Tootfinder

State and Input Constrained Model Reference Adaptive Control with Robustness and Feasibility Analysis
Poulomee Ghosh, Shubhendu Bhasin
https://arxiv.org/abs/2508.21584 https://

State and Input Constrained Model Reference Adaptive Control with Robustness and Feasibility Analysis
We propose a model reference adaptive controller (MRAC) for uncertain linear time-invariant (LTI) plants with user-defined state and input constraints in the presence of unmatched bounded disturbances. Unlike popular optimization-based approaches for constrained control, such as model predictive control (MPC) and control barrier function (CBF) that solve a constrained optimization problem at each step using the system model, our approach is optimization-free and adaptive; it combines a saturate…

PDE-constrained optimal control of a leader-follower opinion formation model
Bertram D\"uring, Oliver Wright
https://arxiv.org/abs/2508.21674 https://…

PDE-constrained optimal control of a leader-follower opinion formation model
We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and Fokker-Planck-type systems of equations associated with the controlled leader-follower opinion formation model. In a function space setting we derive first-order optimality conditions associated with the PDE-constrained optimal control problem, yielding an optimality system…

Bayesian Neural Networks for Functional ANOVA model
Seokhun Park, Choeun Kim, Jihu Lee, Yunseop Shin, Insung Kong, Yongdai Kim
https://arxiv.org/abs/2510.00545 https://

Bayesian Neural Networks for Functional ANOVA model
With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal the contributions of different variable groups. Recently, Tensor Product Neural Network (TPNN) has been developed and applied as basis functions in the functional ANOVA model, referred to as ANOVA-TPNN. A disadvantage of ANOVA-TPNN, however, is that the compone…

A Function-Set Framework: General Properties and Applications to Modal Logic
Luke Bayzid (University of Aveiro), Alexandre Madeira (University of Aveiro), Manuel A. Martins (University of Aveiro)
https://arxiv.org/abs/2509.25880

A Function-Set Framework: General Properties and Applications to Modal Logic
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results between these representations can be non-trivial, as different frameworks are used for different contexts. We present a general structure based on set-theoretic concepts that accommodates many situations related to logical and semantic frameworks. We show the…

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.

Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights
A. J. E. M. Janssen
https://arxiv.org/abs/2508.21409 h…

Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights
We consider in this work the crucial quantity $t_c$ that determines the critical inverse temperature $β_c$ in the $q$-state Potts model on sparse rank-1 random graphs where the vertices are equipped with a Pareto weight density $(τ-1)\,w^{-τ}\,{\cal X}_{[1,\infty)}(w)$. It is shown in \cite{ref1} that this $t_c$ is the unique positive zero of a function ${\cal K}$ that is obtained by an appropriate combination of the stationarity condition and the criticality condition for the case the exter…

A Data-Adaptive Factor Model Using Composite Quantile Approach
Seeun Park, Hee-Seok Oh
https://arxiv.org/abs/2510.00558 https://arxiv.org/pdf/2510.00558

A Data-Adaptive Factor Model Using Composite Quantile Approach
This paper proposes a data-adaptive factor model (DAFM), a novel framework for extracting common factors that explain the structures of high-dimensional data. DAFM adopts a composite quantile strategy to adaptively capture the full distributional structure of the data, thereby enhancing estimation accuracy and revealing latent patterns that are invisible to conventional factor models. In this paper, we develop a practical algorithm for estimating DAFM by minimizing an objective function based o…

Brain Harmony: A Multimodal Foundation Model Unifying Morphology and Function into 1D Tokens
Zijian Dong, Ruilin Li, Joanna Su Xian Chong, Niousha Dehestani, Yinghui Teng, Yi Lin, Zhizhou Li, Yichi Zhang, Yapei Xie, Leon Qi Rong Ooi, B. T. Thomas Yeo, Juan Helen Zhou
https://arxiv.org/abs/2509.24693

Brain Harmony: A Multimodal Foundation Model Unifying Morphology and Function into 1D Tokens
We present Brain Harmony (BrainHarmonix), the first multimodal brain foundation model that unifies structural morphology and functional dynamics into compact 1D token representations. The model was pretrained on two of the largest neuroimaging datasets to date, encompassing 64,594 T1-weighted structural MRI 3D volumes (~ 14 million images) and 70,933 functional MRI (fMRI) time series. BrainHarmonix is grounded in two foundational neuroscience principles: structure complements function - structu…

Braneworlds in Einstein-Scalar-Gauss-Bonnet gravity
Jos\'e Euclides G. Silva, Leandro A. Lessa, Roberto V. Maluf
https://arxiv.org/abs/2508.21725 https://

Braneworlds in Einstein-Scalar-Gauss-Bonnet gravity
We explore the features of a thick braneworld model in five dimensions governed by a Einstein-Gauss-Bonnet gravity with a non-minimal coupling to a dynamical scalar field. We consider two possible scalar-GB coupling function $χ(ϕ)$, one parity-even and another parity-odd function of the scalar field $ϕ$. For both choices, the scalar-Gauss-Bonnet non-minimal coupling produces a warped asymptotically $AdS_5$ spacetime even in the absence of a bulk cosmological constant. Outside the brane core,…

A Graph-based Hybrid Beamforming Framework for MIMO Cell-Free ISAC Networks
Yanan Du, Sai Xu, Jagmohan Chauhan
https://arxiv.org/abs/2509.25385 https://arx…

A Graph-based Hybrid Beamforming Framework for MIMO Cell-Free ISAC Networks
This paper develops a graph-based hybrid beamforming framework for multiple-input multiple-output (MIMO) cell-free integrated sensing and communication (ISAC) networks. Specifically, we construct a novel MIMO cell-free ISAC network model. In this model, multiple dual-function base station (BS) transmitters employ distributed hybrid beamforming to enable simultaneous communication and sensing, while maintaining physical separation between the transmitters and the radar receiver. Building on this…

Source Separation for A Cappella Music
Luca A. Lanzend\"orfer, Constantin Pinkl, Florian Gr\"otschla
https://arxiv.org/abs/2509.26580 https://arx…

Source Separation for A Cappella Music
In this work, we study the task of multi-singer separation in a cappella music, where the number of active singers varies across mixtures. To address this, we use a power set-based data augmentation strategy that expands limited multi-singer datasets into exponentially more training samples. To separate singers, we introduce SepACap, an adaptation of SepReformer, a state-of-the-art speaker separation model architecture. We adapt the model with periodic activations and a composite loss function …

Convergence and Divergence of Language Models under Different Random Seeds
Finlay Fehlauer (ETH Zurich), Kyle Mahowald (University of Texas at Austin), Tiago Pimentel (ETH Zurich)
https://arxiv.org/abs/2509.26643

Convergence and Divergence of Language Models under Different Random Seeds
In this paper, we investigate the convergence of language models (LMs) trained under different random seeds, measuring convergence as the expected per-token Kullback--Leibler (KL) divergence across seeds. By comparing LM convergence as a function of model size and training checkpoint, we identify a four-phase convergence pattern: (i) an initial uniform phase, (ii) a sharp-convergence phase, (iii) a sharp-divergence phase, and (iv) a slow-reconvergence phase. Further, we observe that larger mode…

The properties of a Leontief production technology for Health System Modeling: the Thanzi la Onse model for Malawi
Martin Chalkley, Sakshi Mohan, Margherita Molaro, Bingling She, Wiktoria Tafesse
https://arxiv.org/abs/2508.21699

The properties of a Leontief production technology for Health System Modeling: the Thanzi la Onse model for Malawi
As health system modeling (HSM) advances to include more complete descriptions of the production of healthcare, it is important to establish a robust conceptual characterisation of the production process. For the Thanzi La Onse model in Malawi we have incorporated an approach to production that is based on a form of Leontief technology -- fixed input proportions. At first sight, this form of technology appears restrictive relative to the general conception of a production function employed in e…

Model Reference Adaptive Control with Time-Varying State and Input Constraints
Poulomee Ghosh, Shubhendu Bhasin
https://arxiv.org/abs/2508.21586 https://ar…

Model Reference Adaptive Control with Time-Varying State and Input Constraints
This paper presents a model reference adaptive control (MRAC) framework for uncertain linear time-invariant (LTI) systems subject to user-defined, time-varying state and input constraints. The proposed design seamlessly integrates a time-varying barrier Lyapunov function (TVBLF) to enforce state constraints with a time-varying saturation function to handle input limits. These time-varying constraints can be designed as performance functions to shape transient and steady-state behaviors for both…

Stochastic diffusive energy balance climate model with a multiplicative noise modeling the Solar variability
Gregorio D\'iaz, Jes\'us Ildefonso D\'iaz
https://arxiv.org/abs/2509.23153

Stochastic diffusive energy balance climate model with a multiplicative noise modeling the Solar variability
We prove the existence, uniqueness, and comparison of solutions for a nonlinear stochastic parabolic partial differential equation that includes the Solar variability in terms of a multiplicative Wiener cylindrical noise in the term of the absorbed radiative energy in a simplified diffusive one-dimensional Energy Balance Model. We introduce a hybrid co-albedo nonlinear term, which has the advantages of both the Sellers model, as it is a continuous function, and the Budyko model, as it has an in…

Correlation function metrology for warm dense matter: Recent developments and practical guidelines
Maximilian Peter B\"ohme, Willow Martin, Hannah Bellenbaum, Magaret Berrens, Jan Vorberger, Sebastian Schwalbe, Zhandos Moldabekov, Thomas Gawne, Sebastien Hamel, Brianna Aguilar-Solis, Abhiraj Sharma, Frank Graziani, Tilo D\"oppner, Siegfried Glenzer, Tobias Dornheim, David Bishel

Correlation function metrology for warm dense matter: Recent developments and practical guidelines
X-ray Thomson scattering (XRTS) has emerged as a valuable diagnostic for matter under extreme conditions, as it captures the intricate many-body physics of the probed sample. Recent advances, such as the model-free temperature diagnostic of Dornheim et al. [Nat.Commun. 13, 7911 (2022)], have demonstrated how much information can be extracted directly within the imaginary-time formalism. However, since the imaginary-time formalism is a concept often difficult to grasp, we provide here a systemat…

Epsilon-saturation for stable graphs and Littlestone classes
Maryanthe Malliaris, Olga Medrano Mart\'in del Campo, Shay Moran
https://arxiv.org/abs/2508.21807 https://

Epsilon-saturation for stable graphs and Littlestone classes
Any Littlestone class, or stable graph, has finite sets which function as ``virtual elements'': these can be seen from the learning side as representing hypotheses which are expressible as weighted majority opinions of hypotheses in the class, and from the model-theoretic side as an approximate finitary version of realizing types. We introduce and study the epsilon-saturation of a Littlestone class, or stable graph, which is essentially the closure of the class under inductively adding all such…

Noise estimation of SDE from a single data trajectory
Munawar Ali, Purba Das, Qi Feng, Liyao Gao, Guang Lin
https://arxiv.org/abs/2509.25484 https://arxiv.…

Noise estimation of SDE from a single data trajectory
In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By combining (stochastic) Taylor expansions with Girsanov transformations, and using the drift function's initial value as input, we construct drift estimators while simultaneously recovering the model noise. This allows us to recover the underlying $\mathbb P$ B…

Spin-stripes in the Hubbard model: a combined DMFT and Bethe-Salpeter analysis
Ruslan Mushkaev, Francesco Petocchi, Shintaro Hoshino, Philipp Werner
https://arxiv.org/abs/2509.24439

Spin-stripes in the Hubbard model: a combined DMFT and Bethe-Salpeter analysis
The Hubbard model is known to accommodate various electronic orders, including stripes, which are important for understanding the physics of cuprates. We study spin-stripe order in the square lattice Hubbard model as a function of doping and temperature, by solving the Bethe-Salpeter equa- tion with the local vertex from dynamical mean field theory (DMFT), both inside and outside the antiferromagnetic phase. We find broad regions of horizontal/vertical spin stripes at low tempera- tures for the…

Boosting Pointer Analysis With Large Language Model-Enhanced Allocation Function Detection
Baijun Cheng, Kailong Wang, Ling Shi, Haoyu Wang, Peng Di, Yao Guo, Ding Li, Xiangqun Chen
https://arxiv.org/abs/2509.22530

Boosting Pointer Analysis With Large Language Model-Enhanced Allocation Function Detection
Pointer analysis is foundational for many static analysis tasks, yet its effectiveness is often hindered by imprecise modeling of heap allocations, particularly in C/C++ programs where user-defined allocation functions (AFs) are pervasive. Existing approaches largely overlook these custom allocators, leading to coarse aliasing and reduced analysis precision. In this paper, we present AFD, a novel technique that enhances pointer analysis by automatically identifying and modeling custom allocatio…

Catwalk: Unary Top-K for Efficient Ramp-No-Leak Neuron Design for Temporal Neural Networks
Devon Lister, Prabhu Vellaisamy, John Paul Shen, Di Wu
https://arxiv.org/abs/2508.21267

Catwalk: Unary Top-K for Efficient Ramp-No-Leak Neuron Design for Temporal Neural Networks
Temporal neural networks (TNNs) are neuromorphic neural networks that utilize bit-serial temporal coding. TNNs are composed of columns, which in turn employ neurons as their building blocks. Each neuron processes volleys of input spikes, modulated by associated synaptic weights, on its dendritic inputs. Recently proposed neuron implementation in CMOS employs a Spike Response Model (SRM) with a ramp-no-leak (RNL) response function and assumes all the inputs can carry spikes. However, in actual s…

Dynamical model of Praesepe and its tidal tails
L. Weis, C. West, A. Just, P. Berczik, M. Ishchenko, S. R\"oser, E. Schilbach, B. Shukirgaliyev
https://arxiv.org/abs/2509.24584

Dynamical model of Praesepe and its tidal tails
Context. The dynamical evolution of open clusters in the tidal field of the Milky Way and the feeding of the disc field star population depend strongly on the initial conditions at the time of gas removal. Detailed dynamical models tailored to individual clusters help us understand the role of open clusters in the Galactic disc evolution. Aims. We present a detailed dynamical model of Praesepe, which reproduces the mass profile, the stellar mass function, and the mass segregation observed with …

Lifshitz transition in a holographic ffnite density ffavour brane Weyl semimetal
Cheng-Yuan Lu, Xian-Hui Ge, Sang-Jin Sin
https://arxiv.org/abs/2509.24287 https://

Lifshitz transition in a holographic ffnite density ffavour brane Weyl semimetal
We extend a top-down holographic model of a Weyl semimetal to finite charge density and compute the fermionic spectral function by introducing two probe fermions of opposite chirality. The model is controlled by the boundary fermion mass M and the chemical potential $μ$. In the zero density, small-M limit, we recover four energy bands, two Weyl points, and linear dispersion in their vicinity, the hallmarks of a Weyl semimetal. As M increases, the bands between the Weyl points become progressiv…

Activation Function Design Sustains Plasticity in Continual Learning
Lute Lillo, Nick Cheney
https://arxiv.org/abs/2509.22562 https://arxiv.org/pdf/2509.22…

Activation Function Design Sustains Plasticity in Continual Learning
In independent, identically distributed (i.i.d.) training regimes, activation functions have been benchmarked extensively, and their differences often shrink once model size and optimization are tuned. In continual learning, however, the picture is different: beyond catastrophic forgetting, models can progressively lose the ability to adapt (referred to as loss of plasticity) and the role of the non-linearity in this failure mode remains underexplored. We show that activation choice is a primar…

Fluctuation theorem and optimal control of an active tracking particle with information processing
Tai Han, Fanlong Meng
https://arxiv.org/abs/2508.21487 https://

Fluctuation theorem and optimal control of an active tracking particle with information processing
Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling.We propose the model of an active tracking particle with information processing, based on which the entropy production, information flow, and generalised fluctuation theorem are derived.Moreover, the system performance, in terms of the first passage steps and the total energy consumption, are analysed in th…

Modular Heights of Unitary Shimura Varieties
Ziqi Guo
https://arxiv.org/abs/2509.24363 https://arxiv.org/pdf/2509.24363

Modular Heights of Unitary Shimura Varieties
The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific term, we will introduce a global canonical integral model of such a unitary Shimura variety, and compute the arithmetic top self-intersection number of a canonical arithmetic line bundle with Hermitian metric on such integral model. At the same time, we also…

Sparse Deep Additive Model with Interactions: Enhancing Interpretability and Predictability
Yi-Ting Hung, Li-Hsiang Lin, Vince D. Calhoun
https://arxiv.org/abs/2509.23068 https:…

Sparse Deep Additive Model with Interactions: Enhancing Interpretability and Predictability
Recent advances in deep learning highlight the need for personalized models that can learn from small or moderate samples, handle high dimensional features, and remain interpretable. To address this challenge, we propose the Sparse Deep Additive Model with Interactions (SDAMI), a framework that combines sparsity driven feature selection with deep subnetworks for flexible function approximation. Unlike conventional deep learning models, which often function as black boxes, SDAMI explicitly disen…

A brief introduction to dispersive methods
Gilberto Colangelo
https://arxiv.org/abs/2509.24548 https://arxiv.org/pdf/2509.24548

A brief introduction to dispersive methods
These lectures aim to provide a basic introduction to dispersive methods and their modern applications to the phenomenology of the Standard Model at low energy. This approach exploits analyticity properties of Green functions and scattering amplitude, often combined with unitarity constraints. To find a logically coherent set of topics in this vast subject, I start with the two-point Green's function, show that this needs the three-point function as input which in turn needs the four-point func…

Microscopic study of the asymptotic behavior of the reduced width amplitude in $^7$Li and $^7$Be
H. J. Zhu, M. J. Lyu, Q. Zhao, Z. Cheng, J. Q. Tian, M. Kimura, T. Myo, H. Horiuchi, H. Toki, M. Isaka, H. Takemoto, Akinobu Dot\'e, N. Wan
https://arxiv.org/abs/2509.23613

Microscopic study of the asymptotic behavior of the reduced width amplitude in $^7$Li and $^7$Be
We investigate the effects of different basis model spaces on the calculation of reduced width amplitude (RWA) and asymptotic normalization coefficient (ANC) for the $^{7}$Li and $^{7}$Be nuclei. The two-cluster model ($α+t/^3$He) and three-cluster model ($α+d+n/p$) with the generator coordinates method (GCM) are applied to calculate the wave function of $^7$Li and $^7$Be. Specifically, the model space for the three-cluster model is constructed upon a sufficiently broad space of two-cluster c…

Weakly model-independent determination of total expansion during inflation
Dayeong Choi, Subin Jeon, Jinn-Ouk Gong
https://arxiv.org/abs/2509.21850 https://

Weakly model-independent determination of total expansion during inflation
We study systematically the total expansion experienced by a certain perturbation mode during single-field inflation, not resorting to explicit models of inflation or reheating. By assuming that during the reheating stage the equation of state w{rh} can be written as a function of e-folds, the unknown dynamics during reheating parametrized by w{rh} is confined within a time integral so that any dependence on the models of inflation and reheating is isolated from model-independent contributions.…

Chat to Chip: Large Language Model Based Design of Arbitrarily Shaped Metasurfaces
Huanshu Zhang, Lei Kang, Sawyer D. Campbell, Douglas H. Werner
https://arxiv.org/abs/2509.24196

Chat to Chip: Large Language Model Based Design of Arbitrarily Shaped Metasurfaces
Traditional metasurface design is limited by the computational cost of full-wave simulations, preventing thorough exploration of complex configurations. Data-driven approaches have emerged as a solution to this bottleneck, replacing costly simulations with rapid neural network evaluations and enabling near-instant design for meta-atoms. Despite advances, implementing a new optical function still requires building and training a task-specific network, along with exhaustive searches for suitable …

Deep learning CAT bond valuation
Julian Sester, Huansang Xu
https://arxiv.org/abs/2509.25899 https://arxiv.org/pdf/2509.25899

Stones, Bones, and Snakes: Tilability of the hexagonal grid via the double dimer model
Leigh Foster
https://arxiv.org/abs/2509.21700 https://arxiv.org/pdf/…

Stones, Bones, and Snakes: Tilability of the hexagonal grid via the double dimer model
The question of whether a given region can be successfully filled by a finite set of tiles has been commonly studied, and there are many available arguments for whether a given finite region can be tiled. We can show that there is no domino tiling of the mutilated chessboard via a coloring argument, and a slightly more subtle argument for other two-colored square-grid regions using a height function of Thurston. In this paper, we examine finite regions of the hexagonal grid and a set of tiles k…

An Approach to Estimating Quadratic Logistic Model Parameters of Fractal Dimension Curves
Yanguang Chen
https://arxiv.org/abs/2508.19917 https://arxiv.org/…

An Approach to Estimating Quadratic Logistic Model Parameters of Fractal Dimension Curves
The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of the ordinary logistic model has been developed. However, how to estimate the parameter of quadratic logistic model is still a problem. This paper is devoted to finding a nonlinear regressive approach for estimating parameter values of quadratic logistic model …

Safe-by-Design: Approximate Nonlinear Model Predictive Control with Real Time Feasibility
Jan Olucak, Arthur Castello B. de Oliveira, Torbj{\o}rn Cunis
https://arxiv.org/abs/2509.22422

Safe-by-Design: Approximate Nonlinear Model Predictive Control with Real Time Feasibility
This paper establishes relationships between continuous-time, receding horizon, nonlinear model predictive control (MPC) and control Lyapunov and control barrier functions (CLF/CBF). We show that, if the cost function "behaves well" for points in the terminal set, then the optimal value function and the feasible set, respectively, define a compatible CLF/CBF pair on the MPC's region of attraction. We then proceed to prove that any approximation of the value function and the feasible set also de…

A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions
Hugo Kruiniger
https://arxiv.org/abs/2508.20753 https://

A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions
In this paper we consider two kinds of generalizations of Lancaster's (Review of Economic Studies, 2002) Modified ML estimator (MMLE) for the panel AR(1) model with fixed effects and arbitrary initial conditions and possibly covariates when the time dimension, T, is fixed. When the autoregressive parameter rho=1, the limiting modified profile log-likelihood function for this model has a stationary point of inflection, and rho is first-order underidentified but second-order identified. We show t…

Classification of global structures of evaporating regular black holes with infinite periods of time
Kensuke Sueto, Hirotaka Yoshino
https://arxiv.org/abs/2508.21315 https://

Classification of global structures of evaporating regular black holes with infinite periods of time
We carry out model independent analyses for global structures of spherically symmetric regular black holes that evaporate and approach the extremal state spending infinite periods of time due to Hawking radiation. We assume the radius of the outer apparent horizon (outer AH) to be a decreasing function of ingoing null coordinate, and consider the three cases, Cases 1, 2, and 3, where the radius of the inner AH is a constant, increases, and decreases, respectively. A complete classification …

Development of an Optimized Parameter Set for Monovalent Ions in the Reference Interaction Site Model of Solvation
Felipe Silva Carvalho, Alexander McMahon, David A. Case, Tyler Luchko
https://arxiv.org/abs/2509.22430

Development of an Optimized Parameter Set for Monovalent Ions in the Reference Interaction Site Model of Solvation
Accurate modeling of aqueous monovalent ions is essential for understanding the function of biomolecules, such as nucleic acid stability and binding of charged drugs to protein targets. The 1D and 3D reference interaction site models (1D- and 3D-RISM) of molecular solvation, as implemented in the AmberTools molecular modeling suite, are well suited for modeling mixtures of ionic species around biomolecules across a wide range of concentrations. However, the available ion model parameters were o…

Finite temperature single-particle Green's function in the Lieb-Liniger model
Riccardo Senese, Fabian H. L. Essler
https://arxiv.org/abs/2508.17908 https://

Finite temperature single-particle Green's function in the Lieb-Liniger model
We develop a Monte Carlo sampling algorithm to numerically evaluate the Lehmann representation for the finite temperature single-particle Green's function in the repulsive Lieb-Liniger model. This allows us to determine the spectral function in the full range of temperatures and interactions, as well as in generalized Gibbs ensembles. We test our results against the known limit of infinite interaction strength and find excellent agreement.

Integrating Background Knowledge in Medical Semantic Segmentation with Logic Tensor Networks
Luca Bergamin, Giovanna Maria Dimitri, Fabio Aiolli
https://arxiv.org/abs/2509.22399

Integrating Background Knowledge in Medical Semantic Segmentation with Logic Tensor Networks
Semantic segmentation is a fundamental task in medical image analysis, aiding medical decision-making by helping radiologists distinguish objects in an image. Research in this field has been driven by deep learning applications, which have the potential to scale these systems even in the presence of noise and artifacts. However, these systems are not yet perfected. We argue that performance can be improved by incorporating common medical knowledge into the segmentation model's loss function. To…

A Generative Model for Controllable Feature Heterophily in Graphs
Haoyu Wang, Renyuan Ma, Gonzalo Mateos, Luana Ruiz
https://arxiv.org/abs/2509.23230 https://

A Generative Model for Controllable Feature Heterophily in Graphs
We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of t…

Unifying local and nonlocal corrosion frameworks: A convergent nonlocal extension of the KKS phase-field model
Christian J. Cyron, Marvin Fritz, Alexander Hermann, Tobias K\"oppl, Arman Shojaei, Stewart Silling
https://arxiv.org/abs/2509.23503

Unifying local and nonlocal corrosion frameworks: A convergent nonlocal extension of the KKS phase-field model
We introduce a nonlocal extension of the Kim-Kim-Suzuki (KKS) phase-field corrosion model aimed at bridging local and nonlocal corrosion modeling approaches, such as phase-field and peridynamic frameworks. In this formulation, classical gradient operators are replaced with integral operators defined over a finite interaction horizon, naturally embedding an intrinsic length scale that aligns with nonlocal theories like peridynamics. Under precise assumptions on function spaces and kernel functio…

Computational study of Adhesion and Friction Behavior of Crosslinked Polymer Network
Ajay Kumar, Manoj Kumar Maurya, Manjesh K. Singh
https://arxiv.org/abs/2508.21360 https://…

Computational study of Adhesion and Friction Behavior of Crosslinked Polymer Network
In this study, we have utilized a molecular dynamics simulation approach to understand adhesion and friction behaviour of crosslinked polymer networks. We have used breakable quartic bond to model crosslinked polymers. We explored the structural characteristics and evaluated the coefficient of friction (CoF) as a function of crosslinked monomer fraction (cross-linking bond density) in four-fold cross-linked polymer networks. To estimate CoF, a rigid indenter was inserted to different depths of …

Crossing probabilities in geometric inhomogeneous random graphs
Emmanuel Jacob, C\'eline Kerriou, Amitai Linker, Peter M\"orters
https://arxiv.org/abs/2509.23496 https:…

Crossing probabilities in geometric inhomogeneous random graphs
In a geometric inhomogeneous random graph vertices are given by the points of a Poisson process and are equipped with independent weights following a heavy tailed distribution. Any pair of distinct vertices is independently forming an edge with a probability decaying as a function of the product of the weights divided by the distance of the vertices. For this continuum percolation model we study the crossing probabilities of annuli, i.e. the probabilities that there exist paths starting inside …

Fast Convergence Rates for Subsampled Natural Gradient Algorithms on Quadratic Model Problems
Gil Goldshlager, Jiang Hu, Lin Lin
https://arxiv.org/abs/2508.21022 https://…

Fast Convergence Rates for Subsampled Natural Gradient Algorithms on Quadratic Model Problems
Subsampled natural gradient descent (SNGD) has shown impressive results for parametric optimization tasks in scientific machine learning, such as neural network wavefunctions and physics-informed neural networks, but it has lacked a theoretical explanation. We address this gap by analyzing the convergence of SNGD and its accelerated variant, SPRING, for idealized parametric optimization problems where the model is linear and the loss function is strongly convex and quadratic. In the special cas…

Model-Free Dynamic Consensus in Multi-Agent Systems: A Q-Function Perspective
Maryam Babazadeh, Naim Bajcinca
https://arxiv.org/abs/2509.24598 https://arxi…

Model-Free Dynamic Consensus in Multi-Agent Systems: A Q-Function Perspective
This paper presents a new method for achieving dynamic consensus in linear discrete-time homogeneous multi-agent systems (MAS) with marginally stable or unstable dynamics. The guarantee of consensus in this setting involves a set of constraints based on the graph's spectral properties, complicating the design of the coupling gains. This challenge intensifies for large-scale systems with diverse graph Laplacian spectra. The proposed approach reformulates the dynamic consensus problem with a pres…

The Non-Attainment Phenomenon in Robust SOCPs
Vinh Nguyen
https://arxiv.org/abs/2510.00318 https://arxiv.org/pdf/2510.00318

The Non-Attainment Phenomenon in Robust SOCPs
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this crucial guarantee does not extend to Second-Order Cone Programs (SOCPs), a workhorse model in robust and convex optimization. We construct and analyze a rigorous counterexample derived from a robust linear optimization problem with ellipsoidal uncertainty. The re…

Two-particle number and transverse momentum balance function with event-topology in pp collisions at $\sqrt{s}=13$ TeV
Subash Chandra Behera, Arvind Khuntia
https://arxiv.org/abs/2508.20198

Two-particle number and transverse momentum balance function with event-topology in pp collisions at $\sqrt{s}=13$ TeV
The first study of charge-dependent two-particle differential number ($B$) and momentum balance functions ($P_{2}^{CD}$) with respect to an event shape variable, transverse spherocity, is reported. Results are presented from PYTHIA8 and EPOS-LHC model calculations in proton-proton (pp) collisions at $\sqrt{s} = 13$ TeV. To distinguish between back-to-back jet-like topologies and isotropic events, low and high transverse spherocity values are chosen. The correlation functions are measured as a f…

How many qubits does a machine learning problem require?
Sydney Leither, Michael Kubal, Sonika Johri
https://arxiv.org/abs/2508.20992 https://arxiv.org/pdf…

How many qubits does a machine learning problem require?
For a machine learning paradigm to be generally applicable, it should have the property of universal approximation, that is, it should be able to approximate any target function to any desired degree of accuracy. In variational quantum machine learning, the class of functions that can be learned depend on both the data encoding scheme as well as the architecture of the optimizable part of the model. Here, we show that the property of universal approximation is constructively and efficiently rea…

Towards Large-Spin Effective Theory II: $O(2)$ model in $d=4-\epsilon$
Giulia Fardelli, A. Liam Fitzpatrick, Wei Li
https://arxiv.org/abs/2508.20160 https://

Towards Large-Spin Effective Theory II: $O(2)$ model in $d=4-ε$
We show how to construct a holographic effective theory for the leading-twist operators in the $O(2)$ model in the $4-d=ε$ expansion up to $O(ε^2)$, based on the separation of short-distance and long-distance effects that arises as a function of spin $J$. We obtain the Hamiltonian of the theory and show that it correctly reproduces all the dimensions at $O(ε^2)$ of the leading twist operators for all values of the charge $Q$ and spin $J$. The holographic Hamiltonian is given by the bulk exch…

Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization
Jonathan A. Moran, Pablo G. Morato
https://arxiv.org/abs/2508.18170

Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization
Reliability assessment of engineering systems is often hindered by the need to evaluate limit-state functions through computationally expensive simulations, rendering standard sampling impractical. An effective solution is to approximate the limit-state function with a surrogate model iteratively refined through active learning, thereby reducing the number of expensive simulations. At each iteration, an acquisition strategy selects the next sample by balancing two competing goals: exploration, …

JPResUnet: A Joint Probability Density Function Translation Model in Partially Premixed Flames
Hanying Yang, James C. Massey, Nedunchezhian Swaminathan
https://arxiv.org/abs/2509.17297

JPResUnet: A Joint Probability Density Function Translation Model in Partially Premixed Flames
Machine learning (ML) models are often constrained by their limitations in extrapolation, which restricts their applicability in engineering contexts. Conversely, while exhibiting broad generality, many established scientific models seem to lack the necessary accuracy. This study addresses these challenges by introducing JPResUnet (Joint PDF Residual U-net), a novel model that integrates the strengths of both ML and traditional scientific approaches to predict sub-grid joint probability density…

Exponential Discounting under Partial Efficiency
Charles Gauthier
https://arxiv.org/abs/2508.20249 https://arxiv.org/pdf/2508.20249

Exponential Discounting under Partial Efficiency
This paper derives a novel representation of the exponential discounting model that allows one to assess departures from the model via a measure of efficiency. The approach uses a revealed preference methodology that does not make any parametric assumption on the utility function and allows for unrestricted heterogeneity. The method is illustrated using longitudinal data from checkout scanners and gives insights into sources of departure from exponential discounting.

FlashGMM: Fast Gaussian Mixture Entropy Model for Learned Image Compression
Shimon Murai, Fangzheng Lin, Jiro Katto
https://arxiv.org/abs/2509.18815 https://

Judicial Requirements for Generative AI in Legal Reasoning
Eljas Linna, Tuula Linna
https://arxiv.org/abs/2508.18880 https://arxiv.org/pdf/2508.18880

Judicial Requirements for Generative AI in Legal Reasoning
Large Language Models (LLMs) are being integrated into professional domains, yet their limitations in high-stakes fields like law remain poorly understood. This paper defines the core capabilities that an AI system must possess to function as a reliable reasoning tool in judicial decision-making. Using the IRAC (Issue-Rule-Application-Conclusion) model as an analytical framework, the study focuses on the most challenging phases of legal adjudication: determining the applicable Rule (R) and perf…

Criticality of a stochastic modern Hopfield network model with exponential interaction function
Marco Cafiso, Paolo Paradisi
https://arxiv.org/abs/2509.17152 https://

Criticality of a stochastic modern Hopfield network model with exponential interaction function
The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian learning rule, and retrieval corresponds to convergence towards these minima. Modern Hopfield Networks (MHNs) introduce p-body interactions among neurons with p greater than 2 and, more recently, also exponential interaction functions, which significantly improve …

On parameterized nonlocal-fractional transmission problems and associated function spaces
Qiang Du, Zhaolong Han, Tadele Mengesha, James M. Scott, Xiaochuan Tian
https://arxiv.org/abs/2509.22987

On parameterized nonlocal-fractional transmission problems and associated function spaces
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a fractional type Dirichlet energy on one subdomain and a nonlocal Dirichlet energy involving a finite range of interactions on another subdomain. We present the rigorous mathematical formulation and its well-posedness. We also investigate the behavior of the model in v…

An Interpretable Single-Index Mixed-Effects Model for Non-Gaussian National Survey Data
Qingyang Liu, Debdeep Pati, Dipankar Bandyopadhyay
https://arxiv.org/abs/2509.20638 https…

An Interpretable Single-Index Mixed-Effects Model for Non-Gaussian National Survey Data
This manuscript presents an innovative statistical model to quantify periodontal disease in the context of complex medical data. A mixed-effects model incorporating skewed random effects and heavy-tailed residuals is introduced, ensuring robust handling of non-normal data distributions. The fixed effect is modeled as a combination of a slope parameter and a single index function, constrained to be monotonic increasing for meaningful interpretation. This approach captures different dimensions of…

Guided Multi-Fidelity Bayesian Optimization for Data-driven Controller Tuning with Digital Twins
Mahdi Nobar, J\"urg Keller, Alessandro Forino, John Lygeros, Alisa Rupenyan
https://arxiv.org/abs/2509.17952

Guided Multi-Fidelity Bayesian Optimization for Data-driven Controller Tuning with Digital Twins
We propose a \textit{guided multi-fidelity Bayesian optimization} framework for data-efficient controller tuning that integrates corrected digital twin (DT) simulations with real-world measurements. The method targets closed-loop systems with limited-fidelity simulations or inexpensive approximations. To address model mismatch, we build a multi-fidelity surrogate with a learned correction model that refines DT estimates from real data. An adaptive cost-aware acquisition function balances expect…

Converting IEC 61131-3 LD into SFC Using Large Language Model: Dataset and Testing
Yimin Zhang, Mario de Sousa
https://arxiv.org/abs/2509.12593 https://arx…

Converting IEC 61131-3 LD into SFC Using Large Language Model: Dataset and Testing
In the domain of Programmable Logic Controller (PLC) programming, converting a Ladder Diagram (LD) into a Sequential Function Chart (SFC) is an inherently challenging problem, primarily due to the lack of domain-specific knowledge and the issue of state explosion in existing algorithms. However, the rapid development of Artificial Intelligence (AI) - especially Large Language Model (LLM) - offers a promising new approach. Despite this potential, data-driven approaches in this field have been …

Wartime Media Dynamics in Emerging Democracies: Case Study of Pakistani Media in May 2025 Indo-Pak Conflict
Taaha Saleem Bajwa
https://arxiv.org/abs/2509.20419 https://

Wartime Media Dynamics in Emerging Democracies: Case Study of Pakistani Media in May 2025 Indo-Pak Conflict
Democracies rely on opposition and dissent to function, but in emerging democracies, freedom of speech is often restricted. This effect intensifies during regional conflicts. This study examines how the India-Pakistan conflict of May 2025 influenced Pakistani media coverage. Analyzing approximately 2,600 news articles from three major newspapers using a large language model (LLM), the study found that war-related reporting significantly overshadowed coverage of political opposition and dissent.…

Holographic defect CFTs with Dirichlet end-of-the-world branes
Haruki Nakayama, Tatsuma Nishioka
https://arxiv.org/abs/2509.22270 https://arxiv.org/pdf/250…

Holographic defect CFTs with Dirichlet end-of-the-world branes
We construct a holographic model of defect conformal field theories (DCFTs) with defects of codimension greater than one. Our construction generalizes the AdS/BCFT model by anchoring the end-of-the-world brane on defects at the asymptotic AdS boundary and imposing Dirichlet boundary conditions for the metric on the brane. We compute the defect entropy and defect free energy and show that the defect $\mathcal{C}$-function is always non-negative. We further study holographic defect-localized RG f…

Nonlinear Hall effect in topological Dirac semimetals in parallel magnetic field
Maxim Dzero, Maxim Khodas, Alex Levchenko, Vladyslav Kozii
https://arxiv.org/abs/2508.20159 http…

Nonlinear Hall effect in topological Dirac semimetals in parallel magnetic field
We compute the second-harmonic response of two-dimensional topological Dirac semimetals subjected to an external in-plane magnetic field. The quantum kinetic equation for the Wigner distribution function is derived and then solved to evaluate the second-order electric-field contributions to the current density. Both the Berry curvature dipole and the field-induced terms in the current are analyzed across a broad range of model parameters. We propose that our theory can be tested experimentally …

Quasi-isometric Higman embeddings and the Dehn function
Francis Wagner
https://arxiv.org/abs/2509.17841 https://arxiv.org/pdf/2509.17841

Quasi-isometric Higman embeddings and the Dehn function
This is the first of a sequence of papers devoted to studying the link between the complexity of the Word Problem for a finitely generated recursively presented group $G$ and the isoperimetric functions of the finitely presented groups in which $G$ embeds. We prove here that if a finitely generated group has a presentation $\mathcal{P}$ whose relators can be enumerated by a computational model satisfying certain technical requirements, then the group embeds quasi-isometrically into a finitely p…

BeNNS: A Surrogate Model for Hybrid Online-Offline Evolution of SFC Embedding
Theviyanthan Krishnamohan, Lauritz Thamsen, Paul Harvey
https://arxiv.org/abs/2509.16856 https://…

BeNNS: A Surrogate Model for Hybrid Online-Offline Evolution of SFC Embedding
Service Function Chains (SFCs) enable programmatic control of the functions and services in a computer network. By leveraging Software Defined Networking to control the links between virtualised network functions, SFCs provide a scalable approach to dealing with the increased pressures on network operation and management. Unfortunately, the challenge of embedding SFCs onto the underlying physical network and compute infrastructure is an NP-hard problem. Genetic Algorithms (GAs) have been used t…

The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime
Alexander Alban, Fu-Hsuan Ho, Justin Ko
https://arxiv.org/abs/2508.17313 https://

The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime
We revisit the proof of the limiting free energy of the continuous random energy model (CREM) using the Hamilton--Jacobi approach for mean-field disordered systems. To achieve this, we introduce an enriched model that interpolates between the CREM and the Ruelle probability cascade. We focus on the weak correlation regime, where the CREM's covariance function $A$ is bounded above by the identity function. In the weak correlation regime, we show that the free energy is given by the Hopf formul…

Digging Into the Internal: Causality-Based Analysis of LLM Function Calling
Zhenlan Ji, Daoyuan Wu, Wenxuan Wang, Pingchuan Ma, Shuai Wang, Lei Ma
https://arxiv.org/abs/2509.16268

Digging Into the Internal: Causality-Based Analysis of LLM Function Calling
Function calling (FC) has emerged as a powerful technique for facilitating large language models (LLMs) to interact with external systems and perform structured tasks. However, the mechanisms through which it influences model behavior remain largely under-explored. Besides, we discover that in addition to the regular usage of FC, this technique can substantially enhance the compliance of LLMs with user instructions. These observations motivate us to leverage causality, a canonical analysis meth…

Preference-Based Dynamic Ranking Structure Recognition
Nan Lu, Jian Shi, Xin-Yu Tian
https://arxiv.org/abs/2509.24493 https://arxiv.org/pdf/2509.24493

Preference-Based Dynamic Ranking Structure Recognition
Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to identify dynamic ranking groups by incorporating temporal penalties into a spectral estimation for the celebrated Bradley-Terry model. To detect structural changes, we introduce an innovative objective function and present a practicable algorithm based on dynamic…

SU(N) integrals and tau functions
A. Yu. Orlov
https://arxiv.org/abs/2509.20213 https://arxiv.org/pdf/2509.20213 …

SU(N) integrals and tau functions
We present a family of solvable multi-matrix models associated with an arbitrary embedded graph $Γ$ with a single vertex. The graph with $n$ edges is equipped with $2n$ corner matrices. The partition function of each member of the family depends on the set of eigenvalues of monodromies of corner matrices around the vertices of the dual graph $Γ^*$ and sets of parameters attached to each vertex of $Γ$. We select the cases where the partition function of a model is a tau function of KP, 2KP an…

The quantum XY chain with boundary fields: finite-size gap and phase behavior
Aldo Coraggio, Andrea Pelissetto
https://arxiv.org/abs/2509.22226 https://arx…

The quantum XY chain with boundary fields: finite-size gap and phase behavior
We present a detailed study of the finite-size one-dimensional quantum XY chain in a transverse field in the presence of boundary fields coupled with the order-parameter spin operator. We consider fields located at the chain boundaries that have the same strength and that are oppositely aligned. We derive exact expressions for the gap $Δ$ as a function of the model parameters for large values of the chain length $L$. These results allow us to characterize the nature of the ordered phases of th…

Analysis of the Rarefied Flow at Micro-Step using a DeepONet Surrogate Model with a Physics-Guided Zonal Loss Function
Ehsan Roohi, Amirmehran Mahdavi
https://arxiv.org/abs/2509.17254

Analysis of the Rarefied Flow at Micro-Step using a DeepONet Surrogate Model with a Physics-Guided Zonal Loss Function
The Direct Simulation Monte Carlo (DSMC) method remains the gold standard for simulating rarefied gas flows but is prohibitively expensive for parametric and many-query applications. To address this limitation, we introduce a Deep Operator Network (DeepONet) surrogate framework featuring an innovative, physics-guided zonal loss function. The zonal loss prioritizes physical fidelity in critical flow regions over global error metrics, leading to predictions with greater engineering relevance. It …

Interpretable Scalar-on-Image Linear Regression Models via the Generalized Dantzig Selector
Sijia Liao, Xiaoxiao Sun, Ning Hao, Hao Helen Zhang
https://arxiv.org/abs/2508.20278 …

Interpretable Scalar-on-Image Linear Regression Models via the Generalized Dantzig Selector
The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness constraints to control the bias-variance trade-off, and thus prevent overfitting. However, such assumptions can hinder interpretability, especially when only certain regions of an image influence changes in the response. In such a scenario, interpretability can be be…

Stabilization of Perturbed Loss Function: Differential Privacy without Gradient Noise
Salman Habib, Remi Chou, Taejoon Kim
https://arxiv.org/abs/2508.15523 https://

Stabilization of Perturbed Loss Function: Differential Privacy without Gradient Noise
We propose SPOF (Stabilization of Perturbed Loss Function), a differentially private training mechanism intended for multi-user local differential privacy (LDP). SPOF perturbs a stabilized Taylor expanded polynomial approximation of a model's training loss function, where each user's data is privatized by calibrated noise added to the coefficients of the polynomial. Unlike gradient-based mechanisms such as differentially private stochastic gradient descent (DP-SGD), SPOF does not require inject…

Exact Solutions for a Teleparallel Cosmological Model with Vector Field via Noether Symmetry
Yusuf Kucukakca, Fereshteh Omidvar, Amin Rezaei Akbarieh
https://arxiv.org/abs/2508.17795

Exact Solutions for a Teleparallel Cosmological Model with Vector Field via Noether Symmetry
We study a cosmological model in the framework of teleparallel gravity, where a vector field $A_μ$ is non-minimally coupled to the torsion scalar $T$ in a flat Friedmann-Robertson-Walker (FRW) universe. Using the Noether symmetry approach, we identify specific forms for the coupling function $g(ξ)$ and the potential $V(ξ) = V_0 ξ^n$, with $ξ\equiv A_μA^μ$. The method allows us to find exact analytical solutions for the scale factor $a(t)$ and the scalar function $ξ(t)$. General solution…

From Pheromones to Policies: Reinforcement Learning for Engineered Biological Swarms
Aymeric Vellinger, Nemanja Antonic, Elio Tuci
https://arxiv.org/abs/2509.20095 https://

From Pheromones to Policies: Reinforcement Learning for Engineered Biological Swarms
Swarm intelligence emerges from decentralised interactions among simple agents, enabling collective problem-solving. This study establishes a theoretical equivalence between pheromone-mediated aggregation in \celeg\ and reinforcement learning (RL), demonstrating how stigmergic signals function as distributed reward mechanisms. We model engineered nematode swarms performing foraging tasks, showing that pheromone dynamics mathematically mirror cross-learning updates, a fundamental RL algorithm. E…

Sensitivity Analysis for Antenna Devices through Interval Arithmetic -- A Generalized Approach
Nicola Anselmi, Paolo Rocca, Andrea Massa
https://arxiv.org/abs/2509.23361 https:/…

Sensitivity Analysis for Antenna Devices through Interval Arithmetic -- A Generalized Approach
This paper presents a novel method for the sensitivity analysis of electromagnetic (EM) systems whose transfer function (TF), that is the input-output (I/O) relationship between the input parameters affected by tolerance and the system response (i.e., the arising EM performance of interest), is not available in closed (or explicit) form. The method is a generalized analytic technique based on the Interval Analysis (IA). First, an analytic surrogate model (SM) of the TF is defined by means of a …

A generative model of function growth explains hidden self-similarities across biological and social systems
James Holehouse, S. Redner, Vicky Chuqiao Yang, P. L. Krapivsky, Jose Ignacio Arroyo, Geoffrey B West, Chris Kempes, Hyejin Youn
https://arxiv.org/abs/2509.14468

A generative model of function growth explains hidden self-similarities across biological and social systems
From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by including: (i) a size-dependent probability of introducing new functions, and (ii) a generalized preferential attachment mechanism for expanding existing ones. We uncover a shared underlying structure that helps explain how function diversity evolves in empirical…

Bootstrapping transport in the Drude-Kadanoff-Martin model
Subham Dutta Chowdhury, Sean A. Hartnoll, Aditya Hebbar, Ruby Khondaker
https://arxiv.org/abs/2509.18255 https://

An improved nonlocal electron heat transport model for magnetized plasmas
Z. H. Chen, Z. Q. Zhao, X. H. Yang, L. R. Li, B. Zeng, Z. Li, B. H. Xu, G. B. Zhang, H. H. Ma, M. Tang, Y. Y. Ma, H. Xu, F. Q. Shao, J. Zhang
https://arxiv.org/abs/2508.17309

An improved nonlocal electron heat transport model for magnetized plasmas
Distortions in the electron distribution function driven by intense temperature gradients critically influence the generation and evolution of heat flux and magnetic fields in plasmas under the condition of inertial confinement fusion. Describing such kinetic behaviors at large spatiotemporal scales typically requires multigroup models based on simplified Vlasov-Fokker-Planck equations. However, the accuracy of existing multigroup models remains uncertain, without a well-defined methodology for…

Multi-Agent Guided Policy Search for Non-Cooperative Dynamic Games
Jingqi Li, Gechen Qu, Jason J. Choi, Somayeh Sojoudi, Claire Tomlin
https://arxiv.org/abs/2509.24226 https://

Multi-Agent Guided Policy Search for Non-Cooperative Dynamic Games
Multi-agent reinforcement learning (MARL) optimizes strategic interactions in non-cooperative dynamic games, where agents have misaligned objectives. However, data-driven methods such as multi-agent policy gradients (MA-PG) often suffer from instability and limit-cycle behaviors. Prior stabilization techniques typically rely on entropy-based exploration, which slows learning and increases variance. We propose a model-based approach that incorporates approximate priors into the reward function a…

Choquet rank-dependent utility
Zachary Van Oosten, Ruodu Wang
https://arxiv.org/abs/2509.10788 https://arxiv.org/pdf/2509.10788

Choquet rank-dependent utility
We propose a new decision model under ambiguity, called the Choquet rank-dependent utility model. The model extends the Choquet expected utility model by allowing for the reduction to the rank-dependent utility model in the absence of ambiguity, rather than to the expected utility model. The model has three major components: a utility function $u$ and a probability distortion $g$, which together capture the risk component of the preferences, and generalized probabilistic beliefs $ν$, which cap…

EB-MBD: Emerging-Barrier Model-Based Diffusion for Safe Trajectory Optimization in Highly Constrained Environments
Raghav Mishra, Ian R. Manchester
https://arxiv.org/abs/2510.07700

EB-MBD: Emerging-Barrier Model-Based Diffusion for Safe Trajectory Optimization in Highly Constrained Environments
We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We show that constraints on Model-Based Diffusion can lead to catastrophic performance degradation, even on simple 2D systems due to sample inefficiency in the Monte Carlo approximation of the score function. We introduce Emerging-Barrier Model-Based Diffusion (EB-MBD) which uses progressively introduced barrier constraints to avoid these problems, significantl…

The Courant-Hilbert construction in 4D Chern-Simons theory
Osamu Fukushima, Takaki Matsumoto, Kentaroh Yoshida
https://arxiv.org/abs/2509.22080 https://arx…

The Courant-Hilbert construction in 4D Chern-Simons theory
We consider the Courant-Hilbert (CH) construction of integrable deformations of a two-dimensional principal chiral model (2D PCM) in the context of the four-dimensional Chern-Simons (4D CS) theory. According to this construction, an integrable deformation of 2D PCM is characterized by a boundary function. As a result, the master formula obtained from the 4D CS theory should be corrected by the trace of the energy-momentum tensor so as to support the CH construction. We present some examples of …

Koopman-Operator-Based Model Predictive Control for Drag-free Satellite
Yankai Wang, Ti Chen
https://arxiv.org/abs/2509.20100 https://arxiv.org/pdf/2509.20…

Koopman-Operator-Based Model Predictive Control for Drag-free Satellite
This paper presents a data-driven modelling method for nonlinear dynamics of drag-free satellite based on Koopman operator theory, and a model predictive controller is designed based on the identified model. The nonlinear dynamics of drag-free satellite are identified and controlled based on Sparse Identification of Nonlinear Dynamics (SINDy). Using the manually constructed nonlinear function dictionary as observables, the system approximation is obtained by SINDy algorithm, and a linear Model …

Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits
Matthieu Cornillault, Samuel Belliard
https://arxiv.org/abs/2509.11797

Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits
We continue the work of Belliard, Pimenta and Slavnov (2024) studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified Izergin one and a Vandermonde one. This expression enables us to compute the partition function in the homogeneous limit for the rectangular lattice, and then to study the thermodynamic limit. It leads to a new result, we obtain the first order of free energy wi…

From Pheromones to Policies: Reinforcement Learning for Engineered Biological Swarms
Aymeric Vellinger, Nemanja Antonic, Elio Tuci
https://arxiv.org/abs/2509.20095 https://

From Pheromones to Policies: Reinforcement Learning for Engineered Biological Swarms
Swarm intelligence emerges from decentralised interactions among simple agents, enabling collective problem-solving. This study establishes a theoretical equivalence between pheromone-mediated aggregation in \celeg\ and reinforcement learning (RL), demonstrating how stigmergic signals function as distributed reward mechanisms. We model engineered nematode swarms performing foraging tasks, showing that pheromone dynamics mathematically mirror cross-learning updates, a fundamental RL algorithm. E…

A Stable and Principled Loss Function for Direct Language Model Alignment
Yuandong Tan
https://arxiv.org/abs/2508.07137 https://arxiv.org/pdf/2508.07137

A Stable and Principled Loss Function for Direct Language Model Alignment
The alignment of large language models (LLMs) with human preferences is commonly achieved through Reinforcement Learning from Human Feedback (RLHF). Direct Preference Optimization (DPO) simplified this paradigm by establishing a direct mapping between the optimal policy and a reward function, eliminating the need for an explicit reward model. However, we argue that the DPO loss function is theoretically misaligned with its own derivation, as it promotes the indefinite maximization of a logits d…

The Liouville model in the $L^1$ phase: coupling and extreme values
Michael Hofstetter, Ofer Zeitouni
https://arxiv.org/abs/2508.15689 https://arxiv.org/pd…

The Liouville model in the $L^1$ phase: coupling and extreme values
We establish a strong coupling between the Liouville model and the Gaussian free field on the two dimensional torus in the $L^1$ phase $β\in (0, 8π)$, such that the difference of the two fields is a Hölder continuous function. The coupling originates from a Polchinski renormalisation group approach, which was previously used to prove analogous results for other Euclidean field theories in dimension two. Our main observations for the Liouville model are that the Polchinski flow has a definite…

Scalar fields from nonlinear sigma models on black hole spacetimes
Ludovico Machet, Llibert Arest\'e Sal\'o
https://arxiv.org/abs/2508.18362 https://

Scalar fields from nonlinear sigma models on black hole spacetimes
Scalar fields with non-trivial kinetic term derived from a nonlinear sigma model are motivated by UV completions of gravity such as string theory. We discuss the $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{O}(3)$ sigma models with interacting potentials and simulate their full nonlinear dynamics on black hole spacetimes. We study the properties of the field as a function of the curvature of the sigma model with respect to the free massive scalar case. In the accretion process, the $\mathrm{SL}(2,\…

Value Function Approximation for Nonlinear MPC: Learning a Terminal Cost Function with a Descent Property
T. M. J. T. Baltussen, C. A. Orrico, A. Katriniok, W. P. M. H. Heemels, D. Krishnamoorthy
https://arxiv.org/abs/2508.05804

Value Function Approximation for Nonlinear MPC: Learning a Terminal Cost Function with a Descent Property
We present a novel method to synthesize a terminal cost function for a nonlinear model predictive controller (MPC) through value function approximation using supervised learning. Existing methods enforce a descent property on the terminal cost function by construction, thereby restricting the class of terminal cost functions, which in turn can limit the performance and applicability of the MPC. We present a method to approximate the true cost-to-go with a general function approximator that is c…

On function-on-function linear quantile regression
Muge Mutis, Ufuk Beyaztas, Filiz Karaman, Han Lin Shang
https://arxiv.org/abs/2510.10792 https://arxiv.o…

On function-on-function linear quantile regression
We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated …

A multiple occupancy cell fluid model with competing attraction and repulsion interactions
R. V. Romanik, O. A. Dobush, M. P. Kozlovskii, I. V. Pylyuk, M. A. Shpot
https://arxiv.org/abs/2508.12613

A multiple occupancy cell fluid model with competing attraction and repulsion interactions
An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie-Weiss-type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral representation of the grand partition function, we apply Laplace's method to obtain asymptotically exact expressions for the pressure, density and equation of state. The model exhibits a hierarchy of first-order transitions, each terminating at a critical po…

Generalization Bound for a General Class of Neural Ordinary Differential Equations
Madhusudan Verma, Manoj Kumar
https://arxiv.org/abs/2508.18920 https://a…

Generalization Bound for a General Class of Neural Ordinary Differential Equations
Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their generalization error bounds. Previous research primarily focused on the linear case for the dynamics function in neural ODEs - Marion, P. (2023), or provided bounds for Neural Controlled ODEs that depend on the sampling interval Bleistein et al. (2023). In this wor…

High to low temperature: $O(N)$ model at large $N$
Justin R. David, Srijan Kumar
https://arxiv.org/abs/2508.14872 https://arxiv.org/pdf/2508.14872

High to low temperature: $O(N)$ model at large $N$
We study the $O(N)$ vector model for scalars with quartic interaction at large $N$ on $S^1\times S^2$ without the singlet constraint. The non-trivial fixed point of the model is described by a thermal mass satisfying the gap equation at large $N$. We obtain the partition function and the energy density for the model as a series at low temperature in units of the radius of the sphere. We show these results agree with the Borel-Padé extrapolations of the high temperature expansions of the partit…

Green Inventory Management: Leveraging Multiobjective Reverse Logistics
M. M. Rizvi, I. B. Wadhawan
https://arxiv.org/abs/2509.19639 https://arxiv.org/pdf/…

Green Inventory Management: Leveraging Multiobjective Reverse Logistics
The paper proposes a novel Economic Production Quantity (EPQ) inventory model within a reverse logistics framework, addressing new and repaired products with varying quality and demand patterns. The model integrates production and remanufacturing rates as functions of lot sizes and cycle numbers to develop a feasible inventory cost function. A key contribution of the study is formulating a multiobjective optimization framework that simultaneously minimizes inventory costs and accounts for envir…

Exploring Wormhole Structures within the Framework of $f(R,L_{m})$ Gravity
A. S. Agrawal, Baljeet Kaur Lotte, Reshma Kapse, B. Mishra
https://arxiv.org/abs/2509.17497 https://…

Exploring Wormhole Structures within the Framework of $f(R,L_{m})$ Gravity
In this work, we investigate wormhole geometries within the framework of $f(R,\mathcal{L}_{m})$ gravity by considering a specific form of the model. From the corresponding field equations, the shape function is derived, and the traversability conditions are examined for suitable choices of the model parameters. The obtained shape function is shown to satisfy all the necessary requirements for a traversable wormhole, including the energy conditions. The geometric properties of the wormhole are a…

A model free approach for continuous-time optimal tracking control with unknown user-define cost and constrained control input via advantage function
Duc Cuong Nguyen, Quang Huy Dao, Phuong Nam Dao
https://arxiv.org/abs/2509.16821

A model free approach for continuous-time optimal tracking control with unknown user-define cost and constrained control input via advantage function
This paper presents a pioneering approach to solving the linear quadratic regulation (LQR) and linear quadratic tracking (LQT) problems with constrained inputs using a novel off-policy continuous-time Q-learning framework. The proposed methodology leverages a novel concept of the Advantage function for linear continuous systems, enabling solutions to be obtained without the need for prior knowledge of the reward matrix weights, state resetting, or assuming the existence of a predefined admissib…

Cox Regression on the Plane
Yael Travis-Lumer, Micha Mandel, Rebecca A. Betensky, Malka Gorfine
https://arxiv.org/abs/2509.12473 https://arxiv.org/pdf/2509…

Cox Regression on the Plane
The Cox proportional hazards model is the most widely used regression model in univariate survival analysis. Extensions of the Cox model to bivariate survival data, however, remain scarce. We propose two novel extensions based on a Lehmann-type representation of the survival function. The first, the simple Lehmann model, is a direct extension that retains a straightforward structure. The second, the generalized Lehmann model, allows greater flexibility by incorporating three distinct regression…

Minimization of Nonsmooth Weakly Convex Function over Prox-regular Set for Robust Low-rank Matrix Recovery
Keita Kume, Isao Yamada
https://arxiv.org/abs/2509.17549 https://

Minimization of Nonsmooth Weakly Convex Function over Prox-regular Set for Robust Low-rank Matrix Recovery
We propose a prox-regular-type low-rank constrained nonconvex nonsmooth optimization model for Robust Low-Rank Matrix Recovery (RLRMR), i.e., estimate problem of low-rank matrix from an observed signal corrupted by outliers. For RLRMR, the $\ell_{1}$-norm has been utilized as a convex loss to detect outliers as well as to keep tractability of optimization models. Nevertheless, the $\ell_{1}$-norm is not necessarily an ideal robust loss because the $\ell_{1}$-norm tends to overpenalize entries c…

Least squares-based methods to bias adjustment in scalar-on-function regression model using a functional instrumental variable
Xiwei Chen, Ufuk Beyaztas, Caihong Qin, Heyang Ji, Gilson Honvoh, Roger S. Zoh, Lan Xue, Carmen D. Tekwe
https://arxiv.org/abs/2509.12122

Least squares-based methods to bias adjustment in scalar-on-function regression model using a functional instrumental variable
Instrumental variables are widely used to adjust for measurement error bias when assessing associations of health outcomes with ME prone independent variables. IV approaches addressing ME in longitudinal models are well established, but few methods exist for functional regression. We develop two methods to adjust for ME bias in scalar on function linear models. We regress a scalar outcome on an ME prone functional variable using a functional IV for model identification and propose two least squ…