Tootfinder

Kahan's Automatic Step-Size Control for Unconstrained Optimization
Yifeng Meng, Chungen Shen, Linuo Xue, Lei-Hong Zhang
https://arxiv.org/abs/2508.06002 https://

Kahan's Automatic Step-Size Control for Unconstrained Optimization
The Barzilai and Borwein (BB) gradient method is one of the most widely-used line-search gradient methods. It computes the step-size for the current iterate by using the information carried in the previous iteration. Recently, William Kahan [Kahan, Automatic Step-Size Control for Minimization Iterations, Technical report, University of California, Berkeley CA, USA, 2019] proposed new Gradient Descent (KGD) step-size strategies which iterate the step-size itself by effectively utilizing the info…

Condition number for finite element discretisation of nonlocal PDE systems with applications to biology
Olusegun E. Adebayo, Raluca Eftimie, Dumitru Trucu
https://arxiv.org/abs/2508.09781

Condition number for finite element discretisation of nonlocal PDE systems with applications to biology
In this work, we investigate the condition number for a system of coupled non-local reaction-diffusion-advection equations developed in the context of modelling normal and abnormal wound healing. Following a finite element discretisation of the coupled non-local system, we establish bounds for this condition number. We further discuss how model parameter choices affect the conditioning of the system. Finally, we discuss how the step size of the chosen time-stepping scheme and the spatial gr…

This https://arxiv.org/abs/2504.01759 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter
The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $αβ$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dyna…

Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space
Jiyoung Park, Abhishek Roy, Jonathan W. Siegel, Anirban Bhattacharya
https://arxiv.org/abs/2506.06160

Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space
There is extensive literature on accelerating first-order optimization methods in a Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimization problems is an active area of research. Motivated by the recent success of varying step-size methods in the Euclidean setting, we undertake a study of such algorithms in the Riemannian setting. We show that varying step-size acceleration can be achieved in non-negatively curved Riemannian manifolds under geodesic s…

Improving population size adapting CMA-ES algorithm on step-size blow-up in weakly-structured multimodal functions
Chandula Fernando, Kushani De Silva
https://arxiv.org/abs/2506.00825

Improving population size adapting CMA-ES algorithm on step-size blow-up in weakly-structured multimodal functions
Multimodal optimization requires both exploration and exploitation. Exploration identifies promising attraction basins, while exploitation finds the best solutions within these basins. The balance between exploration and exploitation can be maintained by adjusting parameter settings. The population size adaptation covariance matrix adaption evolutionary strategy algorithm (PSA-CMA-ES) achieves this balance by dynamically adjusting population size. PSA-CMA-ES performs well on well-structured mul…

Design and optimization of neural networks for multifidelity cosmological emulation
Yanhui Yang, Simeon Bird, Ming-Feng Ho, Mahdi Qezlou
https://arxiv.org/abs/2507.07184

Design and optimization of neural networks for multifidelity cosmological emulation
Accurate and efficient simulation-based emulators are essential for interpreting cosmological survey data down to nonlinear scales. Multifidelity emulation techniques reduce simulation costs by combining high- and low-fidelity data, but traditional regression methods such as Gaussian processes struggle with scalability in sample size and dimensionality. In this work, we present T2N-MusE, a neural network framework characterized by (i) a novel 2-step multifidelity architecture, (ii) a 2-stage Ba…

A Study of Non-linear Flows and Shear Banding in Wormlike Micelles Under Varying Elasticity, Flow Curvature, and Surfactant Chemistry
Alfredo Scigliani, Hadi Mohammadigoushki
https://arxiv.org/abs/2507.07218

A Study of Non-linear Flows and Shear Banding in Wormlike Micelles Under Varying Elasticity, Flow Curvature, and Surfactant Chemistry
We report the flow dynamics of two shear-banding wormlike micellar solutions with distinct surfactant chemistries in a Taylor-Couette (TC) setup following a startup shear. The solutions, formulated with CTAB/NaSal and CPyCl/NaSal, exhibit comparable bulk rheology and equilibrium microstructural properties. By varying the TC gap size, we systematically examine elasticity number over a range of 128000-4470000, while flow curvature spans from 0.022 to 0.171. Under a step shear into the stress plat…

This https://arxiv.org/abs/2502.13943 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

AdaptiveStep: Automatically Dividing Reasoning Step through Model Confidence
Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length into a fixed size. These approaches overlook the fact that specific words do not typically mark true decision points in a text. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model's confidence in predicting the …

High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation
Ilya Levin, Alexey Naumov, Sergey Samsonov
https://arxiv.org/abs/2508.05570 https://

High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation
In this paper, we study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size $α$ and propose a novel decomposition of the bias via a linearization technique. We analyze the structure of the bias and show that the leading-order term is linear in $α$ and cannot be eliminated by PR averaging. To address this, we apply the Richardson-Rom…

Reservoir computing with large valid prediction time for the Lorenz system
Lauren A Hurley, Sean E Shaheen
https://arxiv.org/abs/2508.06730 https://arxiv.o…

Reservoir computing with large valid prediction time for the Lorenz system
We study the dependence of the Valid Prediction Time (VPT) of Reservoir Computers (RCs) on hyperparameters including the regularization coefficient, reservoir size, and spectral radius. Under carefully chosen conditions, the RC can achieve approximately 70% of a benchmark performance, based on the output of a single prediction step used as initial conditions for the Lorenz equations. We report high VPT values (>30 Lyapunov times), as we are predicting a noiseless system where overfitting can be…

This https://arxiv.org/abs/2505.21700 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

Rethinking Chunk Size For Long-Document Retrieval: A Multi-Dataset Analysis
Chunking is a crucial preprocessing step in retrieval-augmented generation (RAG) systems, significantly impacting retrieval effectiveness across diverse datasets. In this study, we systematically evaluate fixed-size chunking strategies and their influence on retrieval performance using multiple embedding models. Our experiments, conducted on both short-form and long-form datasets, reveal that chunk size plays a critical role in retrieval effectiveness -- smaller chunks (64-128 tokens) are optim…

Online Learning for Vibration Suppression in Physical Robot Interaction using Power Tools
Gokhan Solak, Arash Ajoudani
https://arxiv.org/abs/2508.03559 https://

Online Learning for Vibration Suppression in Physical Robot Interaction using Power Tools
Vibration suppression is an important capability for collaborative robots deployed in challenging environments such as construction sites. We study the active suppression of vibration caused by external sources such as power tools. We adopt the band-limited multiple Fourier linear combiner (BMFLC) algorithm to learn the vibration online and counter it by feedforward force control. We propose the damped BMFLC method, extending BMFLC with a novel adaptive step-size approach that improves the conv…

On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape
Lei Qin, Ye Pu
https://arxiv.org/abs/2508.06922 https://…

On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape
This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method, Laplacian-weighted Gradient Descent, we propose to add random perturbations to the gradient iteration to enable efficient escape from saddle points and achieve second-order convergence guarantees. We show that, with a sufficiently small fixed step size, the it…

This https://arxiv.org/abs/2504.01759 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter
The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $αβ$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dyna…

Effective sample size estimation based on concordance between p-value and posterior probability of the null hypothesis
Han Wang, Yan Dora Zhang, Guosheng Yin
https://arxiv.org/abs/2507.16422

Effective sample size estimation based on concordance between p-value and posterior probability of the null hypothesis
Estimating the effective sample size (ESS) of a prior distribution is an age-old yet pivotal challenge, with great implications for clinical trials and various biomedical applications. Although numerous endeavors have been dedicated to this pursuit, most of them neglect the likelihood context in which the prior is embedded, thereby considering all priors as "beneficial". In the limited studies of addressing harmful priors, specifying a baseline prior remains an indispensable step. In this paper…

Cauchy problem for the localized wave propagation in continuous model of the one-dimensional diatomic crystal
Sergey Sergeev
https://arxiv.org/abs/2507.02729

Cauchy problem for the localized wave propagation in continuous model of the one-dimensional diatomic crystal
We study the continuous model of the localized wave propagation corresponding to the one-dimensional diatomic crystal lattice. From the mathematical point of view the problem can be described in terms of the Cauchy problem with localized initial data for a system of two pseudo-differential equations. We assume two small parameters in this formulation -- the lattice step and the size if the initial perturbation. We construct the asymptotic solution of the continuous Cauchy problem with respect t…

Beyond the MaxCut problem in $H$-free graphs
Zhihan Jin, Aleksa Milojevi\'c, Istv\'an Tomon
https://arxiv.org/abs/2507.13298 https://

Beyond the MaxCut problem in $H$-free graphs
In a recent breakthrough, Zhang proves that if $G$ is an $H$-free graph with $m$ edges, then $G$ has a cut of size at least $m/2+c_Hm^{0.5001}$, making a significant step towards a well known conjecture of Alon, Bollobás, Krivelevich and Sudakov. We show that the methods of Zhang can be further boosted, and prove the following strengthening. If $G$ is a graph with $m$ edges and no clique of size $m^{1/2-δ}$, then $G$ has a cut of size at least $m/2+m^{1/2+\varepsilon}$ for some $\varepsilon=\…

Statistical microlocal analysis in two-dimensional X-ray CT
Anuj Abhishek, Alexander Katsevich, James W. Webber
https://arxiv.org/abs/2506.05113 https://…

Statistical microlocal analysis in two-dimensional X-ray CT
In many imaging applications it is important to assess how well the edges of the original object, $f$, are resolved in an image, $f^\text{rec}$, reconstructed from the measured data, $g$. In this paper we consider the case of image reconstruction in 2D X-ray Computed Tomography (CT). Let $f$ be a function describing the object being scanned, and $g=Rf + η$ be the Radon transform data in $\mathbb{R}^2$ corrupted by noise, $η$, and sampled with step size $\simε$. Conventional microlocal analys…

Uniform semiclassical observable error bound of Trotterization without the Egorov theorem: a simple algebraic proof
Di Fang, Conrad Qu
https://arxiv.org/abs/2507.02783

Uniform semiclassical observable error bound of Trotterization without the Egorov theorem: a simple algebraic proof
Efficient simulation of the semiclassical Schrödinger equation has garnered significant attention in the numerical analysis community. While controlling the error in the unitary evolution or the wavefunction typically requires the time step size to shrink as the semiclassical parameter $h$ decreases, it has been observed -- and proved for first- and second-order Trotterization schemes -- that the error in certain classes of observables admits a time step size independent of $h$. In this work, …

Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation
Haiquan Zhao, Chengjin Li
https://arxiv.org/abs/2506.00403 https://

Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation
Recently, the proposal of the least mean square (LMS) and recursive least squares (RLS) algorithm for graph signal processing (GSP) provides excellent solutions for processing signals defined on irregular structures such as sensor networks. The existing work has completed the steady state error analysis of the GSP LMS algorithm and GSP RLS algorithm in Gaussian noise scenarios, and a range of values for the step size of the GSP LMS algorithm has also been given. Meanwhile, the transient error a…

An evaluation of level of detail degradation in head-mounted display peripheries
Benjamin Watson, Neff Walker, Larry F Hodges, Martin Reddy
https://arxiv.org/abs/2506.21441

An evaluation of level of detail degradation in head-mounted display peripheries
A paradigm for the design of systems that manage level of detail in virtual environments is proposed. As an example of the prototyping step in this paradigm, a user study was performed to evaluate the effectiveness of high detail insets used with head-mounted displays. Ten subjects were given a simple search task that required the location and identification of a single target object. All subjects used seven different displays (the independent variable), varying in inset size and peripheral det…

Subelliptic Random Walks on Riemannian Manifolds and Their Convergence to Equilibrium
Davide Tramontana
https://arxiv.org/abs/2506.22869 https://

Subelliptic Random Walks on Riemannian Manifolds and Their Convergence to Equilibrium
The aim of this work is to study the convergence to equilibrium of an $(h,ρ)$-subelliptic random walk on a closed, connected Riemannian manifold $(M,g)$ associated with a subelliptic second-order differential operator $A$ on $M$. In such a random walk, $h$ roughly represents the step size and $ρ$ the speed at which it is carried out. To construct the random walk and prove the convergence result, we employ a technique due to Fefferman and Phong, which reduces the problem to the study of a cons…

Two-dimensional Rademacher walk
Satyaki Bhattacharya, Stanislav Volkov
https://arxiv.org/abs/2506.16259 https://arxiv.org/pdf/2506.16…

Two-dimensional Rademacher walk
We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (2023) to $\mathbb{Z}^2$ (for $d\ge 3$, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Englander and Volkov (2025)). This walk is defined as the sum of a sequence of independent steps, where each step goes in one of the four possible directions with equal probability, and the size of the $n$th step is $a_n$ where $\{a_n\}$ is a given sequence of positive …

Axisymmetric Gyrokinetic Simulation of ASDEX-Upgrade Scrape-off Layer Using a Conservative Implicit BGK Collision Operator
D. Liu, J. Juno, G. W. Hammett, A. Hakim, A. Shukla, M. Francisquez
https://arxiv.org/abs/2507.22821

Axisymmetric Gyrokinetic Simulation of ASDEX-Upgrade Scrape-off Layer Using a Conservative Implicit BGK Collision Operator
Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar-Gross-Krook (BGK) collision operator for use in the discontinuous Galerkin (DG) …

Comparing and Scaling fMRI Features for Brain-Behavior Prediction
Mikkel Sch\"ottner Sieler, Thomas A. W. Bolton, Jagruti Patel, Patric Hagmann
https://arxiv.org/abs/2507.20601

Comparing and Scaling fMRI Features for Brain-Behavior Prediction
Predicting behavioral variables from neuroimaging modalities such as magnetic resonance imaging (MRI) has the potential to allow the development of neuroimaging biomarkers of mental and neurological disorders. A crucial processing step to this aim is the extraction of suitable features. These can differ in how well they predict the target of interest, and how this prediction scales with sample size and scan time. Here, we compare nine feature subtypes extracted from resting-state functional MRI…

Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation
Matteo Ferrari, Ilaria Perugia, Enrico Zampa
https://arxiv.org/abs/2506.05886

Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation
In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We analyze the method, showing its stability without imposing any restrictions on the mesh size or time step, and proving quasi-optimal convergence for any choice of space-time tensor product discrete spaces that satisfies standard approximation assumptions. Numerical examples are provided to support the theoretical findin…

A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization
A. A. Vyguzov, F. S. Stonyakin
https://arxiv.org/abs/2507.05669

A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization
We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth and relatively strongly convex objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step size based on both the relative smoothness constant and the Triangle Scaling Exponent (TSE) of the Bregman divergence. Our method does not require prior knowledge of the function parameters and guarantees convergence using only loc…

Relaxing Direct Ptychography Sampling Requirements via Parallax Imaging Insights
Georgios Varnavides, Julie Marie Bekkevold, Stephanie M Ribet, Mary C Scott, Lewys Jones, Colin Ophus
https://arxiv.org/abs/2507.18610

Relaxing Direct Ptychography Sampling Requirements via Parallax Imaging Insights
Direct ptychography enables the retrieval of information encoded in the phase of an electron wave passing through a thin sample by deconvolving the interference effect of a converged probe with known aberrations. Under the weak phase object approximation, this permits the optimal transfer of information using non-iterative techniques. However, the achievable resolution of the technique is traditionally limited by the probe step size -- setting stringent Nyquist sampling requirements. At the sam…

An Atlas of Spectroheliograms from 3641 to 6600 \AA
P. V\'aradi Nagy, A. G. M. Pietrow
https://arxiv.org/abs/2507.13025 https://a…

An Atlas of Spectroheliograms from 3641 to 6600 Å
We present a spectral atlas of solar spectroheliograms covering the wavelength range from 3641 to 6600 Å, with continuous coverage between 3711 and 5300 Å, and sparser coverage beyond this range. The spectral resolution varies between R $\sim$ 20 000 and 40 000, with a spectral step size between 60 and 90 mÅ, while the spatial resolution averages around 2.5 arcseconds. These observations were acquired over three months during the 2025 solar maximum, using amateur spectroheliographs (Sol'Ex a…

RSB bounds on the maximum cut
Viktor Harangi
https://arxiv.org/abs/2506.21296 https://arxiv.org/pdf/2506.21296

RSB bounds on the maximum cut
In the context of random regular graphs, the size of the maximum cut is probably the second most studied graph parameter after the independence ratio. Zdeborová and Boettcher used the cavity method, a non-rigorous statistical physics technique, to predict one-step replica symmetry breaking (1-RSB) formulas. Coja-Ohglan et al. confirmed these predictions as rigorous upper bounds using the interpolation method. While these upper bounds were not expected to be exact, they may be very close to the…

Tracking the rotation of light magnetic particles in turbulence
Chunlai Wu, Rudie P. J. Kunnen, Ziqi Wang, Xander M. de Wit, Federico Toschi, Herman J. H. Clercx
https://arxiv.org/abs/2506.21769

Tracking the rotation of light magnetic particles in turbulence
Particle-laden turbulence involves complex interactions between the dispersed and continuous phases. Given that particles can exhibit a wide range of properties, such as varying density, size, and shape, their interplay with the flow can lead to various modifications of the turbulence. Therefore, understanding the dynamics of particles is a necessary first step toward revealing the behavior of the multiphase system. Within the context of particle dynamics, accurately resolving rotational motion…

Multireference equation-of-motion driven similarity renormalization group: theoretical foundations and applications to ionized states
Zijun Zhao, Shuhang Li, Francesco A. Evangelista
https://arxiv.org/abs/2506.13693

Multireference equation-of-motion driven similarity renormalization group: theoretical foundations and applications to ionized states
We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for systems with strongly correlated ground and excited states. The EOM step scales as $O(N^5)$ with the basis set size $N$, allowing for efficient calculation of spect…

Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Els\"asser Variables
Zhen Yao, Catalin Trenchea, Wenlong Pei
https://arxiv.org/abs/2507.12700

Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables
Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Elsässer variables. We reduce the computational cost of the iterative non-linear solver, at each time step, by partitioning the coupled system into two subproblems of half size, solved in parallel. We prove that the iterations converge linearly, under a time step restriction similar…

Consistency of tug-of-war type operators on random data clouds
Jeongmin Han, Huajie Liu
https://arxiv.org/abs/2507.18383 https://arxiv.org/pdf/2507.18383…

Consistency of tug-of-war type operators on random data clouds
In this paper, we study a tug-of-war type operator on geometric graphs and its associated Dirichlet problem on a random data cloud. Specifically, we analyze the convergence of the value functions as the number of data points increases and the step size of the game shrinks. This analysis reveals the connection between our tug-of-war type operator and the corresponding model problem. A key ingredient in establishing this result is the consistency of the operator.

This https://arxiv.org/abs/2502.03701 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

First-ish Order Methods: Hessian-aware Scalings of Gradient Descent
Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural scaling, which often necessitates expensive line searches or heuristic tuning to determine an appropriate step size. In this paper, we address this limitation by incorporating Hessian information to scale the gradient direction. By accounting for the curvatur…

Gradient descent avoids strict saddles with a simple line-search method too
Andreea-Alexandra Mu\c{s}at, Nicolas Boumal
https://arxiv.org/abs/2507.13804 ht…

Gradient descent avoids strict saddles with a simple line-search method too
It is known that gradient descent (GD) on a $C^2$ cost function generically avoids strict saddle points when using a small, constant step size. However, no such guarantee existed for GD with a line-search method. We provide one for a modified version of the standard Armijo backtracking method with generic, arbitrarily large initial step size. In contrast to previous works, our analysis does not require a globally Lipschitz gradient. We extend this to the Riemannian setting (RGD), assuming the…

The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler
Nawaf Bou-Rabee, Bob Carpenter, Tore Selland Kleppe, Sifan Liu
https://arxiv.org/abs/2506.18746 https:…

The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler
Locally adapting parameters within Markov chain Monte Carlo methods while preserving reversibility is notoriously difficult. The success of the No-U-Turn Sampler (NUTS) largely stems from its clever local adaptation of the integration time in Hamiltonian Monte Carlo via a geometric U-turn condition. However, posterior distributions frequently exhibit multi-scale geometries with extreme variations in scale, making it necessary to also adapt the leapfrog integrator's step size locally and dynamic…

A predictive model for bubble-particle collisions in turbulence
Timothy T. K. Chan (Physics of Fluids Group, University of Twente), Linfeng Jiang (Physics of Fluids Group, University of Twente, Institute of Aerodynamics, RWTH Aachen University), Dominik Krug (Physics of Fluids Group, University of Twente, Institute of Aerodynamics, RWTH Aachen University)

A predictive model for bubble-particle collisions in turbulence
The modelling of bubble-particle collisions is crucial to improving the efficiency of industrial processes such as froth flotation. Although such systems usually have turbulent flows and the bubbles are typically much larger than the particles, there currently exist no predictive models for this case which consistently include finite-size effects in the interaction with the bubbles as well as inertial effects for the particles simultaneously. As a first step, Jiang and Krug (J. Fluid Mech., vol…

Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
Qiujiang Jin, Aryan Mokhtari
https://arxiv.org/abs/2507.00361 ht…

Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
In this paper, we establish global non-asymptotic convergence guarantees for the BFGS quasi-Newton method without requiring strong convexity or the Lipschitz continuity of the gradient or Hessian. Instead, we consider the setting where the objective function is strictly convex and strongly self-concordant. For an arbitrary initial point and any arbitrary positive-definite initial Hessian approximation, we prove global linear and superlinear convergence guarantees for BFGS when the step size is …

Popov Mirror-Prox Method for Variational Inequalities
Abhishek Chakraborty, Angelia Nedi\'c
https://arxiv.org/abs/2507.23395 https://arxiv.org/pdf/2507…

Popov Mirror-Prox Method for Variational Inequalities
This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing methods that require prior knowledge of problem-specific parameters, we propose step-size schemes that are entirely parameter-free in both constant and diminishing forms. For stochastic and deterministic monotone VIs, we establish optimal convergence rates in term…

Explicit Monotone Stable Super-Time-Stepping Methods for Finite Time Singularities
Zheng Tan, Tariq D. Aslam, Andrea L. Bertozzi
https://arxiv.org/abs/2507.17062 https://…

Explicit Monotone Stable Super-Time-Stepping Methods for Finite Time Singularities
We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge--Kutta--Legendre (RKL) and Runge--Kutta--Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multi-stage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the timestep size for stability scales with stage number $s$ as $…

Learning Acceleration Algorithms for Fast Parametric Convex Optimization with Certified Robustness
Rajiv Sambharya, Jinho Bok, Nikolai Matni, George Pappas
https://arxiv.org/abs/2507.16264

Learning Acceleration Algorithms for Fast Parametric Convex Optimization with Certified Robustness
We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization problems with certified robustness. We obtain a strong form of robustness guarantee -- certification of worst-case performance over all parameters within a set after a given number of iterations -- through regularization-based training. The regularization term is …

Optimized Qubit Routing for Commuting Gates via Integer Programming
Moritz Stargalla, Friedrich Wagner
https://arxiv.org/abs/2507.12199 https://

Optimized Qubit Routing for Commuting Gates via Integer Programming
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum resources. In this work, we address the problem of qubit routing for commuting gates, which arises, for example, during the compilation of the well-known Quantum Approximate Optimization Algorithm. We propose a two-step decomposition approach based on integer pro…