Tootfinder

Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels
Wenjun Yu, Yubo Sun, Zixiang Xu, Gennian Ge, Moshe Schwartz
https://arxiv.org/abs/2506.12924

Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the code, the number of reads used in the reconstruction process, and the decoding list size. We show that over a channel that introduces at most $t$ bursts, we can use a length-$n$ code capable of correcting $ε$ errors, with $Θ(n^ρ)$ reads, and decoding with a list of size $O(n^λ)$, where $t-1=ε+ρ+λ$. In the proc…

Near optimal controls for partially observed stochastic linear quadratic problems
Jingrui Sun, Jiaqiang Wen, Jie Xiong, Wen Xu
https://arxiv.org/abs/2506.11778

Near optimal controls for partially observed stochastic linear quadratic problems
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the diffusion term of the state equation, the circular dependence between the control process and the filtration generated by the observation, and the observation process contains an unbounded drift term. We address these difficulties by first restricting the contro…

Robust Optimal Task Planning to Maximize Battery Life
Jiachen Li, Chu Jian, Feiyang Zhao, Shihao Li, Wei Li, Dongmei Chen
https://arxiv.org/abs/2506.11264 …

Robust Optimal Task Planning to Maximize Battery Life
This paper proposes a control-oriented optimization platform for autonomous mobile robots (AMRs), focusing on extending battery life while ensuring task completion. The requirement of fast AMR task planning while maintaining minimum battery state of charge, thus maximizing the battery life, renders a bilinear optimization problem. McCormick envelop technique is proposed to linearize the bilinear term. A novel planning algorithm with relaxed constraints is also developed to handle parameter unce…

Achieving Optimal Locomotion using Self-Generated Waves
D. O'Donovan, M. D. Bustamante, O. Devauchelle, G. P. Benham
https://arxiv.org/abs/2506.11961 h…

Achieving Optimal Locomotion using Self-Generated Waves
An oscillating body floating at the water surface produces a wave-field of self-generated waves. When the oscillation induces a difference in fore-aft wave amplitude squared, these self-generated waves can be used as a mechanism to propel the body horizontally across the surface (Longuet-Higgins and Stewart 1964). The optimisation of this wave-driven propulsion (WDP) is the interest of this work. To study the conditions necessary to produce optimal thrust we will utilise a shallow water set-up …

Optimal tax is close to Pigou in a duopoly https://www.sciencedirect.com/science/article/pii/S0140988325003688 @…

Optimal experiment design for practical parameter identifiability and model discrimination
Yue Liu (University of Oxford, Purdue University), Philip K. Maini (University of Oxford), Ruth E. Baker (University of Oxford)
https://arxiv.org/abs/2506.11311

Optimal experiment design for practical parameter identifiability and model discrimination
Mechanistic mathematical models of biological systems usually contain a number of unknown parameters whose values need to be estimated from available experimental data in order for the models to be validated and used to make quantitative predictions. This requires that the models are practically identifiable, that is, the values of the parameters can be confidently determined, given available data. A well-designed experiment can produce data that are much more informative for the purpose of inf…

Optimal Execution under Liquidity Uncertainty
Etienne Chevalier, Yadh Hafsi, Vathana Ly Vath, Sergio Pulido
https://arxiv.org/abs/2506.11813 https://

Optimal Execution under Liquidity Uncertainty
We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. This resilience is modeled through a potentially arbitrary limit-order book shape. To account for liquidity dynamics, we introduce a stochastic volume effect governing the recovery of the deviation process, which represents the difference between the impacted and unaffected price. A…

Optimal trace norms for Helmholtz problems
Benedikt Gr\"a{\ss}le
https://arxiv.org/abs/2506.11944 https://arxiv.org/pdf/2506.119…

Optimal trace norms for Helmholtz problems
The natural $H^1(Ω)$ energy norm for Helmholtz problems is weighted with the wavenumber modulus $σ$ and induces natural weighted norms on the trace spaces $H^{\pm1/2}(Γ)$ by minimial extension to $Ω\subset\mathbb R^n$. This paper presents a rigorous analysis for these trace norms with an explicit characterisation by weighted Sobolev-Slobodeckij norms and scaling estimates, highlighting their dependence on the geometry of the extension set $Ω\subset\mathbb R^n$ and the weight $σ$. The anal…

State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations
Alfredo Berm\'udez, Iago Pad\'in
https://arxiv.org/abs/2506.11765

State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations
With the growing global emphasis on sustainability and the implementation of contemporary environmental policies, the penetration of renewable energy sources has significantly increased --primarily due to their inexhaustible nature. In this context, integrating photovoltaic (PV) modules with energy storage systems offers a means to mitigate the inherent variability of solar energy. This paper proposes an optimal methodology for power management and market bidding strategies tailored to PV power…

Maximally-Informative Retrieval for State Space Model Generation
Evan Becker, Benjamin Bowman, Matthew Trager, Tian Yu Liu, Luca Zancato, Wei Xia, Stefano Soatto
https://arxiv.org/abs/2506.12149

Maximally-Informative Retrieval for State Space Model Generation
Given a query and dataset, the optimal way of answering the query is to make use all the information available. Modern LLMs exhibit impressive ability to memorize training data, but data not deemed important during training is forgotten, and information outside that training set cannot be made use of. Processing an entire dataset at inference time is infeasible due to the bounded nature of model resources (e.g. context size in transformers or states in state space models), meaning we must resor…

AdaptiveLLM: A Framework for Selecting Optimal Cost-Efficient LLM for Code-Generation Based on CoT Length
Junhang Cheng, Fang Liu, Chengru Wu, Li Zhang
https://arxiv.org/abs/2506.10525

AdaptiveLLM: A Framework for Selecting Optimal Cost-Efficient LLM for Code-Generation Based on CoT Length
While Large Language Models (LLMs) have significantly advanced code generation efficiency, they face inherent challenges in balancing performance and inference costs across diverse programming tasks. Dynamically selecting the optimal LLM based on task difficulty and resource constraints offers a promising approach to achieve an optimal balance between efficiency and performance. However, existing model selection methods are resource-intensive and often neglect cost efficiency. Moreover, these a…

Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective
Sergio Mu\~niz Subi\~nas, Jorge Mart\'inez Mart\'in, Alejandro Mata Ali, Javier Sedano, \'Angel Miguel Garc\'ia-Vico
https://arxiv.org/abs/2506.11711

Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective
In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal solution of the problems. As in other tensor network algorithms for combinatorial optimization problems, the method is based on imaginary time evolution and the implementation of restrictions in the tensor network. In addition, we introduce the use of symmetrie…

Optimal and Suboptimal Decoders under Finite-Alphabet Interference: A Mismatched Decoding Perspective
Sibo Zhang, Bruno Clerckx
https://arxiv.org/abs/2506.12646

Optimal and Suboptimal Decoders under Finite-Alphabet Interference: A Mismatched Decoding Perspective
Interference widely exists in communication systems and is often not optimally treated at the receivers due to limited knowledge and/or computational burden. Evolutions of receivers have been proposed to balance complexity and spectral efficiency, for example, for 6G, while commonly used performance metrics, such as capacity and mutual information, fail to capture the suboptimal treatment of interference, leading to potentially inaccurate performance evaluations. Mismatched decoding is an infor…

Learning-Based Stable Optimal Control for Infinite-Time Nonlinear Regulation Problems
Han Wang, Di Wu, Lin Cheng, Shengping Gong, Xu Huang
https://arxiv.org/abs/2506.10291

Learning-Based Stable Optimal Control for Infinite-Time Nonlinear Regulation Problems
Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent learning-based approaches rarely consider stability guarantees. This paper proposes a learning-based framework to learn a stable optimal controller for nonlinear optimal regulation problems. First, leveraging the equivalence between Pontryagin Maximum Principle…

Enter: Graduated Realism: A Pedagogical Framework for AI-Powered Avatars in Virtual Reality Teacher Training
Judson Leroy Dean Haynes IV
https://arxiv.org/abs/2506.11890

Enter: Graduated Realism: A Pedagogical Framework for AI-Powered Avatars in Virtual Reality Teacher Training
Virtual Reality simulators offer a powerful tool for teacher training, yet the integration of AI-powered student avatars presents a critical challenge: determining the optimal level of avatar realism for effective pedagogy. This literature review examines the evolution of avatar realism in VR teacher training, synthesizes its theoretical implications, and proposes a new pedagogical framework to guide future design. Through a systematic review, this paper traces the progression from human-contro…

This https://arxiv.org/abs/2501.07581 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Optimal Execution Strategies Incorporating Internal Liquidity Through Market Making
This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{cartea2015algorithmic} framework, we incorporate market impact in interbank orders while excluding it for internal market-making transactions. Our model aims to optimize the balance between interbank and internal liquidity, reducing market impact and improving execution efficiency.

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

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

Minimum-hop Constellation Design for Low Earth Orbit Satellite Networks
Chirag Rao, Eytan Modiano
https://arxiv.org/abs/2506.11995 https://

Minimum-hop Constellation Design for Low Earth Orbit Satellite Networks
We consider a Low Earth Orbit (LEO) satellite network with each satellite capable of establishing inter-satellite link (ISL) connections for satellite-to-satellite communication. Since ISLs can be reoriented to change the topology, we optimize the topology to minimize the average shortest path length (ASPL). We characterize the optimal ASPL ISL topology in two families of topologies, 1) vertex-symmetric in which the ISL connections at a satellite node represent a motif that is repeated at all o…

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
Jiarui Gan, Rupak Majumdar
https://arxiv.org/abs/2506.07186

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
We study the problem of computing optimal correlated equilibria (CEs) in infinite-horizon multi-player stochastic games, where correlation signals are provided over time. In this setting, optimal CEs require history-dependent policies; this poses new representational and algorithmic challenges as the number of possible histories grows exponentially with the number of time steps. We focus on computing $(ε, δ)$-optimal CEs -- solutions that achieve a value within $ε$ of an optimal CE, while al…

A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data
Max Winkler, Hamdullah Y\"ucel
https://arxiv.org/abs/2506.11479

A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data
The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error estimates are derived for the control variable in $L^2(\partial \mathcal D)$-norm and state variable in $L^2(Ω\times\mathcal D)$-norm. To solve large linear systems, appropriate preconditioners are proposed for both unconstrained and constrained scenarios. To …

Quenched limit for diffusive biased random walks in random environment
Carlo Scali
https://arxiv.org/abs/2506.11799 https://arxiv.org…

Quenched limit for diffusive biased random walks in random environment
We prove that every directionally transient random walk in random i.i.d.\ environment, under condition $(T)_γ$, which admits an annealed functional limit towards Brownian motion also admits the corresponding quenched limit in $d \ge 2$. We exploit a classical strategy that was introduced by Bolthausen and Sznitman but, with respect to the existing literature, we get almost-optimal bounds on the variance of the quenched expectation of certain functionals of the random walk.

Ray Optics Approach to Holography
Andrii Torchylo
https://arxiv.org/abs/2506.11352 https://arxiv.org/pdf/2506.11352

Ray Optics Approach to Holography
Retrieving the phase of a complex-valued field from the measurements of its amplitude is a crucial problem with a wide range of applications in microscopy and ultracold atomic physics. In particular, obtaining an accurate and efficient solution to this problem is a key step in shaping laser beams for trapping atoms in optical tweezer arrays and applying high-fidelity entangling gates on a neutral atom quantum computer. Current approaches to this problem fail to converge on the optimal solution …

A Robust Local Fr\'echet Regression Using Unbalanced Neural Optimal Transport with Applications to Dynamic Single-cell Genomics Data
Binghao Yan, Hongzhe Li
https://arxiv.org/abs/2506.11969

A Robust Local Fréchet Regression Using Unbalanced Neural Optimal Transport with Applications to Dynamic Single-cell Genomics Data
Single-cell RNA sequencing (scRNA-seq) technologies have enabled the profiling of gene expression for a collection of cells across time during a dynamic biological process. Given that each time point provides only a static snapshot, modeling and understanding the underlying cellular dynamics remains a central yet challenging task in modern genomics. To associate biological time with single cell distributions, we develop a robust local Fréchet regression for interpolating the high-dimensional c…

Training-Free Voice Conversion with Factorized Optimal Transport
Alexander Lobashev, Assel Yermekova, Maria Larchenko
https://arxiv.org/abs/2506.09709 http…

Training-Free Voice Conversion with Factorized Optimal Transport
This paper introduces Factorized MKL-VC, a training-free modification for kNN-VC pipeline. In contrast with original pipeline, our algorithm performs high quality any-to-any cross-lingual voice conversion with only 5 second of reference audio. MKL-VC replaces kNN regression with a factorized optimal transport map in WavLM embedding subspaces, derived from Monge-Kantorovich Linear solution. Factorization addresses non-uniform variance across dimensions, ensuring effective feature transformation.…

Constrained Denoising, Empirical Bayes, and Optimal Transport
Adam Quinn Jaffe, Nikolaos Ignatiadis, Bodhisattva Sen
https://arxiv.org/abs/2506.09986 https…

Constrained Denoising, Empirical Bayes, and Optimal Transport
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At the oracle level, i.e., when the latent variable distribution is assumed known, we apply tools from the theory of optimal transport to characterize the solution to (i) variance-constrained, (ii) distribution-constrained, and (iii) general-constrained denoisin…

Demonstration Sidetracks: Categorizing Systematic Non-Optimality in Human Demonstrations
Shijie Fang, Hang Yu, Qidi Fang, Reuben M. Aronson, Elaine S. Short
https://arxiv.org/abs/2506.11262

Demonstration Sidetracks: Categorizing Systematic Non-Optimality in Human Demonstrations
Learning from Demonstration (LfD) is a popular approach for robots to acquire new skills, but most LfD methods suffer from imperfections in human demonstrations. Prior work typically treats these suboptimalities as random noise. In this paper we study non-optimal behaviors in non-expert demonstrations and show that they are systematic, forming what we call demonstration sidetracks. Using a public space study with 40 participants performing a long-horizon robot task, we recreated the setup in si…

Completeness Stability of Quantum Measurements
Rakesh Saini, Jukka Kiukas, Daniel Burgarth, Alexei Gilchrist
https://arxiv.org/abs/2506.11539 https://

Completeness Stability of Quantum Measurements
We introduce a resource monotone, the completeness stability, to quantify the quality of quantum measurements within a resource-theoretic framework. By viewing a quantum measurement as a frame, the minimum eigenvalue of a frame operator emerges as a significant monotone. It captures bounds on estimation errors and the numerical stability of inverting the frame operator to calculate the optimal dual for state reconstruction. Maximizing this monotone identifies a well-characterized class of quant…

Optimal Transport for $e/\pi^0$ Particle Classification in LArTPC Neutrino Experiments
David Caratelli, Nathaniel Craig, Chuyue Fang, Jessica N. Howard
https://arxiv.org/abs/2506.09238

Optimal Transport for $e/π^0$ Particle Classification in LArTPC Neutrino Experiments
The efficient classification of electromagnetic activity from $π^0$ and electrons remains an open problem in the reconstruction of neutrino interactions in Liquid Argon Time Projection Chamber (LArTPC) detectors. We address this problem using the mathematical framework of Optimal Transport (OT), which has been successfully employed for event classification in other HEP contexts and is ideally suited to the high-resolution calorimetry of LArTPCs. Using a publicly available simulated dataset fro…

Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
Vahan Arsenyan, Elen Vardanyan, Arnak Dalalyan
https://arxiv.org/abs/2506.09681

Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guara…

Towards universally optimal sorting algorithms
Sandeep Sen
https://arxiv.org/abs/2506.08261 https://arxiv.org/pdf/2506.08261

Towards universally optimal sorting algorithms
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this perspective, and also present a novel measure of sortedness that leads to an optimal algorithm based on partition sort. This paradigm of measuring efficiency of algorithms looks promising for further interesting applications beyond the existing ones.

An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications
Kai Ding, Xun Li, Siyu Lv, Xin Zhang
https://arxiv.org/abs/2506.11523 …

An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the asymptotic property of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a d…

Ja echt heel belangrijk
🤣

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new/
[2/6]:
A User's Guide to Sampling Strategies for Sliced Optimal Transport

Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points
Nikolai Nikolov, Pascal J. Thomas
https://arxiv.org/abs/2506.06507 htt…

Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points
It is shown that the optimal upper and lower bounds for the Kobayashi distance near $\mathcal C^{2,α}$-smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Nikolov, A.Y. Okten: "Precise estimates of invariant distances on strongly pseudoconvex domains", Adv. Math. 478 (2025), 110388, remain true in the general $\mathcal C^2$ strongly pseudoconvex setting. In fact, the upper bound is extended to the general $\mathcal C^{1,1}$-smooth case. We also give upper and lower bounds …

Linear programs help to find optimal solutions based on a set of constrains. I used {ompr} before, but the new package {tidyLP} looks promising and integrates with the tidyverse. #rstats #linearprograms #optimization

GitHub - colin-fraser/tidyLP: Tidy Linear Programs
Tidy Linear Programs. Contribute to colin-fraser/tidyLP development by creating an account on GitHub.

This https://arxiv.org/abs/2505.13809 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Characterization of Efficient Influence Function for Off-Policy Evaluation Under Optimal Policies
Off-policy evaluation (OPE) provides a powerful framework for estimating the value of a counterfactual policy using observational data, without the need for additional experimentation. Despite recent progress in robust and efficient OPE across various settings, rigorous efficiency analysis of OPE under an estimated optimal policy remains limited. In this paper, we establish a concise characterization of the efficient influence function (EIF) for the value function under optimal policy within ca…

Optimal Transport Driven Asymmetric Image-to-Image Translation for Nuclei Segmentation of Histological Images
Suman Mahapatra, Pradipta Maji
https://arxiv.org/abs/2506.07023

Optimal Transport Driven Asymmetric Image-to-Image Translation for Nuclei Segmentation of Histological Images
Segmentation of nuclei regions from histological images enables morphometric analysis of nuclei structures, which in turn helps in the detection and diagnosis of diseases under consideration. To develop a nuclei segmentation algorithm, applicable to different types of target domain representations, image-to-image translation networks can be considered as they are invariant to target domain image representations. One of the important issues with image-to-image translation models is that they fai…

On the cross-correlation properties of large-size families of Costas arrays
Runfeng Liu, Qi Wang
https://arxiv.org/abs/2506.12559 https://

On the cross-correlation properties of large-size families of Costas arrays
Costas arrays have been an interesting combinatorial object for decades because of their optimal aperiodic auto-correlation properties. Meanwhile, it is interesting to find families of Costas arrays or extended arrays with small maximal cross-correlation values, since for applications in multi-user systems, the cross-interferences between different signals should also be small. The objective of this paper is to study several large-size families of Costas arrays or extended arrays, and their val…

Optimal protocol for collisional Brownian engines
Gustavo A. L. For\~ao
https://arxiv.org/abs/2506.05078 https://arxiv.org/pdf/2506.0…

Optimal protocol for collisional Brownian engines
Collisional Brownian engines have recently gained attention as alternatives to conventional nanoscale engines. However, a comprehensive optimization of their performance, which could serve as a benchmark for future engine designs, is still lacking. In this work, we address this gap by deriving and analyzing the optimal driving protocol for a collisional Brownian engine. By maximizing the average output work, we show that the optimal protocol consists of linear force segments separated by impuls…

Sind #Holzschneidbretter wirklich unhygienisch? 🪵 Oder sind sie doch die bessere Wahl gegenüber Kunststoffschneidbrettern? Holz setzt zumindest keine Mikroplastikpartikel frei und ist bei richtiger Pflege langlebig und sicher. Wie reinigt man Holzschneidbretter optimal und sorgt für eine hygienische Lagerung? Tipps für den Umgang mit Holzschneidbrettern dazu im Beitrag. 🌿🍴

Küchen-Mythos: Holzschneidbretter sind unhygienisch
Holzschneidbretter sind hygienisch und frei von Mikroplastik. Tipps zur richtigen Reinigung und Lagerung.

Seeding an Uncertain Technology
Eric Gao
https://arxiv.org/abs/2506.10340 https://arxiv.org/pdf/2506.10340

Seeding an Uncertain Technology
I study how a startup with uncertainty over product quality and no knowledge of the underlying diffusion network optimally chooses initial seeds. To ensure widespread adoption when the product is good while minimizing negative perceptions when it is bad, the optimal number of initial seeds should grow logarithmically with network size. When there are agents of different types that govern their connectivity, it is asymptotically optimal to seed agents of a single type: the type that minimizes th…

Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
Matthias Beckmann, Robert Beinert, Jonas Bresch
https://arxiv.org/abs/2506.08761

Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is closely related to the sliced Wasserstein distance and provably guaranties the linear separability of image classes that emerge from translations or scalings. In many real-world applications, like the recognition of watermarks in filigranology, however, the data is subject to general affine transformations originating…

Optimal Task Offloading with Firm Deadlines for Mobile Edge Computing Systems
Khai Doan, Wesley Araujo, Evangelos Kranakis, Ioannis Lambadaris, Yannis Viniotis, Wonjae Shin
https://arxiv.org/abs/2506.09180

Optimal Task Offloading with Firm Deadlines for Mobile Edge Computing Systems
Under a dramatic increase in mobile data traffic, a promising solution for edge computing systems to maintain their local service is the task migration that may be implemented by means of Autonomous mobile agents (AMA). In designing an optimal scheme for task offloading to AMA, we define a system cost as a minimization objective function that comprises two parts. First, an offloading cost which can be interpreted as the cost of using computational resources from the AMA. Second, a penalty cost …

FlowHFT: Flow Policy Induced Optimal High-Frequency Trading under Diverse Market Conditions
Yang Li, Zhi Chen, Steve Yang
https://arxiv.org/abs/2505.05784 …

FlowHFT: Flow Policy Induced Optimal High-Frequency Trading under Diverse Market Conditions
High-frequency trading (HFT) is an investing strategy that continuously monitors market states and places bid and ask orders at millisecond speeds. Traditional HFT approaches fit models with historical data and assume that future market states follow similar patterns. This limits the effectiveness of any single model to the specific conditions it was trained for. Additionally, these models achieve optimal solutions only under specific market conditions, such as assumptions about stock price's s…

Optimal quantum metrology under energy constraints
Longyun Chen, Yuxiang Yang
https://arxiv.org/abs/2506.09436 https://arxiv.org/pdf/…

Optimal quantum metrology under energy constraints
Quantum metrology promises enhanced precision in parameter estimation by exploiting quantum effects. The traditional framework of metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein are often infeasible in practice. Here, we investigate quantum metrology where the total energy consumption of the probe state preparation, intermediate control operations, and the final measurement is subject to a…

Optimal decay of global strong solutions to nematic liquid crystal flows in the half-space
Haokun Chen, Yong Wang
https://arxiv.org/abs/2506.10255 https://…

Optimal decay of global strong solutions to nematic liquid crystal flows in the half-space
We study asymptotic behaviors of the higher-order spatial derivatives and the first-order time derivatives for the strong solution to nematic liquid crystal flows in the half-space $\mathbb{R}_+^3$. Furthermore, when the initial data lie in an appropriately weighted Sobolev space, we obtain the decay rates that are faster than the heat kernel. The main tools employed in this paper are the $L^p-L^q$ estimates of the Stokes semigroup, the a priori estimates of the steady Stokes system in $\mathbb…

Fast Estimation of Globally Optimal Independent Contact Regions for Robust Grasping and Manipulation
Jonathan P. King, Harnoor Ahluwalia, Michael Zhang, Nancy S. Pollard
https://arxiv.org/abs/2506.08856

Fast Estimation of Globally Optimal Independent Contact Regions for Robust Grasping and Manipulation
This work presents a fast anytime algorithm for computing globally optimal independent contact regions (ICRs). ICRs are regions such that one contact within each region enables a valid grasp. Locations of ICRs can provide guidance for grasp and manipulation planning, learning, and policy transfer. However, ICRs for modern applications have been little explored, in part due to the expense of computing them, as they have a search space exponential in the number of contacts. We present a divide an…

Optimal Voltage Control Using Online Exponential Barrier Method
Peng Zhang, Baosen Zhang
https://arxiv.org/abs/2506.10247 https://arx…

Optimal Voltage Control Using Online Exponential Barrier Method
This paper address the optimal voltage control problem of distribution systems with high penetration of inverter-based renewable energy resources, under inaccurate model information. We propose the online exponential barrier method that explicitly leverages the online feedback from grids to enhance the robustness to model inaccuracy and incorporates the voltage constraints to maintain the safety requirements. We provide analytical results on the optimal barrier parameter selection and sufficien…

Optimal Adjustment Sets for Nonparametric Estimation of Weighted Controlled Direct Effect
Ruiyang Lin (University of Science,Technology of China), Yongyi Guo (University of Wisconsin-Madison), Kyra Gan (Cornell Tech)
https://arxiv.org/abs/2506.09871

Optimal Adjustment Sets for Nonparametric Estimation of Weighted Controlled Direct Effect
The weighted controlled direct effect (WCDE) generalizes the standard controlled direct effect (CDE) by averaging over the mediator distribution, providing a robust estimate when treatment effects vary across mediator levels. This makes the WCDE especially relevant in fairness analysis, where it isolates the direct effect of an exposure on an outcome, independent of mediating pathways. This work establishes three fundamental advances for WCDE in observational studies: First, we establish necess…

Technical Report with Proofs for A Full Picture in Conformance Checking: Efficiently Summarizing All Optimal Alignments
Philipp B\"ar, Moe T. Wynn, Sander J. J. Leemans
https://arxiv.org/abs/2506.10345

Technical Report with Proofs for A Full Picture in Conformance Checking: Efficiently Summarizing All Optimal Alignments
This technical report provides proofs for the claims in the paper "A Full Picture in Conformance Checking: Efficiently Summarizing All Optimal Alignments".

Optimal Graph Reconstruction by Counting Connected Components in Induced Subgraphs
Hadley Black, Arya Mazumdar, Barna Saha, Yinzhan Xu
https://arxiv.org/abs/2506.08405

Optimal Graph Reconstruction by Counting Connected Components in Induced Subgraphs
The graph reconstruction problem has been extensively studied under various query models. In this paper, we propose a new query model regarding the number of connected components, which is one of the most basic and fundamental graph parameters. Formally, we consider the problem of reconstructing an $n$-node $m$-edge graph with oracle queries of the following form: provided with a subset of vertices, the oracle returns the number of connected components in the induced subgraph. We show $Θ(\frac…

Regret-Optimal Q-Learning with Low Cost for Single-Agent and Federated Reinforcement Learning
Haochen Zhang, Zhong Zheng, Lingzhou Xue
https://arxiv.org/abs/2506.04626

Regret-Optimal Q-Learning with Low Cost for Single-Agent and Federated Reinforcement Learning
Motivated by real-world settings where data collection and policy deployment -- whether for a single agent or across multiple agents -- are costly, we study the problem of on-policy single-agent reinforcement learning (RL) and federated RL (FRL) with a focus on minimizing burn-in costs (the sample sizes needed to reach near-optimal regret) and policy switching or communication costs. In parallel finite-horizon episodic Markov Decision Processes (MDPs) with $S$ states and $A$ actions, existing m…

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited
Guillaume Boutoille, Gilles Pag\`es
https://arxiv.org/abs/2506.01746

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited
In this paper we revisit the exsistence theorem for $L^r$-optimal quantization, $r\ge 2$, with respect to a Bregman divergence: we establish the existence of optimal quantizaers under lighter assumptions onthe strictly convex function which generates the divergence, espcially in the quadratic case ($r=2$). We then prove a uniqueness theorem ``à la Trushkin'' in one dimension for strongly unimodal distributions and divergences gerated by strictly convex functions whiose thire dervative is eithe…

Optimal hedging of an informed broker facing many traders
Philippe Bergault, Pierre Cardaliaguet, Wenbin Yan
https://arxiv.org/abs/2506.08992 https://

Optimal hedging of an informed broker facing many traders
This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset's price, engages with traders whose trading activities impact the market price. Using a mean-field game approach, we derive the equilibrium strategies for both the broker and the traders, illustrating the intricate dynamics of their interactions. …

Model Predictive Control-Based Optimal Energy Management of Autonomous Electric Vehicles Under Cold Temperatures
Shanthan Kumar Padisala, Satadru Dey
https://arxiv.org/abs/2506.10221

Model Predictive Control-Based Optimal Energy Management of Autonomous Electric Vehicles Under Cold Temperatures
In autonomous electric vehicles (AEVs), battery energy must be judiciously allocated to satisfy primary propulsion demands and secondary auxiliary demands, particularly the Heating, Ventilation, and Air Conditioning (HVAC) system. This becomes especially critical when the battery is in a low state of charge under cold ambient conditions, and cabin heating and battery preconditioning (prior to actual charging) can consume a significant percentage of available energy, directly impacting the drivi…

Almost-Optimal Local-Search Methods for Sparse Tensor PCA
Max Lovig, Conor Sheehan, Konstantinos Tsirkas, Ilias Zadik
https://arxiv.org/abs/2506.09959 http…

Almost-Optimal Local-Search Methods for Sparse Tensor PCA
Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods. Of note, among the few existing results recent studies have revealed a significant "local-computational" gap in the context of a well-studied sparse tensor principal component analysis (PCA), where a broad class of local Markov chain methods exhibits a notab…

Semantic Communication for Cooperative Multi-Tasking over Rate-Limited Wireless Channels with Implicit Optimal Prior
Ahmad Halimi Razlighi, Carsten Bockelmann, Armin Dekorsy
https://arxiv.org/abs/2506.08944

Semantic Communication for Cooperative Multi-Tasking over Rate-Limited Wireless Channels with Implicit Optimal Prior
In this work, we expand the cooperative multi-task semantic communication framework (CMT-SemCom) introduced in [1], which divides the semantic encoder on the transmitter side into a common unit (CU) and multiple specific units (SUs), to a more applicable design. Our proposed system model addresses real-world constraints by introducing a general design that operates over rate-limited wireless channels. Further, we aim to tackle the rate-limit constraint, represented through the Kullback-Leibler …

Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\L}ojasiewicz condition
Vassilis Apidopoulos, Vasiliki Mavrogeorgou, Theodoros G. Tsironis
https://arxiv.org/abs/2506.11705

Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the Łojasiewicz condition
In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a Łojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the Łojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they sug…

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…

EnerBridge-DPO: Energy-Guided Protein Inverse Folding with Markov Bridges and Direct Preference Optimization
Dingyi Rong, Haotian Lu, Wenzhuo Zheng, Fan Zhang, Shuangjia Zheng, Ning Liu
https://arxiv.org/abs/2506.09496

EnerBridge-DPO: Energy-Guided Protein Inverse Folding with Markov Bridges and Direct Preference Optimization
Designing protein sequences with optimal energetic stability is a key challenge in protein inverse folding, as current deep learning methods are primarily trained by maximizing sequence recovery rates, often neglecting the energy of the generated sequences. This work aims to overcome this limitation by developing a model that directly generates low-energy, stable protein sequences. We propose EnerBridge-DPO, a novel inverse folding framework focused on generating low-energy, high-stability prot…

Optimal designs for identifying effective doses in drug combination studies
Leonie Sch\"urmeyer, Ludger Sandig, Leonie Theresa Hezler, Bernd-Wolfgang Igl, Kirsten Schorning
https://arxiv.org/abs/2506.05913

Optimal designs for identifying effective doses in drug combination studies
We consider the optimal design problem for identifying effective dose combinations within drug combination studies where the effect of the combination of two drugs is investigated. Drug combination studies are becoming increasingly important as they investigate potential interaction effects rather than the individual impacts of the drugs. In this situation, identifying effective dose combinations that yield a prespecified effect is of special interest. If nonlinear surface models are used to de…

On the Ding and Helleseth's 8th open problem about optimal ternary cyclic codes
Dong He, Peipei Zheng, Qunying Liao
https://arxiv.org/abs/2506.09651 ht…

On the Ding and Helleseth's 8th open problem about optimal ternary cyclic codes
The cyclic code is a subclass of linear codes and has applications in consumer electronics, data storage systems and communication systems due to the efficient encoding and decoding algorithms. In 2013, Ding, et al. presented nine open problems about optimal ternary cyclic codes. Till now, the 1st, 2nd, 6th and 7th problems were completely solved, the 3rd, 8th and 9th problems were incompletely solved. In this manuscript, we focus on the 8th problem. By determining the root set of some special …

Wasserstein Distances on Quantum Structures: an Overview
Emily Beatty
https://arxiv.org/abs/2506.09794 https://arxiv.org/pdf/2506.097…

Wasserstein Distances on Quantum Structures: an Overview
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal transport tools from probability measures to quantum states has shown great promise over the last few years, particularly in the development of the theory of Wasserstein-style distances and divergences between quantum states. Such distances have already led to a…

Pattern-preserving optimal control problems with increasing time horizon
Matteo Della Rossa, Lorenzo Freddi
https://arxiv.org/abs/2506.09970 https://

Pattern-preserving optimal control problems with increasing time horizon
We establish a general framework that guarantees the preservation of optimal control patterns as the time horizon $[0,T]$ increases and becomes unbounded. A concept of pattern-preserving family of optimal control problems is introduced and the goal is achieved by analyzing the $Γ$-convergence of the corresponding variational formulations as $T\to\infty$. Special attention is given to scenarios involving state constraints. To illustrate the results, examples and applications are provided, with …

Locomotion on Constrained Footholds via Layered Architectures and Model Predictive Control
Zachary Olkin, Aaron D. Ames
https://arxiv.org/abs/2506.09979 ht…

Locomotion on Constrained Footholds via Layered Architectures and Model Predictive Control
Computing stabilizing and optimal control actions for legged locomotion in real time is difficult due to the nonlinear, hybrid, and high dimensional nature of these robots. The hybrid nature of the system introduces a combination of discrete and continuous variables which causes issues for numerical optimal control. To address these challenges, we propose a layered architecture that separates the choice of discrete variables and a smooth Model Predictive Controller (MPC). The layered formulatio…

An optimal class of domains permitting inner boundaries in a divergence theorem for rough integrands
Thomas Ruf
https://arxiv.org/abs/2506.09978 https://…

An optimal class of domains permitting inner boundaries in a divergence theorem for rough integrands
The divergence theorem on an open domain $U \subset \mathbb{R}^m$ of finite measure is investigated for the rough class $\mathcal{DM}_\infty(U)$ of bounded vector fields $u \, \colon \, U \to \mathbb{R}^m$ with a finite Radon measure divergence. Let $\mathcal{DB}(U)$ denote the closure of $\mathcal{DM}_\infty(U)$ in the Lebesgue space $L_\infty(U)$. Equivalent conditions are proved for the domain $U$ to admit the divergence theorem \begin{equation} \exists ! \ell \in \mathcal{DB}'(U) \, \colon …

This https://arxiv.org/abs/2410.08850 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Learning to Stop: Deep Learning for Mean Field Optimal Stopping
Optimal stopping is a fundamental problem in optimization with applications in risk management, finance, robotics, and machine learning. We extend the standard framework to a multi-agent setting, named multi-agent optimal stopping (MAOS), where agents cooperate to make optimal stopping decisions in a finite-space, discrete-time environment. Since solving MAOS becomes computationally prohibitive as the number of agents is very large, we study the mean-field optimal stopping (MFOS) problem, obtai…

Logarithmic Smoothing for Adaptive PAC-Bayesian Off-Policy Learning
Maxime Haddouche, Otmane Sakhi
https://arxiv.org/abs/2506.10664 https://

Logarithmic Smoothing for Adaptive PAC-Bayesian Off-Policy Learning
Off-policy learning serves as the primary framework for learning optimal policies from logged interactions collected under a static behavior policy. In this work, we investigate the more practical and flexible setting of adaptive off-policy learning, where policies are iteratively refined and re-deployed to collect higher-quality data. Building on the success of PAC-Bayesian learning with Logarithmic Smoothing (LS) in static settings, we extend this framework to the adaptive scenario using tool…

This https://arxiv.org/abs/2409.05191 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Generalization of Geometric Graph Neural Networks with Lipschitz Loss Functions
In this paper, we study the generalization capabilities of geometric graph neural networks (GNNs). We consider GNNs over a geometric graph constructed from a finite set of randomly sampled points over an embedded manifold with topological information captured. We prove a generalization gap between the optimal empirical risk and the optimal statistical risk of this GNN, which decreases with the number of sampled points from the manifold and increases with the dimension of the underlying manifold…

Optimal Non-Adaptive Group Testing with One-Sided Error Guarantees
Daniel McMorrow, Jonathan Scarlett
https://arxiv.org/abs/2506.10374 https://

Optimal Non-Adaptive Group Testing with One-Sided Error Guarantees
The group testing problem consists of determining a sparse subset of defective items from within a larger set of items via a series of tests, where each test outcome indicates whether at least one defective item is included in the test. We study the approximate recovery setting, where the recovery criterion of the defective set is relaxed to allow a small number of items to be misclassified. In particular, we consider one-sided approximate recovery criteria, where we allow either only false neg…

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
Hongwei Mei, Rui Wang, Jiongmin Yong
https://arxiv.org/abs/2506.09337

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike properties for the optimal pairs. The key is to prove a proper convergence of the solutions to the differential Riccati equations to the algebraic Riccati equation. Even for the problems without regime switchings, our result provides a refined estimate compared to t…

Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions
Jonathan R. Cangelosi, Matthias Heinkenschloss
https://arxiv.org/abs/2506.10804

Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions
This work establishes sensitivities of the solution of an optimal control problem (OCP) and a corresponding quantity of interest (QoI) to perturbations in a state/control-dependent component function that appears in the governing ODEs and the objective function. This extends existing OCP sensitivity results, which consider the sensitivity of the OCP solution with respect to state/control-independent parameters. It is shown that with Carathéodory-type assumptions, the Implicit Function Theorem …

Optimal quantum sampling on distributed databases
Longyun Chen, Jingcheng Liu, Penghui Yao
https://arxiv.org/abs/2506.07724 https://a…

Optimal quantum sampling on distributed databases
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of quantum sampling in a distributed setting. Specifically, we assume that the data is distributed among multiple machines, and each machine solely maintains a basic oracle that counts the multiplicity of individual elements. Given a quantum sampling task, which …

A potential-theoretic approach to optimal stopping in a spectrally L\'evy Model
Masahiko Egami, Tomohiro Koike
https://arxiv.org/abs/2506.10538 https:/…

A potential-theoretic approach to optimal stopping in a spectrally Lévy Model
We present a systematic solution method for optimal stopping problem of one-dimensional spectrally negative Lévy processes. Our main tools are based on potential theory, particularly the Riesz decomposition and the maximum principle. This novel approach allows us to handle a broad class of reward functions. That is, we solve the problem in a general setup without relying on specific form of the reward function or on the fluctuation identities. We provide a step-by-step solution procedure, whic…

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…

This https://arxiv.org/abs/2202.01956 has been replaced.
link: https://scholar.google.com/scholar?q=a

Maximum Likelihood Estimation of Optimal Receiver Operating Characteristic Curves from Likelihood Ratio Observations
The optimal receiver operating characteristic (ROC) curve, giving the maximum probability of detection as a function of the probability of false alarm, is a key information-theoretic indicator of the difficulty of a binary hypothesis testing problem (BHT). It is well known that the optimal ROC curve for a given BHT, corresponding to the likelihood ratio test, is determined by the probability distribution of the observed data under each of the two hypotheses. In some cases, these two distributio…

Estimation of Optimal Causal Bounds via Covariate-Assisted Optimal Transport
Sirui Lin, Zijun Gao, Jose Blanchet, Peter Glynn
https://arxiv.org/abs/2506.00257

Estimation of Optimal Causal Bounds via Covariate-Assisted Optimal Transport
We study the estimation of causal estimand involving the joint distribution of treatment and control outcomes for a single unit. In typical causal inference settings, it is impossible to observe both outcomes simultaneously, which places our estimation within the domain of partial identification (PI). Pre-treatment covariates can substantially reduce estimation uncertainty by shrinking the partially identified set. Recently, it was shown that covariate-assisted PI sets can be characterized thro…

Optimal Robotic Velcro Peeling with Force Feedback
Jiacheng Yuan, Changhyun Choi, Volkan Isler
https://arxiv.org/abs/2506.05812 https://

Optimal Robotic Velcro Peeling with Force Feedback
We study the problem of peeling a Velcro strap from a surface using a robotic manipulator. The surface geometry is arbitrary and unknown. The robot has access to only the force feedback and its end-effector position. This problem is challenging due to the partial observability of the environment and the incompleteness of the sensor feedback. To solve it, we first model the system with simple analytic state and action models based on quasi-static dynamics assumptions. We then study the fully-obs…

On a mean-field Pontryagin minimum principle for stochastic optimal control
Manfred Opper, Sebastian Reich
https://arxiv.org/abs/2506.10506 https://…

On a mean-field Pontryagin minimum principle for stochastic optimal control
This papers outlines a novel extension of the classical Pontryagin minimum (maximum) principle to stochastic optimal control problems. Contrary to the well-known stochastic Pontryagin minimum principle involving forward-backward stochastic differential equations, the proposed formulation is deterministic and of mean-field type. The Hamiltonian structure of the proposed Pontryagin minimum principle is achieved via the introduction of an appropriate gauge variable. The gauge freedom can be used t…

Optimal T depth quantum circuits for implementing arbitrary Boolean functions
Suman Dutta, Anik Basu Bhaumik, Anupam Chattopadhyay, Subhamoy Maitra
https://arxiv.org/abs/2506.01542

Optimal T depth quantum circuits for implementing arbitrary Boolean functions
In this paper we present a generic construction to obtain an optimal T depth quantum circuit for any arbitrary $n$-input $m$-output Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}^m$ having algebraic degree $k\leq n$, and it achieves an exact Toffoli (and T) depth of $\lceil \log_2 k \rceil$. This is a broader generalization of the recent result establishing the optimal Toffoli (and consequently T) depth for multi-controlled Toffoli decompositions (Dutta et al., Phys. Rev. A, 2025). We achie…

Criss-Cross Deletion Correcting Codes: Optimal Constructions with Efficient Decoders
Yubo Sun, Gennian Ge
https://arxiv.org/abs/2506.07607 https://

Criss-Cross Deletion Correcting Codes: Optimal Constructions with Efficient Decoders
This paper addresses fundamental challenges in two-dimensional error correction by constructing optimal codes for \emph{criss-cross deletions}. We consider an $ n \times n $ array over a $ q $-ary alphabet $Σ_q := \{0, 1, \ldots, q-1\}$ that is subject to a \emph{$(t_r, t_c)$-criss-cross deletion}, which involves the simultaneous removal of $ t_r $ rows and $ t_c $ columns. A code $\mathcal{C} \subseteq Σ_q^{n \times n}$ is defined as a \emph{$(t_r,t_c)$-criss-cross deletion correcting code} …

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization
Quang Huy Nguyen, Phuong Cuc Hoang, Van Chien Le, Thi Thanh Mai Ta
https://arxiv.org/abs/2506.10924

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and adjoint. This problem is shown to be equivalent to our optimal control problem. Based on fully unstructured, space-time interface-fitted meshes, we propose and analyze a Petrov-Galerkin approximation of the problem. An optimal error estimate with respect to a …

An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists
Andreas Mueller
https://arxiv.org/abs/2506.10686

An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists
Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required computational efficiency, recursive $O(n)$-algorithms were proposed to this end. Aiming at compact yet efficient formulations, a Lie group formulation was recently proposed, making use of body-fixed and hybrid representation of twists and wrenches. In this paper…

Optimal absorption and emission of itinerant fields into a spin ensemble memory
Linda Greggio, Tristan Lorriaux, Alexandru Petrescu, Mazyar Mirrahimi, Audrey Bienfait
https://arxiv.org/abs/2506.06107

Optimal absorption and emission of itinerant fields into a spin ensemble memory
Quantum memories integrated in a modular quantum processing architecture can rationalize the resources required for quantum computation. This work focuses on spin-based quantum memories, where itinerant electromagnetic fields are stored in large ensembles of effective two-level systems, such as atomic or solid-state spin ensembles, embedded in a cavity. Using a mean-field framework, we model the ensemble as an effective spin communication channel and develop a cascaded quantum model to describe…

Vulnerability-Based Optimal Grid Defense Strategies for Enhancing Cyber-Physical Energy System Resilience
Eric T\"onges, Philipp H\"artel, Martin Braun
https://arxiv.org/abs/2506.09766

Vulnerability-Based Optimal Grid Defense Strategies for Enhancing Cyber-Physical Energy System Resilience
An approach is proposed to identify optimal asset protection strategies based on vulnerability assessment outcomes. Traditional bilevel attacker-defender models emphasize worstcase scenarios but offer limited defensive guidance. In contrast, trilevel models introduce high computational complexity and rely on fixed network configurations. The proposed critical-components method leverages vulnerability assessment results to determine protection strategies, effectively outsourcing the upper-level …

Optimal Control of Pseudo-Parabolic KWC Systems for Grain Boundary Motion
Harbir Antil, Daiki Mizuno, Ken Shirakawa
https://arxiv.org/abs/2506.09407 https:…

Optimal Control of Pseudo-Parabolic KWC Systems for Grain Boundary Motion
The KWC system is a well-known generic framework for phase-field models of grain boundary motion, whose original formulation is given as a parabolic gradient flow of a free energy. In the original KWC system, the results of uniqueness have been relatively scarce compared to other issues, such as existence, qualitative behavior, and numerics. This lack of progress has posed a significant challenge for more advanced topics, including optimal control. To overcome this, the authors have recently in…

Remarks on multi-period martingale optimal transport
Brendan Pass, Joshua Hiew
https://arxiv.org/abs/2506.05505 https://arxiv.org/pdf…

Remarks on multi-period martingale optimal transport
We study the structural properties of multi-period martingale optimal transport (MOT). We develop new tools to address these problems, and use them to prove several uniqueness and structural results on three-period martingale optimal transport. More precisely, we establish lemmas on how and when two-period martingale couplings may be glued together to obtain multi-period martingales and which among these glueings are optimal for particular MOT problems. We use these optimality results to study …

$C^{1,\alpha}$-regularity for Schr\"odinger potentials of Shannon-entropy regularized Optimal Transport
Sumiya Baasandorj, Simone Di Marino, Augusto Gerolin
https://arxiv.org/abs/2506.09302

$C^{1,α}$-regularity for Schrödinger potentials of Shannon-entropy regularized Optimal Transport
We provide the stability of $C^{1,α}$ regularity of Schrödinger potentials of Boltzmann-Shannon entropy regularized Optimal Transport under the classical assumption of marginals supported on bounded convex sets and whose densities are bounded above and below.

Constructions of Optimal Frequency-Hopping Sequences with Controlled Minimum Gaps
Chen Li, Chunlei Li, Xiangyong Zeng, Dian Li
https://arxiv.org/abs/2506.00945

Constructions of Optimal Frequency-Hopping Sequences with Controlled Minimum Gaps
Frequency-hopping sequences (FHSs) with low Hamming correlation and wide gaps significantly contribute to the anti-interference performance in FH communication systems. This paper investigates FHSs with optimal Hamming correlation and controlled minimum gaps. We start with the discussion of the upper bounds on the minimum gaps of uniform FHSs and then propose a general construction of optimal uniform wide-gap FHSs with length 2l and 3l, which includes the work by Li et al. in IEEE Trans. Inf. T…

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…

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
Liang Chen, Youyicun Lin, Yuxuan Zhou
https://arxiv.org/abs/2506.08988

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path. Building on the convex DOT model of Benamou and Brenier, we first properly reformulate its dual problem, discretized on a triangular mesh for space together with a staggered grid for time, to a linear second-order cone programming. Then the resulting finite-dimen…

This https://arxiv.org/abs/2412.01012 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime
We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function $c_2$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is the Riemannian distance squared. Building on insights from previous studies on the Riemannian and Lorentzian case, our main goal is to investigate the regularity of $π$-solutions (weak versions of Kantorovich potentials), from which we can conclude, in a classical way,…

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/7})$ Second-Order Oracle Complexity
Lesi Chen, Chengchang Liu, Luo Luo, Jingzhao Zhang
https://arxiv.org/abs/2506.08362

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(ε^{-4/7})$ Second-Order Oracle Complexity
Previous algorithms can solve convex-concave minimax problems $\min_{x \in \mathcal{X}} \max_{y \in \mathcal{Y}} f(x,y)$ with $\mathcal{O}(ε^{-2/3})$ second-order oracle calls using Newton-type methods. This result has been speculated to be optimal because the upper bound is achieved by a natural generalization of the optimal first-order method. In this work, we show an improved upper bound of $\tilde{\mathcal{O}}(ε^{-4/7})$ by generalizing the optimal second-order method for convex optimizat…

A Branch-and-Cut Algorithm for the Optimal Design of Parking Lots with One-way and Two-way Lanes
Helen Thomas, Tarun Rambha
https://arxiv.org/abs/2506.09961

A Branch-and-Cut Algorithm for the Optimal Design of Parking Lots with One-way and Two-way Lanes
We address the problem of maximizing the number of stalls in parking lots where vehicles park perpendicular to the driveways. Building on recent research, we first formulate a mixed integer program to maximize the number of parking stalls using a flow-based approach. Parking lots are rasterized into a grid, and the proposed MIP model optimizes them in a generic manner, adapting to the grid resolution and stall size without the need for custom formulations. The constraints ensure the connectivit…

Stochastic maximum principle for optimal control problem of non exchangeable mean field systems
Idris Kharroubi, Samy Mekkaoui, Huy\^en Pham
https://arxiv.org/abs/2506.05595

Stochastic maximum principle for optimal control problem of non exchangeable mean field systems
We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-q…

Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning
Yuhua Zhu, Yuming Zhang, Haoyu Zhang
https://arxiv.org/abs/2506.05208

Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning
This paper addresses continuous-time reinforcement learning (CTRL) where the system dynamics are governed by a stochastic differential equation but are unknown, and only discrete-time observations are available. Existing approaches face limitations: model-based PDE methods suffer from non-identifiability, while model-free methods based on the optimal Bellman equation (Optimal-BE) are prone to large discretization errors sensitive to both the dynamics and reward structure. To overcome these chal…

Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
Oliver G. S. Lundqvist, Fabricio Oliveira
https://arxiv.org/abs/2506.04742

Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
Neural networks have been used to solve optimal control problems, typically by training neural networks using a combined loss function that considers data, differential equation residuals, and objective costs. We show that including cost functions in the training process is unnecessary, advocating for a simpler architecture and streamlined approach by decoupling the optimal control problem from the training process. Thus, our work shows that a simple neural operator architecture, such as DeepON…

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…

Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence
Qi Feng, Gu Wang
https://arxiv.org/abs/2506.08121 https://…

Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework applies to both the entropy-regularized relaxed control problems and the classical control problems, with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control under the monotonicity condition of the Hamiltonian. By …

Achieving Linear Speedup and Near-Optimal Complexity for Decentralized Optimization over Row-stochastic Networks
Liyuan Liang, Xinyi Chen, Gan Luo, Kun Yuan
https://arxiv.org/abs/2506.04600

Achieving Linear Speedup and Near-Optimal Complexity for Decentralized Optimization over Row-stochastic Networks
A key challenge in decentralized optimization is determining the optimal convergence rate and designing algorithms to achieve it. While this problem has been extensively addressed for doubly-stochastic and column-stochastic mixing matrices, the row-stochastic scenario remains unexplored. This paper bridges this gap by introducing effective metrics to capture the influence of row-stochastic mixing matrices and establishing the first convergence lower bound for decentralized learning over row-sto…