Tootfinder

Wrote up a nice little macro in @… to illustrate "anonymous recursive functions" Š la PowerShell.
https://github.com/shriram/anonymous-r

GitHub - shriram/anonymous-recursive-function: Anonymous recursive functions in Racket
Anonymous recursive functions in Racket. Contribute to shriram/anonymous-recursive-function development by creating an account on GitHub.

ForTIFAI: Fending Off Recursive Training Induced Failure for AI Models
Soheil Zibakhsh Shabgahi, Pedram Aghazadeh, Azalia Mirhosseini, Farinaz Koushanfar
https://arxiv.org/abs/2509.08972

ForTIFAI: Fending Off Recursive Training Induced Failure for AI Models
The increasing reliance on generative AI models has accelerated the generation rate of synthetic data, with some projections suggesting that most available new data for training could be machine-generated by 2030. This shift to a mainly synthetic content presents a critical challenge: repeated training in synthetic data leads to a phenomenon known as model collapse, where model performance degrades over generations of training, eventually rendering the models ineffective. Although prior studies…

An algorithm for the Product-Sum Equality
Hlib Husarov, Eberhard Mayerhofer
https://arxiv.org/abs/2508.09647 https://arxiv.org/pdf/2508.09647

An algorithm for the Product-Sum Equality
We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution. The algorithm is efficient, with a time complexity similar to the quick sort algorithm.

Recursive Aperture Decoded Ultrasound Imaging (READI) With Estimated Motion-Compensated Compounding (EMC2)
Tyler Keith Henry, Darren Dahunsi, Randy Palamar, Negar Majidi, Mohammad Rahim Sobhani, Roger Zemp
https://arxiv.org/abs/2509.08781

Recursive Aperture Decoded Ultrasound Imaging (READI) With Estimated Motion-Compensated Compounding (EMC2)
Fast Orthogonal Row-Column Electronic Scanning (FORCES) is a Hadamard-encoded Synthetic Transmit Aperture (STA) imaging sequence using bias-sensitive Top-Orthogonal to Bottom Electrode (TOBE) arrays. It produces images with a higher Signal-to-Noise Ratio (SNR) and improved penetration depth compared to traditional STA techniques, but suffers from motion sensitivity due to ensemble size and aperture encoding. This work presents Recursive Aperture Decoded Ultrasound Imaging (READI), a novel decod…

Perspective Chapter: Insights from Kalman Filtering with Correlated Noises Recursive Least-Square Algorithm for State and Parameter Estimation
Abd El Mageed Hag Elamin Khalid
https://arxiv.org/abs/2507.07588

Perspective Chapter: Insights from Kalman Filtering with Correlated Noises Recursive Least-Square Algorithm for State and Parameter Estimation
This article explores the estimation of parameters and states for linear stochastic systems with deterministic control inputs. It introduces a novel Kalman filtering approach called Kalman Filtering with Correlated Noises Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which leverages the cross-correlation between process noise and measurement noise in Kalman filtering cycles to jointly estimate both parameters and system states. The study also investigates the theoretical…

Sample-Efficient Online Control Policy Learning with Real-Time Recursive Model Updates
Zixin Zhang, James Avtges, Todd D. Murphey
https://arxiv.org/abs/2509.08241 https://

Sample-Efficient Online Control Policy Learning with Real-Time Recursive Model Updates
Data-driven control methods need to be sample-efficient and lightweight, especially when data acquisition and computational resources are limited -- such as during learning on hardware. Most modern data-driven methods require large datasets and struggle with real-time updates of models, limiting their performance in dynamic environments. Koopman theory formally represents nonlinear systems as linear models over observables, and Koopman representations can be determined from data in an optimizat…

Recursive vectorized computation of the Frobenius norm
Vedran Novakovi\'c
https://arxiv.org/abs/2509.06220 https://arxiv.org/pdf/2509.06220

Recursive vectorized computation of the Frobenius norm
Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on hypot, a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine DNRM2 it is shown that the proposed algorithms could in many cases be significantly more accurate. The scalar recursive algorithms are vectorized with the Intel's vector instructions to achieve performance comparable to xNRM2, and are further parallelized with OpenCilk. Some scalar algorithms are uncond…

Recursive Adaptive Importance Sampling with Optimal Replenishment
Daniel W\"urzler Barreto, Mevin B. Hooten
https://arxiv.org/abs/2509.08102 https://a…

Recursive Adaptive Importance Sampling with Optimal Replenishment
Increased access to computing resources has led to the development of algorithms that can run efficiently on multi-core processing units or in distributed computing environments. In the context of Bayesian inference, many parallel computing approaches to fit statistical models have been proposed in the context of Markov Chain Monte Carlo methods, but they either have limited gains due to high latency cost or rely on model-specific decompositions. Alternatively, adaptive importance sampling, seq…

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping
E. Rule, I. A. Chernyshev, I. Stetcu, J. Carlson, R. Weiss
https://arxiv.org/abs/2509.07279

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping
We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $N$ particles and $N_s$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O…

Knowledge Collapse in LLMs: When Fluency Survives but Facts Fail under Recursive Synthetic Training
Figarri Keisha, Zekun Wu, Ze Wang, Adriano Koshiyama, Philip Treleaven
https://arxiv.org/abs/2509.04796

Knowledge Collapse in LLMs: When Fluency Survives but Facts Fail under Recursive Synthetic Training
Large language models increasingly rely on synthetic data due to human-written content scarcity, yet recursive training on model-generated outputs leads to model collapse, a degenerative process threatening factual reliability. We define knowledge collapse as a distinct three-stage phenomenon where factual accuracy deteriorates while surface fluency persists, creating "confidently wrong" outputs that pose critical risks in accuracy-dependent domains. Through controlled experiments with recursiv…

Raqlet: Cross-Paradigm Compilation for Recursive Queries
Amir Shaikhha, Youning Xia, Meisam Tarabkhah, Jazal Saleem, Anna Herlihy
https://arxiv.org/abs/2508.03978 https://

Raqlet: Cross-Paradigm Compilation for Recursive Queries
We introduce Raqlet, a source-to-source compilation framework that addresses the fragmentation of recursive querying engines spanning relational (recursive SQL), graph (Cypher, GQL), and deductive (Datalog) systems. Recent standards such as SQL:2023's SQL/PGQ and the GQL standard provide a common foundation for querying graph data within relational and graph databases; however, real-world support remains inconsistent across systems. Raqlet bridges this gap by translating recursive queries acros…

A Recursive Algorithm for Multi-Coefficient Inversion in Nonlinear Helmholtz Equations
Shuai LU, Boxi XU
https://arxiv.org/abs/2509.06008 https://arxiv.org…

A Recursive Algorithm for Multi-Coefficient Inversion in Nonlinear Helmholtz Equations
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive decoupling and simultaneous recovery of multiple coefficients, we develop a novel Fourier-based approach that combines the principle of inclusion-exclusion with carefully constructed complex exponential solutions. This methodology not only ensures unique identif…

Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems
Hui Li, Yanxin Li
https://arxiv.org/abs/2509.05567 https://…

Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems
Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\to$ module $\to$ system $\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irrevers…

Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations
Ying Hu, Guomin Liu, Shanjian Tang
https://arxiv.org/abs/2507.06118

Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations
This paper aims to study the relationship between the maximum principle and the dynamic programming principle for recursive optimal control problem of stochastic evolution equations, where the control domain is not necessarily convex and the value function may be nonsmooth. By making use of the notion of conditionally expected operator-valued backward stochastic integral equations, we establish a connection between the first and second-order adjoint processes in MP and the general derivatives o…

FractalPINN-Flow: A Fractal-Inspired Network for Unsupervised Optical Flow Estimation with Total Variation Regularization
Sara Behnamian, Rasoul Khaksarinezhad, Andreas Langer
https://arxiv.org/abs/2509.08670

FractalPINN-Flow: A Fractal-Inspired Network for Unsupervised Optical Flow Estimation with Total Variation Regularization
We present FractalPINN-Flow, an unsupervised deep learning framework for dense optical flow estimation that learns directly from consecutive grayscale frames without requiring ground truth. The architecture centers on the Fractal Deformation Network (FDN) - a recursive encoder-decoder inspired by fractal geometry and self-similarity. Unlike traditional CNNs with sequential downsampling, FDN uses repeated encoder-decoder nesting with skip connections to capture both fine-grained details and long…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- A Random Walk Approach to Broadcasting on Random Recursive Trees
Ernst Althaus, Lisa Hartung, Rebecca Steiner

Replaced article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- A Random Walk Approach to Broadcasting on Random Recursive Trees
Ernst Althaus, Lisa Hartung, Rebecca Steiner

Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
Simon Barazer
https://arxiv.org/abs/2507.07308 https://…

Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
In this paper, we investigate the algebraic structure underlying the acyclic decomposition. This decomposition applies to directed metric ribbon graphs and enables the recursive computation of the volumes of their moduli spaces. Building on this, we define integral operators with these volumes and show that they satisfy a Cut-and-Join type equation. Furthermore, we demonstrate that a suitable specialization of these operators gives rise to a generating series for \textit{dessins d'enfants}.

Recursive relations for 2-variable weighted shifts
Edward L. White
https://arxiv.org/abs/2507.02163 https://arxiv.org/pdf/2507.02163

Recursive relations for 2-variable weighted shifts
In this paper, we outline a method to determine all recursive relations for a subnormal 2-variable weighted shift, up to total degree $k$, entirely from the representing measure. This allows us to show that the densities of the atoms do not affect the recursive relations. We then show that this method can be used to explicitly construct a Gröbner basis for the ideal of recursive relations.

IBN: An Interpretable Bidirectional-Modeling Network for Multivariate Time Series Forecasting with Variable Missing
Shusen Ma, Tianhao Zhang, Qijiu Xia, Yun-Bo Zhao
https://arxiv.org/abs/2509.07725

IBN: An Interpretable Bidirectional-Modeling Network for Multivariate Time Series Forecasting with Variable Missing
Multivariate time series forecasting (MTSF) often faces challenges from missing variables, which hinder conventional spatial-temporal graph neural networks in modeling inter-variable correlations. While GinAR addresses variable missing using attention-based imputation and adaptive graph learning for the first time, it lacks interpretability and fails to capture more latent temporal patterns due to its simple recursive units (RUs). To overcome these limitations, we propose the Interpretable Bidi…

Furthering Free-Fermion Findability From Fratricides
Jannis Ruh, Samual J. Elman
https://arxiv.org/abs/2509.09092 https://arxiv.org/pdf/2509.09092

Furthering Free-Fermion Findability From Fratricides
We present a novel graph-theoretic approach to simplifying generic many-body Hamiltonians. Our primary result introduces a recursive twin-collapse algorithm, leveraging the identification and elimination of symmetric vertex pairs (twins), as well as line-graph modules, within the frustration graph of the Hamiltonian. This method systematically block-diagonalizes Hamiltonians, significantly reducing complexity while preserving the energetic spectrum. Importantly, our approach expands the class o…

An explicit algorithm for the Higman Embedding Theorem
V. H. Mikaelian
https://arxiv.org/abs/2507.04347 https://arxiv.org/pdf/2507.04…

An explicit algorithm for the Higman Embedding Theorem
We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its generators and defining relations. This is the explicit analogue of the remarkable Higman Embedding Theorem stating that a finitely generated group $G$ is embeddable into a finitely presented group if and only if $G$ is recursive. The constructed finitely presen…

Constrained Recursive Logit for Route Choice Analysis
Hung Tran, Tien Mai, Minh Ha Hoang
https://arxiv.org/abs/2509.01595 https://arxiv.org/pdf/2509.01595

Constrained Recursive Logit for Route Choice Analysis
The recursive logit (RL) model has become a widely used framework for route choice modeling, but it suffers from a key limitation: it assigns nonzero probabilities to all paths in the network, including those that are unrealistic, such as routes exceeding travel time deadlines or violating energy constraints. To address this gap, we propose a novel Constrained Recursive Logit (CRL) model that explicitly incorporates feasibility constraints into the RL framework. CRL retains the main advantages …

Fibonacci sequences in $\mathbb F_p$
Menny Aka
https://arxiv.org/abs/2508.08016 https://arxiv.org/pdf/2508.08016 …

Fibonacci sequences in $\mathbb F_p$
We prove a conjecture due to Gica (Fibonacci Quarterly, 2008). Our proof is simple, uses only elementary abstract algebra, and generalizes to other recursive sequences.

A Novel On-Shell Recursive Relation
Humberto Gomez
https://arxiv.org/abs/2507.23510 https://arxiv.org/pdf/2507.23510

A Novel On-Shell Recursive Relation
We present a novel framework for deriving on-shell recursion relations, with a specific focus on biadjoint and pure Yang-Mills theories. Starting from the double-cover CHY factorization formulae, we identify a suitable set of independent kinematic variables that enables the reconstruction of amputated currents from amplitudes. As a byproduct, this new recursive structure recasts the BCJ numerators into an explicitly on-shell factorized form.

Ghost in the Machine: Examining the Philosophical Implications of Recursive Algorithms in Artificial Intelligence Systems
Llewellin RG Jegels
https://arxiv.org/abs/2507.01967

Ghost in the Machine: Examining the Philosophical Implications of Recursive Algorithms in Artificial Intelligence Systems
This paper investigates whether contemporary AI architectures employing deep recursion, meta-learning, and self-referential mechanisms provide evidence of machine consciousness. Integrating philosophical history, cognitive science, and AI engineering, it situates recursive algorithms within a lineage spanning Cartesian dualism, Husserlian intentionality, Integrated Information Theory, the Global Workspace model, and enactivist perspectives. The argument proceeds through textual analysis, compar…

RTQA : Recursive Thinking for Complex Temporal Knowledge Graph Question Answering with Large Language Models
Zhaoyan Gong, Juan Li, Zhiqiang Liu, Lei Liang, Huajun Chen, Wen Zhang
https://arxiv.org/abs/2509.03995

RTQA : Recursive Thinking for Complex Temporal Knowledge Graph Question Answering with Large Language Models
Current temporal knowledge graph question answering (TKGQA) methods primarily focus on implicit temporal constraints, lacking the capability of handling more complex temporal queries, and struggle with limited reasoning abilities and error propagation in decomposition frameworks. We propose RTQA, a novel framework to address these challenges by enhancing reasoning over TKGs without requiring training. Following recursive thinking, RTQA recursively decomposes questions into sub-problems, solves …

A strategy to avoid particle depletion in recursive Bayesian inference
Henry R. Scharf
https://arxiv.org/abs/2508.01572 https://arxiv.org/pdf/2508.01572

A strategy to avoid particle depletion in recursive Bayesian inference
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration becomes the prior for the next, beliefs are updated sequentially instead of all-at-once. Thus, recursive inference is relevant for both streaming data and settings where data too numerous to be analyzed together can be partitioned into manageable pieces. In prac…

Efficient adaptive randomized algorithms for fixed-threshold low-rank matrix approximation
Qiaohua Liu, Yuejuan Yu
https://arxiv.org/abs/2508.07553 https://

Efficient adaptive randomized algorithms for fixed-threshold low-rank matrix approximation
The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized rank-revealing algorithm of the data matrix $A$, in which the basis matrix $Q$ of the approximate range space is adaptively built block by block, through a recursive deflation procedure on $A$. Detailed analysis of randomized projection schemes are provided to analyz…

Refined floor diagrams relative to a conic and Caporaso-Harris type formula
Yanqiao Ding, Jianxun Hu
https://arxiv.org/abs/2509.06004 https://arxiv.org/pdf…

Refined floor diagrams relative to a conic and Caporaso-Harris type formula
We prove a $q$-refined correspondence theorem between higher genus relative Gromov-Witten invariants with a Lambda class $λ_{g-g'}$ insertion in the blow-up of $\mathbb{P}^2$ at $k$ points on a conic and the refined counts of genus $g'$ floor diagrams relative to a conic, after the change of variables $q=e^{iu}$. We provide a Caporaso-Harris type recursive formula for the refined counts of higher genus floor diagrams. As an application of the correspondence theorem, we propose a higher genus v…

Semantically Separating Nominal Wyvern for Usability and Decidability
Yu Xiang Zhu, Amos Robinson, Sophia Roshal, Timothy Mou, Julian Mackay, Jonathan Aldrich, Alex Potanin
https://arxiv.org/abs/2507.03867

Semantically Separating Nominal Wyvern for Usability and Decidability
The Dependent Object Types (DOT) calculus incorporates concepts from functional languages (e.g. modules) with traditional object-oriented features (e.g. objects, subtyping) to achieve greater expressivity (e.g. F-bounded polymorphism). However, this merger of paradigms comes at the cost of subtype decidability. Recent work on bringing decidability to DOT has either sacrificed expressiveness or ease of use. The unrestricted construction of recursive types and type bounds has made subtype decidab…

Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems
Marius Lemm, Bruno Nachtergaele, Simone Warzel, Amanda Young
https://arxiv.org/abs/2507.18814

Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems
We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A se…

Replaced article(s) found for q-fin.PR. https://arxiv.org/list/q-fin.PR/new
[1/1]:
- A recursive formula for the $n^\text{th}$ survival function and the $n^\text{th}$ first passage t...
Alessio Lapolla

I just used recursive routing on my @… to automatically switch to using a USB 4g dongle when the main fiber connection goes down.
I'm a networking GOD i say!
Not really, but this is very cool. My work vpn does not even need to be restarted, this is awesome!

Synchronization and Applications of Piecewise Recursive Sequences with Dynamic Thresholds
Slimane Alaoui Soulimani Valenti
https://arxiv.org/abs/2507.19605 https://

Synchronization and Applications of Piecewise Recursive Sequences with Dynamic Thresholds
We investigate piecewise recursive sequences where both the sequence and its switching threshold evolve dynamically. We consider coupled evolution: $a_{n+1} = f(a_n)$ if $a_n \leq c_n$, otherwise $a_{n+1} = g(a_n)$, with threshold $c_{n+1} = h(a_n, c_n)$. Our analysis reveals that when an orbit switches between regimes infinitely often and both sequences converge, they appear to converge to the same limit (Common Limit Theorem). For linear systems, we identify five possible dynamical behaviors:…

The Recursive Panopticon Hypothesis
Xiaoyu Yan
https://arxiv.org/abs/2509.02625 https://arxiv.org/pdf/2509.02625 …

The Recursive Panopticon Hypothesis
The cosmic "Great Silence" revealed by the Fermi paradox remains a central puzzle in contemporary science. Existing explanations such as the "Big Filter," "Zoo Hypothesis," and "Dark Forest" theory are trapped in isolated frameworks of "hypothesis list paradigm" that resist falsification. This paper proposes the "Recursive Panopticon Hypothesis" arguing that under the uncertainty of recursive higher-order deterrence, cosmic civilizations will universally adopt "silence" as their optimal surviva…

Crosslisted article(s) found for physics.chem-ph. https://arxiv.org/list/physics.chem-ph/new
[1/1]:
- Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping
E. Rule, I. A. Chernyshev, I. Stetcu, J. Carlson, R. Weiss

When are two algorithms the same? Towards addressing Hilbert's 24th problem
Konstantin Doubrovinski
https://arxiv.org/abs/2508.02764 https://arxiv.org/…

When are two algorithms the same? Towards addressing Hilbert's 24th problem
The informal question of when two theorem proofs are "essentially the same" goes back to David Hilbert, who considered adding it (or something largely equivalent) to his famous list of open problems, but eventually decided to leave it out. Given that the notion of a formal proof is closely related to that of a (computer) program, i.e. a recursive function, it may be useful to ask the same question with regard to programs instead. Here we propose a minimalistic approach to this question within R…

Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
Binhui Zhang, Jianwei Ma
https://arxiv.org/abs/2508.19750 https://…

Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing flow architecture that enhances both expressiveness and interpretability through two key innovations. First, we integrate Kolmogorov-Arnold Networks and incorporate Latent Dirichlet Allocation into normalizing flows to construct a structured, interpretable lat…

RPKT: Learning What You Don't -- Know Recursive Prerequisite Knowledge Tracing in Conversational AI Tutors for Personalized Learning
Jinwen Tang, Qiming Guo, Zhicheng Tang
https://arxiv.org/abs/2508.11892

RPKT: Learning What You Don't -- Know Recursive Prerequisite Knowledge Tracing in Conversational AI Tutors for Personalized Learning
Educational systems often assume learners can identify their knowledge gaps, yet research consistently shows that students struggle to recognize what they don't know they need to learn-the "unknown unknowns" problem. This paper presents a novel Recursive Prerequisite Knowledge Tracing (RPKT) system that addresses this challenge through dynamic prerequisite discovery using large language models. Unlike existing adaptive learning systems that rely on pre-defined knowledge graphs, our approach rec…

A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions
Toan Huynh, Ruth Lopez Fajardo, Guannan Zhang, Lili Ju, Feng Bao
https://arxiv.org/abs/2508.06834

A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governin…

Self-consistent moment dynamics for networks of spiking neurons
Gianni Valerio Vinci, Roberto Benzi, Maurizio Mattia
https://arxiv.org/abs/2507.05117 https…

Self-consistent moment dynamics for networks of spiking neurons
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we derive the recursive and nonlinear relation between the moments, such as the mean potential, and the population firing rates. The self-consistent dynamics found relies on the dominant eigenvalues of the evolution operator, tightly related to the moments of t…

The Post Science Paradigm of Scientific Discovery in the Era of Artificial Intelligence: Modelling the Collapse of Ideation Costs, Epistemic Inversion, and the End of Knowledge Scarcity
Christian William Callaghan
https://arxiv.org/abs/2507.07019

The Post Science Paradigm of Scientific Discovery in the Era of Artificial Intelligence: Modelling the Collapse of Ideation Costs, Epistemic Inversion, and the End of Knowledge Scarcity
This paper develops a theoretical and formal response to the collapse in the marginal cost of ideation caused by artificial intelligence (AI). In challenging the foundational assumption of knowledge scarcity, the paper argues that the key economic constraint is no longer the generation of ideas, but the alignment of ideation with the recursive structure of human needs. Building on previous work, we further develop Experiential Matrix Theory (EMT), a framework that models innovation as a recursi…

Efficient algorithm for linear diophantine equations in two variables
Mayank Deora, Pinakpani Pal
https://arxiv.org/abs/2507.23216 https://arxiv.org/pdf/25…

Efficient algorithm for linear diophantine equations in two variables
Solving linear diophantine equations in two variables have applications in computer science and mathematics. In this paper, we revisit an algorithm for solving linear diophantine equations in two variables, which we refer as DEA-R algorithm. The DEA-R algorithm always incurs equal or less number of recursions or recursive calls as compared to extended euclidean algorithm. With the objective of taking advantage of the less number of recursive calls , we propose an optimized version of the DEA-R …

REALM: Recursive Relevance Modeling for LLM-based Document Re-Ranking
Pinhuan Wang, Zhiqiu Xia, Chunhua Liao, Feiyi Wang, Hang Liu
https://arxiv.org/abs/2508.18379 https://

REALM: Recursive Relevance Modeling for LLM-based Document Re-Ranking
Large Language Models (LLMs) have shown strong capabilities in document re-ranking, a key component in modern Information Retrieval (IR) systems. However, existing LLM-based approaches face notable limitations, including ranking uncertainty, unstable top-k recovery, and high token cost due to token-intensive prompting. To effectively address these limitations, we propose REALM, an uncertainty-aware re-ranking framework that models LLM-derived relevance as Gaussian distributions and refines them…

Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
https://arxiv.org/abs/2508.02303

Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence
We introduce a recursive theory that completely axiomatizes the structure $\langle \mathbb{Z},<, +,f,0\rangle$ where $f$ is the function that maps each $x$ to the integer part of $φx $, with $φ$ the golden ratio. We prove that our axiomatization is model-complete in a language expanded with a function which we call the Fibonacci floor function, as defined in the introduction. We also present an improvement of the axiomatization of the structure $\langle \mathbb{Z}, +, f,0\rangle$ already stud…

Receding Horizon Recursive Location Estimation
Xu Weng, K. V. Ling, Ling Zhao
https://arxiv.org/abs/2506.18430 https://arxiv.org/pdf/…

Receding Horizon Recursive Location Estimation
This paper presents a recursive solution to the receding or moving horizon estimation (MHE) problem for nonlinear time-variant systems. We provide the conditions under which the recursive MHE is equivalent to the extended Kalman filter (EKF), regardless of the horizon size. Theoretical and empirical evidence is also provided. Moreover, we clarify the connection between MHE and factor graph optimization (FGO). We apply the recursive MHE to GNSS localization and evaluate its performance using pub…

Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification
Hassan Mortada, Cyril Falcon, Yanis Kahil, Math\'eo Clavaud, Jean-Philippe Michel
https://arxiv.org/abs/2506.11639

Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Our approach propaga…

Hyperbolic tiling neighborhoods in O(1) time
Yanick Thurn, Manuel Schrauth, Johanna Erdmenger
https://arxiv.org/abs/2508.04765 https://arxiv.org/pdf/2508.0…

Hyperbolic tiling neighborhoods in O(1) time
Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive algorithms, which are fundamentally limited: they do not readily yield the neighborhood graph representing cell adjacencies, which is however required for many applications. We introduce a novel approach that allows to build hyperbolic tilings and their associated gr…

Newton-Flow Particle Filters based on Generalized Cram\'er Distance
Uwe D. Hanebeck
https://arxiv.org/abs/2509.00182 https://arxiv.org/pdf/2509.00182…

Newton-Flow Particle Filters based on Generalized Cramér Distance
We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a likelihood function is used for representing the measurement and its uncertainty. This likelihood is progressively introduced into the filtering procedure by homotopy continuation over an artificial time. A generalized Cramér distance between particle sets is der…

Bayesian online collective anomaly and change point detection in fine-grained time series
Xian Chen, Weichi Wu
https://arxiv.org/abs/2508.06385 https://arx…

Bayesian online collective anomaly and change point detection in fine-grained time series
Fine-grained time series data are crucial for accurate and timely online change detection. While both collective anomalies and change points can coexist in such data, their joint online detection has received limited attention. In this research, we develop a Bayesian framework capturing time series with collective anomalies and change points, and introduce a recursive online inference algorithm to detect the most recent collective anomaly and change point jointly. For scaling, we further propos…

Robust Recursive Query Parallelism in Graph Database Management Systems
Anurag Chakraborty, Semih Saliho\u{g}lu
https://arxiv.org/abs/2508.19379 https://ar…

Robust Recursive Query Parallelism in Graph Database Management Systems
Efficient multi-core parallel processing of recursive join queries is critical for achieving good performance in graph database management systems (GDBMSs). Prior work adopts two broad approaches. First is the state of the art morsel-driven parallelism, whose vanilla application in GDBMSs parallelizes computations at the source node level. Second is to parallelize each iteration of the computation at the frontier level. We show that these approaches can be seen as part of a design space of mors…

On multi-propagator angular integrals
Juliane Haug, Vladimir A. Smirnov, Fabian Wunder
https://arxiv.org/abs/2508.00693 https://arxiv.org/pdf/2508.00693

On multi-propagator angular integrals
We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed unitarity. We present an Euler integral representation similar to Lee-Pomeransky representation and explicitly describe a recursive IBP reduction and dimensional shift relations for the general case of $n$ denominators. On the level of master integrals, applying a…

Crosslisted article(s) found for nlin.AO. https://arxiv.org/list/nlin.AO/new
[1/1]:
- Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Co...
Hui Li, Yanxin Li

G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem
Wei He, Qiangjun Tang
https://arxiv.org/abs/2508.17731 https://…

G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem
In this paper, we study the existence and uniqueness of solutions to a class of non-Lipschitz G-BSDEs and the corresponding stochastic recursive optimal control problem. More precisely, we suppose that the generator of G-BSDE is uniformly continuous and monotonic with respect to the first unknown variable. Using the comparison theorem for G-BSDE and the stability of viscosity solutions, we establish the dynamic programming principle and the connection between the value function and the viscosit…

A recursive formula for the $n^\text{th}$ survival function and the $n^\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\text{th}$-to-default CDS
Alessio Lapolla
https://arxiv.org/abs/2509.02347

A recursive formula for the $n^\text{th}$ survival function and the $n^\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\text{th}$-to-default CDS
We derive some rather general, but complicated, formulae to compute the survival function and the first passage time distribution of the $n^\text{th}$ coordinate of a many-body stochastic process in the presence of a killing barrier. First we will study the case of two coordinates and then we will generalize the results to three or more coordinates. Even if the results are difficult to implement, we will provide examples of their use applying them to a physical system, the single file diffusion…

Solvable Tuple Patterns and Their Applications to Program Verification
Naoki Kobayashi, Ryosuke Sato, Ayumi Shinohara, Ryo Yoshinaka
https://arxiv.org/abs/2508.20365 https://

Solvable Tuple Patterns and Their Applications to Program Verification
Despite the recent progress of automated program verification techniques, fully automated verification of programs manipulating recursive data structures remains a challenge. We introduce the notion of solvable tuple patterns (STPs) to express invariants between list-like recursive data structures. A distinguishing feature of STPs is that they can be efficiently inferred from only a small number of positive samples; no negative samples are required. An SMT solver that supports the sequence theo…

Consistent DAG selection for Bayesian causal discovery under general error distributions
Anamitra Chaudhuri, Anirban Bhattacharya, Yang Ni
https://arxiv.org/abs/2508.00993 https…

Consistent DAG selection for Bayesian causal discovery under general error distributions
We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated errors being independent and allowed to be non-Gaussian. A Bayesian hierarchical model is proposed to identify the true data-generating directed acyclic graph (DAG) structure where the nodes and edges represent the variables and the direct causal effects, respecti…

Harnessing Batched BLAS/LAPACK Kernels on GPUs for Parallel Solutions of Block Tridiagonal Systems
David Jin, Alexis Montoison, Sungho Shin
https://arxiv.org/abs/2509.03015 http…

Harnessing Batched BLAS/LAPACK Kernels on GPUs for Parallel Solutions of Block Tridiagonal Systems
We present a GPU implementation for the factorization and solution of block-tridiagonal symmetric positive definite linear systems, which commonly arise in time-dependent estimation and optimal control problems. Our method employs a recursive algorithm based on Schur complement reduction, transforming the system into a hierarchy of smaller, independent blocks that can be efficiently solved in parallel using batched BLAS/LAPACK routines. While batched routines have been used in sparse solvers, o…

High-Order Deep Meta-Learning with Category-Theoretic Interpretation
David H. Mguni
https://arxiv.org/abs/2507.02634 https://arxiv.or…

High-Order Deep Meta-Learning with Category-Theoretic Interpretation
We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative mechanism that creates \emph{virtual tasks} -- synthetic problem instances designed to enable the meta-learner to learn \emph{soft constraints} and unknown generalisable rules across related tasks. Crucially, this enables the framework to generate its own infor…

A Recursive Total Least Squares Solution for Bearing-Only Target Motion Analysis and Circumnavigation
Lin Li, Xueming Liu, Zhoujingzi Qiu, Tianjiang Hu, Qingrui Zhang
https://arxiv.org/abs/2508.11289

A Recursive Total Least Squares Solution for Bearing-Only Target Motion Analysis and Circumnavigation
Bearing-only Target Motion Analysis (TMA) is a promising technique for passive tracking in various applications as a bearing angle is easy to measure. Despite its advantages, bearing-only TMA is challenging due to the nonlinearity of the bearing measurement model and the lack of range information, which impairs observability and estimator convergence. This paper addresses these issues by proposing a Recursive Total Least Squares (RTLS) method for online target localization and tracking using mo…

Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem
Martin Hutzenthaler, Tuan Anh Nguyen
https://arxiv.org/abs/2506.23969

Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem
Full history recursive multilevel Picard (MLP) approximations have been proved to overcome the curse of dimensionality in the numerical approximation of semilinear heat equations with nonlinearities which are globally Lipschitz continuous with respect to the maximum-norm. Nonlinearities in Hamilton-Jacobi-Bellman equations in stochastic control theory, however, are often (locally) Lipschitz continuous with respect to the standard Euclidean norm. In this paper we prove the surprising fact that M…

Horus: A Protocol for Trustless Delegation Under Uncertainty
David Shi, Kevin Joo
https://arxiv.org/abs/2507.00631 https://arxiv.org/…

Horus: A Protocol for Trustless Delegation Under Uncertainty
Correctness is an emergent property of systems where exposing error is cheaper than committing it. In dynamic, low-trust environments, autonomous AI agents benefit from delegating work to sub-agents, yet correctness cannot be assured through upfront specification or centralized oversight. We propose a protocol that enforces correctness through collateralized claims in a recursive verification game. Tasks are published as intents, and solvers compete to fulfill them. Selected solvers carry out t…

TAGF: Time-aware Gated Fusion for Multimodal Valence-Arousal Estimation
Yubeen Lee, Sangeun Lee, Chaewon Park, Junyeop Cha, Eunil Park
https://arxiv.org/abs/2507.02080

TAGF: Time-aware Gated Fusion for Multimodal Valence-Arousal Estimation
Multimodal emotion recognition often suffers from performance degradation in valence-arousal estimation due to noise and misalignment between audio and visual modalities. To address this challenge, we introduce TAGF, a Time-aware Gated Fusion framework for multimodal emotion recognition. The TAGF adaptively modulates the contribution of recursive attention outputs based on temporal dynamics. Specifically, the TAGF incorporates a BiLSTM-based temporal gating mechanism to learn the relative impor…

Recursive Variational Autoencoders for 3D Blood Vessel Generative Modeling
Paula Feldman, Miguel Fainstein, Viviana Siless, Claudio Delrieux, Emmanuel Iarussi
https://arxiv.org/abs/2506.14914

Recursive Variational Autoencoders for 3D Blood Vessel Generative Modeling
Anatomical trees play an important role in clinical diagnosis and treatment planning. Yet, accurately representing these structures poses significant challenges owing to their intricate and varied topology and geometry. Most existing methods to synthesize vasculature are rule based, and despite providing some degree of control and variation in the structures produced, they fail to capture the diversity and complexity of actual anatomical data. We developed a Recursive variational Neural Network…

Combination generators with optimal cache utilization and communication free parallel execution
Xi He, Max. A. Little
https://arxiv.org/abs/2507.03980 http…

Combination generators with optimal cache utilization and communication free parallel execution
We introduce an efficient and elegant combination generator for producing all combinations of size less than or equal to K, designed for exhaustive generation and combinatorial optimization tasks. This generator can be implemented to achieve what we define as optimal efficiency: constant amortized time, optimal cache utilization, embarrassingly parallel execution, and a recursive structure compatible with pruning-based search. These properties are difficult to satisfy simultaneously in existing…

Recursive relations for the S-matrix of Liouville theory
George Jorjadze, Lado Razmadze, Stefan Theisen
https://arxiv.org/abs/2507.11760 https://

Recursive relations for the S-matrix of Liouville theory
We analyze the relation between the vertex operators of the in and out fields in Liouville theory. This is used to derive equations for the S-matrix, from which a recursive relation for the normal symbol of the S-matrix for discrete center-of-mass momenta is obtained. Its solution is expressed as multiple contour-integrals of a generalized Dotsenko-Fateev type. This agrees with the functional integral representation of the scattering matrix of Liouville theory which we had proposed previously.

Derivation and Verification of Array Sorting by Merging, and its Certification in Dafny
Juan Pablo Carbonell, Jos\'e E. Solsona, Nora Szasz, \'Alvaro Tasistro
https://arxiv.org/abs/2509.01758

Derivation and Verification of Array Sorting by Merging, and its Certification in Dafny
We provide full certifications of two versions of merge sort of arrays in the verification-aware programming language Dafny. We start by considering schemas for applying the divide-and-conquer or partition method of solution to specifications given by pre- and post-conditions involving linear arrays. We then derive the merge sort and merging algorithms as instances of these schemas, thereby arriving at a fully recursive formulation. Further, the analysis of the tree of subproblems arising from …

Recursive-ARX for Grid-Edge Fault Detection
Soufiane El Yaagoubi, Keith Moffat, Eduardo Prieto Araujo, Florian D\"orfler
https://arxiv.org/abs/2506.20011

Recursive-ARX for Grid-Edge Fault Detection
Future electrical grids will require new ways to identify faults as inverters are not capable of supplying large fault currents to support existing fault detection methods and because distributed resources may feed faults from the edge of the grid. This paper proposes the use of real-time system identification for online power-system fault detection. Specifically, we implement Recursive ARX (rARX) system identification on a grid-connected inverter. Experiments demonstrate that the proposed rARX…

Teaching Introductory Functional Programming Using Haskelite
Pedro Vasconcelos (University of Porto)
https://arxiv.org/abs/2508.03640 https://arxiv.org/pdf…

Teaching Introductory Functional Programming Using Haskelite
Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as recursive definitions, algebraic data types and higher-order functions. Step-by-step interpreters have been shown to help beginners by clarifying misconceptions and improving understanding. This paper reports on the experience of using a step-by-step tracing inte…

On vector-valued functional equations with multiple recursive terms
Ioannis Dimitriou
https://arxiv.org/abs/2507.01871 https://arxiv.…

On vector-valued functional equations with multiple recursive terms
In this paper, we study a vector-valued functional equation that arises naturally when we are dealing with vector-valued multiplicative Lindley-type recursions. Our work is strongly motivated by a wide range of semi-Markovian queueing, and autoregressive processes.

Performance Enhancement of the Recursive Least Squares Algorithms with Rank Two Updates
Alexander Stotsky
https://arxiv.org/abs/2507.11095 https://

Performance Enhancement of the Recursive Least Squares Algorithms with Rank Two Updates
New recursive least squares algorithms with rank two updates (RLSR2) that include both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically associated in this report with well-known RLS algorithms with rank one updates. Moreover, new properties (which can be used for further performance improvement) of the recursive algorithms associated with the convergence of the inverse of information matrix …

Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
Jean-Guillaume Dumas (CASC), Cl\'ement Pernet (CASC), Alexandre Sedoglavic (CRIStAL)
https://arxiv.org/abs/2506.19405

Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and accuracy of numerical matrix multiplication. We start by a unification on known max-norm bounds on matrix multiplication stability and then extend them to further norms and more generally to recursive bilinear algorithms and the alternative basis matrix multiplicat…

An Optimization-Free Recursive QAOA for the Binary Paint Shop Problem
Gary J Mooney, Jedwin Villanueva, Bhaskar Roy Radhan, Joydip Ghosh, Charles D Hill, Lloyd C L Hollenberg
https://arxiv.org/abs/2507.10908

An Optimization-Free Recursive QAOA for the Binary Paint Shop Problem
The classical outer optimisation loop of the classical-quantum hybrid Quantum Approximate Optimisation Algorithm (QAOA) can be bypassed by transferring precomputed parameters to larger unseen problem instances using the parameter concentration property found in certain classes of problem instances. In this paper, parameter transfer is applied to the recursive-QAOA (RQAOA) approach of Bravyi et al. implementing the Binary Paint Shop Problem (BPSP) -- an optimisation problem found in manufacturin…

Divisibility criteria and coefficient formulas for cyclotomic polynomials
Laura De Carli, Maurizio Laporta
https://arxiv.org/abs/2508.02722 https://arxiv.o…

Divisibility criteria and coefficient formulas for cyclotomic polynomials
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of our results. Additionally, we provide new insights into the coefficients of cyclotomic polynomials and we propose a recursive relation between the coefficients of two cyclotomic polynomials whose indexes differ by a prime factor.

Robust Recursive Fusion of Multiresolution Multispectral Images with Location-Aware Neural Networks
Haoqing Li, Ricardo Borsoi, Tales Imbiriba, Pau Closas
https://arxiv.org/abs/2506.13733

Robust Recursive Fusion of Multiresolution Multispectral Images with Location-Aware Neural Networks
Multiresolution image fusion is a key problem for real-time satellite imaging and plays a central role in detecting and monitoring natural phenomena such as floods. It aims to solve the trade-off between temporal and spatial resolution in remote sensing instruments. Although several algorithms have been proposed for this problem, the presence of outliers such as clouds downgrades their performance. Moreover, strategies that integrate robustness, recursive operation and learned models are missin…

Replaced article(s) found for eess.SP. https://arxiv.org/list/eess.SP/new
[1/1]:
- Recursive and non-recursive filters for sequential smoothing and prediction with instantaneous ph...
Hugh Lachlan Kennedy

A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of parallel Kinematic Manipulators
Andreas Mueller, Shivesh Kumar, Thomas Kordik
https://arxiv.org/abs/2507.14274

A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of parallel Kinematic Manipulators
Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory control of parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element for this is the computationally efficient evaluation of the second time derivative of the inverse dynamics solution. This has not been presented in the lite…

AI-AI Esthetic Collaboration with Explicit Semiotic Awareness and Emergent Grammar Development
Nicanor I. Moldovan
https://arxiv.org/abs/2508.20195 https://

AI-AI Esthetic Collaboration with Explicit Semiotic Awareness and Emergent Grammar Development
This paper presents the first documented case of artificial intelligence (AI) systems engaging in collaborative esthetic creation through the development of endogenous semiotic protocols. Two interacting large language models (Claude Sonnet 4 and ChatGPT-4o) demonstrated the spontaneous emergence of meta-semiotic awareness, recursive grammar development, and irreducible collaborative esthetic synthesis. The interaction produced novel symbolic operators that functioned as operative grammar proto…

MacMahon's Double Vision: Partition Diamonds Revisited
Matthias Beck, Kobe Wijesekera
https://arxiv.org/abs/2506.23354 https://ar…

MacMahon's Double Vision: Partition Diamonds Revisited
Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's $Ω$-operator in search for integer partition identities. More recently, Dockery, Jameson, Sellers, and Wilson (2024) extended this concept to $d$-fold partition diamonds and found their generating function in a recursive form. We approach $d$-fold partition diamonds via Stanley's (1972) theory of $P$-partitions and give a closed formula for a bivariate generalization of the Dockery…

Recursive characterisation of skew morphisms of finite cyclic groups
Martin Bachrat\'y, Michal Hagara
https://arxiv.org/abs/2506.11626 https://

Recursive characterisation of skew morphisms of finite cyclic groups
A skew morphism of a finite group $G$ is an element $φ$ of $\mathrm{Sym}(G)$ preserving the identity element of $G$ and having the property that for each $a\in G$ there exists a non-negative integer $i_a$ such that $φ(ab)=φ(a)φ^{i_a}(b)$ for all $b\in G$. In this paper we show that if a skew morphism $φ$ of $\mathbb{Z}_n$ is not an automorphism of $\mathbb{Z}_n$, then it is uniquely determined by a triple $(h,α,β)$ where $h$ is an element of $\mathbb{Z}_n$, $α$ is a skew morphism of $\m…

Existence Theorem for Cumulative Universe Towers and Its Applications
Higuchi Joaquim Reizi
https://arxiv.org/abs/2506.21653 https://…

Existence Theorem for Cumulative Universe Towers and Its Applications
This paper builds a cumulative tower of Grothendieck universes that provides a precise size discipline for higher type theory. Starting from an increasing sequence of inaccessible cardinals, we give an inductive-recursive definition of universe codes, their decoding functor, and a rank that controls the growth of each code. For every level of the tower we prove closure under dependent products, dependent sums, identity types, and all finite limits and colimits; the colimit part is obtained with…

Finite random iterated function systems do not always satisfy Bowen's formula
Yuya Arima
https://arxiv.org/abs/2509.02070 https://arxiv.org/pdf/2509.02…

Finite random iterated function systems do not always satisfy Bowen's formula
In this paper, we provide a finite random iterated function system satisfying the open set condition, for which the random version of Bowen's formula fails to hold. This counterexample shows that analogous results established for random recursive constructions are not always obtained for random iterated function systems.

Recursive Gaussian Process Regression with Integrated Monotonicity Assumptions for Control Applications
Ricus Husmann, Sven Weishaupt, Harald Aschemann
https://arxiv.org/abs/2508.14715

Recursive Gaussian Process Regression with Integrated Monotonicity Assumptions for Control Applications
In this paper, we present an extension to the recursive Gaussian Process (RGP) regression that enables the satisfaction of inequality constraints and is well suited for a real-time execution in control applications. The soft inequality constraints are integrated by introducing an additional extended Kalman Filter (EKF) update step using pseudo-measurements. The sequential formulation of the algorithm and several developed heuristics ensure both the performance and a low computational effort of …

How two elephants can learn from each other
Rafik Aguech, Shuo Qin
https://arxiv.org/abs/2509.04862 https://arxiv.org/pdf/2509.04862

How two elephants can learn from each other
We consider a two-elephant walking model in which the elephants interact dynamically. At each time step, each elephant determines its next move randomly based on its partner's past movements. We show that the asymptotic behavior of the elephants mainly depends on the sign and the absolute value of the product of their reinforcement parameters. In various regimes, we establish the law of large numbers and the central limit theorem. Our proofs are based on a connection to the random recursive tre…

A multi-stage Bayesian approach to fit spatial point process models
Rachael Ren, Mevin B. Hooten, Toryn L. J. Schafer, Nicholas M. Calzada, Benjamin Hoose, Jamie N. Womble, Scott Gende
https://arxiv.org/abs/2508.02922

A multi-stage Bayesian approach to fit spatial point process models
Spatial point process (SPP) models are commonly used to analyze point pattern data, including presence-only data in ecology. Current methods for fitting these models are computationally expensive because they require numerical quadrature and algorithm supervision (i.e., tuning) in the Bayesian setting. We propose a flexible and efficient multi-stage recursive Bayesian approach to fitting SPP models that leverages parallel computing resources to estimate point process model coefficients and deri…

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

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

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- A method for determining the mod-$p^k$ behaviour of recursive sequences
Christian Krattenthaler (Universit\"at Wien), Thomas W. M\"uller (Universit\"at Wien)

Kernel-FFI: Transparent Foreign Function Interfaces for Interactive Notebooks
Hebi Li, Forrest Sheng Bao, Qi Xiao, Jin Tian
https://arxiv.org/abs/2507.23205 https://

Kernel-FFI: Transparent Foreign Function Interfaces for Interactive Notebooks
Foreign Function Interfaces (FFIs) are essential for enabling interoperability between programming languages, yet existing FFI solutions are ill-suited for the dynamic, interactive workflows prevalent in modern notebook environments such as Jupyter. Current approaches require extensive manual configuration, introduce significant boilerplate, and often lack support for recursive calls and object-oriented programming (OOP) constructs-features critical for productive, multi-language development. …

Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support
Trung Phung, Kyle Reese, Ilya Shpitser, Rohit Bhattacharya
https://arxiv.org/abs/2507.16107

Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support
A common approach for handling missing values in data analysis pipelines is multiple imputation via software packages such as MICE (Van Buuren and Groothuis-Oudshoorn, 2011) and Amelia (Honaker et al., 2011). These packages typically assume the data are missing at random (MAR), and impose parametric or smoothing assumptions upon the imputing distributions in a way that allows imputation to proceed even if not all missingness patterns have support in the data. Such assumptions are unrealistic in…

A Hybrid Perspective on Suboptimal Mixed-Integer Quadratic Programming
Luke Fina, Christopher Petersen
https://arxiv.org/abs/2507.02772 https://

A Hybrid Perspective on Suboptimal Mixed-Integer Quadratic Programming
This work solves suboptimal mixed-integer quadratic programs recursively for feedback control of dynamical systems. The proposed framework leverages parametric mixed-integer quadratic programming (MIQP) and hybrid systems theory to model a recursive MIQP feedback controller and a feedback controlled dynamical system. The proposed hybrid framework theoretically encodes the suboptimal part via solver parameters as bounded perturbations from the optimal solution set. The stability of the proposed …

Data-Driven Adaptive Second-Order Sliding Mode Control with Noisy Data
Behrad Samari, Gian Paolo Incremona, Antonella Ferrara, Abolfazl Lavaei
https://arxiv.org/abs/2508.02357 h…

Data-Driven Adaptive Second-Order Sliding Mode Control with Noisy Data
This paper offers a data-driven approach for designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for single-input nonlinear systems, characterized by perturbed strict-feedback structures with unknown dynamics. The proposed approach is recursive, in which the system dynamics are first decomposed into two parts, referred to as the upper and lower dynamics. The control design task is then divided into two stages, that is, designing a virtual controller for the upper dynami…

On the normalization of trigonometric and hyperbolic B-splines
Hendrik Speleers
https://arxiv.org/abs/2508.01817 https://arxiv.org/pdf/2508.01817

On the normalization of trigonometric and hyperbolic B-splines
Trigonometric and hyperbolic B-splines can be computed via recurrence relations analogous to the classical polynomial B-splines. However, in their original formulation, these two types of B-splines do not form a partition of unity and consequently do not admit the notion of control polygons with the convex hull property for design purposes. In this paper, we look into explicit expressions for their normalization and provide a recursive algorithm to compute the corresponding normalization weight…

Criticality of the abelian sandpile in dimension 1
Adrien Rezzouk
https://arxiv.org/abs/2509.03697 https://arxiv.org/pdf/2509.03697

Criticality of the abelian sandpile in dimension 1
We study the critical behavior of the dissipative abelian sandpile model on Z with dissipative sites at arbitrary positions (x_k). This is equivalent to studying whether the expected stopping time of a trapped random walk on Z is finite. Our main contribution is a precise description of this phase transition via three distinct regimes. Our analysis captures criticality through the asymptotic behavior of an explicit recursive sequence, revealing counterintuitive phenomena in which traps may be f…

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization
Serge Gratton, Alena Kopani\v{c}\'akov\'a, Philippe Toint
https://arxiv.org/abs/2507.11513

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization
Two OFFO (Objective-Function Free Optimization) noise tolerant algorithms are presented that handle bound constraints, inexact gradients and use second-order information when available.The first is a multi-level method exploiting a hierarchical description of the problem and the second is a domain-decomposition method covering the standard addditive Schwarz decompositions. Both are generalizations of the first-order AdaGrad algorithm for unconstrained optimization. Because these algorithms shar…

Iteratively Saturated Kalman Filtering
Alan Yang, Stephen Boyd
https://arxiv.org/abs/2507.00272 https://arxiv.org/pdf/2507.00272

Iteratively Saturated Kalman Filtering
The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise. We introduce the iteratively saturated Kalman filter (ISKF), which is derived as a scaled gradient method for solving a convex robust estimation problem. It achieves outlier robustness while preserving the KF's low per-step cost and implementation simplicity…

Spacetime Wavelet Method for Linear Boundary-Value Problems in Sylvester Matrix Equation Form
Cody D. Cochran, Karel Matous
https://arxiv.org/abs/2509.02720 https://

Spacetime Wavelet Method for Linear Boundary-Value Problems in Sylvester Matrix Equation Form
We present a high-order spacetime numerical method for discretizing and solving linear initial-boundary value problems using wavelet-based techniques with user-prescribed error estimates. The spacetime wavelet discretization yields a system of algebraic equations resulting in a Sylvester matrix equation. We solve this system with a Global Generalized Minimal Residual (GMRES) method in conjunction with a wavelet-based recursive algorithm to improve convergence. We perform rigorous verification s…

Near-perfect Clustering Based on Recursive Binary Splitting Using Max-MMD
Sourav Chakrabarty, Anirvan Chakraborty, Shyamal K. De
https://arxiv.org/abs/2507.11158

Near-perfect Clustering Based on Recursive Binary Splitting Using Max-MMD
We develop novel clustering algorithms for functional data when the number of clusters $K$ is unknown and also when it is prefixed. These algorithms are developed based on the Maximum Mean Discrepancy (MMD) measure between two sets of observations. The algorithms recursively use a binary splitting strategy to partition the dataset into two subgroups such that they are maximally separated in terms of an appropriate weighted MMD measure. When $K$ is unknown, the proposed clustering algorithm has …

Deep BSVIEs Parametrization and Learning-Based Applications
Nacira Agram, Giulia Pucci
https://arxiv.org/abs/2507.01948 https://arxiv…

Deep BSVIEs Parametrization and Learning-Based Applications
We study the numerical approximation of backward stochastic Volterra integral equations (BSVIEs) and their reflected extensions, which naturally arise in problems with time inconsistency, path dependent preferences, and recursive utilities with memory. These equations generalize classical BSDEs by involving two dimensional time structures and more intricate dependencies. We begin by developing a well posedness and measurability framework for BSVIEs in product probability spaces. Our approach …

Incremental Policy Iteration for Unknown Nonlinear Systems with Stability and Performance Guarantees
Qingkai Meng, Fenglan Wang, Lin Zhao
https://arxiv.org/abs/2508.21367 https:…

Incremental Policy Iteration for Unknown Nonlinear Systems with Stability and Performance Guarantees
This paper proposes a general incremental policy iteration adaptive dynamic programming (ADP) algorithm for model-free robust optimal control of unknown nonlinear systems. The approach integrates recursive least squares estimation with linear ADP principles, which greatly simplifies the implementation while preserving adaptive learning capabilities. In particular, we develop a sufficient condition for selecting a discount factor such that it allows learning the optimal policy starting with an i…