Tootfinder

So I'm working on building a device that will trigger something with each revolution of a wheel. Originally I was thinking each rotation would cause the trigger, but now I am wondering if I should calculate the RPM and average it.
I'm not great at math, so you know, it'll take more work, but it should be doable.
I guess I would use one function to determine how frequently a spot on the wheel passes a certain point, then use the result as one input to trigger the ou…

Quantum optical shallow networks
Simone Roncallo, Angela Rosy Morgillo, Seth Lloyd, Chiara Macchiavello, Lorenzo Maccone
https://arxiv.org/abs/2507.21036 https://

Quantum optical shallow networks
Classical shallow networks are universal approximators. Given a sufficient number of neurons, they can reproduce any continuous function to arbitrary precision, with a resource cost that scales linearly in both the input size and the number of trainable parameters. In this work, we present a quantum optical protocol that implements a shallow network with an arbitrary number of neurons. Both the input data and the parameters are encoded into single-photon states. Leveraging the Hong-Ou-Mandel ef…

Parallel Hierarchical Agglomerative Clustering in Low Dimensions
MohammadHossein Bateni, Laxman Dhulipala, Willem Fletcher, Kishen N Gowda, D Ellis Hershkowitz, Rajesh Jayaram, Jakub {\L}\k{a}cki
https://arxiv.org/abs/2507.20047

Parallel Hierarchical Agglomerative Clustering in Low Dimensions
Hierarchical Agglomerative Clustering (HAC) is an extensively studied and widely used method for hierarchical clustering in $\mathbb{R}^k$ based on repeatedly merging the closest pair of clusters according to an input linkage function $d$. Highly parallel (i.e., NC) algorithms are known for $(1+ε)$-approximate HAC (where near-minimum rather than minimum pairs are merged) for certain linkage functions that monotonically increase as merges are performed. However, no such algorithms are known for…

TextOnly: A Unified Function Portal for Text-Related Functions on Smartphones
Minghao Tu, Chun Yu, Xiyuan Shen, Zhi Zheng, Li Chen, Yuanchun Shi
https://arxiv.org/abs/2508.16926

TextOnly: A Unified Function Portal for Text-Related Functions on Smartphones
Text boxes serve as portals to diverse functionalities in today's smartphone applications. However, when it comes to specific functionalities, users always need to navigate through multiple steps to access particular text boxes for input. We propose TextOnly, a unified function portal that enables users to access text-related functions from various applications by simply inputting text into a sole text box. For instance, entering a restaurant name could trigger a Google Maps search, while a gre…

Modeling the Path of Structural Strategic Deterrence: A Sand Table Simulation and Research Report on China's Military-Industrial Capability System against the United States Based on Rare Earth Supply Disconnection
Wei Meng
https://arxiv.org/abs/2505.21579

Modeling the Path of Structural Strategic Deterrence: A Sand Table Simulation and Research Report on China's Military-Industrial Capability System against the United States Based on Rare Earth Supply Disconnection
This study proposes a systematic non-kinetic deterrence path modeling framework based on strategic rare earth supply cut-off, aiming to assess the strategic effects of China's export control policy against the United States at the military system level. The model adopts a four-layer structure of "policy input -- resource node -- equipment system -- capability output" and integrates path dependency modeling, degradation function design, and capability lag prediction mechanisms to form a strategi…

Blocklisted Oblivious Pseudorandom Functions
Xinyuan Zhang, Anrin Chakraborti, Michael Reiter
https://arxiv.org/abs/2507.16040 https://

Blocklisted Oblivious Pseudorandom Functions
An oblivious pseudorandom function (OPRF) is a protocol by which a client and server interact to evaluate a pseudorandom function on a key provided by the server and an input provided by the client, without divulging the key or input to the other party. We extend this notion by enabling the server to specify a blocklist, such that OPRF evaluation succeeds only if the client's input is not on the blocklist. More specifically, our design gains performance by embedding the client input into a metr…

🔧 Strict-Mode Function Calling
Beta API now supports strict-mode for function calling, ensuring the output always complies with the defined JSON schema.
🔗 Anthropic API Compatibility
The API is now compatible with Anthropic API, allowing seamless integration with Claude Code.
💰 Pricing Adjustment (Effective Sept. 5, 2025, 16:00 UTC)
Input tokens: $ 0.07/million (cache hit) / $ 0.56/million (cache miss)
Output tokens: $ 1.68/million
The off-peak discount e…

Safe Navigation under State Uncertainty: Online Adaptation for Robust Control Barrier Functions
Ersin Das, Rahal Nanayakkara, Xiao Tan, Ryan M. Bena, Joel W. Burdick, Paulo Tabuada, Aaron D. Ames
https://arxiv.org/abs/2508.19159

Safe Navigation under State Uncertainty: Online Adaptation for Robust Control Barrier Functions
Measurements and state estimates are often imperfect in control practice, posing challenges for safety-critical applications, where safety guarantees rely on accurate state information. In the presence of estimation errors, several prior robust control barrier function (R-CBF) formulations have imposed strict conditions on the input. These methods can be overly conservative and can introduce issues such as infeasibility, high control effort, etc. This work proposes a systematic method to improv…

Attention Mechanism in Randomized Time Warping
Yutaro Hiraoka, Kazuya Okamura, Kota Suto, Kazuhiro Fukui
https://arxiv.org/abs/2508.16366 https://arxiv.org…

Attention Mechanism in Randomized Time Warping
This paper reveals that we can interpret the fundamental function of Randomized Time Warping (RTW) as a type of self-attention mechanism, a core technology of Transformers in motion recognition. The self-attention is a mechanism that enables models to identify and weigh the importance of different parts of an input sequential pattern. On the other hand, RTW is a general extension of Dynamic Time Warping (DTW), a technique commonly used for matching and comparing sequential patterns. In essence,…

Why Compressed Metal Hydrides are Near-room-temperature Superconductors
Warren E. Pickett
https://arxiv.org/abs/2508.18429 https://arxiv.org/pdf/2508.18429…

Why Compressed Metal Hydrides are Near-room-temperature Superconductors
This contribution provides a partial response to the titular statement since, it will be claimed,the ``why'' is not yet understood, but there is a pathway for achieving a more complete understanding. The sense of the community has been that, given a prospective metal hydride and pressure, the energy landscape can be surveyed computationally for thermodynamic and dynamic stability, the Eliashberg spectral function with its required input (energy bands, phonon modes, coupling matrix elements) can…

Optimal Convergence Rates of Deep Neural Network Classifiers
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
https://arxiv.org/abs/2506.14899 https://

Optimal Convergence Rates of Deep Neural Network Classifiers
In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s \in [0,\infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of $q+1$ vector-valued multivariate functions, where each component function is either a maximum value function or a Hölder-$β$ smooth function that depends only on $d_*$ of its input variables. Notably, $d_…

Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Tewodros Amdeberhan, Leonid G. Fel, Ken Ono
https://arxiv.org/abs/2507.12352

Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Ramanujan derived a sequence of even weight $2n$ quasimodular forms $U_{2n}(q)$ from derivatives of Jacobi's weight $3/2$ theta function. Using the generating function for this sequence, one can construct sequences of quasimodular forms of all nonnegative integer weights with minimal input: a weight 1 modular form and a power series $F(X)$. Using the weight 1 form $θ(q)^2$ and $F(X)=e^{X/2}$, we obtain a sequence $\{Y_n(q)\}$ of weight $n$ quasimodular forms on $Γ_0(4)$ whose symmetric functi…

Polynomial Property Testing
Lior Gishboliner, Asaf Shapira
https://arxiv.org/abs/2508.16878 https://arxiv.org/pdf/2508.16878…

Polynomial Property Testing
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing, it is known that many properties can be tested with query complexity that depends only on the error parameter $\varepsilon$ (and not on the size of the input), but the current bounds on the query complexity grow extremely quickly as a function of $1/\varepsil…

Stabilizing simulation-based cosmological Fisher forecasts: a case study using the Voronoi volume function
Saee Dhawalikar (IUCAA), Aseem Paranjape (IUCAA), Shadab Alam (TIFR)
https://arxiv.org/abs/2506.16408

Stabilizing simulation-based cosmological Fisher forecasts: a case study using the Voronoi volume function
Forecasting cosmological constraints from halo-based statistics often suffers from instability in derivative estimates, especially when the number of simulations is limited. This instability reduces the reliability of Fisher forecasts and machine learning based approaches that use derivatives. We introduce a general framework that addresses this challenge by stabilizing the input statistic and then systematically identifying the optimal subset of summary statistics that maximizes cosmological i…

Jump Complexity of Deterministic Finite Automata with Translucent Letters
Szil\'ard Zsolt Fazekas, Victor Mitrana, Andrei P\u{a}un, Mihaela P\u{a}un
https://arxiv.org/abs/2506.18393

Jump Complexity of Deterministic Finite Automata with Translucent Letters
We investigate a dynamical complexity measure defined for finite automata with translucent letters (FAwtl). Roughly, this measure counts the minimal number of necessary jumps for such an automaton in order to accept an input. The model considered here is the deterministic finite automaton with translucent letters (DFAwtl). Unlike in the case of the nondeterministic variant, the function describing the jump complexity of any DFAwtl is either bounded by a constant or it is linear. We give a polyn…

Filter Equivariant Functions: A symmetric account of length-general extrapolation on lists
Owen Lewis, Neil Ghani, Andrew Dudzik, Christos Perivolaropoulos, Razvan Pascanu, Petar Veli\v{c}kovi\'c
https://arxiv.org/abs/2507.08796

Filter Equivariant Functions: A symmetric account of length-general extrapolation on lists
What should a function that extrapolates beyond known input/output examples look like? This is a tricky question to answer in general, as any function matching the outputs on those examples can in principle be a correct extrapolant. We argue that a "good" extrapolant should follow certain kinds of rules, and here we study a particularly appealing criterion for rule-following in list functions: that the function should behave predictably even when certain elements are removed. In functional prog…

The receptron is a nonlinear threshold logic gate with intrinsic multi-dimensional selective capabilities for analog inputs
B. Paroli, F. Borghi, M. A. C. Potenza, P. Milani
https://arxiv.org/abs/2506.19642

The receptron is a nonlinear threshold logic gate with intrinsic multi-dimensional selective capabilities for analog inputs
Threshold logic gates (TLGs) have been proposed as artificial counterparts of biological neurons with classification capabilities based on a linear predictor function combining a set of weights with the feature vector. The linearity of TLGs limits their classification capabilities requiring the use of networks for the accomplishment of complex tasks. A generalization of the TLG model called receptron, characterized by input-dependent weight functions allows for a significant enhancement of clas…

Conservative quantum offline model-based optimization
Kristian Sotirov, Annie E. Paine, Savvas Varsamopoulos, Antonio A. Gentile, Osvaldo Simeone
https://arxiv.org/abs/2506.19714 …

Conservative quantum offline model-based optimization
Offline model-based optimization (MBO) refers to the task of optimizing a black-box objective function using only a fixed set of prior input-output data, without any active experimentation. Recent work has introduced quantum extremal learning (QEL), which leverages the expressive power of variational quantum circuits to learn accurate surrogate functions by training on a few data points. However, as widely studied in the classical machine learning literature, predictive models may incorrectly e…

from my link log —
Dynamic witnesses for static type errors in OCaml, or, ill-typed programs usually go wrong.
https://arxiv.org/abs/1606.07557
saved 2025-05-31

Dynamic Witnesses for Static Type Errors (or, Ill-Typed Programs Usually Go Wrong)
Static type errors are a common stumbling block for newcomers to typed functional languages. We present a dynamic approach to explaining type errors by generating counterexample witness inputs that illustrate how an ill-typed program goes wrong. First, given an ill-typed function, we symbolically execute the body to synthesize witness values that make the program go wrong. We prove that our procedure synthesizes general witnesses in that if a witness is found, then for all inhabited input types…

Source Wavefront Generation for a Non-Interferometric Reconfigurable Null Test using a Photonic Lantern
Nikolas Romer, Jannick P. Rolland
https://arxiv.org/abs/2507.15171

Source Wavefront Generation for a Non-Interferometric Reconfigurable Null Test using a Photonic Lantern
A method is presented to use a fiber-optic device known as a photonic lantern to generate a reconfigurable custom wavefront for a null test of spherical, aspheric, and freeform optical surfaces. By modulating input intensity and phases at single mode fiber input ports, the wavefront of the output light field from the multimode end can be controlled to generate a custom nulling phase function. Generation of a desired wavefront is demonstrated by simulating a nineteen-port non-mode-selective phot…

Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder
Shoichi Koyama, Kenji Ishizuka
https://arxiv.org/abs/2506.16729 https://…

Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder
A learning-based method for estimating the magnitude distribution of sound fields from spatially sparse measurements is proposed. Estimating the magnitude distribution of acoustic transfer function (ATF) is useful when phase measurements are unreliable or inaccessible and has a wide range of applications related to spatial audio. We propose a neural-network-based method for the ATF magnitude estimation. The key feature of our network architecture is the input and output layers conditioned on so…

Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain
Mohab Safey El Din (PolSys), Georgy Scholten (LJLL), Emmanuel Tr\'elat (LJLL)
https://arxiv.org/abs/2507.13071

Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain
Let K be the unit-cube in Rn and f\,: K $\rightarrow$ R^n be a Morse function. We assume that the function f is given by an evaluation program $Γ$ in the noisy model, i.e., the evaluation program $Γ$ takes an extra parameter $η$ as input and returns an approximation that is $η$-close to the true value of f . In this article, we design an algorithm able to compute all local minimizers of f on K . Our algorithm takes as input $Γ$, $η$, a numerical accuracy parameter $ε$ as well as some ext…

A robust and versatile deep learning model for prediction of the arterial input function in dynamic small animal $\left[^{18}\text{F}\right]$FDG PET imaging
Christian Salomonsen, Luigi Tommaso Luppino, Fredrik Aspheim, Kristoffer Wickstr{\o}m, Elisabeth Wetzer, Michael Kampffmeyer, Rodrigo Berzaghi, Rune Sundset, Robert Jenssen, Samuel Kuttner
https:…

A robust and versatile deep learning model for prediction of the arterial input function in dynamic small animal $\left[^{18}\text{F}\right]$FDG PET imaging
Dynamic positron emission tomography (PET) and kinetic modeling are pivotal in advancing tracer development research in small animal studies. Accurate kinetic modeling requires precise input function estimation, traditionally achieved via arterial blood sampling. However, arterial cannulation in small animals like mice, involves intricate, time-consuming, and terminal procedures, precluding longitudinal studies. This work proposes a non-invasive, fully convolutional deep learning-based approach…

An effective physics-informed neural operator framework for predicting wavefields
Xiao Ma, Tariq Alkhalifah
https://arxiv.org/abs/2507.16431 https://

An effective physics-informed neural operator framework for predicting wavefields
Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional neural operator (PICNO) to solve the Helmholtz equation efficiently. The PICNO takes both the background wavefield corresponding to a homogeneous medium and the velocity model as input function space, generating the scattered wavefield as the output function spa…

Robust output stability and input-to-output stability based on output dissipation
Antoine Chaillet (IUF, L2S), Iasson Karafyllis (NTUA), Yuan Wang
https://arxiv.org/abs/2506.10479

Robust output stability and input-to-output stability based on output dissipation
LaSalle techniques to ensure the convergence of a given output usually fail at guaranteeing uniform convergence time, which induces robustness issues. Recent works have provided extra conditions under which a Lyapunov function that dissipates in terms of only the output guarantees this uniformity. In this paper, we extend these results to systems with inputs in order to establish either robust stability or input-to-output stability. In addition, we show that a recent relaxation of Barb__lat's l…

Quality control in sublinear time: a case study via random graphs
Cassandra Marcussen, Ronitt Rubinfeld, Madhu Sudan
https://arxiv.org/abs/2508.16531 https://

Quality control in sublinear time: a case study via random graphs
Many algorithms are designed to work well on average over inputs. When running such an algorithm on an arbitrary input, we must ask: Can we trust the algorithm on this input? We identify a new class of algorithmic problems addressing this, which we call "Quality Control Problems." These problems are specified by a (positive, real-valued) "quality function" $ρ$ and a distribution $D$ such that, with high probability, a sample drawn from $D$ is "high quality," meaning its $ρ$-value is near $1$.…

Automating MD simulations for Proteins using Large language Models: NAMD-Agent
Achuth Chandrasekhar, Amir Barati Farimani
https://arxiv.org/abs/2507.07887 …

Automating MD simulations for Proteins using Large language Models: NAMD-Agent
Molecular dynamics simulations are an essential tool in understanding protein structure, dynamics, and function at the atomic level. However, preparing high quality input files for MD simulations can be a time consuming and error prone process. In this work, we introduce an automated pipeline that leverages Large Language Models (LLMs), specifically Gemini 2.0 Flash, in conjunction with python scripting and Selenium based web automation to streamline the generation of MD input files. The pipeli…

Design of OTFS Signals with Pulse Shaping and Window Function for OTFS-Based Radar
Liangchen Sun, Yutaka Jitsumatsu
https://arxiv.org/abs/2506.04861 https:…

Design of OTFS Signals with Pulse Shaping and Window Function for OTFS-Based Radar
We propose a pulse radar system that employs a generalized window function derived from the root raised cosine (RRC), which relaxes the conventional constraint that the window values are within the range [0, 1]. The proposed window allows both negative values and values exceeding 1, enabling greater flexibility in signal design. The system transmits orthogonal time frequency space (OTFS) signals intermittently, establishing a flexible input-output relationship that captures both fractional dela…

Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network
Shin-ichi Ito
https://arxiv.org/abs/2507.11799 ht…

Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network
This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation. The proposed method directly maps input parameters to the corresponding probability density function without numerically solving the governing equation, thereby significantly reducing computational costs. Specifically, it enables efficient evaluation of the density function in Monte Carlo simulations while maintaining accuracy comparable to or even exceeding t…

On the Gaussian Limit of the Output of IIR Filters
Yashaswini Murthy, Bassam Bamieh, R. Srikant
https://arxiv.org/abs/2508.12705 https://arxiv.org/pdf/2508…

On the Gaussian Limit of the Output of IIR Filters
We study the asymptotic distribution of the output of a stable Linear Time-Invariant (LTI) system driven by a non-Gaussian stochastic input. Motivated by longstanding heuristics in the stochastic describing function method, we rigorously characterize when the output process becomes approximately Gaussian, even when the input is not. Using the Wasserstein-1 distance as a quantitative measure of non-Gaussianity, we derive upper bounds on the distance between the appropriately scaled output and a …

Deep learning-derived arterial input function
Junyu Chen, Zirui Jiang, Jennifer M. Coughlin, Martin G. Pomper, Yong Du
https://arxiv.org/abs/2505.24166 htt…

Deep learning-derived arterial input function
Dynamic positron emission tomography (PET) imaging combined with radiotracer kinetic modeling is a powerful technique for visualizing biological processes in the brain, offering valuable insights into brain functions and neurological disorders such as Alzheimer's and Parkinson's diseases. Accurate kinetic modeling relies heavily on the use of a metabolite-corrected arterial input function (AIF), which typically requires invasive and labor-intensive arterial blood sampling. While alternative non…

NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling
Pengfei Wang, Qiujie Dong, Fangtian Liang, Hao Pan, Lei Yang, Congyi Zhang, Guying Lin, Caiming Zhang, Yuanfeng Zhou, Changhe Tu, Shiqing Xin, Alla Sheffer, Xin Li, Wenping Wang
https://arxiv.org/abs/2506.13050

NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling
Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the zero-level set of a neural signed distance function (SDF), with sparse geometric control is still a challenging task. Sparse input shape control typically includes 3D curve networks or, more generally, 3D curve sketches, which are unstructured and cannot be …

p-adic congruences in iterated derivatives of the Weierstrass elliptic function
Kiran Luecke, Eric Peterson
https://arxiv.org/abs/2506.07420 https://

p-adic congruences in iterated derivatives of the Weierstrass elliptic function
We use homotopy theoretic methods to prove congruence relations of number theoretic interest. Specifically, we use the theory of $\mathbb E_\infty$ complex orientations to establish $p$-adic Kümmer congruences among iterated derivatives of the Weierstrass elliptic function. The machinery of Ando, Hopkins, and Rezk was developed with the intended application of taking congruence relations as input and producing $\mathbb E_\infty$-orientations as output. We run their machine in reverse, using …

Rethinking Growth: An Extension of the Solow-Swan Model
Timothy F. Power, Roman G. Smirnov
https://arxiv.org/abs/2506.10864 https://a…

Rethinking Growth: An Extension of the Solow-Swan Model
The aggregate Cobb-Douglas production function stands as a central element in the renowned Solow-Swan model in economics, providing a crucial theoretical framework for comprehending the determinants of economic growth. This model not only guides policymakers and economists but also influences their decisions, fostering sustainable and inclusive development. In this study, we utilize a one-input version of a new generalization of the Cobb-Douglas production function proposed recently, thereby ex…

Learning to cluster neuronal function
Nina S. Nellen, Polina Turishcheva, Michaela Vystr\v{c}ilov\'a, Shashwat Sridhar, Tim Gollisch, Andreas S. Tolias, Alexander S. Ecker
https://arxiv.org/abs/2506.03293

Learning to cluster neuronal function
Deep neural networks trained to predict neural activity from visual input and behaviour have shown great potential to serve as digital twins of the visual cortex. Per-neuron embeddings derived from these models could potentially be used to map the functional landscape or identify cell types. However, state-of-the-art predictive models of mouse V1 do not generate functional embeddings that exhibit clear clustering patterns which would correspond to cell types. This raises the question whether th…

Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence
Jes\'us Due\~nas, Carmen N\'u\~nez, Rafael Obaya
https://arxiv.org/abs/2507.00545

Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence
The long-term dynamics of a Bonifacio-Lugiato model of optical superfluorescence is investigated. The scalar ordinary differential equation modelling the phenomenon is given by a concave-convex autonomous function of the state variable that is excited by a time-dependent input, $I(t)$. The system's response is described in terms of the dynamical characteristics of the input function, with particular focus on uniform stability or bistability cases. Building on previous published results, the ope…

This https://arxiv.org/abs/2402.07660 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Rényi Resolvability, Noise Stability, and Anti-contractivity
This paper investigates three closely related topics -- Rényi resolvability, noise stability, and anti-contractivity. The Rényi resolvability problem refers to approximating a target output distribution of a given channel in the Rényi divergence when the input is set to a function of a given uniform random variable. This problem for the Rényi parameter in $(0,2]\cup\{\infty\}$ was first studied by the present author and Tan in 2019. In the present paper, we provide a complete solution to th…

On Random Fields Associated with Analytic Wavelet Transform
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
https://arxiv.org/abs/2508.10495 https://arxiv.org/pd…

On Random Fields Associated with Analytic Wavelet Transform
Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process remains underexplored. In this work, we study the magnitude and phase of the AWT as random fields on the time-frequency domain when the observed signal is a deterministic function plus additive stationary Gaussian noise. We derive their marginal and joint distribu…

Computability of a Whitney Extension
Andrea Brun, Guido Gherardi, Alberto Marcone
https://arxiv.org/abs/2507.02113 https://arxiv.org/…

Computability of a Whitney Extension
We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if $F \subseteq \mathbb{R}^n$ is a closed set represented so that the distance function $x \mapsto d(x,F)$ can be computed, and $(f^{(\bar{k})})_{|\bar{k}| \le m}$ is a Whitney jet of order $m$ on $F$, then we can compute $g \in C^{m}(\mathbb{R}^n)$ such that $g$ and its partial derivatives coincide on $F$ with the corresponding functions of $(f^{(\bar{k})})_{|…

PBE Meets LLM: When Few Examples Aren't Few-Shot Enough
Shuning Zhang, Yongjoo Park
https://arxiv.org/abs/2507.05403 https://arxi…

PBE Meets LLM: When Few Examples Aren't Few-Shot Enough
Large language models (LLMs) can generate code from natural language descriptions. Their performance is typically evaluated using programming benchmarks that simulate real-world tasks. These benchmarks provide specifications in the form of docstrings, function signatures, or bug reports. The model then generates a program, which is tested against predefined test cases. In contrast, Programming by Example (PBE) uses input-output examples as the specification. Traditional PBE systems rely on sear…

A Hybrid Multi-Well Hopfield-CNN with Feature Extraction and K-Means for MNIST Classification
Ahmed Farooq
https://arxiv.org/abs/2507.08766 https://…

A Hybrid Multi-Well Hopfield-CNN with Feature Extraction and K-Means for MNIST Classification
This study presents a hybrid model for classifying handwritten digits in the MNIST dataset, combining convolutional neural networks (CNNs) with a multi-well Hopfield network. The approach employs a CNN to extract high-dimensional features from input images, which are then clustered into class-specific prototypes using k-means clustering. These prototypes serve as attractors in a multi-well energy landscape, where a Hopfield network performs classification by minimizing an energy function that b…

Tropical solution of discrete best approximation problems
Nikolai Krivulin
https://arxiv.org/abs/2507.22634 https://arxiv.org/pdf/2507.22634

Tropical solution of discrete best approximation problems
We consider discrete best approximation problems in the setting of tropical algebra that is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input-output pairs of an unknown function defined on a tropical semifield, the problem is to determine an approximating rational function formed by two Puiseux polynomials as numerator and denominator. With specified numbers of monomials in both polynomials, the approximation aims at evaluating the e…

Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag, Richard D. Braatz
https://arxiv.org/abs/2507.02131

Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
This article investigates the robustness of gradient descent algorithms under perturbations. The concept of small-disturbance input-to-state stability (ISS) for discrete-time nonlinear dynamical systems is introduced, along with its Lyapunov characterization. The conventional linear Polyak-Lojasiewicz (PL) condition is then extended to a nonlinear version, and it is shown that the gradient descent algorithm is small-disturbance ISS provided the objective function satisfies the generalized nonli…

A generalization of Deterministic Finite Automata related to discharging
John M. Campbell
https://arxiv.org/abs/2506.14072 https://ar…

A generalization of Deterministic Finite Automata related to discharging
Deterministic Finite Automata (DFAs) are of central importance in automata theory. In view of how state diagrams for DFAs are defined using directed graphs, this leads us to introduce a generalization of DFAs related to a method widely used in graph theory referred to as the discharging method. Given a DFA $(Q, Σ, δ, q_{0}, F)$, the transition function $δ\colon Q \times Σ\to Q$ determines a directed path in the corresponding state diagram based on an input string $a_{1} a_{2} \cdots a_{n}$ …

A Note on Single-Cut Full-Open Protocols
Kazumasa Shinagawa, Koji Nuida
https://arxiv.org/abs/2507.03323 https://arxiv.org/pdf/2507.0…

A Note on Single-Cut Full-Open Protocols
Card-based cryptography is a research area that realizes cryptographic protocols such as secure computation by applying shuffles to sequences of cards that encode input values. A single-cut full-open protocol is one that obtains an output value by applying a random cut to an input sequence of cards, after which all cards are opened. In this paper, we propose three single-cut full-open protocols: two protocols for three-variable functions and one protocol for a four-variable function.

Asymptotic convexity of wide and shallow neural networks
Vivek Borkar, Parthe Pandit
https://arxiv.org/abs/2507.01044 https://arxiv.o…

Asymptotic convexity of wide and shallow neural networks
For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible explanation of their observed good performance.

Binaural Sound Event Localization and Detection Neural Network based on HRTF Localization Cues for Humanoid Robots
Gyeong-Tae Lee
https://arxiv.org/abs/2508.04333 https://

Binaural Sound Event Localization and Detection Neural Network based on HRTF Localization Cues for Humanoid Robots
Humanoid robots require simultaneous sound event type and direction estimation for situational awareness, but conventional two-channel input struggles with elevation estimation and front-back confusion. This paper proposes a binaural sound event localization and detection (BiSELD) neural network to address these challenges. BiSELDnet learns time-frequency patterns and head-related transfer function (HRTF) localization cues from binaural input features. A novel eight-channel binaural time-freque…

Sensitivity and Query Complexity under Uncertainty
Deepu Benson, Balagopal Komarath, Nikhil Mande, Sai Soumya Nalli, Jayalal Sarma, Karteek Sreenivasaiah
https://arxiv.org/abs/2507.00148

Sensitivity and Query Complexity under Uncertainty
In this paper, we study the query complexity of Boolean functions in the presence of uncertainty, motivated by parallel computation with an unlimited number of processors where inputs are allowed to be unknown. We allow each query to produce three results: zero, one, or unknown. The output could also be: zero, one, or unknown, with the constraint that we should output ''unknown'' only when we cannot determine the answer from the revealed input bits. Such an extension of a Boolean function is ca…

Physics-inspired neural networks as quasi inverse of quantum channels
Sameen Aziz, Muhammad Faryad
https://arxiv.org/abs/2506.11716 https://

Physics-inspired neural networks as quasi inverse of quantum channels
Quantum channels are not invertible in general. A quasi-inverse allows for a partial recovery of the input state, but its analytical results are found only in a restricted space of its parameters. This work explores the potential of neural networks to find the quasi-inverse of qubit channels for any values of the channel parameters while keeping the quasi-inverse as a physically realizable quantum operation. We introduce a physics-inspired loss function based on the mean of the square of the mo…

Multi-Symbol Digital AirComp via Modulation Design and Power Adaptation
Xiaojing Yan, Saeed Razavikia, Carlo Fischione
https://arxiv.org/abs/2507.08670 htt…

Multi-Symbol Digital AirComp via Modulation Design and Power Adaptation
In this paper, we consider digital over-the-air computation (AirComp) and introduce a new multi-symbol modulation framework called sequential modulation for AirComp (SeMAC). Building upon ChannelComp, a general framework for designing modulation schemes to support arbitrary function computation over a multiple access channel (MAC), SeMAC maps each input value to a sequence of modulated symbols using distinct constellation diagrams across multiple time slots. This extension generalizes ChannelCo…

Improved girth approximation in weighted undirected graphs
Avi Kadria, Liam Roditty, Aaron Sidford, Virginia Vassilevska Williams, Uri Zwick
https://arxiv.org/abs/2507.13869

Improved girth approximation in weighted undirected graphs
Let $G = (V,E,\ell)$ be a $n$-node $m$-edge weighted undirected graph, where $\ell: E \rightarrow (0,\infty)$ is a real \emph{length} function defined on its edges, and let $g$ denote the girth of $G$, i.e., the length of its shortest cycle. We present an algorithm that, for any input, integer $k \geq 1$, in $O(kn^{1+1/k}\log{n} + m(k+\log{n}))$ expected time finds a cycle of length at most $\frac{4k}{3}g$. This algorithm nearly matches a $O(n^{1+1/k}\log{n})$-time algorithm of \cite{KadriaRSWZ…

Nonlinear Oscillatory Response of Automated Vehicle Car-following: Theoretical Analysis with Traffic State and Control Input Limits
Sixu Li, Yang Zhou
https://arxiv.org/abs/2505.24029

Nonlinear Oscillatory Response of Automated Vehicle Car-following: Theoretical Analysis with Traffic State and Control Input Limits
This paper presents a framework grounded in the theory of describing function (DF) and incremental-input DF to theoretically analyze the nonlinear oscillatory response of automated vehicles (AVs) car-following (CF) amidst traffic oscillations, considering the limits of traffic state and control input. While prevailing approaches largely ignore these limits (i.e., saturation of acceleration/deceleration and speed) and focus on linear string stability analysis, this framework establishes a basis …

Fast Forward and Inverse Thermal Modeling for Parameter Estimation of Multi-Layer Composites -- Part II: Inverse Modeling and Applications
Gan Fu, Mitrofan Curti, Calina Ciuhu, Elena A. Lomonova
https://arxiv.org/abs/2507.06746

Fast Forward and Inverse Thermal Modeling for Parameter Estimation of Multi-Layer Composites -- Part II: Inverse Modeling and Applications
A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I. Transient temperature at a single point is used as input, with the objective function minimized through an interior-point optimization algorithm. The IHCM accurately estimates thermal properties such as thermal conductivity, specific heat capacity, density, and h…

Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators
Alexander Yeung, Peter DelMastro, Arjun Karuvally, Hava Siegelmann, Edward Rietman, Hananel Hazan
https://arxiv.org/abs/2507.21377

Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators
Reservoir Computing is a machine learning approach that uses the rich repertoire of complex system dynamics for function approximation. Current approaches to reservoir computing use a network of coupled integrating neurons that require a steady current to maintain activity. Here, we introduce a small world graph of differentiating neurons that are active only when there are changes in input as an alternative to integrating neurons as a reservoir computing substrate. We find the coupling strengt…

This https://arxiv.org/abs/2504.17108 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Computational Physics in the Advanced Lab: Experiment and Simulation of Thermal Diffusion in Metal Rods
We present a simple experiment on thermal diffusion in metal rods that can be used to integrate computation into the advanced lab. An analytical solution exists for the transient heat conduction in an infinite rod with a delta function heat input, but no analytical solution exists for short rods or for long duration heat inputs. Our apparatus is a copper rod with a heater and thermometers attached to the rod. The temperature of the metal rod due to transient heat conduction can be modeled using…

Circular Holographic MIMO Beamforming for Integrated Data and Energy Multicast Systems
Qingxiao Huang, Yizhe Zhao, Jie Hu, Kun Yang, Yuguang Fang
https://arxiv.org/abs/2507.05057 …

Circular Holographic MIMO Beamforming for Integrated Data and Energy Multicast Systems
Thanks to the application of metamaterials, holographic multiple-input multiple-output (H-MIMO) is expected to achieve a higher spatial diversity gain with lower hardware complexity. With the aid of a circular antenna arrangement of H-MIMO, integrated data and energy multicast (IDEM) can fully exploit the near-field channel to realize wider range of energy focusing and higher achievable rate. In this paper, we derive the closed-form near-field resolution function in 3D space and show the asympt…

Replacement dynamics of binary quadratic forms
Raghav Bhutani, Frederick Saia
https://arxiv.org/abs/2508.05816 https://arxiv.org/pdf/2508.05816

Replacement dynamics of binary quadratic forms
For an $S$-valued function $f$ of $m \geq 1$ variables we define a dynamical process in which the output $f(\overline{v})$ replaces exactly one entry of the input $\overline{v} \in S^m$ at each step in the iterative process. Our study focuses on periodic vectors with respect to this process. We define a stratification of periodic vectors according to their type, and characterize types for which the determination of periodic vectors comes down to dynamics of univariate polynomials. We then restr…

This https://arxiv.org/abs/2403.06708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tikhonov Regularization for Stochastic Non-Smooth Convex Optimization in Hilbert Spaces
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one being differentiable and the other potentially non-smooth. We then use stochastic differential inclusions where the drift term is minus the subgradient of the objective function, and the diffusion term is either bounded or square-integrable. In this context, un…

The Frequency Response of Networks as Open Systems
Amirhossein Nazerian, Malbor Asllani, Melvyn Tyloo, Wai Lim Ku, Francesco Sorrentino
https://arxiv.org/abs/2507.04180

The Frequency Response of Networks as Open Systems
Many biological, technological, and social systems are effectively networks of interacting individual systems. Typically, these networks are not isolated objects, but interact with their environment through both signals and information that is received by specific nodes with an input function or released to the environment by other nodes with an output function. An important question is whether the structure of different networks, together with the particular selection of input and output nodes…

Analysis of (p,$\gamma$) capture cross-sections relevant to p-process using TALYS for A=75-110
Satabdi Mondal, Enakshi Senapati, Deepak Pandit, Balaram Dey, Pampa Das, Alokkumar De, Srijit Bhattacharya
https://arxiv.org/abs/2508.05054

Analysis of (p,$γ$) capture cross-sections relevant to p-process using TALYS for A=75-110
The proton capture (p, $γ$) cross-sections for eight different atomic nuclei in the mass region A=75-110 were calculated within the nuclear reaction model code TALYS. For all the reactions, we tested different combinations of inputs for level density (l.d) parameter and gamma strength function ($γ_{sf}$). Finally, it was observed that application of hybrid input in TALYS (macroscopic l.d and microscopic or semi-microscopic $γ_{sf}$ or in abbreviation mac-mic) resulted successful agreement of…

A 1/2-Approximation for Budgeted $k$-Submodular Maximization
Chenhao Wang
https://arxiv.org/abs/2507.12875 https://arxiv.org/pdf/2507…

A 1/2-Approximation for Budgeted $k$-Submodular Maximization
A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution, $k$-submodular maximization adds the challenge of determining the subset to which each selected element belongs. Prior research has shown that the greedy algorithm is a 1/2-approximation for the monotone $k$-submodular maximization problem under cardinality or m…

Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation
Rei Sakuma, Kaito Wada, Shu Kanno, Kimberlee Keithley, Kenji Sugisaki, Takashi Abe, Hajime Nakamura, Naoki Yamamoto
https://arxiv.org/abs/2507.01361

Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation
Filtering is an important technique in quantum computing used for isolating or enhancing some specific states of quantum many-body systems. In this paper, we analyze the performance of filters based on the quantum phase estimation (QPE) algorithm, in which filtering removes states associated with bitstrings in the ancilla register above a given threshold. We show that when the conventional rectangular window function is used for the QPE input state, the resulting filter function exhibits an osc…

Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance
Eduardo Figueiredo, Steven Adams, Peyman Mohajerin Esfahani, Luca Laurenti
https://arxiv.org/abs/2506.08689

Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input set of distributions close in the Wasserstein distance, we compute a set of distributions centered at a discrete distribution that is guaranteed to contain the pushforward of any distribution in the input set. Our approach is based on approximating a nominal di…

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

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

A Novel Intensity-Based Criterion for Determining Exceptional Point in PT-Symmetry Coupled Array of Optical Waveguides
Mahla Bahar, Mojtaba Golshani, Mostafa Motamedifar
https://arxiv.org/abs/2507.01200

A Novel Intensity-Based Criterion for Determining Exceptional Point in PT-Symmetry Coupled Array of Optical Waveguides
In this study, we investigated the propagation pattern and the site-to-site correlation function in a PT-symmetric waveguide array with different input quantum states. Recognizing the stark difference in propagation pattern before and after the PT symmetry-breaking point, we have developed a novel, straightforward intensity-based criterion to determine the exceptional point (EP). This new criterion shows excellent agreement with those obtained by directly computing the Hamiltonian's eigenvalues…

Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem
Hao-Chung Cheng, Po-Chieh Liu
https://arxiv.org/abs/2507.06232 https://

Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem
In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998. By choosing the optimal input distribution, we recover the optimal error exponent (i.e., the reliability function) of classical-quantum channels for rates above the critical rate. Our result extends to various quantum packing-type problems, including classical communication over any fully quantum channel with or without entanglement-assistance, const…

This https://arxiv.org/abs/2407.04562 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An SDE Perspective on Stochastic Inertial Gradient Dynamics with Time-Dependent Viscosity and Geometric Damping
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the gradient of the objective function. This will provide a general mathematical framework for analyzing fast optimization algorithms with stochastic gradient input. Our study is a natural extension of our previous work devoted to the first-order in time stochas…

Inverse matroid optimization under subset constraints
Krist\'of \'iB\'erczi, Lydia Mirabel Mendoza-Cadena, Jos\'e Soto
https://arxiv.org/abs/2507.00930

Inverse matroid optimization under subset constraints
In the Inverse Matroid problem, we are given a matroid, a fixed basis $B$, and an initial weight function, and the goal is to minimally modify the weights -- measured by some function -- so that $B$ becomes a maximum-weight basis. The problem arises naturally in settings where one wishes to explain or enforce a given solution by minimally perturbing the input. We extend this classical problem by replacing the fixed basis with a subset $S_0$ of the ground set and imposing various structural co…

This https://arxiv.org/abs/2301.10637 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Complexity of Geometric programming in the Turing model and application to nonnegative tensors
We consider a version of geometric programming problem consisting in minimizing a function given by the maximum of finitely many log-Laplace transforms of discrete nonnegative measures on a Euclidean space. Under a coerciveness assumption, we show that an $\varepsilon$-minimizer can be computed in a time that is polynomial in the input size and in $|\log\varepsilon|$. This is obtained by establishing bit-size estimates on approximate minimizers and by applying the ellipsoid method. We…

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…

This https://arxiv.org/abs/2007.13121 has been replaced.
link: https://scholar.google.com/scholar?q=a

Efficient Approximation Schemes for Stochastic Probing and Selection-Stopping Problems
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $ε>0$, such algorithmic schemes attain a $(1-ε)$-approximation in $t(ε)\cdot poly(|{\cal I}|)$ time, where $t(\cdot)$ is a function that depends only on $ε$ and $|{\cal I}|$ denotes the input length. Technically speaking, our approach relies on presenting tailor-made redu…