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arXiv 2023年

作者： Nguyen, Kyle Rutter, Erica M. Flores, Kevin Biomathematics Graduate Program North Carolina State University RaleighNC United States Center for Research in Scientific Computation North Carolina State University RaleighNC United States Department of Applied Mathematics University of California Merced MercedCA United States Department of Mathematics North Carolina State University RaleighNC United States

Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates, however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of Glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models’ performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions. © 2023, CC BY.

关键词： Parameter estimation

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Realistic-science, technology, engineering, and mathematics assisted by google classroom as a learning innovation in the new normal era to improve statistical thinking skill

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Journal of Physics: Conference Series 2021年第4期1918卷

作者： A S Ardiansyah N A Novita H Zhintya D Kurnianto Mathematics Education Study Program Universitas Negeri Semarang Applied Statistics and Computation Study Program Universitas Negeri Semarang

Based on government policies regarding the implementation of learning from home, it is necessary the learning innovation to continue learning in the new normal era by utilizing existing technological advances. In this digital era, statistics thinking is important because it is needed to be able to interpret and understand and make good decisions from the statistical data obtained. From these problems, one of the innovations that can be done is by implementing Realistic mathematics Education integrated Science, Technology, Engineering, and mathematics assisted by Google Classroom (R-STEM-GC). This paper aims to determine the effect of R-STEM-GC learning on students' statistical thinking skills. This paper uses literature review method research that identifies, assesses, and interprets all findings on a research topic to answer existing research questions. It can concluded that realistic learning was more effective in terms of students' mathematical reasoning and communication than conventional learning; learning with the application of STEM can improve students' problem solving abilities compared to conventional learning; and the use of google classrooms that can improve communication skills. From the results of this analysis, the application of R-STEM-GC learning can be an innovative solution in improving students' statistical thinking skills in new normal era.

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A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

arXiv

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arXiv 2023年

作者： Herrala, Olli Gabriel, Steven A. Oliveira, Fabricio Ekholm, Tommi Aalto University Department of Mathematics and Systems Analysis Espoo Finland University of Maryland Department of Mechanical Engineering/Applied Mathematics Statistics & Scientific Computing Program College ParkMD United States Norwegian University of Science and Technology Department of Industrial Economics and Technology Management Trondheim Norway Finnish Meteorological Institute Helsinki Finland

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio. Copyright © 2023, The Authors. All rights reserved.

关键词： Energy resources

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A bicriteria perspective on l-penalty approaches a corrigendum to siddiqui and gabriel's L-Penalty Approach for Solving MPECs

arXiv

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arXiv 2018年

作者： Dächert, D. Siddiqui, Kerstin Saez-Gallego, Sauleh Gabriel, Javier Morales, Steven A. Miguel, Juan University of Duisburg-Essen Faculty of Economics and Business Administration Department for Management Science and Energy Economics Berliner Platz 6-8 Essen45127 Germany Departments of Civil Engineering and Applied Mathematics Statisitics Johns Hopkins University 3400 N Charles Street BaltimoreMD21218 United States Siemens Wind Power A/S Borupvang 9 Ballerup2750 Denmark Department of Mechanical Engineering Applied Mathematics Statistics and Scientific Computation Program University of Maryland College ParkMD20742-3021 United States University of Málaga Department of Applied Mathematics School of Industrial Engineers Málagaroom 2.556L-B

This paper presents a corrigendumto Theorems 2 and 3 in Siddiqui and Gabriel (2013). In brief, we revise the claim that their L-penalty approach yields a so-lution satisfying complementarity for any positive value of L, in general. This becomes evident when interpreting the L-penalty method as a weighted-sum scalarization of a bicriteria optimization problem. We also elaborate further assumptions under which the L-penalty approach yields a solution satisfying complementarity. Copyright © 2018, The Authors. All rights reserved.

关键词： Constrained optimization

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A Simulation-Based Model for Optimal Demand Response Load Shifting: A Case Study for the Texas Power Market

SSRN

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SSRN 2019年

作者： Schaperow, Jacob R. Gabriel, Steven A. Siemann, Michael Crawford, Jaden Civil and Environmental Engineering University of California Los Angeles 420 Westwood Plaza 6722 Boelter Hall Los AngelesCA90095 United States Mechanical Engineering/Applied Mathematics Statistics & Scientific Computing Program University of Maryland College ParkMD20742 United States Whisker Labs 12410 Milestone Center Drive GermantownMD20876 United States

This paper describes a prototype Monte Carlo simulation tool that we use to evaluate retail demand response (DR) programs for the Texas power market (the Electric Reliability Council of Texas/ERCOT), but which could also be applied to other regions. The model simulates a direct load control technique in which customers’ power consumption is adjusted during certain time periods called DR events. During a DR event, smart thermostats automatically increase participating customers’ temperature setpoints, reducing air-conditioning loads and thus potentially shielding retail electric providers (REPs) from financial losses during times of peak load. This study identified a Pareto optimal load control schedule based on forecasted load, settlement point prices and weather variables, taking into account stochastic load and prices as well as gray-box thermodynamic modeling. A Pareto optimal schedule is defined as the schedule that maximizes profit to the REP and minimizes its risk of low profits. We show how much benefit REPs stand to gain by following an optimal load schedule and how much they stand to lose by enacting DR events at the wrong times. © 2019, The Authors. All rights reserved.

关键词： Sales

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A Stochastic MPEC Approach for Grid Tariff Design with Demand Side Flexibility

TechRxiv

引用

TechRxiv 2019年

作者： Askeland, Magnus Burandt, Thorsten Gabriel, Steven A. SINTEF Energy Research Department of Electric Power Engineering Norwegian University of Science and Technology Trondheim Norway Technical University of Berlin The Energy Transportation Environment Department German Institute for Economic Research DIW Berlin Berlin Germany Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim Norway Department of Mechanical Engineering Applied Math & Statistics Scientific Computation Program University of Maryland College Park Maryland United States

As the end-users increasingly can provide flexibility to the power system, it is important to consider how this flexibility can be activated as a resource for the grid. Electricity network tariffs are one option that can be used to activate this flexibility. Therefore, by designing efficient grid tariffs, it might be possible to reduce the total costs in the power system by incentivizing a change in consumption patterns. This paper provides a methodology for optimal grid tariff design under decentralized decision-making and uncertainty in demand, power prices, and renewable generation. A bilevel model is formulated to adequately describe the interaction between the end-users and a distribution system operator. In addition, a centralized decision-making model is provided for benchmarking purposes. The bilevel model is reformulated as a mixed-integer linear problem solvable by branch-and-cut techniques. Results for a deterministic example and a stochastic case study are presented and discussed. © 2019, CC BY-SA.

关键词： Decision making

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The estimation of the effective reproductive number from disease outbreak data

arXiv

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arXiv 2020年

作者： Cintrón-Arias, Ariel Castillo-Chávez, Carlos Bettencourt, Luís M.A. Lloyd, Alun L. Banks, H.T. Statistical and Applied Mathematical Sciences Institute 19 T. W. Alexander Drive P.O. Box 14006 Research Triangle ParkNC27709-4006 United States Department of Mathematics and Statistics Arizona State University P.O. Box 871804 TempeAZ85287 - 1804 Los Alamos National Laboratory Mail Stop B284 Los AlamosNM87545 United States Biomathematics Graduate Program Department of Mathematics North Carolina State University RaleighNC27695 United States Center for Research in Scientific Computation North Carolina State University P.O. Box 8205 RaleighNC27695

We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets. Copyright © 2020, The Authors. All rights reserved.

关键词： Parameter estimation

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Potential numerical techniques and challenges for atmospheric modeling

Potential numerical techniques and challenges for atmospheri...

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作者： Li, J. Steppeler, J. Fang, F. Pain, C.C. Zhu, J. Peng, X. Dong, L. Li, Y. Tao, L. Leng, W. Wang, Y. Zheng, J. International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Hamburg Germany Applied Modelling and Computation Group Department of Earth Science and Engineering Imperial College London London United Kingdom International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Department of Atmospheric Sciences University of Chinese Academy of Sciences Beijing China State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China School of Mathematics and Statistics Henan University Kaifeng China Center for Excellence in Regional Atmospheric Environment Institute of Urban Environment Chinese Academy of Sciences Xiamen China

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Resonant responses to variance modulation in stochastic integrate-and-fire neurons

引用

BMC Neuroscience 2007年第2期8卷 1-1页

作者： Joanna Pressley Todd W Troyer Applied Mathematics and Scientific Computation Program University of Maryland College Park MD 20742 USA Neuroscience and Cognitive Science Program University of Maryland College Park MD 20742 USA Department of Psychology University of Maryland College Park MD 20742 USA

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Noise induces continuous and noncontinuous transitions in neuronal interspike intervals range

arXiv

引用

arXiv 2020年

作者： Protachevicz, P.R. Santos, M.S. Seifert, E.G. Gabrick, E.C. Borges, F.S. Borges, R.R. Trobia, J. Szezech, J.D. Iarosz, K.C. Caldas, I.L. Antonopoulos, C.G. Xu, Y. Viana, R.L. Batista, A.M. Graduate Program in Science-Physics State University of Ponta Grossa Ponta Grossa84030-900 Institute of Physics University of Saõ Paulo Saõ Paulo05508-900 Brazil Department of Physics State University of Ponta Grossa Ponta Grossa84030-900 Center ForMathematics Computation and Cognition Federal University of ABC Sao Bernardo do Campo09606-045 Department of Mathematics Federal University of Technology Paraná Ponta Grossa84016-210 Department of Mathematics and Statistics State University of Ponta Grossa Ponta Grossa84030-900 Faculdade de Telêmaco Borba FATEB Telemaco Borba84266-010 Brazil Department of Mathematical Sciences University of Essex Wivenhoe ParkCO43SQ United Kingdom Department of Applied Mathematics Northwestern Polytechnical University Xi'an710072 Department of Physics Federal University of Paraná Curitiba82590-300 Brazil

Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to model firing patterns of neurons subject to noise. In this work, we consider perturbing noise in the adaptive exponential integrate-and-fire (AEIF) neuron. The AEIF is a two-dimensional model that describes different neuronal firing patterns by varying its parameters. Noise is added in the equation related to the membrane potential. We show that a noise current can induce continuous and noncontinuous transitions in neuronal interspike intervals. Moreover, we show that the noncontinuous transition occurs mainly for parameters close to the border between tonic spiking and burst activities of the neuron without noise. Copyright © 2020, The Authors. All rights reserved.

关键词： Neurons

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