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PRECISE: PRivacy-loss-Efficient and Consistent Inference based on poSterior quantilEs

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arXiv 2025年

作者： Zhou, Ruyu Liu, Fang Department of Applied and Computational Mathematics and Statistics University of Notre Dame IN46556 United States

Differential privacy (DP) is a mathematical framework for releasing information with formal privacy guarantees. Despite the existence of various DP procedures for performing a wide range of statistical analysis and machine learning tasks, methods of good utility are still lacking for obtaining valid statistical inference with DP guarantees. We address this gap by introducing the notion of valid Privacy-Preserving Interval Estimation (PPIE) and proposing PRivacy-loss-Efficient and Consistent Inference based on poSterior quantilEs (PRECISE). PRECISE is a general-purpose Bayesian approach for constructing privacy-preserving posterior intervals. We establish the Mean-Squared-Error (MSE) consistency for our proposed private posterior quantiles converging to the population posterior quantile as sample size or privacy loss increases. We conduct extensive experiments to compare the utilities of PRECISE with common existing privacy-preserving inferential approaches in various inferential tasks, data types and sizes, privacy loss levels. The results demonstrated a significant advantage of PRECISE with its nominal coverage and substantially narrower intervals than the existing methods, which are prone to either under-coverage or impractically wide intervals. © 2025, CC BY.

关键词： Differential privacy

Synergetic effects of multiple junction and surface hydroxyl in Cu/CuO/Cu2O/TiO2 heterostructures towards highly efficient photocatalysts for hydrogen generation

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Materials Science for Energy Technologies 2025年 8卷 131-142页

作者： Subagyo, Riki Anindika, Garcelina Rizky Aufkani, Afif Akmal Zhang, Lei Ardhyananta, Hosta Burhan, R.Y. Perry Nugraheni, Zjahra Vianita Akhlus, Syafsir Bahruji, Hasliza Prasetyoko, Didik Wellia, Diana Vanda Ivansyah, Atthar Luqman Arramel Kusumawati, Yuly Department of Chemistry Faculty of Science and Analytic Data Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Center of Excellence Applied Physics and Chemistry Nano Center Indonesia Jl PUSPIPTEK South Tangerang Banten15314 Indonesia Department of Physics National University of Singapore Singapore117551 Singapore Department of Materials and Metallurgical Engineering Faculty of Industrial Technology and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Centre of Advanced Material and Energy Science Universiti Brunei Darussalam Jalan Tungku Link BE 1410 Brunei Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Andalas Padang25163 Indonesia Master Program in Computational Science Faculty of Mathematics and Natural Science Institut Teknologi Bandung Jalan Ganesha No. 10 Bandung40132 Indonesia Instrumentation and Computational Physics Research Group Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesha No.10 West Java Bandung40132 Indonesia

The implementation of titanium dioxide (TiO2) as a photocatalyst material in hydrogen (H2) evolution reaction (HER) has embarked renewed interest in the past decade. Rapid electron-hole pairs recombination and wide band gap of a photo-sensitive material of TiO2 are detrimental toward the targeted catalytical reaction. In this study, we present the rational design, fabrication, photocatalytic performance of TiO2-Cu/CuO/Cu2O heterostructures (CuTi) using viable chemical reduction method. The Z-scheme and S-scheme are succesfully generated across the TiO2/CuO/Cu2O interfaces, while the Schottky junction arises on the Cu perimeters. This is evidenced from the blue shifted about 0.3 eV of Cu 2p core level determined by using X-ray photoemission spectroscopy (XPS), in combination with the formation of inverse V-shape of the Mott-Schottky plots. In addition, we find that Cu/CuO/Cu2O facilitates photon absorption range up to the visible region. The multiple heterojunction and the large number of OHsurface enhanced charge carrier transfer are associated to the suppression of photoluminescence (PL) intensity, high surface hydroxyl (OHsurface) density in CuTi probed by XPS, and fast electron transfer based on the electrochemical measurements. The presence of OHsurface inhibits the recombination of electron. A significant H2 photogeneration rate enhancement is achieved when an optimized 5 wt% Cu/CuO/Cu2O concentration is used on TiO2 to achieve 7,157.19 μmol·g−1 (1,789.30 μmol·g−1·h−1). Based on this finding, zero emission energy innitiative could be materialized under multiple heterojunctions in photocatalytic process is beneficial for enhancing the H2 production. © 2025 The Authors

关键词： Titanium dioxide

Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation

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Bulletin of Mathematical Biology 2025年第6期87卷 1-32页

作者： Srivastava, Kashvi Eilertsen, Justin Booth, Victoria Schnell, Santiago Department of Mathematics University of Michigan Ann Arbor USA Mathematical Reviews American Mathematical Society Ann Arbor USA Department of Biological Sciences and Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame USA

The application of the standard quasi-steady-state approximation to the Michaelis-Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific biochemical conditions that dictate the validity of the standard quasi-steady-state approximation remains a challenging endeavor. Emerging research suggests that the accuracy of the standard quasi-steady-state approximation improves as the ratio of the initial enzyme concentration, $$e_0$$ , to the Michaelis constant, $$K_M$$ , decreases. In this work, we examine this ratio and its implications for the accuracy and validity of the standard quasi-steady-state approximation as compared to other quasi-steady-state reductions in its proximity. Using standard tools from the analysis of ordinary differential equations, we show that while $$e_0/K_M$$ provides an indication of the standard quasi-steady-state approximation’s asymptotic accuracy, the standard quasi-steady-state approximation’s predominance relies on a small ratio of $$e_0$$ to the Van Slyke-Cullen constant, K. Here, we define the predominance of a quasi-steady-state reduction when it offers the highest approximation accuracy among other well-known reductions with overlapping validity conditions. We conclude that the magnitude of $$e_0/K$$ offers the most accurate measure of the validity of the standard quasi-steady-state approximation.

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Independence, induced subgraphs, and domination in K1,r-free graphs

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arXiv 2025年

作者： Caro, Yair Davila, Randy Henning, Michael A. Pepper, Ryan Department of Mathematics University of Haifa–Oranim Tivon36006 Israel Department of Computational Applied Mathematics & Operations Research Rice University HoustonTX77005 United States Department of Mathematics and Applied Mathematics University of Johannesburg Auckland Park2006 South Africa Department of Mathematics and Statistics University of Houston–Downtown HoustonTX77002 United States

Let G be a graph and F a family of graphs. Define αF(G) as the maximum order of any induced subgraph of G that belongs to the family F. For the family F of graphs with chromatic number at most k, we prove that if G is K1,r-free, then αF(G) ≤ (r − 1)kγ(G), where γ(G) is the domination number. When F is the family of empty graphs, this bound simplifies to α(G) ≤ 2γ(G) for K1,3free (claw-free) graphs, where α(G) is the independence number of G. For d-regular graphs, this is further refined to the bound α(G) ≤ 2 (d+1/d+2) γ(G), which is tight for d ∈ {2, 3, 4}. Using Ramsey theory, we extend this framework to edge-hereditary graph families, showing that for K1,r-free graphs, we have αF(G) ≤ r(Kr, F∗)γ(G), where F∗ is the set of graphs not in F. Specializing to Kq-free graphs, we show αF(G) ≤ (r(Kq, Kr) − 1)γ(G). Finally, for the k-independence number αk(G), we prove that if G is K1,r-free with order n and minimum degree δ ≥ k + 1, (formula presented) and this bound is sharp for all parameters. Copyright © 2025, The Authors. All rights reserved.

关键词： Graph theory

Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup

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arXiv 2025年

作者： Hu, Nan Hwang, Jonghyun Ruangkriengsin, Tachin Stone, Howard A. Department of Mechanical and Aerospace Engineering Princeton University NJ08544 United States Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions. The results refine capillary breakup rheometry for viscoelastic fluids and advance the understanding of breakup dynamics across scales. Copyright © 2025, The Authors. All rights reserved.

关键词： Relaxation time

THE NO-UNDERRUN SAMPLER: A LOCALLY ADAPTIVE, GRADIENT-FREE MCMC METHOD

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arXiv 2025年

作者： Bou-Rabee, Nawaf Carpenter, Bob Liu, Sifan Oberdörster, Stefan Department of Mathematical Sciences Rutgers University United States Center for Computational Mathematics Flatiron Institute United States Institute for Applied Mathematics University of Bonn Germany

In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal’s funnel, a challenging multi-scale distribution from Bayesian hierarchical *** Codes 60J05, 65C05 Copyright © 2025, The Authors. All rights reserved.

关键词： Monte Carlo methods

GLOBAL WELL-POSEDNESS OF VLASOV-POISSON-BOLTZMANN EQUATIONS WITH NEUTRAL INITIAL DATA AND SMALL RELATIVE ENTROPY

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arXiv 2025年

作者： Jiang, Zaihong Wang, Yong Xiong, Hang Department of Mathematics Zhejiang Normal University Jinhua321004 China Institute of Applied Mathematics AMSS CAS Beijing100190 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China

The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the self-induced electric field. In this paper, we are concerned with global well-posedness of mild solutions of the equations. We establish the global existence and uniqueness of mild solutions to the two species Vlasov-Poisson-Boltzmann equations in the torus for a class of initial data with bounded time-velocity weighted L∞ norm under nearly neutral condition and some smallness condition on L1xL∞v norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Due to the nonlinear effect of electric field, we consider the problem in Wx,v1,∞ with large amplitude data, new difficulty arises when establishing globally uniform Wx,v1,∞ bound, which has been overcome based on nearly neutral condition, time-velocity weight function and a logarithmic estimate. Moreover, the large time behavior of solutions in Wx,v1,∞ norm with exponential decay rates of convergence is also obtained. Copyright © 2025, The Authors. All rights reserved.

关键词： Entropy

SEMIALGEBRAIC NEURAL NETWORKS: FROM ROOTS TO REPRESENTATIONS

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arXiv 2025年

作者： Mis, S. David Lassas, Matti de Hoop, Maarten V. Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX77005 United States Department of Mathematics and Statistics University of Helsinki P.O. Box 68 HelsinkiFI-00014 Finland Simons Chair in Computational Applied Mathematics and Earth Science Rice University HoustonTX77005 United States

Many numerical algorithms in scientific computing—particularly in areas like numerical linear algebra, PDE simulation, and inverse problems—produce outputs that can be represented by semialgebraic functions;that is, the graph of the computed function can be described by finitely many polynomial equalities and inequalities. In this work, we introduce Semialgebraic Neural Networks (SANNs), a neural network architecture capable of representing any bounded semialgebraic function, and computing such functions up to the accuracy of a numerical ODE solver chosen by the programmer. Conceptually, we encode the graph of the learned function as the kernel of a piecewise polynomial selected from a class of functions whose roots can be evaluated using a particular homotopy continuation method. We show by construction that the SANN architecture is able to execute this continuation method, thus evaluating the learned semialgebraic function. Furthermore, the architecture can exactly represent even discontinuous semialgebraic functions by executing a continuation method on each connected component of the target function. Lastly, we provide example applications of these networks and show they can be trained with traditional deep-learning techniques. © 2025, CC BY.

关键词： Inverse problems

INEXACT SUBSPACE PROJECTION METHODS FOR LOW-RANK TENSOR EIGENVALUE PROBLEMS

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arXiv 2025年

作者： Dektor, Alec Delmastro, Peter Ye, Erika van Beeumen, Roel Yang, Chao Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Department of Mathematics Virginia Tech BlacksburgVA United States

We compare two approaches for solving high-dimensional eigenvalue problems with low-rank structure: the inexact Lanczos method and inexact polynomial-filtered subspace iteration. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor format. A primary challenge in these methods is that standard operations, such as matrix-vector products and linear combinations, increase tensor rank, necessitating rank truncation and hence approximation. The Lanczos method constructs an approximate orthonormal Krylov basis, which is often difficult to represent accurately using low-rank tensor formats, even when the eigenvectors themselves exhibit low-rank structure. In contrast, the low-rank polynomial-filtered subspace iteration uses approximate eigenvectors (Ritz vectors) directly as a subspace basis, bypassing the need for an orthonormal Krylov basis. Our analysis and numerical experiments demonstrate that inexact subspace iteration is much more robust to rank-truncation errors compared to the inexact Lanczos method. We further demonstrate that rank-truncated subspace iteration can converge for problems where the density matrix renormalization group method (DMRG) *** Codes 65F15, 15A69 © 2025, CC BY.

关键词： Tensors