Tootfinder

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Weijian Li, Panagiotis Kounatidis, Zhong-Ping Jiang, Andreas A. Malikopoulos
https://arxiv.org/abs/2506.12596

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing the robustness of derivative-free methods for solving an infinite-horizon LQR problem. To be specific, we estimate policy gradients by cost values, and study the effect of perturbations on the estimations, where the perturbations may arise from function approx…

Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
Gregory Bellchambers
https://arxiv.org/abs/2506.13614 https://…

Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
The success of diffusion models has driven interest in performing conditional sampling via training-free guidance of the denoising process to solve image restoration and other inverse problems. A popular class of methods, based on Diffusion Posterior Sampling (DPS), attempts to approximate the intractable posterior score function directly. In this work, we present a novel expression for the exact posterior score for purely denoising tasks that is tractable in terms of the unconditional score fu…

A fast mesh-free boundary integral method for two-phase flow with soluble surfactant
Samantha G. Evans, Michael Siegel, Johannes Tausch, Michael R. Booty
https://arxiv.org/abs/2506.11282

A fast mesh-free boundary integral method for two-phase flow with soluble surfactant
We present an accurate and efficient boundary integral (BI) method for simulating the deformation of drops and bubbles in Stokes flow with soluble surfactant. Soluble surfactant advects and diffuses in bulk fluids while adsorbing and desorbing at interfaces. Since the fluid velocity is coupled to the surfactant concentration, the advection-diffusion equation governing the bulk surfactant concentration $C$ is nonlinear, precluding the Green's function formulation necessary for a BI method. Howev…

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
Meghanil Sinha, S. Surendra Singh
https://arxiv.org/abs/2506.11171

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
This paper presents a study on gravitational vacuum stars (gravastars) with an isotropic matter distribution in de Rham-Gabadadze-Tolley (dRGT) massive gravity incorporating Buchdahl metric function. Here we have conducted an analysis on thin-shell singularity-free gravastar configuration. The study demonstrates the viability of gravastars as alternatives to black holes (BHs) in this massive gravity. Our research yields singularity free analytical solutions for gravastar interior and without ev…

Towards Biosignals-Free Autonomous Prosthetic Hand Control via Imitation Learning
Kaijie Shi, Wanglong Lu, Hanli Zhao, Vinicius Prado da Fonseca, Ting Zou, Xianta Jiang
https://arxiv.org/abs/2506.08795

Towards Biosignals-Free Autonomous Prosthetic Hand Control via Imitation Learning
Limb loss affects millions globally, impairing physical function and reducing quality of life. Most traditional surface electromyographic (sEMG) and semi-autonomous methods require users to generate myoelectric signals for each control, imposing physically and mentally taxing demands. This study aims to develop a fully autonomous control system that enables a prosthetic hand to automatically grasp and release objects of various shapes using only a camera attached to the wrist. By placing the ha…

A note on $\mathscr{B}$-free sets and the existence of natural density
Aurelia Dymek, Stanis{\l}aw Kasjan, Joanna Ku{\l}aga-Przymus
https://arxiv.org/abs/2506.10218

A note on $\mathscr{B}$-free sets and the existence of natural density
Given $\mathscr{B}\subseteq \mathbb{N}$, let $\mathcal{M}_\mathscr{B}=\bigcup_{b\in\mathscr{B}}b\mathbb{Z}$ be the correspoding set of multiples. We say that $\mathscr{B}$ is taut if the logarithmic density of $\mathcal{M}_\mathscr{B}$ decreases after removing any element from $\mathscr{B}$. We say that $\mathscr{B}$ is minimal if it is primitive (i.e.\ $b| b'$ for $b,b'\in\mathscr{B}$ implies $b=b'$) and the characteristic function $η$ of $\mathcal{M}_\mathscr{B}$ is a Toeplitz sequence …

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes
Thomas J. Ringstrom, Paul R. Schrater
https://arxiv.org/abs/2506.09499

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes
We introduce Option Kernel Bellman Equations (OKBEs) for a new reward-free Markov Decision Process. Rather than a value function, OKBEs directly construct and optimize a predictive map called a state-time option kernel (STOK) to maximize the probability of completing a goal while avoiding constraint violations. STOKs are compositional, modular, and interpretable initiation-to-termination transition kernels for policies in the Options Framework of Reinforcement Learning. This means: 1) STOKs can…

Oh god, the picture invokes some very mousetrap-adjacent vibes, in the @… sense of the word. https://mamot.fr/@pluralistic/114440131512138899

The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function
Songlin Han
https://arxiv.org/abs/2505.23795 https:…

The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function
We study the error bound for a smooth weighted prime number theorem, and its implication to the zero-free region for the Riemann zeta function using the method of Pintz. We also give an application to the average number of smooth weighted Goldbach representations and generalize the result to the case of smooth weighted average k-Goldbach representations.

Into the Unknown: From Structure to Disorder in Protein Function Prediction
{\DJ}esika Kolari\'c, Chi Fung Willis Chow, Rita Zi Zhu, Agnes Toth-Petroczy, T. Reid Alderson, Iva Priti\v{s}anac
https://arxiv.org/abs/2506.06004

Into the Unknown: From Structure to Disorder in Protein Function Prediction
Intrinsically disordered regions (IDRs) account for one-third of the human proteome and play essential biological roles. However, predicting the functions of IDRs remains a major challenge due to their lack of stable structures, rapid sequence evolution, and context-dependent behavior. Many predictors of protein function neglect or underperform on IDRs. Recent advances in computational biology and machine learning, including protein language models, alignment-free approaches, and IDR-specific m…

Happy #PrideMonth! 🏳️‍⚧️🏳️‍🌈
I’m just too fabulously queer and genderfluid to function like anyone expects. My identity is a whole spectrum, shifting and sparkling with every color and every gender. 🌈✨
Some days I’m femme, some days I’m masc, and some days I’m something totally unique and undefined. 💖💙🤍
My

Unveiling the role of vector potential in the Aharonov-Bohm effect
Masashi Wakamatsu
https://arxiv.org/abs/2506.07018 https://arxiv.o…

Unveiling the role of vector potential in the Aharonov-Bohm effect
The most popular interpretation of the Aharonov-Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle's wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, not a few researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-loc…

Spectrally accurate and efficient convolution with the 3D free-space Laplace Green's function via the super-potential
Lukas Exl, Sebastian Schaffer
https://arxiv.org/abs/2506.04489

Spectrally accurate and efficient convolution with the 3D free-space Laplace Green's function via the super-potential
We present a high-accuracy spectral method for solving the unbounded three-dimensional Poisson equation with smooth, compactly supported sources. The approach is based on a super-potential formulation, where the solution is obtained by applying the Laplacian to a convolution with the biharmonic Green's function. A separable Gaussian-sum (GS) approximation enables efficient FFT-based computation with quasi-linear complexity. Owing to the improved regularity of the biharmonic kernel, the GS cutof…

The asymptotic $\chi$-boundedness of hereditary families
Bruce Reed, Yelena Yuditsky
https://arxiv.org/abs/2506.01070 https://arxiv.o…

The asymptotic $χ$-boundedness of hereditary families
A family ${\cal F}$ of graphs is asymptotically $χ$-bounded with bounding function $f$ if almost every graph $G$ in the family satisfies $χ(G) \le f(ω(G))$. A graph is $H$-free if it does not contain $H$ as an induced subgraph. We ask which hereditary families are asymptotically $χ$-bounded, and discuss some related questions. We show that for every tree $T$, almost all $T$-free graphs $G$ satisfy $χ(G)=ω(G)$. We show that for every cycle $C_k$ except $C_6$, almost every $C_k$-free graph …

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Xia Liao, Xiping Zhang
https://arxiv.org/abs/2505.24236 https://

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(γ\cdot \ind_U)$ of the restriction of a constructible function $γ$ on $U$. We globalise Ginzburg's local sharp construction and introduce the log transversality condition, which is a new transversality condition about the relative position of $γ$ and $D$. We prove that the log transversality condition is satisfied if either $D$ is normal…

Free Askey--Wilson functionals and geometric last passage percolation on a strip
Wlodek Bryc, Kamil Szpojankowski, Jacek Wesolowski
https://arxiv.org/abs/2506.01879

Free Askey--Wilson functionals and geometric last passage percolation on a strip
Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of $\mathbb{Z}^2$ has a unique stationary measure. Building on this, Barraquand arXiv:2409.08927 derived explicit contour integral formulas for the model's multipoint probability generating function. In this paper, we introduce free Askey--Wilson functionals and use them to extend these generating function formulas. Our framework yields explicit expressions valid over a broader ran…

This https://arxiv.org/abs/2212.12237 has been replaced.
link: https://scholar.google.com/scholar?q=a

Electron-phonon interaction and phonons in 2d doped semiconductors
Electron-phonon interaction and phonon frequencies of doped polar semiconductors are sensitive to long-range Coulomb forces and can be strongly affected by screening effects of free carriers, the latter changing significantly when approaching the two-dimensional limit. We tackle this problem within a linear-response dielectric-matrix formalism, where screening effects can be properly taken into account by generalized effective charge functions and the inverse scalar dielectric function, allowin…

This https://arxiv.org/abs/2503.22733 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

RBFleX-NAS: Training-Free Neural Architecture Search Using Radial Basis Function Kernel and Hyperparameter Detection
Neural Architecture Search (NAS) is an automated technique to design optimal neural network architectures for a specific workload. Conventionally, evaluating candidate networks in NAS involves extensive training, which requires significant time and computational resources. To address this, training-free NAS has been proposed to expedite network evaluation with minimal search time. However, state-of-the-art training-free NAS algorithms struggle to precisely distinguish well-performing networks f…

Nonvanishing of $L$--functions associated to fixed order characters over function fields
Chantal David, Alexandra Florea, Matilde Lalin
https://arxiv.org/abs/2506.07815

Nonvanishing of $L$--functions associated to fixed order characters over function fields
We show that a positive proportion of the values $L(1/2,χ_c)$ are non-zero, where $χ_c$ is the $\ell^{\text{th}}$ residue symbol for $\ell \geq 3$ over $\mathbb{F}_q[t]$, when averaging over square-free polynomials $c$ in $\mathbb{F}_q[t]$, as $q \equiv 1(\textrm{mod}\,{2\ell})$ is fixed and the degree of $c$ goes to infinity. In the case of $\ell=3$, we show that at least $1/6$ of $L(1/2,χ_c)\neq 0$, while for $\ell>3$, the proportion depends on the order of the character. This improves a p…

A Real-time 3D Desktop Display
Livio Tenze, Enrique Canessa
https://arxiv.org/abs/2506.08064 https://arxiv.org/pdf/2506.08064

A Real-time 3D Desktop Display
A new extended version of the altiro3D C++ Library -- initially developed to get glass-free holographic displays starting from 2D images -- is here introduced aiming to deal with 3D video streams from either 2D webcam images or flat video files. These streams are processed in real-time to synthesize light-fields (in Native format) and feed realistic 3D experiences. The core function needed to recreate multiviews consists on the use of MiDaS Convolutional Neural Network (CNN), which allows to ex…

Symmetry breaking for local minimizers of a free discontinuity problem
Massimo Gobbino, Nicola Picenni
https://arxiv.org/abs/2506.05270 https://

Symmetry breaking for local minimizers of a free discontinuity problem
We study a functional defined on the class of piecewise constant functions, combining a jump penalization, which discourages discontinuities, with a fidelity term that penalizes deviations from a given linear function, called the forcing term. In one dimension, it is not difficult to see that local minimizers form staircases that approximate the forcing term. Here we show that in two dimensions symmetry breaking occurs, leading to the emergence of exotic minimizers whose level sets are not si…

This https://arxiv.org/abs/2403.06006 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Real-time observables in de Sitter thermodynamics
We study real-time finite-temperature correlators for free scalars of any mass in a $dS_{d+1}$ static patch in any dimension. We show that whenever the inverse temperature is a rational multiple of the inverse de Sitter temperature, certain Matsubara poles of the symmetric Wightman function disappear. At the de Sitter temperature, we explicitly show how the Lorentzian thermal correlators can all be obtained by analytic continuations from the round $S^{d+1}$. We establish the precise relation be…

Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process
Jason J. Lambe, Feng Chen, Tom Stindl, Tsz-Kit Jeffrey Kwan
https://arxiv.org/abs/2506.01258

Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based inference in this setting, we propose to use a likelihood-free approach to parameter estimation, where a fully connected neural network (NN) is trained using simulated data to estimate the parameters of the Hawkes process from a summary statistic of the count data. A…

This https://arxiv.org/abs/2505.22166 has been replaced.
initial toot: https://mastoxiv.page/@…

Critical and Nonpercolating Phases in Bond Percolation on the Song-Havlin-Makse Network
We investigate bond percolation on the Song-Havlin-Makse (SHM) network, a scale-free tree with a tunable degree exponent and dimensionality. Using a generating function approach, we analytically derive the average size and the fractal exponent of the root cluster for deterministic cases. Our analysis reveals that bond percolation on the SHM network remains in a nonpercolating phase for all $p < 1$ when the network is fractal (i.e., finite-dimensional), whereas it exhibits a critical phase, wher…

Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law
Sampurna Karmakar, Amulya Ratnakar, Sourin Das
https://arxiv.org/abs/2506.01930

Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law
Quantum transport anomalies in systems obeying Haldane-Wu fractional exclusion statistics, characterized by the statistical interactions parameter $g$ are investigated. We identify particle-hole symmetry breaking of the Haldane-Wu distribution function via its deviations of the maximum entropy ($\mathcal{S}_{g}^{max}$), evaluated at the chemical potential, from the value ${k_B} \ln 2$ (a value that holds only at the free fermion limit, $g=1$). A duality relation, $g\,\mathcal{S}_{g}^{max}=\math…

On General Principal Symmetric Ideals
Noah Walker
https://arxiv.org/abs/2505.21802 https://arxiv.org/pdf/2505.21802

On General Principal Symmetric Ideals
In a recent paper by Harada, Seceleanu, and Şega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is sufficiently large. In this paper, we strengthen that result by giving a effective bound on the number of variables needed for their conclusion to hold. The bound is related to a well-known integer sequence involving partition numbers (OEIS A000070). Along the way, we …

This https://arxiv.org/abs/2403.05322 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms
Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct-search methods, is particularly popular thanks to its simplicity of im…

On General Principal Symmetric Ideals
Noah Walker
https://arxiv.org/abs/2505.21802 https://arxiv.org/pdf/2505.21802

On General Principal Symmetric Ideals
In a recent paper by Harada, Seceleanu, and Şega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is sufficiently large. In this paper, we strengthen that result by giving a effective bound on the number of variables needed for their conclusion to hold. The bound is related to a well-known integer sequence involving partition numbers (OEIS A000070). Along the way, we …