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Fairness Through Matching

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arXiv 2025年

作者： Kim, Kunwoong Kong, Insung Lee, Jongjin Chae, Minwoo Park, Sangchul Kim, Yongdai Department of Statistics Seoul National University Korea Republic of Department of Applied Mathematics University of Twente Netherlands Samsung Research Korea Republic of School of Law Seoul National University Korea Republic of Department of Statistics Interdisciplinary Program in Artificial Intelligence Seoul National University Korea Republic of Seoul National University Korea Republic of

Group fairness requires that different protected groups, characterized by a given sensitive attribute, receive equal outcomes overall. Typically, the level of group fairness is measured by the statistical gap between predictions from different protected groups. In this study, we reveal an implicit property of existing group fairness measures, which provides an insight into how the group-fair models behave. Then, we develop a new group-fair constraint based on this implicit property to learn group-fair models. To do so, we first introduce a notable theoretical observation: every group-fair model has an implicitly corresponding transport map between the input spaces of each protected group. Based on this observation, we introduce a new group fairness measure termed Matched Demographic Parity (MDP), which quantifies the averaged gap between predictions of two individuals (from different protected groups) matched by a given transport map. Then, we prove that any transport map can be used in MDP to learn group-fair models, and develop a novel algorithm called Fairness Through Matching (FTM)1, which learns a group-fair model using MDP constraint with an user-specified transport map. We specifically propose two favorable types of transport maps for MDP, based on the optimal transport theory, and discuss their advantages. Experiments reveal that FTM successfully trains group-fair models with certain desirable properties by choosing the transport map accordingly. © 2025, CC BY.

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An Algorithm for Illuminating n Nonoverlapping Circular Discs’ Boundaries on the Plane with Application to Tree Stem Illumination Problem

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arXiv 2025年

作者： Sukkasem, Phapaengmuang Chaidee, Supanut Khokthong, Watit Program in Applied Mathematics Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai50200 Thailand Department of Mathematics Faculty of Science Chiang Mai University Thailand Forest Restoration Research Unit Department of Biology Faculty of Science Chiang Mai University Chiang Mai50200 Thailand Environmental Science Research Centre Faculty of Science Chiang Mai University Chiang Mai50200 Thailand

Given a set of n nonoverlapping circular discs on a plane, we aim to determine possible positions of points (referred to as cameras) that could fully illuminate all the circular discs’ boundaries. This work presents a geometric approach for determining feasible camera positions that would provide total illumination of all circular discs. The Laguerre Delaunay triangulation, coupled with the intersection of slabs formed by the boundaries of circular discs, is employed to form the region that satisfies the given conditions. The experiment is conducted using a set of randomly positioned circular discs on a plane. This study has the potential to address the issue of illumination in forests by utilizing a LiDAR camera to determine the possible number and placement of cameras that can effectively illuminate trees within a forest. © 2025, CC BY.

关键词： Laser recording

A simple yet effective approach for predicting disease spread using mathematically-inspired diffusion-informed neural networks

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Scientific Reports 2025年第1期15卷 1-14页

作者： Jeong, ByeongChang Lee, Yeon Ju Han, Cheol E. Department of Electronics and Information Engineering Korea University Sejong South Korea Interdisciplinary Graduate Program for Artificial Intelligence Smart Convergence Technology Korea University 2511 Sejong-ro Sejong 30019 South Korea Department of Applied Mathematics Korea University Sejong South Korea

The COVID-19 outbreak has highlighted the importance of mathematical epidemic models like the Susceptible-Infected-Recovered (SIR) model, for understanding disease spread dynamics. However, enhancing their predictive accuracy complicates parameter estimation. To address this, we proposed a novel model that integrates traditional mathematical modeling with deep learning which has shown improved predicted power across diverse fields. The proposed model includes a simple artificial neural network (ANN) for regional disease incidences, and a graph convolutional neural network (GCN) to capture spread to adjacent regions. GCNs are a recent deep learning algorithm designed to learn spatial relationship from graph-structured data. We applied the model to COVID-19 incidences in Spain to evaluate its performance. It achieved a 0.9679 correlation with the test data, outperforming previous models with fewer parameters. By leveraging the efficient training methods of deep learning, the model simplifies parameter estimation while maintaining alignment with the mathematical framework to ensure interpretability. The proposed model may allow the more robust and insightful analyses by leveraging the generalization power of deep learning and theoretical foundations of the mathematical models. © The Author(s) 2025.

关键词： Artificial neural networks COVID-19 Deep learning Graph convolutional neural network

Solutions with prescribed mass for L2-supercritical NLS equations under Neumann boundary conditions

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arXiv 2025年

作者： Chang, Xiaojun Rǎdulescu, Vicenţiu D. Zhang, Yuxuan School of Mathematics and Statistics Center for Mathematics and Interdisciplinary Sciences Northeast Normal University Jilin Changchun130024 China Faculty of Applied Mathematics AGH University of Kraków al. Mickiewicza 30 Kraków30-059 Poland Simion Stoilow Institute of Mathematics the Romanian Academy 21 Calea Grivit ¸ei Bucharest010702 Romania Department of Mathematics University of Craiova Street A.I. Cuza 13 Craiova200585 Romania Brno University of Technology Faculty of Electrical Engineering and Communication Technická 3058/10 Brno61600 Czech Republic School of Mathematics Zhejiang Normal University Zhejiang Jinhua321004 China

In this paper, we investigate the following nonlinear Schrödinger equation with Neumann boundary conditions: (Fermula presented) coupled with a constraint condition: ZΩ |u|2dx = c, where (Fermula presented) denotes a smooth bounded domain, ν represents the unit outer normal vector to ∂Ω, c is a positive constant, and λ acts as a Lagrange multiplier. When the nonlinearity f exhibits a general mass supercritical growth at infinity, we establish the existence of normalized solutions, which are not necessarily positive solutions and can be characterized as mountain pass type critical points of the associated constraint functional. Our approach provides a uniform treatment of various nonlinearities, including cases such as f (u) = |u|p−2u, |u|q−2u + |u|p−2u, and −|u|q−2u + |u|p−2u, where 2 N4 ∗. The result is obtained through a combination of a minimax principle with Morse index information for constrained functionals and a novel blow-up analysis for the NLS equation under Neumann boundary conditions. Copyright © 2025, The Authors. All rights reserved.

关键词： Schrodinger equation

Carbon-modified zeolite derivates based filler in mixed matrix membrane adsorbers (MMMAs) for enhancing urea and creatinine removal from hemodialysis spent dialysate

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Journal of Industrial and Engineering Chemistry 2025年 147卷 584-597页

作者： Widiastuti, Nurul Rahman, Reca Ardiyanti Cipta Dharma, Hadi Nugraha Widyanto, Alvin Rahmad Nareswari, Cininta Kayadoe, Victor Raharjo, Yanuardi Saiful Nomura, Mikihiro Department of Chemistry Faculty of Science and Data Analytics Institut Teknologi Sepuluh Nopember Kampus ITS Keputih-Sukolilo Jl. Arif Rahman Hakim Surabaya60111 Indonesia Advanced Nanolithography Lab Department of System Semiconductor Science Dongguk University 30 Pildong-ro 1-gil Jung-gu Seoul04620 Korea Republic of Department of Applied Chemistry Shibaura Institute of Technology 3-7-5 Toyosu Koto-ku Tokyo135-8548 Japan Chemical Education Study Program Faculty of Teaching and Education Sciences University of Pattimura Ambon97233 Indonesia Chemistry Department Faculty of Science and Technology Universitas Airlangga Surabaya Indonesia Chemistry Department Faculty of Mathematics and Natural Science Universitas Syiah Kuala Banda Aceh Indonesia

Conventional dialysate recycling methods struggle to effectively remove creatinine, urea, and other minor contaminants. This study explores mixed matrix membrane adsorbers (MMMAs) as a novel approach to address these challenges. MMMAs, which integrate adsorbents into filtration membranes, function as both filters and impurity scavengers. Zeolite carbon composite (ZCC) and zeolite-templated carbon (ZTC) were incorporated into MMMAs using the non-solvent induced phase separation (NIPS) technique. Characterization by SEM and XRD confirmed the successful synthesis of ZCC and ZTC, retaining the zeolite-Y structure and amorphous nature, with notable differences in particle sizes (680 and 379 nm) and crystallite sizes (0.45 and 0.02 nm). FTIR revealed hydrogen bonding interactions between ZCC and PVP, absent in ZTC. SEM and AFM analyses of the membranes indicated increased hydrophilicity and porosity with ZCC, while ZTC reduced surface roughness. MMMAs significantly outperformed pristine membranes in removing urea and creatinine. The PPK-0.2 membrane achieved superior rejection rates (93.05 % for urea and 98.95 % for creatinine), attributed to microporous entrapment of ZTC and polymer matrix adsorption. In contrast, PPZ-0.2 showed lower rejection rates (84.24 % for urea and 85.79 % for creatinine), relying solely on physical adsorption. These findings highlight MMMAs, especially ZTC-based ones, as promising candidates for enhancing dialysate reuse efficiency. © 2024 The Korean Society of Industrial and Engineering Chemistry

关键词： Hydrogen bonds

Unbiased Parameter Estimation for Bayesian Inverse Problems

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

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arXiv 2025年

作者： Geadah, Victor Arbelaiz, Juncal Ritz, Harrison Daw, Nathaniel D. Cohen, Jonathan D. Pillow, Jonathan W. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ United States Princeton Neuroscience Institute Princeton University PrincetonNJ United States

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic state-space model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finite-horizon setting. We further illustrate the performance of our methodology through numerical examples. © 2025, CC BY.

关键词： Stochastic systems

A SIZE-STRUCTURED MODEL FOR CANNIBALISM

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THEORETICAL POPULATION BIOLOGY 1992年第3期42卷 347-361页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a “life-boat strategy” phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.

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A DISCRETE MODEL FOR COMPETING STAGE-STRUCTURED SPECIES

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THEORETICAL POPULATION BIOLOGY 1992年第3期41卷 372-387页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

This paper deals with the problem of relating physiological properties of individual organisms to the dynamics at the total population level. A general nonlinear matrix difference equation is described which accounts for the dynamics of stage-structured populations under the assumption that individuals in the populations can be placed into well defined descriptive stages. Density feedback is modeled through an assumption that (stage-specific) fertilities and transitions are proportional to a resource uptake functional which is dependent upon a total weighted population size. It is shown how, if stage-specific differences in mortality are insignificant compared to stage-specific differences in fertility and inter-stage transitions, a nonlinear version of the strong ergodic theorem of demography mathematically separates the population level dynamics from the dynamics of the stage distribution vector, which is shown to stabilize independently of the population level dynamics. The nonlinear dynamics at the population level are governed by a key parameter π that encapsulates the stage-specific parameters and thereby affords a means by which population level dynamics can be linked to properties of individual organisms. The method is applied to a community of stagestructured populations competing for a common limiting resource, and it is seen how the parameter π determines the competitively superior species. An example of size structured competitors illustrates how the method can relate the competitive success of a species to such size-specific properties as resource conversion efficiencies and allocation fractions for individual growth and reproduction, largest adult body size, and size at birth and maturation.

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