Tootfinder

Optimal control of the Poisson equation with transport regularization: Properties of optimal transport plans and transport map
Christian Meyer, Gerd Wachsmuth
https://arxiv.org/abs/2506.02808

Optimal control of the Poisson equation with transport regularization: Properties of optimal transport plans and transport map
An optimal control problem in the space of Borel measures governed by the Poisson equation is investigated. The characteristic feature of the problem under consideration is the Tikhonov regularization term in form of the transportation distance of the control to a given prior. Existence of optimal solutions is shown and first-order necessary optimality conditions are derived. The latter are used to deduce structural a priori information about the optimal control and its support based on propert…

Energy-optimal control of discrete-time port-Hamiltonian systems
Arijit Sarkar, Vaibhav Kumar Singh, Manuel Schaller, Karl Worthmann
https://arxiv.org/abs/2509.01345 https://

Energy-optimal control of discrete-time port-Hamiltonian systems
In this letter, we study the energy-optimal control of nonlinear port-Hamiltonian (pH) systems in discrete time. For continuous-time pH systems, energy-optimal control problems are strictly dissipative by design. This property, stating that the system to be optimized is dissipative with the cost functional as a supply rate, implies a stable long-term behavior of optimal solutions and enables stability results in predictive control. In this work, we show that the crucial property of strict dis…

Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space
Paul Freulon, Nikitas Georgakis, Victor Panaretos
https://arxiv.org/abs/2507.01709

Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space
The optimal transport problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupling is often singular with respect to Lebesgue measure. Regularizing the optimal transport problem with an entropy term yields an approximation called entropic optimal transport. Entropic penalties steer the induced coupling toward a reference measure with desired properties. For instance, when seeking a diffuse coupling, …

New Constructions of Optimal $(r,\delta)$-LRCs via Algebraic Function Fields
Yuan Gao, Haoming Shi, Weijun Fang
https://arxiv.org/abs/2509.00302 https://ar…

New Constructions of Optimal $(r,δ)$-LRCs via Algebraic Function Fields
Constructing optimal $(r,δ)$-LRCs that attain the Singleton-type bound is an active and important research direction, particularly due to their practical applications in distributed storage systems. In this paper, we focus on the construction of optimal $(r,δ)$-LRCs with flexible minimum distances, especially for the case $δ\geq 3$. We first extend a general framework -- originally proposed by Li \textit{et al.} (IEEE Trans. Inf. Theory, vol. 65, no. 1, 2019) and Ma and Xing (J. Comb. Theory…

Optimal Dynamic Fees in Automated Market Makers
Leonardo Baggiani, Martin Herdegen, Leandro S\'anchez-Betancourt
https://arxiv.org/abs/2506.02869 https…

Optimal Dynamic Fees in Automated Market Makers
Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show…

A Transformer-Based Neural Network for Optimal Deterministic-Allocation and Anonymous Joint Auction Design
Zhen Zhang, Luowen Liu, Wanzhi Zhang, Zitian Guo, Kun Huang, Qi Qi, Qiang Liu, Xingxing Wang
https://arxiv.org/abs/2506.02435

A Transformer-Based Neural Network for Optimal Deterministic-Allocation and Anonymous Joint Auction Design
With the advancement of machine learning, an increasing number of studies are employing automated mechanism design (AMD) methods for optimal auction design. However, all previous AMD architectures designed to generate optimal mechanisms that satisfy near dominant strategy incentive compatibility (DSIC) fail to achieve deterministic allocation, and some also lack anonymity, thereby impacting the efficiency and fairness of advertising allocation. This has resulted in a notable discrepancy between…

Systematic Evaluation of Trade-Offs in Motion Planning Algorithms for Optimal Industrial Robotic Work Cell Design
G. de Mathelin, C. Hartl-Nesic, A. Kugi
https://arxiv.org/abs/2509.02146

Systematic Evaluation of Trade-Offs in Motion Planning Algorithms for Optimal Industrial Robotic Work Cell Design
The performance of industrial robotic work cells depends on optimizing various hyperparameters referring to the cell layout, such as robot base placement, tool placement, and kinematic design. Achieving this requires a bilevel optimization approach, where the high-level optimization adjusts these hyperparameters, and the low-level optimization computes robot motions. However, computing the optimal robot motion is computationally infeasible, introducing trade-offs in motion planning to make the …

A reduced-IRKA method for large-scale $\mathcal{H}_2$-optimal model order reduction
Yiding Lin, Valeria Simoncini
https://arxiv.org/abs/2508.00242 https://…

A reduced-IRKA method for large-scale $\mathcal{H}_2$-optimal model order reduction
The $\mathcal{H}_2$-optimal Model Order Reduction (MOR) is one of the most significant frameworks for reduction methodologies for linear dynamical systems. In this context, the Iterative Rational Krylov Algorithm (\IRKA) is a well established method for computing an optimal projection space of fixed dimension $r$, when the system has small or medium dimensions. However, for large problems the performance of \IRKA\ is not satisfactory. In this paper, we introduce a new rational Krylov subspace p…

Asymptotically Optimal Inapproximability of E$k$-SAT Reconfiguration
Shuichi Hirahara, Naoto Ohsaka
https://arxiv.org/abs/2508.00276 https://arxiv.org/pdf/…

Asymptotically Optimal Inapproximability of E$k$-SAT Reconfiguration
In the Maxmin E$k$-SAT Reconfiguration problem, we are given a satisfiable $k$-CNF formula $φ$ where each clause contains exactly $k$ literals, along with a pair of its satisfying assignments. The objective is transform one satisfying assignment into the other by repeatedly flipping the value of a single variable, while maximizing the minimum fraction of satisfied clauses of $φ$ throughout the transformation. In this paper, we demonstrate that the optimal approximation factor for Maxmin E$k$-…

A Practical Linear Time Algorithm for Optimal Tree Decomposition of Halin Graphs
J. A. Alejandro-Soto, Joel Antonio Trejo-Sanchez, Carlos Segura
https://arxiv.org/abs/2506.02346

A Practical Linear Time Algorithm for Optimal Tree Decomposition of Halin Graphs
This work proposes \textsc{H-Td}, a practical linear-time algorithm for computing an optimal-width tree decomposition of Halin graphs. Unlike state-of-the-art methods based on reduction rules or separators, \textsc{H-Td} exploits the structural properties of Halin graphs. Although two theoretical linear-time algorithms exist that can be applied to graphs of treewidth three, no practical implementation has been made publicly available. Furthermore, extending reduction-based approaches to partial…

Optimal distillation of photonic indistinguishability
Francesco Hoch, Anita Camillini, Giovanni Rodari, Eugenio Caruccio, Gonzalo Carvacho, Taira Giordani, Riccardo Albiero, Niki Di Giano, Giacomo Corrielli, Francesco Ceccarelli, Roberto Osellame, Marco Robbio, Leonardo Novo, Nicol\`o Spagnolo, Ernesto F. Galv\~ao, Fabio Sciarrino
https://…

Optimal distillation of photonic indistinguishability
Imperfect photons' indistinguishability limits the performance of photonic quantum communication and computation . Distillation protocols, inspired by entanglement purification, enhance photons' indistinguishability by leveraging quantum interference in linear optical circuits. In this work, we present a three-photon distillation protocol optimized to achieve the maximum visibility gain, which requires consideration of multi-photon effects such as collective photonic phases. We employ interfero…

QC-OT: Optimal Transport with Quasiconformal Mapping
Yuping Lv, Qi Zhao, Xuebin Chang, Wei Zeng
https://arxiv.org/abs/2507.01456 https://

QC-OT: Optimal Transport with Quasiconformal Mapping
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in transmission results and processes. Existing numerical and geometric methods for computing OT seldom pays specific attention on this aspect. Especially, when dealing with the triangular mesh data, the known semi-discrete geometric OT (sd-OT) method employs critical op…

Optimal Parallel Scheduling under Concave Speedup Functions
Chengzhang Li, Peizhong Ju, Atilla Eryilmaz, Ness Shroff
https://arxiv.org/abs/2509.01811 https://

Optimal Parallel Scheduling under Concave Speedup Functions
Efficient scheduling of parallel computation resources across multiple jobs is a fundamental problem in modern cloud/edge computing systems for many AI-based applications. Allocating more resources to a job accelerates its completion, but with diminishing returns. Prior work (heSRPT) solved this problem only for some specific speedup functions with an exponential form, providing a closed-form solution. However, the general case with arbitrary concave speedup functions -- which more accurately c…

Using Machine Learning to Compute Constrained Optimal Carbon Tax Rules
Felix K\"ubler, Simon Scheidegger, Oliver Surbek
https://arxiv.org/abs/2507.01704

Using Machine Learning to Compute Constrained Optimal Carbon Tax Rules
We develop a computational framework for deriving Pareto-improving and constrained optimal carbon tax rules in a stochastic overlapping generations (OLG) model with climate change. By integrating Deep Equilibrium Networks for fast policy evaluation and Gaussian process surrogate modeling with Bayesian active learning, the framework systematically locates optimal carbon tax schedules for heterogeneous agents exposed to climate risk. We apply our method to a 12-period OLG model in which exogenous…

DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee
Yingyuan Li, Aokun Wang, Zhongjian Wang
https://arxiv.org/abs/2506.23429

DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min optimization during training and does not impose any restriction on the network structure. Theoretically we establish a weak convergence guarantee and a quantitative error bound between the learned map and the optimal transport map. Our numerical experiments vali…

Totally convex functions, $L^2$-Optimal transport for laws of random measures, and solution to the Monge problem
Alessandro Pinzi, Giuseppe Savar\'e
https://arxiv.org/abs/2509.01768

Totally convex functions, $L^2$-Optimal transport for laws of random measures, and solution to the Monge problem
We study the Optimal Transport problem for laws of random measures in the Kantorovich-Wasserstein space $\mathcal{P}_2(\mathcal{P}_2(\mathrm{H}))$, associated with a Hilbert space $\mathrm{H}$ (with finite or infinite dimension) and for the corresponding quadratic cost induced by the squared Wasserstein metric in $\\mathcal{P}_2(\mathrm{H}).$ Despite the lack of smoothness of the cost, the fact that the space $\mathcal{P}_2(\mathrm{H})$ is not Hilbertian, and the curvature distortion induced …

Optimal sources for elliptic PDEs
Giuseppe Buttazzo, Juan Casado-D\'iaz, Faustino Maestre
https://arxiv.org/abs/2509.01521 https://arxiv.org/pdf/2509.0…

Optimal sources for elliptic PDEs
We investigate optimal control problems governed by the elliptic partial differential equation $-Δu=f$ subject to Dirichlet boundary conditions on a given domain $Ω$. The control variable in this setting is the right-hand side $f$, and the objective is to minimize a cost functional that depends simultaneously on the control $f$ and on the associated state function $u$. We establish the existence of optimal controls and analyze their qualitative properties by deriving necessary conditions fo…

Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
S\'andor Kisfaludi-Bak, Geert van Wordragen
https://arxiv.org/abs/2509.01443 https://

Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
We consider Steiner spanners in Euclidean and non-Euclidean geometries. In the Euclidean setting, a recent line of work initiated by Le and Solomon [FOCS'19] and further improved by Chang et al. [SoCG'24] obtained Steiner $(1+\varepsilon)$-spanners of size $O_d(\varepsilon^{(1-d)/2}\log(1/\varepsilon)n)$, nearly matching the lower bounds of Bhore and Tóth [SIDMA'22]. We obtain Steiner $(1+\varepsilon)$-spanners of size $O_d(\varepsilon^{(1-d)/2}\log(1/\varepsilon)n)$ not only in $d$-dimensio…

Bifurcation in optimal retirement
Bushra Shehnam Ashraf, Thomas S. Salisbury
https://arxiv.org/abs/2506.02155 https://arxiv.org/pdf/2…

Bifurcation in optimal retirement
We study optimal consumption and retirement using a Cobb-Douglas utility and a simple model in which an interesting bifurcation arises. With high wealth, individuals plan to retire. With low wealth they plan to never retire. At a critical level of initial wealth they may choose to defer this decision, leading to a continuum of wealth trajectories with identical utilities.

In West-Nordamerika ist der Einfluss des Menschen auf das #Feuerwetter (heißes, trockenes, windreiches Wetter) jetzt messbar.
Zwischen 81 % und 188 % des Anstiegs in den letzten 50 Jahren gehen auf menschgemachte #Klimaveränderungen zurück.
Temperatur,

Fingerprint of anthropogenic climate change detected in long-term western North American fire weather trends - Communications Earth & Environment
Anthropogenic climate change has been the dominant driver of increasing fire weather trends in western North America over the past 50 years, contributing 81–188% of the observed linear trends, according to regional optimal fingerprinting applied to large ensembles of high-resolution climate models.

Neural Co-state Projection Regulator: A Model-free Paradigm for Real-time Optimal Control with Input Constraints
Lihan Lian, Uduak Inyang-Udoh
https://arxiv.org/abs/2508.00283 h…

Neural Co-state Projection Regulator: A Model-free Paradigm for Real-time Optimal Control with Input Constraints
Learning-based approaches, notably Reinforcement Learning (RL), have shown promise for solving optimal control tasks without explicit system models. However, these approaches are often sample-inefficient, sensitive to reward design and hyperparameters, and prone to poor generalization, especially under input constraints. To address these challenges, we introduce the neural co-state projection regulator (NCPR), a model-free learning-based optimal control framework that is grounded in Pontryagin'…

An adaptive design for optimizing treatment assignment in randomized clinical trials
Wei Zhang, Zhiwei Zhang, Aiyi Liu
https://arxiv.org/abs/2509.00429 https://

An adaptive design for optimizing treatment assignment in randomized clinical trials
The treatment assignment mechanism in a randomized clinical trial can be optimized for statistical efficiency within a specified class of randomization mechanisms. Optimal designs of this type have been characterized in terms of the variances of potential outcomes conditional on baseline covariates. Approximating these optimal designs requires information about the conditional variance functions, which is often unavailable or unreliable at the design stage. As a practical solution to this dilem…

The optimal degree for maximizing rumor spreading on a ring lattice
Ana C. D\'iaz Bacca, Pablo M. Rodriguez, Catalina M. R\'ua-Alvarez
https://arxiv.org/abs/2507.02141

The optimal degree for maximizing rumor spreading on a ring lattice
The ring lattice with $n$ nodes, each connected to the $2k$ nearest neighbors, has been utilized as the basis for several models of small-world networks, obtained by rewiring or adding edges to generate shortcuts. It is well-known that when a rumor process is embedded in these networks, the system exhibits a transition between localization and propagation at a finite value of the network mean degree, emphasizing the importance of incorporating shortcuts to optimize the dissemination process. We…

Removal of Redundant Candidate Points for the Exact D-Optimal Design Problem
Radoslav Harman, Samuel Rosa
https://arxiv.org/abs/2509.00719 https://arxiv.or…

Removal of Redundant Candidate Points for the Exact D-Optimal Design Problem
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods, constructing optimal exact (i.e., finite-sample) designs is a substantially more difficult integer-optimization problem. In this paper, we propose necessary conditions, based on approximate designs, that must be satisfied by any support point of a D-optimal exact d…

Optimal Feedback Schemes for Dirty Paper Channels With State Estimation at the Receiver
Dengfeng Xia, Han Deng, Haonan Zhang, Fan Cheng, Bin Dai, Liuguo Yin
https://arxiv.org/abs/2507.00942

Optimal Feedback Schemes for Dirty Paper Channels With State Estimation at the Receiver
In the literature, it has been shown that feedback does not increase the optimal rate-distortion region of the dirty paper channel with state estimation at the receiver (SE-R). On the other hand, it is well-known that feedback helps to construct low-complexity coding schemes in Gaussian channels, such as the elegant Schalkwijk-Kailath (SK) feedback scheme. This motivates us to explore capacity-achieving SK-type schemes in dirty paper channels with SE-R and feedback. In this paper, we first prop…

OTMol: Robust Molecular Structure Comparison via Optimal Transport
Xiaoqi Wei, Xuhang Dai, Yaqi Wu, Yanxiang Zhao, Yingkai Zhang, Zixuan Cang
https://arxiv.org/abs/2509.01550 ht…

OTMol: Robust Molecular Structure Comparison via Optimal Transport
Root-mean-square deviation (RMSD) is widely used to assess structural similarity in systems ranging from flexible ligand conformers to complex molecular cluster configurations. Despite its wide utility, RMSD calculation is often challenged by inconsistent atom ordering, indistinguishable configurations in molecular clusters, and potential chirality inversion during alignment. These issues highlight the necessity of accurate atom-to-atom correspondence as a prerequisite for meaningful alignment.…

An optimal $L^2$ extension for continuous $L^2$-optimal Hermitian metrics
Zhuo Liu
https://arxiv.org/abs/2506.22840 https://arxiv.org…

An optimal $L^2$ extension for continuous $L^2$-optimal Hermitian metrics
In this paper, we obtain an optimal $L^2$ extension theorem for continuous $L^2$-optimal Hermitian metric on bounded planer domains. As applications, we affirmatively answer a question of Deng-Ning-Wang and a question of Inayama.

Passage-traversing optimal path planning with sampling-based algorithms
Jing Huang, Hao Su, Kwok Wai Samuel Au
https://arxiv.org/abs/2506.23614 https://

Passage-traversing optimal path planning with sampling-based algorithms
This paper introduces a new paradigm of optimal path planning, i.e., passage-traversing optimal path planning (PTOPP), that optimizes paths' traversed passages for specified optimization objectives. In particular, PTOPP is utilized to find the path with optimal accessible free space along its entire length, which represents a basic requirement for paths in robotics. As passages are places where free space shrinks and becomes constrained, the core idea is to leverage the path's passage traversal…

Week 1 NFL survivor pool picks, advice, optimal strategy: NFL expert makes knockout pick, teams to avoid

https://www.cbssports.com/nfl/news/week-1-

Learning Optimal Posted Prices for a Unit-Demand Buyer
Yifeng Teng, Yifan Wang
https://arxiv.org/abs/2506.02284 https://arxiv.org/pdf…

Learning Optimal Posted Prices for a Unit-Demand Buyer
We study the problem of learning the optimal item pricing for a unit-demand buyer with independent item values, and the learner has query access to the buyer's value distributions. We consider two common query models in the literature: the sample access model where the learner can obtain a sample of each item value, and the pricing query model where the learner can set a price for an item and obtain a binary signal on whether the sampled value of the item is greater than our proposed price. In …

Handling Sparse Non-negative Data in Finance
Agostino Capponi, Zhaonan Qu
https://arxiv.org/abs/2509.01478 https://arxiv.org/pdf/2509.01478

Handling Sparse Non-negative Data in Finance
We show that Poisson regression, though often recommended over log-linear regression for modeling count and other non-negative variables in finance and economics, can be far from optimal when heteroskedasticity and sparsity -- two common features of such data -- are both present. We propose a general class of moment estimators, encompassing Poisson regression, that balances the bias-variance trade-off under these conditions. A simple cross-validation procedure selects the optimal estimator. Num…

Curvature-Based Optimal Polynomial Geometric Interpolation of Circular Arcs
Ema \v{C}e\v{s}ek, Ale\v{s} Vavpeti\v{c}
https://arxiv.org/abs/2509.01353 https://

Curvature-Based Optimal Polynomial Geometric Interpolation of Circular Arcs
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is prescribed at the boundary points of the circular arc. Analysis is done for cases of parabolic $G^0$, cubic $G^1$ and quartic $G^2$ interpolation. The comparison of the approximation of circular arcs based on curvature with the approximation based on radial error i…

Optimal Simulation Budget Allocation Under Unknown Sampling Variance
Jianzhong Du, Ilya O. Ryzhov, Siyang Gao
https://arxiv.org/abs/2509.02138 https://arxi…

Optimal Simulation Budget Allocation Under Unknown Sampling Variance
The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed with both its mean and variance being unknown. Using a Bayesian representation of the probability of correct selection, which allows us to explicitly model uncertainty about the variance, we provide a theoretical characterization of the optimal allocation of the…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[10/11]:
- Learning local and global prototypes with optimal transport for unsupervised anomaly detection an...
Robin Trombetta, Carole Lartizien

Near-Optimal Stability for Distributed Transaction Processing in Blockchain Sharding
Ramesh Adhikari, Costas Busch, Dariusz R. Kowalski
https://arxiv.org/abs/2509.02421 https://…

Near-Optimal Stability for Distributed Transaction Processing in Blockchain Sharding
In blockchain sharding, $n$ processing nodes are divided into $s$ shards, and each shard processes transactions in parallel. A key challenge in such a system is to ensure system stability for any ``tractable'' pattern of generated transactions; this is modeled by an adversary generating transactions with a certain rate of at most $ρ$ and burstiness $b$. This model captures worst-case scenarios and even some attacks on transactions' processing, e.g., DoS. A stable system ensures bounded transac…

Offline Reinforcement Learning for Mobility Robustness Optimization
Pegah Alizadeh, Anastasios Giovanidis, Pradeepa Ramachandra, Vasileios Koutsoukis, Osama Arouk
https://arxiv.org/abs/2506.22793

Offline Reinforcement Learning for Mobility Robustness Optimization
In this work we revisit the Mobility Robustness Optimisation (MRO) algorithm and study the possibility of learning the optimal Cell Individual Offset tuning using offline Reinforcement Learning. Such methods make use of collected offline datasets to learn the optimal policy, without further exploration. We adapt and apply a sequence-based method called Decision Transformers as well as a value-based method called Conservative Q-Learning to learn the optimal policy for the same target reward as t…

Explicit Constructions of Maximal 3-Zero-Sum-Free Subsets in $(\mathbb{Z}/4\mathbb{Z})^n$
Alfonso Davila Vera
https://arxiv.org/abs/2509.01735 https://arxi…

Explicit Constructions of Maximal 3-Zero-Sum-Free Subsets in $(\mathbb{Z}/4\mathbb{Z})^n$
We address Nathan Kaplan's 2014 CANT problem: the largest $H \subseteq (\mathbb{Z}/4\mathbb{Z})^n$ with no distinct $x, y, z \in H$ such that $x + y + z \equiv 0 \pmod{4}$. A universal optimal construction, $H = \{ v \mid v_1 \equiv 1 \text{ or } 3 \pmod{4} \}$, achieves size $4^n/2$ and density 0.5 for all $n$, proven maximal via $|H|^2 \leq (4^n - |H|) \cdot |H|$. Verified computationally to $n=10$; code at https://github.com/DynMEP/ZeroSumFreeSets-Z4/releases/ta…

Approximate Solution Methods for the Average Reward Criterion in Optimal Tracking Control of Linear Systems
Duc Cuong Nguyen
https://arxiv.org/abs/2507.01556

Approximate Solution Methods for the Average Reward Criterion in Optimal Tracking Control of Linear Systems
This paper studies optimal control under the average-reward/cost criterion for deterministic linear systems. We derive the value function and optimal policy, and propose an approximate solution using Model Predictive Control to enable practical implementation.

Introducing HALC: A general pipeline for finding optimal prompting strategies for automated coding with LLMs in the computational social sciences
Andreas Reich, Claudia Thoms, Tobias Schrimpf
https://arxiv.org/abs/2507.21831

Introducing HALC: A general pipeline for finding optimal prompting strategies for automated coding with LLMs in the computational social sciences
LLMs are seeing widespread use for task automation, including automated coding in the social sciences. However, even though researchers have proposed different prompting strategies, their effectiveness varies across LLMs and tasks. Often trial and error practices are still widespread. We propose HALC$-$a general pipeline that allows for the systematic and reliable construction of optimal prompts for any given coding task and model, permitting the integration of any prompting strategy deemed rel…

HCQA: Hybrid Classical-Quantum Agent for Generating Optimal Quantum Sensor Circuits
Ahmad Alomari, Sathish A. P. Kumar
https://arxiv.org/abs/2508.21246 https://

HCQA: Hybrid Classical-Quantum Agent for Generating Optimal Quantum Sensor Circuits
This study proposes an HCQA for designing optimal Quantum Sensor Circuits (QSCs) to address complex quantum physics problems. The HCQA integrates computational intelligence techniques by leveraging a Deep Q-Network (DQN) for learning and policy optimization, enhanced by a quantum-based action selection mechanism based on the Q-values. A quantum circuit encodes the agent current state using Ry gates, and then creates a superposition of possible actions. Measurement of the circuit results in prob…

Doubly-Dispersive Continuous MIMO Systems: Channel Modeling and Beamforming Design
Kuranage Roche Rayan Ranasinghe, Zhaolin Wang, Hyeon Seok Rou, Giuseppe Thadeu Freitas de Abreu, Emil Bj\"ornson
https://arxiv.org/abs/2509.00964

Doubly-Dispersive Continuous MIMO Systems: Channel Modeling and Beamforming Design
We address the modeling and optimal beamforming (BF) design for multiple-input multiple-output (MIMO) continuous aperture array (CAPA) systems operating over doubly-dispersive (DD) channels. First, a comprehensive DD continuous MIMO (DDC MIMO) channel model that incorporates CAPAs at both the transmitter (TX) and receiver (RX) is derived, which is used to obtain explicit input-output (I/O) relations for various waveforms well suited to integrated sensing and communications (ISAC) and robust to …

Selection of Optimal Number and Location of PMUs for CNN Based Fault Location and Identification
Khalid Daud Khattak, Muhammad A. Choudhry
https://arxiv.org/abs/2509.02192 https…

Selection of Optimal Number and Location of PMUs for CNN Based Fault Location and Identification
In this paper, we present a data-driven Forward Selection with Neighborhood Refinement (FSNR) algorithm to determine the number and placement of Phasor Measurement Units (PMUs) for maximizing deep-learning-based fault diagnosis performance. Candidate PMU locations are ranked via a cross-validated Support Vector Machine (SVM) classifier, and each selection is refined through local neighborhood exploration to produce a near-optimal sensor set. The resulting PMU subset is then supplied to a 1D Con…

Quasi-optimal error estimates for the approximation of stable stationary states of the elastic energy of inextensible curves
S\"oren Bartels, Bal\'azs Kov\'acs, Dominik Schneider
https://arxiv.org/abs/2509.01287

Quasi-optimal error estimates for the approximation of stable stationary states of the elastic energy of inextensible curves
We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility constraint is only enforced at the nodes of the discretization. We show why this discretization leads to suboptimal convergence rates and we improve on it by also enforcing the constraint in the midpoints of each subinterval. We then use the inverse function the…

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift
Zhen Zhang, Xin Liu, Shaoli Wang, Jiaye Teng
https://arxiv.org/abs/2506.23453

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift
Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its common occurrence in real-world scenarios. In this paper, we investigate the minimax lower bound of the problem when the source and target distributions are known. To achieve the minimax optimal bound (up to a logarithmic factor), we propose a two-stage algorithm…

Geometric Visual Servo Via Optimal Transport
Ethan Canzini, Simon Pope, Ashutosh Tiwari
https://arxiv.org/abs/2506.02768 https://arxi…

Geometric Visual Servo Via Optimal Transport
When developing control laws for robotic systems, the principle factor when examining their performance is choosing inputs that allow smooth tracking to a reference input. In the context of robotic manipulation, this involves translating an object or end-effector from an initial pose to a target pose. Robotic manipulation control laws frequently use vision systems as an error generator to track features and produce control inputs. However, current control algorithms don't take into account the …

Testing maximum entropy models with e-values
Francesca Giuffrida, Diego Garlaschelli, Peter Gr\"unwald
https://arxiv.org/abs/2509.01064 https://arxiv.…

Testing maximum entropy models with e-values
E-values have recently emerged as a robust and flexible alternative to p-values for hypothesis testing, especially under optional continuation, i.e., when additional data from further experiments are collected. In this work, we define optimal e-values for testing between maximum entropy models, both in the microcanonical (hard constraints) and canonical (soft constraints) settings. We show that, when testing between two hypotheses that are both microcanonical, the so-called growth-rate optimal …

Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
Niklas Baumgarten, David Schneiderhan
https://arxiv.org/abs/2506.02647 https:/…

Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a parallel multilevel Monte Carlo method as stochastic gradient estimator. As a result, we achieve precise control over the stochastic gradient's bias, introduced by numerical approximation, and its sampling error, arising from the use of incomplete gradients, wh…

Optimal Dispersion Under Asynchrony
Debasish Pattanayak, Ajay D. Kshemkalyani, Manish Kumar, Anisur Rahaman Molla, Gokarna Sharma
https://arxiv.org/abs/2507.01298

Optimal Dispersion Under Asynchrony
We study the dispersion problem in anonymous port-labeled graphs: $k \leq n$ mobile agents, each with a unique ID and initially located arbitrarily on the nodes of an $n$-node graph with maximum degree $Δ$, must autonomously relocate so that no node hosts more than one agent. Dispersion serves as a fundamental task in distributed computing of mobile agents, and its complexity stems from key challenges in local coordination under anonymity and limited memory. The goal is to minimize both the …

Covariance scanning for adaptively optimal change point detection in high-dimensional linear models
Haeran Cho, Housen Li
https://arxiv.org/abs/2507.02552 …

Covariance scanning for adaptively optimal change point detection in high-dimensional linear models
This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed the sparsity of the covariance-weighted differential parameter. This form of "inherent sparsity" captures a delicate interplay between the covariance structure of the regressors and the change in regression coefficients on the detectability of a change point. Complem…

Re-examining the Legendre-Gauss-Lobatto Pseudospectral Methods for Optimal Control
Yilin Zou, Fanghua Jiang
https://arxiv.org/abs/2507.01660 https://

Re-examining the Legendre-Gauss-Lobatto Pseudospectral Methods for Optimal Control
Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau (LGR) points in terms of convergence properties, this paper presents a rigorous re-examination of LGL-based methods. We introduce an augmented formulation that enhances the standard LGL collocation approach by incorporating an additional degree of freedom (DOF…

Fairly Wired: Towards Leximin-Optimal Division of Electricity
Eden Hartman, Dinesh Kumar Baghel, Erel Segal-Halevi
https://arxiv.org/abs/2506.02193 https:/…

Fairly Wired: Towards Leximin-Optimal Division of Electricity
In many parts of the world - particularly in developing countries - the demand for electricity exceeds the available supply. In such cases, it is impossible to provide electricity to all households simultaneously. This raises a fundamental question: how should electricity be allocated fairly? In this paper, we explore this question through the lens of egalitarianism - a principle that emphasizes equality by prioritizing the welfare of the worst-off households. One natural rule that aligns with …

GridMind: LLMs-Powered Agents for Power System Analysis and Operations
Hongwei Jin, Kibaek Kim, Jonghwan Kwon
https://arxiv.org/abs/2509.02494 https://arxi…

GridMind: LLMs-Powered Agents for Power System Analysis and Operations
The complexity of traditional power system analysis workflows presents significant barriers to efficient decision-making in modern electric grids. This paper presents GridMind, a multi-agent AI system that integrates Large Language Models (LLMs) with deterministic engineering solvers to enable conversational scientific computing for power system analysis. The system employs specialized agents coordinating AC Optimal Power Flow and N-1 contingency analysis through natural language interfaces whi…

Optimal control of SDEs with merely measurable drift: an HJB approach
Kai Du, Qingmeng Wei
https://arxiv.org/abs/2509.01054 https://arxiv.org/pdf/2509.0105…

Optimal control of SDEs with merely measurable drift: an HJB approach
We investigate an optimal control problem for a diffusion whose drift and running cost are merely measurable in the state variable. Such low regularity rules out the use of Pontryagin's maximum principle and also invalidates the standard proof of the Bellman principle of optimality. We address these difficulties by analyzing the associated Hamilton-Jacobi-Bellman (HJB) equation. Using PDE techniques together with a policy iteration scheme, we prove that the HJB equation admits a unique strong s…

Tree decompositions with small width, spread, order and degree
David R. Wood
https://arxiv.org/abs/2509.01140 https://arxiv.org/pdf/2509.01140

Tree decompositions with small width, spread, order and degree
Tree-decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. The main property of tree-decompositions is the width (the maximum size of a bag $-1$). We show that every graph has a tree-decomposition with near-optimal width, plus several additional properties of interest. In particular every graph $G$ with treewidth at most $k$ has a tree-decomposition with width at most $72k+1$, where each vertex $v$ appears in at most $\text{deg}_G(v)+1$ bags, the num…

Robust estimation of optimal dynamic treatment regimes with nonignorable missing covariates
Jian Sun, Bo Fu, Li Su
https://arxiv.org/abs/2506.22892 https:/…

Robust estimation of optimal dynamic treatment regimes with nonignorable missing covariates
Estimating optimal dynamic treatment regimes (DTRs) using observational data is often challenged by nonignorable missing covariates arsing from informative monitoring of patients in clinical practice. To address nonignorable missingness of pseudo-outcomes induced by nonignorable missing covariates, a weighted Q-learning approach using parametric Q-function models and a semiparametric missingness propensity model has recently been proposed. However, misspecification of parametric Q-functions at …

An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions
Zhuo Liu
https://arxiv.org/abs/2506.22834 https://

An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions
In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via the multiple coarse $L^2$-estimate property for (strongly) upper semi-continuous functions and show that (strongly) upper semi-continuous $L^2$-optimal functions satisfy Skoda's integrability theorem and the strong openness property.

An Optimal Least-Square Solver For Scaled Partial-Isometric Linear Systems
Suvendu Kar, Murugesan Venkatapathi
https://arxiv.org/abs/2507.01434 https://

An Optimal Least-Square Solver For Scaled Partial-Isometric Linear Systems
We present an $O(mn)$ direct least-squares solver for $m \times n$ linear systems with a scaled partial isometry. The proposed algorithm is also useful when the system is block diagonal and each block is a scaled partial isometry with distinct scaling factors. We also include numerical experiments as a demonstration.

Covariate balance under Bayesian decision theory
Andr\'e A. F. Fumis, Victor Fossaluza, Rafael B. Stern
https://arxiv.org/abs/2509.01828 https://arxiv.…

Covariate balance under Bayesian decision theory
We study optimal sample allocation between treatment and control groups under Bayesian linear models. We derive an analytic expression for the Bayes risk, which depends jointly on sample size and covariate mean balance across groups. Under a flat conditional prior, the covariate mean balance term simplifies to the Mahalanobis distance. Our results reveal that the optimal allocation does not always correspond to equal sample sizes, and we provide sufficient conditions under which equal allocatio…

Learning-based primal-dual optimal control of discrete-time stochastic systems with multiplicative noise
Xiushan Jiang, Weihai Zhang
https://arxiv.org/abs/2506.02613

Learning-based primal-dual optimal control of discrete-time stochastic systems with multiplicative noise
Reinforcement learning (RL) is an effective approach for solving optimal control problems without knowing the exact information of the system model. However, the classical Q-learning method, a model-free RL algorithm, has its limitations, such as lack of strict theoretical analysis and the need for artificial disturbances during implementation. This paper explores the partially model-free stochastic linear quadratic regulator (SLQR) problem for a system with multiplicative noise from the primal…

Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
Dian Jing, Pablo Sala, Liang Jiang, Ruben Verresen
https://arxiv.org/abs/2507.23765 https://

Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this work, we exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a s…

Optimal Transport Learning: Balancing Value Optimization and Fairness in Individualized Treatment Rules
Wenhai Cui, Xiaoting Ji, Wen Su, Xiaodong Yan, Xingqiu Zhao
https://arxiv.org/abs/2507.23349

Optimal Transport Learning: Balancing Value Optimization and Fairness in Individualized Treatment Rules
Individualized treatment rules (ITRs) have gained significant attention due to their wide-ranging applications in fields such as precision medicine, ridesharing, and advertising recommendations. However, when ITRs are influenced by sensitive attributes such as race, gender, or age, they can lead to outcomes where certain groups are unfairly advantaged or disadvantaged. To address this gap, we propose a flexible approach based on the optimal transport theory, which is capable of transforming any…

Optimal Messaging Strategy for Incentivizing Agents in Dynamic Systems
Renyan Sun, Ashutosh Nayyar
https://arxiv.org/abs/2508.00188 https://arxiv.org/pdf/2…

Optimal Messaging Strategy for Incentivizing Agents in Dynamic Systems
We consider a finite-horizon discrete-time dynamic system jointly controlled by a designer and one or more agents, where the designer can influence the agents' actions through selective information disclosure. At each time step, the designer sends a message to the agent(s) from a prespecified message space. The designer may also take an action that directly influences system dynamics and rewards. Each agent uses its received message (and its own information) to choose its action. We are interes…

Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT)
Usman A. Khan, Mouhacine Benosman, Wenliang Liu, Federico Pecora, Joseph W. Durham
https://arxiv.org/abs/2508.21205

Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT)
In this paper, we propose a novel methodology for path planning and scheduling for multi-robot navigation that is based on optimal transport theory and model predictive control. We consider a setup where $N$ robots are tasked to navigate to $M$ targets in a common space with obstacles. Mapping robots to targets first and then planning paths can result in overlapping paths that lead to deadlocks. We derive a strategy based on optimal transport that not only provides minimum cost paths from robot…

Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs
Ugur G. Abdulla, Jose H. Rodrigues
https://arxiv.org/abs/2509.02050 https://

Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs
We pursue a computational analysis of the biomedical problem on the identification of the cancerous tumor at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial differential equations. Relying on the fact that the electrical conductivity of the cancerous tumor is significantly higher than the conductivity of the healthy tissue, we consider an inverse EIT problem on the identification of the conductivity map in the complete ele…

Asymptotically Optimal Secure Aggregation for Wireless Federated Learning with Multiple Servers
Zhenhao Huang, Kai Liang, Yuanming Shi, Songze Li, Youlong Wu
https://arxiv.org/abs/2506.23680

Asymptotically Optimal Secure Aggregation for Wireless Federated Learning with Multiple Servers
In this paper, we investigate the transmission latency of the secure aggregation problem in a \emph{wireless} federated learning system with multiple curious servers. We propose a privacy-preserving coded aggregation scheme where the servers can not infer any information about the distributed users' local gradients, nor the aggregation value. In our scheme, each user encodes its local gradient into $\sK$ confidential messages intended exclusively for different servers using a multi-secret shari…

Optimal Coordination of Flexible DERs in Local Energy and Flexibility Markets to Ensure Social Equity
Niloofar Pourghaderi, Milad Kabirifar, Payman Dehghanian
https://arxiv.org/abs/2506.02179

Optimal Coordination of Flexible DERs in Local Energy and Flexibility Markets to Ensure Social Equity
Local electricity markets offer a promising solution for integrating renewable energy sources and other distributed energy resources (DERs) into distribution networks. These markets enable the effective utilization of flexible resources by facilitating coordination among various agents. Beyond technical and economic considerations, addressing social equity within these local communities is critical and requires dedicated attention in market-clearing frameworks. This paper proposes a social equi…

The robustness of composite pulses elucidated by classical mechanics: Stability around the globe
Jonathan Berkheim, David J. Tannor
https://arxiv.org/abs/2507.01364

The robustness of composite pulses elucidated by classical mechanics: Stability around the globe
Composite Pulses (CPs) are widely used in Nuclear Magnetic Resonance (NMR), optical spectroscopy, optimal control experiments and quantum computing to manipulate systems that are well-described by a two-level Hamiltonian. A careful design of these pulses can allow the refocusing of an ensemble at a desired state, even if the ensemble experiences imperfections in the magnitude of the external field or resonance offsets. Since the introduction of CPs, several theoretical justifications for their …

CrossPipe: Towards Optimal Pipeline Schedules for Cross-Datacenter Training
Tiancheng Chen, Ales Kubicek, Langwen Huang, Torsten Hoefler
https://arxiv.org/abs/2507.00217

CrossPipe: Towards Optimal Pipeline Schedules for Cross-Datacenter Training
Training large language models (LLMs) now requires resources that exceed a single datacenter, making cross-datacenter strategies increasingly crucial. We present CrossPipe, a framework designed to optimize model training across geographically distributed datacenters by explicitly modeling and mitigating the impact of network latency and limited bandwidth. It enables unified analysis and optimization incorporating both pipeline parallelism (PP) and opportunities for overlapping data parallelism …

An in depth look at the Procrustes-Wasserstein distance: properties and barycenters
Davide Adamo, Marco Corneli, Manon Vuillien, Emmanuelle Vila
https://arxiv.org/abs/2507.00894

An in depth look at the Procrustes-Wasserstein distance: properties and barycenters
Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such as the alignment and comparison of point clouds. Having that application in mind, we carefully build a space of discrete probability measures and show that over that space PW actually is a distance. Algorithms to solve the PW problems already exist, however we…

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs
Youngkyu Lee, Shanqing Liu, Jerome Darbon, George Em Karniadakis
https://arxiv.org/abs/2507.00278

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs
We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after appropriate discretization. By integrating classical numerical methods (e.g., Krylov-based methods) with modern deep learning components, such as neural operators, our approach enables flexible, on-demand solver design tailored to specific problem classes and objectives. The fast solvers tackle the large linear system r…

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes
Ziling Heng, Peng Wang, Chengju Li
https://arxiv.org/abs/2506.23198

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes
Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let $V_n^{(p)}$ be an $n$-dimensional vector space over $\gf_p$ for a prime $p$. In this paper, we study the hybrid character sums of the form \begin{eqnarray*} \sum_{x \in V_n^{(p)}}ψ\left(F(x)\right)χ_1\left(a x\right), \end{eqnarray*} where $F$ is a function fro…

Learning Agile Gate Traversal via Analytical Optimal Policy Gradient
Tianchen Sun, Bingheng Wang, Longbin Tang, Yichao Gao, Lin Zhao
https://arxiv.org/abs/2508.21592 https://

Learning Agile Gate Traversal via Analytical Optimal Policy Gradient
Traversing narrow gates presents a significant challenge and has become a standard benchmark for evaluating agile and precise quadrotor flight. Traditional modularized autonomous flight stacks require extensive design and parameter tuning, while end-to-end reinforcement learning (RL) methods often suffer from low sample efficiency and limited interpretability. In this work, we present a novel hybrid framework that adaptively fine-tunes model predictive control (MPC) parameters online using outp…

Optimal Targeting in Dynamic Systems
Yuchen Hu, Shuangning Li, Stefan Wager
https://arxiv.org/abs/2507.00312 https://arxiv.org/pdf/25…

Optimal Targeting in Dynamic Systems
Modern treatment targeting methods often rely on estimating the conditional average treatment effect (CATE) using machine learning tools. While effective in identifying who benefits from treatment on the individual level, these approaches typically overlook system-level dynamics that may arise when treatments induce strain on shared capacity. We study the problem of targeting in Markovian systems, where treatment decisions must be made one at a time as units arrive, and early decisions can impa…

Low-Power Optimal Strategy for Witsenhausen Counterexample
Mengyuan Zhao, Ma\"el Le Treust, Tobias J. Oechtering
https://arxiv.org/abs/2509.02381 https://

Low-Power Optimal Strategy for Witsenhausen Counterexample
We discuss the Witsenhausen counterexample from the perspective of varying power budgets and propose a low-power estimation (LoPE) strategy. Specifically, our LoPE approach designs the first decision-maker (DM) a quantization step function of the Gaussian source state, making the target system state a piecewise linear function of the source with slope one. This approach contrasts with Witsenhausen's original two-point strategy, which instead designs the system state itself to be a binary step. …

Optimizing digital quantum simulation of open quantum lattice models
Xie-Hang Yu, Hongchao Li, J. Ignacio Cirac, Rahul Trivedi
https://arxiv.org/abs/2509.02268 https://

Optimizing digital quantum simulation of open quantum lattice models
Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated. We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment. Under a smoothness assumption …

Optimal BESS Scheduling for Multi-Market Participation in the Nordics
Zeenat Hameed, Chresten Traeholt
https://arxiv.org/abs/2506.02837 https://

Optimal BESS Scheduling for Multi-Market Participation in the Nordics
Battery energy storage systems BESSs can provide fast frequency reserves and energy arbitrage in Nordic electricity markets but their limited energy capacity requires accurate revenue forecasts and coordinated bidding across multiple submarkets. This paper introduces a unified framework that employs generalized additive models GAMs to generate one week ahead forecasts of spot and FCRN revenues in Denmark, Finland, and Norway using three years of hourly price and volume data. Forecast outputs fe…

Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport
Moaad Khamlich, Francesco Romor, Gianluigi Rozza
https://arxiv.org/abs/2507.23602 https://…

Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a regularized (RSOT) formulation that can be solved efficiently via its convex dual. However, a significant computational challenge emerges when the continuous source measure is discretized via the finite element (FE) method to handle complex geometries or dens…

Lipschitz-Guided Design of Interpolation Schedules in Generative Models
Yifan Chen, Eric Vanden-Eijnden, Jiawei Xu
https://arxiv.org/abs/2509.01629 https://

Lipschitz-Guided Design of Interpolation Schedules in Generative Models
We study the design of interpolation schedules in the stochastic interpolants framework for flow and diffusion-based generative models. We show that while all scalar interpolation schedules achieve identical statistical efficiency under Kullback-Leibler divergence in path space after optimal diffusion coefficient tuning, their numerical efficiency can differ substantially. This observation motivates focusing on numerical properties of the resulting drift fields rather than statistical criteria …

Optimal Motion Scaling for Delayed Telesurgery
Jason Lim, Florian Richter, Zih-Yun Chiu, Jaeyon Lee, Ethan Quist, Nathan Fisher, Jonathan Chambers, Steven Hong, Michael C. Yip
https://arxiv.org/abs/2506.21689

Optimal Motion Scaling for Delayed Telesurgery
Robotic teleoperation over long communication distances poses challenges due to delays in commands and feedback from network latency. One simple yet effective strategy to reduce errors and increase performance under delay is to downscale the relative motion between the operating surgeon and the robot. The question remains as to what is the optimal scaling factor, and how this value changes depending on the level of latency as well as operator tendencies. We present user studies investigating th…

Ocior: Ultra-Fast Asynchronous Leaderless Consensus with Two-Round Finality, Linear Overhead, and Adaptive Security
Jinyuan Chen
https://arxiv.org/abs/2509.01118 https://…

Ocior: Ultra-Fast Asynchronous Leaderless Consensus with Two-Round Finality, Linear Overhead, and Adaptive Security
In this work, we propose Ocior, a practical asynchronous Byzantine fault-tolerant (BFT) consensus protocol that achieves the optimal performance in resilience, communication, computation, and round complexity. Unlike traditional BFT consensus protocols, Ocior processes incoming transactions individually and concurrently using parallel instances of consensus. While leader-based consensus protocols rely on a designated leader to propose transactions, Ocior is a leaderless consensus protocol that …

Limit Analysis Approach for Optimal Reinforcement Design of Masonry Structures: the Weak Reinforcement Concept
Aguinaldo Fraddosio, Celeste Lasorella, Mario Daniele Piccioni, Elio Sacco
https://arxiv.org/abs/2509.02559

Limit Analysis Approach for Optimal Reinforcement Design of Masonry Structures: the Weak Reinforcement Concept
In this paper, first the non-standard limit analysis 2D problem for reinforced masonry structures is suitably reformulated, giving a innovative computational framework for the evaluation of the strengthening effects of tensile reinforcements. This framework is used for designing optimized reinforcements for masonry structures aimed at improving the structural capacity, but without substantial changes in the typical behavior of masonry structural systems, since the reinforcement layout leaves th…

Beyond morphophoricity: $s$-tight IC measurements in geometric generalised probabilistic theories
Anna Szymusiak
https://arxiv.org/abs/2507.01745 https://

Beyond morphophoricity: $s$-tight IC measurements in geometric generalised probabilistic theories
The analysed in this paper new class of $s$-tight IC measurements contains both morphophoric measurements, preserving the geometry of the states space, and tight IC measurements, introduced nearly 20 years ago by Scott in the quantum case as optimal for the task of linear quantum tomography. By looking at the mathematical side of these classes we discover their common feature, which is also preserved in the broader class of $s$-tight IC measurements: a particularly elegant form of the formula t…

RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric
Yu Zhang, Xiao-Song Yang
https://arxiv.org/abs/2506.22170 https://…

RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric
The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or all other nodes based on non-negative edge weights. Numerous studies have focused on the Dijkstra algorithm due to its potential application. However, its application in surface path planning for mobile robots remains largely unexplored. In this letter, a surface optimal path planning algorithm called RM-Dijkstra is p…

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…

A Path Planning Model for Intercepting a Moving Target with Finite Obstacle Avoidance
Masuda Akter, Mohammed Mustafa Rizvi
https://arxiv.org/abs/2507.01447

A Path Planning Model for Intercepting a Moving Target with Finite Obstacle Avoidance
This paper investigates the problem of computing a two-dimensional optimal curvature straight line (CS) shortest path for an unmanned aerial vehicle (UAV) to intercept a moving target, with both the UAV (pursuer) and target travelling at constant speeds. We formulate an optimal control problem that integrates two critical objectives: avoiding static obstacles and successfully intercepting the target. The approach introduces constraints derived from obstacle avoidance and target interception req…

Solving the Pod Repositioning Problem with Deep Reinforced Adaptive Large Neighborhood Search
Lin Xie, Hanyi Li
https://arxiv.org/abs/2506.02746 https://…

Solving the Pod Repositioning Problem with Deep Reinforced Adaptive Large Neighborhood Search
The Pod Repositioning Problem (PRP) in Robotic Mobile Fulfillment Systems (RMFS) involves selecting optimal storage locations for pods returning from pick stations. This work presents an improved solution method that integrates Adaptive Large Neighborhood Search (ALNS) with Deep Reinforcement Learning (DRL). A DRL agent dynamically selects destroy and repair operators and adjusts key parameters such as destruction degree and acceptance thresholds during the search. Specialized heuristics for bo…

An Error Bound for Aggregation in Approximate Dynamic Programming
Yuchao Li, Dimitri Bertsekas
https://arxiv.org/abs/2507.01324 https://

An Error Bound for Aggregation in Approximate Dynamic Programming
We consider a general aggregation framework for discounted finite-state infinite horizon dynamic programming (DP) problems. It defines an aggregate problem whose optimal cost function can be obtained off-line by exact DP and then used as a terminal cost approximation for an on-line reinforcement learning (RL) scheme. We derive a bound on the error between the optimal cost functions of the aggregate problem and the original problem. This bound was first derived by Tsitsiklis and van Roy [TvR96] …

Convergence Rates of Time Discretization in Extended Mean Field Control
Christoph Reisinger, Wolfgang Stockinger, Maria Olympia Tsianni, Yufei Zhang
https://arxiv.org/abs/2509.00904

Convergence Rates of Time Discretization in Extended Mean Field Control
Piecewise constant control approximation provides a practical framework for designing numerical schemes of continuous-time control problems. We analyze the accuracy of such approximations for extended mean field control (MFC) problems, where the dynamics and costs depend on the joint distribution of states and controls. For linear-convex extended MFC problems, we show that the optimal control is $1/2$-Hölder continuous in time. Using this regularity, we prove that the optimal cost of the conti…

LoL-NMPC: Low-Level Dynamics Integration in Nonlinear Model Predictive Control for Unmanned Aerial Vehicles
Parakh M. Gupta, Ond\v{r}ej Proch\'azka, Jan H\v{r}ebec, Matej Novosad, Robert P\v{e}ni\v{c}ka, Martin Saska
https://arxiv.org/abs/2506.02169

LoL-NMPC: Low-Level Dynamics Integration in Nonlinear Model Predictive Control for Unmanned Aerial Vehicles
In this paper, we address the problem of tracking high-speed agile trajectories for Unmanned Aerial Vehicles(UAVs), where model inaccuracies can lead to large tracking errors. Existing Nonlinear Model Predictive Controller(NMPC) methods typically neglect the dynamics of the low-level flight controllers such as underlying PID controller present in many flight stacks, and this results in sub-optimal tracking performance at high speeds and accelerations. To this end, we propose a novel NMPC formul…

Numerical analysis of the convex relaxation of the barrier parameter functional of self-concordant barriers
Vitali Pirau, Roland Hildebrand
https://arxiv.org/abs/2507.01812

Numerical analysis of the convex relaxation of the barrier parameter functional of self-concordant barriers
Self-concordant barriers are essential for interior-point algorithms in conic programming. To speed up the convergence it is of interest to find a barrier with the lowest possible parameter for a given cone. The barrier parameter is a non-convex function on the set of self-concordant barriers on a given cone, and finding an optimal barrier amounts to solving a non-convex infinite-dimensional optimization problem. In this work we study the degradation of the optimal value of the problem when the…

Stability-Constrained AC Optimal Power Flow -- A Gaussian Process-Based Approach
Vincenzo Di Vito, Kaarthik Sundar, Ferdinando Fioretto, Deepjyoti Deka
https://arxiv.org/abs/2507.23094

Stability-Constrained AC Optimal Power Flow -- A Gaussian Process-Based Approach
The Alternating Current Optimal Power Flow (ACOPF) problem is a core task in power system operations, aimed at determining cost-effective generation dispatch while satisfying physical and operational constraints. However, conventional ACOPF formulations rely on steady-state models and neglect the dynamic behavior of generators, which can lead to operating points that are economically optimal but dynamically unstable. This paper proposes a novel, data-driven approach to incorporate generator dyn…

A Reinforcement Learning Framework for Some Singular Stochastic Control Problems
Zongxia Liang, Xiaodong Luo, Xiang Yu
https://arxiv.org/abs/2506.22203 htt…

A Reinforcement Learning Framework for Some Singular Stochastic Control Problems
We develop a continuous-time reinforcement learning framework for a class of singular stochastic control problems without entropy regularization. The optimal singular control is characterized as the optimal singular control law, which is a pair of regions of time and the augmented states. The goal of learning is to identify such an optimal region via the trial-and-error procedure. In this context, we generalize the existing policy evaluation theories with regular controls to learn our optimal s…

Predictive Control Strategies for Sustaining Innovation Adoption on Multilayer Social Networks
Martina Alutto, Qiulin Xu, Fabrizio Dabbene, Hideaki Ishii, Chiara Ravazzi
https://arxiv.org/abs/2509.01457

Predictive Control Strategies for Sustaining Innovation Adoption on Multilayer Social Networks
This paper studies an optimal control problem for an adoption-opinion model that couples innovation adoption with opinion formation on a multilayer network. Adoption spreads through social contagion and perceived benefits, while opinions evolve via social interactions and feedback from adoption levels. Individuals may abandon adoption due to dissatisfaction or external constraints, potentially hindering diffusion. We analyze system equilibria and their stability, identifying conditions under wh…

A Calculus of Variations Approach to Stochastic Control
Matthew Lorig
https://arxiv.org/abs/2509.01744 https://arxiv.org/pdf/2509.01744

A Calculus of Variations Approach to Stochastic Control
We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton portfolio optimization problem.

Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds
Dingqian Gao, Qi L\"u
https://arxiv.org/abs/2507.01407 https://

Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function. We then prove the existence, uniqueness of viscosity solutions to the HJB equation, along with their continuous dependence on initial data and model parameters. Finally, under appropriate regularity conditions on the value function…

On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems
Shoju Enami, Kenji Kashima
https://arxiv.org/abs/2507.21543 https://arxiv.o…

On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems
In recent years, mutual information optimal control has been proposed as an extension of maximum entropy optimal control. Both approaches introduce regularization terms to render the policy stochastic, and it is important to theoretically clarify the relationship between the temperature parameter (i.e., the coefficient of the regularization term) and the stochasticity of the policy. Unlike in maximum entropy optimal control, this relationship remains unexplored in mutual information optimal con…

REAP-T: A MATLAB Toolbox for Implementing Robust-to-Early Termination Model Predictive Control
Mohsen Amiri, Mehdi Hosseinzadeh
https://arxiv.org/abs/2507.00863

REAP-T: A MATLAB Toolbox for Implementing Robust-to-Early Termination Model Predictive Control
This paper presents a MATLAB toolbox for implementing robust-to-early termination model predictive control, abbreviated as REAP, which is designed to ensure a sub-optimal yet feasible solution when MPC computations are prematurely terminated due to limited computational resources. Named REAP-T, this toolbox is a comprehensive, user-friendly, and modular platform that enables users to explore, analyze, and customize various components of REAP for their specific applications. Notable attributes o…

Mirror descent for constrained stochastic control problems
Deven Sethi, David \v{S}i\v{s}ka
https://arxiv.org/abs/2506.02564 https://…

Mirror descent for constrained stochastic control problems
Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control problems with the action space being bounded and convex. We show that if the Hamiltonian is uniformly convex in its action variable then mirror descent converges linearly while if it is uniformly strongly convex relative to an appropriate Bregman divergence, the…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/3]:
- Full characterization of optimal transport plans for concave costs
Paul Pegon (LMO), Davide Piazzoli (LMO), Filippo Santambrogio (LMO)

A Stochastic-Optimization-Based Adaptive-Sampling Scheme for Data-Driven Stability Analysis of Switched Linear Systems
Alexis Vuille, Guillaume O. Berger, Rapha\"el M. Jungers
https://arxiv.org/abs/2508.21617

A Stochastic-Optimization-Based Adaptive-Sampling Scheme for Data-Driven Stability Analysis of Switched Linear Systems
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in particular, the fact that these methods suffer from illconditioning of the optimal Lyapunov function, which was shown in recent work to be a direct consequence of the way the data is collected by sampling uniformly the state space. In this work, we formalize the no…