Clemens-Schmid exact sequence
R. Virk
https://arxiv.org/abs/2509.03700 https://arxiv.org/pdf/2509.03700

On the Clemens-Schmid exact sequence
A treatment of (generalized) Clemens-Schmid exact sequences from the perspective of weights.

Tracing stellar rotation in young massive LMC clusters
Sebastian Kamann, Nate Bastian, Florian Niederhofer, Andrea Bellini, Ivan Cabrera-Ziri, Stefan Dreizler, Fabian G\"ottgens, Vera Kozhurina-Platais, Mattia Libralato, Sven Martens, Sara Saracino
https://arxiv.org/abs/2509.02698

Tracing stellar rotation in young massive LMC clusters
We present a detailed analysis of stellar rotation along the main sequences of NGC 1866 and NGC 1856, two young (~200-300 Myr) massive clusters in the Large Magellanic Cloud, using MUSE integral field spectroscopy. Differences in stellar rotation have been proposed as an explanation for the extended main sequence turn-offs and split main sequences in these clusters. In agreement with this idea, we find strong links between the photometric colours of the cluster stars and their projected rotatio…

Towards Understanding the Shape of Representations in Protein Language Models
Kosio Beshkov, Anders Malthe-S{\o}renssen
https://arxiv.org/abs/2509.24895 https://

Towards Understanding the Shape of Representations in Protein Language Models
While protein language models (PLMs) are one of the most promising avenues of research for future de novo protein design, the way in which they transform sequences to hidden representations, as well as the information encoded in such representations is yet to be fully understood. Several works have attempted to propose interpretability tools for PLMs, but they have focused on understanding how individual sequences are transformed by such models. Therefore, the way in which PLMs transform the wh…

NS-Pep: De novo Peptide Design with Non-Standard Amino Acids
Tao Guo, Junbo Yin, Yu Wang, Xin Gao
https://arxiv.org/abs/2510.03326 https://arxiv.org/pdf/25…

NS-Pep: De novo Peptide Design with Non-Standard Amino Acids
Peptide drugs incorporating non-standard amino acids (NSAAs) offer improved binding affinity and improved pharmacological properties. However, existing peptide design methods are limited to standard amino acids, leaving NSAA-aware design largely unexplored. We introduce NS-Pep, a unified framework for co-designing peptide sequences and structures with NSAAs. The main challenge is that NSAAs are extremely underrepresented-even the most frequent one, SEP, accounts for less than 0.4% of residues-r…

Metric Convergence of Sequences of Static Spacetimes with the Null Distance
Brian Allen
https://arxiv.org/abs/2510.02237 https://arxiv.org/pdf/2510.02237…

Metric Convergence of Sequences of Static Spacetimes with the Null Distance
How should one define metric space notions of convergence for sequences of spacetimes? Since a Lorentzian manifold does not define a metric space directly, the uniform convergence, Gromov-Hausdorff (GH) convergence, and Sormani-Wenger Intrinsic Flat (SWIF) convergence does not extend automatically. One approach is to define a metric space structure, which is compatible with the Lorentzian structure, so that the usual notions of convergence apply. This approach was taken by C. Sormani and C. Veg…

$ L_\infty $-spectral sequences for Hochschild cohomology
Jasper van de Kreeke
https://arxiv.org/abs/2508.21716 https://arxiv.org/pdf/2508.21716

$ L_\infty $-spectral sequences for Hochschild cohomology
Spectral sequences are a common tool to compute cohomology spaces, but higher structure is often lost on the way. In this article we exhibit a strategy to retain the higher structure on the cohomology, which works in case the chain complex with higher structure is presented as the twisting of a simpler chain complex by a Maurer-Cartan element. This works particularly well in case of the Hochschild complex of a minimal $ A_\infty $-category, where the Hochschild complex can be seen as the twisti…

Two-Body Contact Dynamics in a Bose Gas near a Fano-Feshbach Resonance
Alexandre Journeaux, Julie Veschambre, Maxime Lecomte, Ethan Uzan, Jean Dalibard, F\'elix Werner, Dmitry S. Petrov, Raphael Lopes
https://arxiv.org/abs/2509.03567

Two-Body Contact Dynamics in a Bose Gas near a Fano-Feshbach Resonance
We investigate the real-time buildup of short-range correlations in a nondegenerate ultracold Bose gas near a narrow Fano-Feshbach resonance. Using rapid optical control, we quench the closed-channel molecular energy to resonance on sub-microsecond timescales and track the evolution of the two-body contact through photo-dissociation losses. Repeated pulse sequences enhance sensitivity to early-time two-body losses and reveal long-lived coherence between atom pairs and molecular states. The obse…

RawBench: A Comprehensive Benchmarking Framework for Raw Nanopore Signal Analysis Techniques
Furkan Eris, Ulysse McConnell, Can Firtina, Onur Mutlu
https://arxiv.org/abs/2510.03629

RawBench: A Comprehensive Benchmarking Framework for Raw Nanopore Signal Analysis Techniques
Nanopore sequencing technologies continue to advance rapidly, offering critical benefits such as real-time analysis, the ability to sequence extremely long DNA fragments (up to millions of bases in a single read), and the option to selectively stop sequencing a molecule before completion. Traditionally, the raw electrical signals generated during sequencing are converted into DNA sequences through a process called basecalling, which typically relies on large neural network models. Raw signal an…

Morse sequences on stacks and flooding sequences
Gilles Bertrand
https://arxiv.org/abs/2509.01384 https://arxiv.org/pdf/2509.01384

Morse sequences on stacks and flooding sequences
This paper builds upon the framework of \emph{Morse sequences}, a simple and effective approach to discrete Morse theory. A Morse sequence on a simplicial complex consists of a sequence of nested subcomplexes generated by expansions and fillings-two operations originally introduced by Whitehead. Expansions preserve homotopy, while fillings introduce critical simplexes that capture essential topological features. We extend the notion of Morse sequences to \emph{stacks}, which are monotonic funct…

Z-scores-based methods and their application to biological monitoring: An extended analysis of professional soccer players and cyclists athletes
Geoffroy C. B. Berthelot (IRMES - URP\_7329, RELAIS), Brigitte Gelein (ENSAI, IRMAR), Eric Meinadier (FFC), Emmanuel Orhant (FFF), J\'er\^ome Dedecker (MAP5 - UMR 8145)
https://arxiv.org/abs/2…

Z-scores-based methods and their application to biological monitoring: An extended analysis of professional soccer players and cyclists athletes
The increase in the collection of biological data allows for the individual and longitudinal monitoring of hematological or urine biomarkers. However, identifying abnormal behavior in these biological sequences is not trivial. Moreover, the complexity of the biological data (correlation between biomarkers, seasonal effects, etc.) is also an issue. Z-score methods can help assess the abnormality in these longitudinal sequences while capturing some features of the biological complexity. This work…

Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
Trung Chau, Kanoy Kumar Das, Amit Roy, Kamalesh Saha
https://arxiv.org/abs/2510.01366

Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
We introduce the abstract notion of squarefree-power-like functions, which unify the sequences of squarefree ordinary and symbolic powers of squarefree monomial ideals. By employing the Tor-vanishing criteria for mixed sums of ideals, we establish sharp lower bounds for their Castelnuovo-Mumford regularity in terms of what we call the admissible set of the associated hypergraph. As an application, we derive the first general combinatorial lower bound for the regularity of squarefree symbolic po…

Profinite approach to S-adic shift spaces I: Saturating directive sequences
Jorge Almeida, Alfredo Costa, Herman Goulet-Ouellet
https://arxiv.org/abs/2509.00991 https://

Profinite approach to S-adic shift spaces I: Saturating directive sequences
This paper is the first in a series of three, about (relatively) free profinite semigroups and S-adic representations of minimal shift spaces. We associate to each primitive S-adic directive sequence ${\boldsymbolσ}$ a $\textit{profinite image}$ in the free profinite semigroup over the alphabet of the induced minimal shift space. When this profinite image contains a $\mathcal{J}$-maximal maximal subgroup of the free profinite semigroup (which, up to isomorphism, is called the $\t…

On minimal product-one sequences of maximal length over the non-abelian group of order $pq$
Danilo Vilela Avelar, Fabio Enrique Brochero Mart\'inez, S\'avio Ribas
https://arxiv.org/abs/2510.00070

On minimal product-one sequences of maximal length over the non-abelian group of order $pq$
Let $G$ be a finite group. A sequence over $G$ is a finite multiset of elements of $G$, and it is called product-one if its terms can be ordered so that their product is the identity of $G$. The large Davenport constant $\D(G)$ is the maximal length of a minimal product-one sequence, that is, a product-one sequence that cannot be partitioned into two nontrivial product-one subsequences. Let $p,q$ be odd prime numbers with $p \mid q-1$ and let $C_q \rtimes C_p$ denote the non-abelian group of or…

Keypoint-based Diffusion for Robotic Motion Planning on the NICOL Robot
Lennart Clasmeier, Jan-Gerrit Habekost, Connor G\"ade, Philipp Allgeuer, Stefan Wermter
https://arxiv.org/abs/2509.04076

Keypoint-based Diffusion for Robotic Motion Planning on the NICOL Robot
We propose a novel diffusion-based action model for robotic motion planning. Commonly, established numerical planning approaches are used to solve general motion planning problems, but have significant runtime requirements. By leveraging the power of deep learning, we are able to achieve good results in a much smaller runtime by learning from a dataset generated by these planners. While our initial model uses point cloud embeddings in the input to predict keypoint-based joint sequences in its o…

Tauberian Properties of Riesz Means for Sequences of Uncertain Variables
Mehmet Sengonul
https://arxiv.org/abs/2509.03756 https://arxiv.org/pdf/2509.03756

Tauberian Properties of Riesz Means for Sequences of Uncertain Variables
In this study, the Tauberian Properties of Riesz Means for Sequences of Uncertain Variables were examined, and some interesting properties were revealed.

Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras
Alexander Wires, Dev Karan Singh, Shiv Datt Kumar
https://arxiv.org/abs/2509.03019

Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras
For nonabelian $2^{\mathrm{nd}}$-cohomology of multiplicative Lie algebras, we properly generalize from the group case three classic results. We prove a Correspondence theorem which compares $2^{\mathrm{nd}}$-cohomology associated to a realized abstract kernel to the abelian $2^{\mathrm{nd}}$-cohomology group over the algebraic center. For arbitrary extensions, we prove a Wells's Theorem characterizing ideal-preserving automorphisms and establish the 1-dimensional Lyndon-Hochschild-Serre exact …

Just pushed an update for https://thi.ng/genart-api (v0.29.0) which now supports dynamic switching of time providers. This is useful for situations where you want to switch from realtime animation to offline-based timing, e.g. to export high-resolution image sequences and give the browser time to grab & encode e…

thi.ng/genart-api

Evaluating Self-Supervised Speech Models via Text-Based LLMS
Takashi Maekaku, Keita Goto, Jinchuan Tian, Yusuke Shinohara, Shinji Watanabe
https://arxiv.org/abs/2510.04463 https…

Evaluating Self-Supervised Speech Models via Text-Based LLMS
Self-Supervised Learning (SSL) has gained traction for its ability to learn rich representations with low labeling costs, applicable across diverse downstream tasks. However, assessing the downstream-task performance remains challenging due to the cost of extra training and evaluation. Existing methods for task-agnostic evaluation also require extra training or hyperparameter tuning. We propose a novel evaluation metric using large language models (LLMs). By inputting discrete token sequences a…

G-kernels and Crossed Modules
Sergio Gir\'on Pacheco, Masaki Izumi, Ulrich Pennig
https://arxiv.org/abs/2509.04134 https://arxiv.org/pdf/2509.04134

G-kernels and Crossed Modules
We develop a unified framework based on topological crossed modules for various lifting obstructions for $Γ$-kernels. It allows us to identify actions, cocycle actions and $Γ$-kernels up to their natural equivalence relations with cohomology sets. The obstructions then appear as boundary maps in corresponding exact sequences. Since topological crossed modules are topological $2$-groups (in the categorical sense), they have classifying spaces, which come with a natural transformation from the …

Coarse scrambling for Sobol' and Niederreiter sequences
Kosuke Suzuki
https://arxiv.org/abs/2510.02111 https://arxiv.org/pdf/2510.02111

Coarse scrambling for Sobol' and Niederreiter sequences
We introduce \emph{coarse scrambling}, a novel randomization for digital sequences that permutes blocks of digits in a mixed-radix representation. This construction is designed to preserve the powerful $(0,\boldsymbol{e},d)$-sequence property of the underlying points. For sufficiently smooth integrands, we prove that this method achieves the canonical $O(n^{-3+ε})$ variance decay rate, matching that of standard Owen's scrambling. Crucially, we show that its maximal gain coefficient grows only …

Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains
Ninh Van Thu
https://arxiv.org/abs/2509.00301 https://ar…

Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.

Synthetic Dialogue Generation for Interactive Conversational Elicitation & Recommendation (ICER)
Moonkyung Ryu, Chih-Wei Hsu, Yinlam Chow, Mohammad Ghavamzadeh, Craig Boutilier
https://arxiv.org/abs/2510.02331

Synthetic Dialogue Generation for Interactive Conversational Elicitation & Recommendation (ICER)
While language models (LMs) offer great potential for conversational recommender systems (CRSs), the paucity of public CRS data makes fine-tuning LMs for CRSs challenging. In response, LMs as user simulators qua data generators can be used to train LM-based CRSs, but often lack behavioral consistency, generating utterance sequences inconsistent with those of any real user. To address this, we develop a methodology for generating natural dialogues that are consistent with a user's underlying sta…

Approximation of the number of nonunimodular zeros of a self-reciprocal polynomial
Dragan Stankov
https://arxiv.org/abs/2509.01015 https://arxiv.org/pdf/25…

Approximation of the number of nonunimodular zeros of a self-reciprocal polynomial
We introduce the ratio of the number of roots, not equal to 1 in modulus, of a reciprocal polynomial $R_d(x)$ to its degree $d$. For some sequences of reciprocal polynomials we show that the ratio has a limit $L$ when $d$ tends to infinity. Each of these sequences is defined using a two-variable polynomial $P(x,y)$ so that $R_d(x) = P(x,x^n)$. We present a few methods for approximation of the limit ratio, some of them we originally developed. In a previous paper we have calculated the e…

📇 Bringing restartable sequences out of the niche
#linux #operatingsystem

A Nonmonotone Front Descent Method for Bound-Constrained Multi-Objective Optimization
Pierluigi Mansueto
https://arxiv.org/abs/2509.02409 https://arxiv.org…

A Nonmonotone Front Descent Method for Bound-Constrained Multi-Objective Optimization
We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the first descent algorithm employing nonmonotone strategies to generate point sets approximating the Pareto front. We establish convergence properties for the resulting sequences of sets, analogous to the original framework, and present numerical results confirmi…

Directed evolution effectively selects for DNA based physical reservoir computing networks capable of multiple tasks
Tanmay Pandey, Petro Feketa, Jan Steink\"uhler
https://arxiv.org/abs/2509.04000

Directed evolution effectively selects for DNA based physical reservoir computing networks capable of multiple tasks
DNA and other biopolymers are being investigated as new computing substrates and alternative to silicon-based digital computers. However, the established top-down design of biomolecular interaction networks remains challenging and does not fully exploit biomolecular self-assembly capabilities. Outside of the field of computation directed evolution has been used as a tool for goal directed optimization of DNA sequences. Here, we propose integrating directed evolution with DNA-based reservoir com…

Typhoon Path Prediction Using Functional Data Analysis and Clustering-Based Regression
Jimin Kim
https://arxiv.org/abs/2510.02316 https://arxiv.org/pdf/251…

Typhoon Path Prediction Using Functional Data Analysis and Clustering-Based Regression
Accurate prediction of typhoon trajectories is essential for mitigating the impact of these extreme weather events. This study proposes a functional data analysis (FDA) framework for modeling and forecasting typhoon paths using historical trajectory data. Latitude and longitude sequences are represented as smooth functional observations, and a function-on-function regression model is employed to capture the temporal dynamics of typhoon movement. While the baseline model demonstrates reasonable …

Cyclic Vanishing Identities of Sun-Pan Type: Analytic and Modular Perspectives
Ken Nagai
https://arxiv.org/abs/2510.01341 https://arxiv.org/pdf/2510.01341

Cyclic Vanishing Identities of Sun-Pan Type: Analytic and Modular Perspectives
We revisit the cyclic identities of Sun--Pan type for Bernoulli polynomials and their $q$-analogues. From the analytic side, we formulate minimal Appell axioms that force cyclic vanishing identities, extending naturally to $q$-Appell sequences and analytic Bernoulli functions. From the modular side, we show that the same relations arise as period polynomial identities associated with Eisenstein series, reflecting the symmetry $(ST)^3=-I$ of the modular group. These two complementary perspective…

Relative compactness of It\^o integrals on the M1 Skorokhod space with identification of limits
Fabrice Wunderlich
https://arxiv.org/abs/2508.21624 https://

Relative compactness of Itô integrals on the M1 Skorokhod space with identification of limits
We establish general results for weak relative compactness of sequences of Itô integrals with respect to Skorohod's functional M1 topology, under general conditions. Moreover, we are able to explicitly characterise the form of the limit points of all convergent subsequences. This result closes a longstanding gap in the literature, where weak relative compactness had previously only been shown under the significantly more restrictive J1 topology, or the S topology which is too coarse to preserv…

epiGPTope: A machine learning-based epitope generator and classifier
Natalia Flechas Manrique, Alberto Mart\'inez, Elena L\'opez-Mart\'inez, Luc Andrea, Rom\'an Orus, Aitor Manteca, Aitziber L. Cortajarena, Lloren\c{c} Espinosa-Portal\'es
https://arxiv.org/abs/2509.03351

epiGPTope: A machine learning-based epitope generator and classifier
Epitopes are short antigenic peptide sequences which are recognized by antibodies or immune cell receptors. These are central to the development of immunotherapies, vaccines, and diagnostics. However, the rational design of synthetic epitope libraries is challenging due to the large combinatorial sequence space, $20^n$ combinations for linear epitopes of n amino acids, making screening and testing unfeasible, even with high throughput experimental techniques. In this study, we present a large l…

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations
Ljuben Mutafchiev
https://arxiv.org/abs/2509.26129 …

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations
Let $S_n$ be the set of all permutations of $\{1,2,\ldots,n\}$ and let $σ=(σ_1,σ_2,\ldots,σ_n)\in S_n$. The {\it initial longest increasing sequence} (ILIS) in $σ$ has length $m$ if, for $1\le m\le n-1$, $σ_1<σ_2<\ldots<σ_m, σ_m>σ_{m+1}$, and has length $n$ if $σ=(1,2,\ldots,n)$. Let $l(σ)$ be the length of the ILIS in $σ$. We assume that $σ$ is represented in cycle notation, so that the first number in each cycle is the minimum number of this cycle. We also assume that $σ$ is ch…

HIV-1 protease cleavage sites detection with a Quantum convolutional neural network algorithm
Junggu Choi, Junho Lee, Kyle L. Jung, Jae U. Jung
https://arxiv.org/abs/2510.01993 …

HIV-1 protease cleavage sites detection with a Quantum convolutional neural network algorithm
In this study, we propose a quantum convolutional neural network (QCNN)-based framework with the neural quantum embedding (NQE) to predict HIV-1 protease cleavage sites in amino acid sequences from viral and human proteins. To assess the effectiveness and robustness of our framework, we compared the classification performance against classical neural networks under both noiseless and noisy simulations. Among experimental conditions, the QCNN with the angle and amplitude encoding NQE conditions …

InfVSR: Breaking Length Limits of Generic Video Super-Resolution
Ziqing Zhang, Kai Liu, Zheng Chen, Xi Li, Yucong Chen, Bingnan Duan, Linghe Kong, Yulun Zhang
https://arxiv.org/abs/2510.00948

InfVSR: Breaking Length Limits of Generic Video Super-Resolution
Real-world videos often extend over thousands of frames. Existing video super-resolution (VSR) approaches, however, face two persistent challenges when processing long sequences: (1) inefficiency due to the heavy cost of multi-step denoising for full-length sequences; and (2) poor scalability hindered by temporal decomposition that causes artifacts and discontinuities. To break these limits, we propose InfVSR, which novelly reformulates VSR as an autoregressive-one-step-diffusion paradigm. This…

Estimation of Phylogenetic Tree using Gene Sequencing Data
S M Rafiuddin
https://arxiv.org/abs/2509.01407 https://arxiv.org/pdf/2509.01407

Estimation of Phylogenetic Tree using Gene Sequencing Data
A phylogenetic tree is an important way in Bioinformatics to find the evolutionary relationship among biological species. In this research, a proposed model is described for the estimation of a phylogenetic tree for a given set of data. To estimate a phylogenetic tree there are certain necessary steps have to be considered. Gene sequences are useful data resources to estimate the relationship among species at the molecular level. In this research, the approach is to create a fusion between the …

On the Parameterized Complexity of Grundy Domination and Zero Forcing Problems
Robert Scheffler
https://arxiv.org/abs/2508.18104 https://arxiv.org/pdf/2508…

On the Parameterized Complexity of Grundy Domination and Zero Forcing Problems
We consider two different problem families that deal with domination in graphs. On the one hand, we focus on dominating sequences. In such a sequence, every vertex dominates some vertex of the graph that was not dominated by any earlier vertex in the sequence. The problem of finding the longest dominating sequence is known as $\mathsf{Grundy~Domination}$. Depending on whether the closed or the open neighborhoods are used for domination, there are three other versions of this problem. We show th…

AI-Based Stroke Rehabilitation Domiciliary Assessment System with ST_GCN Attention
Suhyeon Lim, Ye-eun Kim, Andrew J. Choi
https://arxiv.org/abs/2510.00049 https://

AI-Based Stroke Rehabilitation Domiciliary Assessment System with ST_GCN Attention
Effective stroke recovery requires continuous rehabilitation integrated with daily living. To support this need, we propose a home-based rehabilitation exercise and feedback system. The system consists of (1) hardware setup with RGB-D camera and wearable sensors to capture Stroke movements, (2) a mobile application for exercise guidance, and (3) an AI server for assessment and feedback. When Stroke user exercises following the application guidance, the system records skeleton sequences, which a…

NoTVLA: Narrowing of Dense Action Trajectories for Generalizable Robot Manipulation
Zheng Huang, Mingyu Liu, Xiaoyi Lin, Muzhi Zhu, Canyu Zhao, Zongze Du, Xiaoman Li, Yiduo Jia, Hao Zhong, Hao Chen, Chunhua Shen
https://arxiv.org/abs/2510.03895

NoTVLA: Narrowing of Dense Action Trajectories for Generalizable Robot Manipulation
Vision-Language-Action (VLA) models represent a pivotal advance in embodied intelligence, yet they confront critical barriers to real-world deployment, most notably catastrophic forgetting. This issue stems from their overreliance on continuous action sequences or action chunks, which inadvertently create isolated data silos that disrupt knowledge retention across tasks. To tackle these challenges, we propose the Narrowing of Trajectory VLA (NoTVLA) framework: a novel approach that narrows its …

A Walk on the Wild Side: a Shape-First Methodology for Orthogonal Drawings
Giordano Andreola, Susanna Caroppo, Giuseppe Di Battista, Fabrizio Grosso, Maurizio Patrignani, Allegra Strippoli
https://arxiv.org/abs/2508.19416

A Walk on the Wild Side: a Shape-First Methodology for Orthogonal Drawings
Several algorithms for the construction of orthogonal drawings of graphs, including those based on the Topology-Shape-Metrics (TSM) paradigm, tend to prioritize the minimization of crossings. This emphasis has two notable side effects: some edges are drawn with unnecessarily long sequences of segments and bends, and the overall drawing area may become excessively large. As a result, the produced drawings often lack geometric uniformity. Moreover, orthogonal crossings are known to have a limited…

Evaluating the Safety and Skill Reasoning of Large Reasoning Models Under Compute Constraints
Adarsha Balaji, Le Chen, Rajeev Thakur, Franck Cappello, Sandeep Madireddy
https://arxiv.org/abs/2509.18382

Capacity-Achieving Codes for Noisy Insertion Channels
Hengfeng Liu, Chunming Tang, Cuiling Fan
https://arxiv.org/abs/2509.24161 https://arxiv.org/pdf/2509.…

Capacity-Achieving Codes for Noisy Insertion Channels
DNA storage has emerged as a promising solution for large-scale and long-term data preservation. Among various error types, insertions are the most frequent errors occurring in DNA sequences, where the inserted symbol is often identical or complementary to the original, and in practical implementations, noise can further cause the inserted symbol to mutate into a random one, which creates significant challenges to reliable data recovery. In this paper, we investigate a new noisy insertion chann…

Eigendecompositions of temporal networks
Lucas Lacasa
https://arxiv.org/abs/2509.03135 https://arxiv.org/pdf/2509.03135

Eigendecompositions of temporal networks
Temporal networks, defined as sequences of time-aggregated adjacency matrices, sample latent graph dynamics and trace trajectories in graph space. By interpreting each adjacency matrix as a different time snapshot of a scalar field, fluid-mechanics theories can be applied to construct two distinct eigendecompositions of temporal networks. The first builds on the proper orthogonal decomposition (POD) of flowfields and decomposes the evolution of a network in terms of a basis of orthogonal networ…

Colored base-3 partitions, sequences of polynomials, and perfect numbers
Karl Dilcher, Larry Ericksen
https://arxiv.org/abs/2509.03147 https://arxiv.org/pd…

Colored base-3 partitions, sequences of polynomials, and perfect numbers
Motivated by the observation that the counting function of a certain base-3 colored partition contains the even perfect numbers as a subsequence, we begin by defining a sequence of polynomials in four variables and discuss their properties and combinatorial interpretations. We then concentrate on certain subsequences that are related to the Chebyshev polynomials of both kinds. Finally, we consider several sequences of single-variable polynomials that have meaningful combinatorial interpretation…

DMGIN: How Multimodal LLMs Enhance Large Recommendation Models for Lifelong User Post-click Behaviors
Zhuoxing Wei, Qingchen Xie, Qi Liu
https://arxiv.org/abs/2508.21801 https:/…

DMGIN: How Multimodal LLMs Enhance Large Recommendation Models for Lifelong User Post-click Behaviors
Modeling user interest based on lifelong user behavior sequences is crucial for enhancing Click-Through Rate (CTR) prediction. However, long post-click behavior sequences themselves pose severe performance issues: the sheer volume of data leads to high computational costs and inefficiencies in model training and inference. Traditional methods address this by introducing two-stage approaches, but this compromises model effectiveness due to incomplete utilization of the full sequence context. Mor…

ChopChop: a Programmable Framework for Semantically Constraining the Output of Language Models
Shaan Nagy, Timothy Zhou, Nadia Polikarpova, Loris D'Antoni
https://arxiv.org/abs/2509.00360

ChopChop: a Programmable Framework for Semantically Constraining the Output of Language Models
Language models (LMs) can generate code, but cannot guarantee its correctness--producing outputs that often violate type safety, program invariants, or semantic equivalence. Constrained decoding offers a solution by restricting generation to programs that satisfy desired properties. Yet, existing methods are limited to shallow syntactic constraints or rely on brittle, ad hoc encodings of semantics over token sequences. We present ChopChop, the first programmable framework for semantic constra…

SALSA-V: Shortcut-Augmented Long-form Synchronized Audio from Videos
Amir Dellali, Luca A. Lanzend\"orfer, Florian Gr\"otschla, Roger Wattenhofer
https://arxiv.org/abs/2510.02916

SALSA-V: Shortcut-Augmented Long-form Synchronized Audio from Videos
We propose SALSA-V, a multimodal video-to-audio generation model capable of synthesizing highly synchronized, high-fidelity long-form audio from silent video content. Our approach introduces a masked diffusion objective, enabling audio-conditioned generation and the seamless synthesis of audio sequences of unconstrained length. Additionally, by integrating a shortcut loss into our training process, we achieve rapid generation of high-quality audio samples in as few as eight sampling steps, pavi…

Sequences of surfaces in $4$-manifolds
Marina Ville
https://arxiv.org/abs/2509.00566 https://arxiv.org/pdf/2509.00566…

Sequences of surfaces in $4$-manifolds
Let $(Σ_n)$ be a sequence of surfaces immersed in a $4$-manifold $M$ which converges to a branched surface $Σ_0$ .\\ We denote by $k^T_p$ (resp. $k^N_p$) the amount of curvature of the tangent bundles $TΣ_n$ (resp. normal bundles $NΣ_n$) which concentrates around a branch point $p$ of $Σ_0$ when $n$ goes to infinity. Alternatively $k^T\pm k^N$ measures how much the twistor degrees drop when we go from $Σ_n$ to $Σ_0$. For complex algebraic curves, $k^T+k^N=0$..\\ In some instances - 1) if…

DLGAN : Time Series Synthesis Based on Dual-Layer Generative Adversarial Networks
Xuan Hou, Shuhan Liu, Zhaohui Peng, Yaohui Chu, Yue Zhang, Yining Wang
https://arxiv.org/abs/2508.21340

DLGAN : Time Series Synthesis Based on Dual-Layer Generative Adversarial Networks
Time series synthesis is an effective approach to ensuring the secure circulation of time series data. Existing time series synthesis methods typically perform temporal modeling based on random sequences to generate target sequences, which often struggle to ensure the temporal dependencies in the generated time series. Additionally, directly modeling temporal features on random sequences makes it challenging to accurately capture the feature information of the original time series. To address t…

A Survey on a Pair of Diophantine Equations
Hung Viet Chu, Rishabh Gulecha, Sicheng Guo, Nathanael Johnson, Steven J. Miller, Yeju Shin
https://arxiv.org/abs/2509.01781 https://…

A Survey on a Pair of Diophantine Equations
Given two relatively prime numbers $a$ and $b$, it is known that exactly one of the two Diophantine equations has a nonnegative integral solution $(x,y)$: $$ ax + by \ =\ \frac{(a-1)(b-1)}{2}\quad \mbox{ and }\quad 1 + ax + by \ =\ \frac{(a-1)(b-1)}{2}. $$ Furthermore, the solution is unique. This paper surveys recent results on finding the solution and determining which equation is used when $a$ and $b$ are taken from certain sequences. We contribute to the literature by finding $(x,y)$ when…

Sampling Theory of Jointly Bandlimited Time-vertex Graph Signals
Hang Sheng, Hui Feng, Junhao Yu, Feng Ji, Bo Hu
https://arxiv.org/abs/2508.21412 https://a…

Sampling Theory of Jointly Bandlimited Time-vertex Graph Signals
Time-vertex graph signal (TVGS) models describe time-varying data with irregular structures. The bandlimitedness in the joint time-vertex Fourier spectral domain reflects smoothness in both temporal and graph topology. In this paper, we study the critical sampling of three types of TVGS including continuous-time signals, infinite-length sequences, and finite-length sequences in the time domain for each vertex on the graph. For a jointly bandlimited TVGS, we prove a lower bound on sampling densi…

Spectral theory of matrix-sequences: perspectives of the GLT analysis and beyond
Stefano Serra-Capizzano
https://arxiv.org/abs/2509.19544 https://arxiv.org…

Spectral theory of matrix-sequences: perspectives of the GLT analysis and beyond
In recent years there has been a growing attention on distribution results in the sense of Weyl for the collective behavior of eigenvalues and singular values of matrix-sequences. Starting from the work of Szegö regarding the case of Toeplitz matrix-sequences, there has been a wealth of associated results, which culminated in the works of Tilli and of Tyrtyshnikov, Zamarashkin, and of the author for preconditioned and non-preconditioned $r$-block $d$-level Toeplitz matrix-sequences with Lebesg…

The Chow ring of a sequence of point and rational curve blow-ups
Daniel Camaz\'on Portela
https://arxiv.org/abs/2509.23138 https://arxiv.org/pdf/2509.2…

The Chow ring of a sequence of point and rational curve blow-ups
Given a sequence of point and rational curve blow-ups blow-ups of smooth $3-$dimensional projective varieties $Z_{i}$ defined over an algebraically closed field $\mathit{k}$, $Z_{s}\xrightarrow{π_{s}} Z_{s-1}\xrightarrow{π_{s-1}}\cdot\cdot\cdot\xrightarrow{π_{2}} Z_{1}\xrightarrow{π_{1}} Z_{0}$, with $Z_{0}\cong\mathbb{P}^{3}$, we give an explicit presentations of the Chow ring $A^{\bullet}(Z_{s})$ of its sky. We prove that, in contrast to the case of sequences of point blow-ups, the skies …

Line bundles and exact sequences for the ideal class group and the Picard group
Abolfazl Tarizadeh
https://arxiv.org/abs/2508.19889 https://arxiv.org/pdf/2…

Line bundles and exact sequences for the ideal class group and the Picard group
For any extension of commutative rings $A\subseteq B$ we first naturally define a group $\Cl(A,B)$, that we call the ideal class group of this extension (we will see that both the classical ideal class group and, surprisingly, the Picard group are special cases of this structure), then, as a first main result, we obtain the following exact sequence of Abelian groups: ...

The hat polykite as an Iterated Function System
Corey de Wit
https://arxiv.org/abs/2510.00409 https://arxiv.org/pdf/2510.00409

The hat polykite as an Iterated Function System
This paper describes the celebrated aperiodic hat tiling by Smith et al. [Comb. Theory 8 (2024), 6] as generated by an overlapping iterated function system. We briefly introduce and study infinite sequences of iterated function systems that converge uniformly in each component, and use this theory to model the hat tiling's associated imperfect substitution system.

Breaking the Euclidean Barrier: Hyperboloid-Based Biological Sequence Analysis
Sarwan Ali, Haris Mansoor, Murray Patterson
https://arxiv.org/abs/2510.01118 https://

Breaking the Euclidean Barrier: Hyperboloid-Based Biological Sequence Analysis
Genomic sequence analysis plays a crucial role in various scientific and medical domains. Traditional machine-learning approaches often struggle to capture the complex relationships and hierarchical structures of sequence data when working in high-dimensional Euclidean spaces. This limitation hinders accurate sequence classification and similarity measurement. To address these challenges, this research proposes a method to transform the feature representation of biological sequences into the hy…

Bayesian Re-Analysis of the Phylogenetic Topology of Early SARS-CoV-2 Case Sequences
Michael B. Weissman
https://arxiv.org/abs/2510.01484 https://arxiv.org…

Bayesian Re-Analysis of the Phylogenetic Topology of Early SARS-CoV-2 Case Sequences
A much-cited 2022 paper by Pekar et al. claimed that Bayesian analysis of the molecular phylogeny of early SARS-CoV-2 cases indicated that it was more likely that two successful introductions to humans had occurred than that just one had. Here I show that after correcting a fundamental error in Bayesian reasoning the results in that paper give larger likelihood for a single introduction than for two.

AutoDrive-R$^2$: Incentivizing Reasoning and Self-Reflection Capacity for VLA Model in Autonomous Driving
Zhenlong Yuan, Jing Tang, Jinguo Luo, Rui Chen, Chengxuan Qian, Lei Sun, Xiangxiang Chu, Yujun Cai, Dapeng Zhang, Shuo Li
https://arxiv.org/abs/2509.01944

AutoDrive-R$^2$: Incentivizing Reasoning and Self-Reflection Capacity for VLA Model in Autonomous Driving
Vision-Language-Action (VLA) models in autonomous driving systems have recently demonstrated transformative potential by integrating multimodal perception with decision-making capabilities. However, the interpretability and coherence of the decision process and the plausibility of action sequences remain largely underexplored. To address these issues, we propose AutoDrive-R$^2$, a novel VLA framework that enhances both reasoning and self-reflection capabilities of autonomous driving systems thr…

TreeMind: Automatically Reproducing Android Bug Reports via LLM-empowered Monte Carlo Tree Search
Zhengyu Chen, Zhaoyi Meng, Wenxiang Zhao, Wansen Wang, Haoyang Zhao, Jiahao Zhan, Jie Cui, Hong Zhong
https://arxiv.org/abs/2509.22431

TreeMind: Automatically Reproducing Android Bug Reports via LLM-empowered Monte Carlo Tree Search
Automatically reproducing Android app crashes from textual bug reports is challenging, particularly when the reports are incomplete and the modern UI exhibits high combinatorial complexity. Existing approaches based on reinforcement learning or large language models (LLMs) exhibit limitations in such scenarios. They struggle to infer unobserved steps and reconstruct the underlying user action sequences to navigate the vast UI interaction space, primarily due to limited goal-directed reasoning a…

Discrete Facial Encoding: : A Framework for Data-driven Facial Display Discovery
Minh Tran, Maksim Siniukov, Zhangyu Jin, Mohammad Soleymani
https://arxiv.org/abs/2510.01662 htt…

Discrete Facial Encoding: : A Framework for Data-driven Facial Display Discovery
Facial expression analysis is central to understanding human behavior, yet existing coding systems such as the Facial Action Coding System (FACS) are constrained by limited coverage and costly manual annotation. In this work, we introduce Discrete Facial Encoding (DFE), an unsupervised, data-driven alternative of compact and interpretable dictionary of facial expressions from 3D mesh sequences learned through a Residual Vector Quantized Variational Autoencoder (RVQ-VAE). Our approach first extr…

Meaningless Tokens, Meaningful Gains: How Activation Shifts Enhance LLM Reasoning
Zeru Shi, Yingjia Wan, Zhenting Wang, Qifan Wang, Fan Yang, Elisa Kreiss, Ruixiang Tang
https://arxiv.org/abs/2510.01032

Meaningless Tokens, Meaningful Gains: How Activation Shifts Enhance LLM Reasoning
Motivated by the puzzling observation that inserting long sequences of meaningless tokens before the query prompt can consistently enhance LLM reasoning performance, this work analyzes the underlying mechanism driving this phenomenon and based on these insights proposes a more principled method that allows for similar performance gains. First, we find that the improvements arise from a redistribution of activations in the LLM's MLP layers, where near zero activations become less frequent while …

Regular Structures in Kronecker Permutations
Fran\c{c}ois Cl\'ement
https://arxiv.org/abs/2509.03782 https://arxiv.org/pdf/2509.03782

Regular Structures in Kronecker Permutations
Kronecker sequences $(k α\mod 1)_{k=1}^{\infty}$ for some irrational $α> 0$ have played an important role in many areas of mathematics. It is possible to associate to each finite segment $(k α\mod 1)_{k=1}^{n}$ a permutation $π\in S_n$ associated with the canonical lifting to two dimensions. We show that these permutations induced by Kronecker sequences based on irrational $α$ are extremely regular for specific choices of $n$ and $α$. In particular, all quadratic irrationals have an infin…

The covering radius of Butson Hadamard codes for the homogeneous metric
Xingxing Xu, Minjia Shi, Patrick Sole
https://arxiv.org/abs/2508.12859 https://arxi…

The covering radius of Butson Hadamard codes for the homogeneous metric
Butson matrices are complex Hadamard matrices with entries in the complex roots of unity of given order. There is an interesting code in phase space related to this matrix (Armario et al. 2023). We study the covering radius of Butson Hadamard codes for the homogeneous metric, a metric defined uniquely, up to scaling, for a commutative ring alphabet that is Quasi Frobenius. An upper bound is derived by an orthogonal array argument. A lower bound relies on the existence of bent sequences in the s…

Constructions of Sequences of Alternating Sum and Difference Dominated Sets
Yorick Herrmann, Connor Hill, Merlin Phillips, Daniel Flores, Steven J. Miller, Steven Senger
https://arxiv.org/abs/2509.00792

Constructions of Sequences of Alternating Sum and Difference Dominated Sets
A More Sums Than Difference (MSTD) set is a finite set of integers $A$ where the cardinality of its sumset, $A+A$, is greater than the cardinality of its difference set, $A-A$. Since addition is commutative while subtraction isn't, it was conjectured that MSTD sets are rare. As Martin and O'Bryant proved a small (but positive) percentage are MSTD, it is natural to ask what additional properties can we impose on a chain of MSTD sets; in particular, can we construct a sequence of sets alternating…

Attributes as Textual Genes: Leveraging LLMs as Genetic Algorithm Simulators for Conditional Synthetic Data Generation
Guangzeng Han, Weisi Liu, Xiaolei Huang
https://arxiv.org/abs/2509.02040

Attributes as Textual Genes: Leveraging LLMs as Genetic Algorithm Simulators for Conditional Synthetic Data Generation
Large Language Models (LLMs) excel at generating synthetic data, but ensuring its quality and diversity remains challenging. We propose Genetic Prompt, a novel framework that combines genetic algorithms with LLMs to augment synthetic data generation. Our approach treats semantic text attributes as gene sequences and leverages the LLM to simulate crossover and mutation operations. This genetic process enhances data quality and diversity by creating novel attribute combinations, yielding syntheti…

Sequences of odd length in strict partitions IV: the combinatorics of parameterized Rogers-Ramanujan type identities
Haijun Li
https://arxiv.org/abs/2509.24942 https://

Sequences of odd length in strict partitions IV: the combinatorics of parameterized Rogers-Ramanujan type identities
In the first three papers, we conducted a series of discussions on the statistics of strict partitions and Rogers-Ramanujan partitions, specifically the sequences of odd length (denoted as $\mathrm{sol}$) and its extensions. We established bijections for some Rogers-Ramanujan type identities. This paper will continue that series of work, and first we will use the bijective method to re-establish several parameterized Rogers-Ramanujan type identities, which appeared in the recent work of Hao-Kua…

The Lie of the Average: How Class Incremental Learning Evaluation Deceives You?
Guannan Lai, Da-Wei Zhou, Xin Yang, Han-Jia Ye
https://arxiv.org/abs/2509.22580 https://

The Lie of the Average: How Class Incremental Learning Evaluation Deceives You?
Class Incremental Learning (CIL) requires models to continuously learn new classes without forgetting previously learned ones, while maintaining stable performance across all possible class sequences. In real-world settings, the order in which classes arrive is diverse and unpredictable, and model performance can vary substantially across different sequences. Yet mainstream evaluation protocols calculate mean and variance from only a small set of randomly sampled sequences. Our theoretical anal…

Pre-Distillation of Magic States via Composite Schemes
Muhammad Erew, Moshe Goldstein, Yaron Oz, Haim Suchowski
https://arxiv.org/abs/2510.00804 https://ar…

Pre-Distillation of Magic States via Composite Schemes
Magic state distillation (MSD) is a cornerstone of fault-tolerant quantum computing, enabling non-Clifford gates via state injection into stabilizer circuits. However, the substantial overhead of current MSD protocols remains a major obstacle to scalable implementations. We propose a general framework for pre-distillation, based on composite pulse sequences that suppress systematic errors in the generation of magic states. Unlike typical composite designs that target simple gates such as $X$, $…

PSTTS: A Plug-and-Play Token Selector for Efficient Event-based Spatio-temporal Representation Learning
Xiangmo Zhao, Nan Yang, Yang Wang, Zhanwen Liu
https://arxiv.org/abs/2509.22481

PSTTS: A Plug-and-Play Token Selector for Efficient Event-based Spatio-temporal Representation Learning
Mainstream event-based spatio-temporal representation learning methods typically process event streams by converting them into sequences of event frames, achieving remarkable performance. However, they neglect the high spatial sparsity and inter-frame motion redundancy inherent in event frame sequences, leading to significant computational overhead. Existing token sparsification methods for RGB videos rely on unreliable intermediate token representations and neglect the influence of event noise…

Quantitative growth of multi-recurrence sequences
Clemens Fuchs, Armand Noubissie
https://arxiv.org/abs/2510.01896 https://arxiv.org/pdf/2510.01896

Quantitative growth of multi-recurrence sequences
In 1982, Schlickewei and Van der Poorten claimed that any multi-recurrence sequence has, essentially, maximal possible growth rate. Fourty years later, Fuchs and Heintze provided a non-effective proof of this statement. In this paper, we prove a quantitative version of that result by giving an explicit upper bound for the maximal possible growth rate of a multi-recurrence. Moreover, we also give a function field analogue of the result, answering a question posed by Fuchs and Heintze when provin…

Degree sequences realizing labelled perfect matchings
Joseph Briggs, Jessica McDonald, Songling Shan
https://arxiv.org/abs/2510.01110 https://arxiv.org/pdf…

Degree sequences realizing labelled perfect matchings
Let $n\in \mathbb{N}$ and $d_1 \geq d_2 \geq d_n\geq 1$ be integers. There is characterization of when $(d_1, d_1, \ldots, d_n)$ is the degree sequence of a graph containing a perfect matching, due to results of Lovász (1974) and Erdős and Gallai (1960). But \emph{which} perfect matchings can be realized in the labelled graph? Here we find the extremal answers to this question, showing that the sequence $(d_1, d_2, \ldots, d_n)$: (1) can realize a perfect matching iff it can realize $\{(1, n)…

GUI-KV: Efficient GUI Agents via KV Cache with Spatio-Temporal Awareness
Kung-Hsiang Huang, Haoyi Qiu, Yutong Dai, Caiming Xiong, Chien-Sheng Wu
https://arxiv.org/abs/2510.00536

GUI-KV: Efficient GUI Agents via KV Cache with Spatio-Temporal Awareness
Graphical user interface (GUI) agents built on vision-language models have emerged as a promising approach to automate human-computer workflows. However, they also face the inefficiency challenge as they process long sequences of high-resolution screenshots and solving long-horizon tasks, making inference slow, costly and memory-bound. While key-value (KV) caching can mitigate this, storing the full cache is prohibitive for image-heavy contexts. Existing cache-compression methods are sub-optima…

Multi-Modal Model Predictive Path Integral Control for Collision Avoidance
Alberto Bertipaglia, Dariu M. Gavrila, Barys Shyrokau
https://arxiv.org/abs/2508.21364 https://…

Multi-Modal Model Predictive Path Integral Control for Collision Avoidance
This paper proposes a novel approach to motion planning and decision-making for automated vehicles, using a multi-modal Model Predictive Path Integral control algorithm. The method samples with Sobol sequences around the prior input and incorporates analytical solutions for collision avoidance. By leveraging multiple modes, the multi-modal control algorithm explores diverse trajectories, such as manoeuvring around obstacles or stopping safely before them, mitigating the risk of sub-optimal solu…

Temporal-Aware Iterative Speech Model for Dementia Detection
Chukwuemeka Ugwu, Oluwafemi Oyeleke
https://arxiv.org/abs/2510.00030 https://arxiv.org/pdf/251…

Temporal-Aware Iterative Speech Model for Dementia Detection
Deep learning systems often struggle with processing long sequences, where computational complexity can become a bottleneck. Current methods for automated dementia detection using speech frequently rely on static, time-agnostic features or aggregated linguistic content, lacking the flexibility to model the subtle, progressive deterioration inherent in speech production. These approaches often miss the dynamic temporal patterns that are critical early indicators of cognitive decline. In this pap…

Signed counting of partition matrices
Shane Chern, Shishuo Fu
https://arxiv.org/abs/2508.21318 https://arxiv.org/pdf/2508.21318

Signed counting of partition matrices
We prove that the signed counting (with respect to the parity of the ``$\operatorname{inv}$'' statistic) of partition matrices equals the cardinality of a subclass of inversion sequences. In the course of establishing this result, we introduce an interesting class of partition matrices called improper partition matrices. We further show that a subset of improper partition matrices is equinumerous with the set of Motzkin paths. Such an equidistribution is established both analytically and biject…

Lacunary sequences whose reciprocal sums represent all rationals in an interval
Wouter van Doorn, Vjekoslav Kova\v{c}
https://arxiv.org/abs/2509.24971 https://

Lacunary sequences whose reciprocal sums represent all rationals in an interval
Answering a question of Michael Bleicher and Paul Erdős, we show that there exists a lacunary sequence of positive integers such that finite sums of reciprocals of its terms attain all rational numbers from a non-empty open interval. We also study several stronger variants of their original problem: determining the value of the optimal lacunarity parameter, representing rationals infinitely many times, finding such lacunary sequences with arbitrarily large jumps, and relating the maximal lengt…

Learning the Wrong Lessons: Syntactic-Domain Spurious Correlations in Language Models
Chantal Shaib, Vinith M. Suriyakumar, Levent Sagun, Byron C. Wallace, Marzyeh Ghassemi
https://arxiv.org/abs/2509.21155

Learning the Wrong Lessons: Syntactic-Domain Spurious Correlations in Language Models
For an LLM to correctly respond to an instruction it must understand both the semantics and the domain (i.e., subject area) of a given task-instruction pair. However, syntax can also convey implicit information Recent work shows that syntactic templates--frequent sequences of Part-of-Speech (PoS) tags--are prevalent in training data and often appear in model outputs. In this work we characterize syntactic templates, domain, and semantics in task-instruction pairs. We identify cases of spurious …

Zeros and Orthogonality of generalized Fibonacci polynomials
Cristian F. Coletti, Rigoberto Fl\'orez, Robinson A. Higuita, Sandra Z. Yepes
https://arxiv.org/abs/2510.00074 h…

Zeros and Orthogonality of generalized Fibonacci polynomials
This paper analyzes the concept of orthogonality in second-order polynomial sequences that have Binet formula similar to that of the Fibonacci and Lucas numbers, referred to as Generalized Fibonacci Polynomials (GFP). We give a technique to find roots of the GFP. As a corollary of this result, we give an alternative proof of a special case of Favard's Theorem. The general case of Favard's Theorem guarantees that there is a measure to determine whether a sequence of second-order polynomials is o…

The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences
Yongkang Wan, Zhonghao Liang, Qunying Liao
https://arxiv.org/abs/2509.14569

The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences
In this paper, for the generalized Fibonacci sequence $\left\{W_n\left(a,b,p,q\right)\right\}$, by using elementary methods and techniques, we give the asymptotic estimation values of $\left(\sum\limits_{k=n}^{\infty}\frac{1}{\sum\limits_{i=0}^{t}s_{i}W_{mk+l_i}}\right)^{-1}$ and $\left(\sum\limits_{k=n}^{\infty}\frac{\left(-1\right)^k}{\sum\limits_{i=0}^{t}s_{i}W_{mk+l_i}}\right)^{-1}$, respectively. In particular, for some special $a,b,p,q,m,t,s_i$ and $l_i\left(0\leq i\leq t \right)$, Theore…

Explicit construction of infinite families of strongly regular digraphs with parameters $((v (2^{n 1}-4)t)2^{n-1}, k (2^n-2)t, t, \lambda, t)$
Viktor A. Byzov, Igor A. Pushkarev
https://arxiv.org/abs/2509.25425

Explicit construction of infinite families of strongly regular digraphs with parameters $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$
An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$ is described. A computer program was used to find the initial digraphs. The remaining terms of the sequence are obtained by the constructed recurrence. Using the described approach, 11 families of strongly regular digraphs were found. In particular, these families contain digraphs $\text{dsrg}(72, 18, 5, 3, 5)$, $\text{dsrg}(76, 19, 5, 4, 5)$, $\text{…

On the structure of solutions graph of the Markoff-Hurwitz equation and recurrence sequences
Ilya V. Vyugin
https://arxiv.org/abs/2509.19289 https://arxiv.…

Delsarte duality on subspaces and applications to rank-metric codes and q-matroids
Martino Borello, Olga Polverino, Ferdinando Zullo
https://arxiv.org/abs/2509.24409 https://

Delsarte duality on subspaces and applications to rank-metric codes and q-matroids
We study the interplay between the lattice of F_{q^m}-subspaces and the lattice of F_{q^m}-subspaces of an F_{q^m}-vector space. Introducing notions of weight and defect relative to an F_q-subspace, we analyze the sequence of maximum non-zero defects. We establish a correspondence between subspaces of positive defect and their Delsarte duals, enabling explicit characterizations of the associated sequences of maximum non-zero defects. Our framework unifies several classes of subspaces studied in…

On Finite Pseudorandom Binary Sequences: Generalized polynomials
Manfred G. Madritsch, Robert F. Tichy
https://arxiv.org/abs/2509.19810 https://arxiv.org/p…

On Finite Pseudorandom Binary Sequences: Generalized polynomials
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but also the floor function. We estimate the well-distribution measure, looking at the ``randomness'' along arithmetic progressions.

Totally positive Toeplitz matrices: classical and modern
Konstanze Rietsch
https://arxiv.org/abs/2509.25163 https://arxiv.org/pdf/2509.25163

Totally positive Toeplitz matrices: classical and modern
By a theorem of Edrei, an infinite, normalised totally nonnegative upper-triangular Toeplitz matrices is determined by a pair of nonnegative parameter sequences, the `Schoenberg parameters', where nonzero parameters correspond to the roots and poles of a naturally associated generating function. These totally nonnegative Toeplitz matrices and their parameters also arise in the classification of characters of the infinite symmetric group by later work of Thoma. Moreover the Schoenberg parameters…

Extremal Bounds on the Properties of Sigma and Albertson Indices for Non-Decreasing Degree Sequences
Jasem Hamoud, Duaa Abdullah
https://arxiv.org/abs/2509.19291 https://…

Schur log-concavity and the quantum Pascal triangle
\'Alvaro Guti\'errez, Christian Krattenthaler
https://arxiv.org/abs/2509.22648 https://arxiv.or…

Schur log-concavity and the quantum Pascal triangle
We say a sequence $f_0, f_1, f_2, \ldots$ of symmetric functions is Schur log-concave if $f_n^2 - f_{n-1}f_{n+1}$ is Schur positive for all $n\ge1$. We conjecture that a very general class of sequences of Schur functions satisfies this property, and show it for sequences of Schur functions indexed by partitions with growing first part and column. Our findings are related to work of Lam, Postnikov and Pylyavskyy on Schur positivity, and of Butler, Sagan, and the second author on $q$-log-concavit…

Ramsey sequences with bounded clique size
Abhishek Girish Aher, Aparna Lakshmanan S
https://arxiv.org/abs/2509.23929 https://arxiv.org/pdf/2509.23929

Ramsey sequences with bounded clique size
A sequence of graphs $ \{G_k\} $ is a Ramsey sequence if for every positive integer $ k $, the graph $ G_k $ is a proper subgraph of $ G_{k+1} $, and there exists an integer $n > k$ such that every red-blue coloring of $ G_n $ contains a monochromatic copy of $ G_k $. Among the wide range of open problems in Ramsey theory, an interesting open question is ``Does there exist an ascending sequence $\{G_k\}$ with $\lim_{k \to \infty} χ(G_k) = \infty$ and $\lim_{k \to \infty} ω(G_k) \neq \infty$ t…