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5th International Conference on Control Systems, mathematical Modeling, Automation and Energy Efficiency, SUMMA 2023

作者： Zhukova, Aleksandra Flerova, Anna Chernov, Aleksey Pilnik, Nikolay FRC CSC of RAS Dept. of Mathematical Modelling of Economic Systems MIPT Moscow Russia FRC CSC RAS Dept. of Mathematical Modelling of Economic Systems Moscow Russia Moscow Institute of Physics and Technology MIPT-School of Applied Mathematics and Computer Science Moscow Russia

ISBN: (纸本)9798350309126

In this paper we present the mathematical formulation of the problem of planning the Asset Liability Management if the Presence of Normative and Internal Constraints. As a nonlinear optimal control problem, it has specifics due to the state constraints. The maximum principle involves verification of regularity property in order to apply computational methods. We reformulate the problem as the problem with convex objective function and linear, but mixed system of constraints. This enables application of optimization methods to compute the optimal controls, and study the dependence of controls on the parameters that describe the external environments and the management objective. © 2023 IEEE.

关键词： Optimal control systems

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SMT-Solving Induction Proofs of Inequalities 7

SMT-Solving Induction Proofs of Inequalities

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7th International Workshop on Satisfiability Checking and Symbolic Computation Square Workshop, SC-Square 2022

作者： Uncu, Ali K. Davenport, James H. England, Matthew Austrian Academy of Science Johann Radon Institute for Computational and Applied Mathematics Linz Austria University of Bath Faculty of Science Department of Computer Science Bath United Kingdom Coventry University Research Centre for Computational Science and Mathematical Modelling Coventry United Kingdom

This paper accompanies a new dataset of non-linear real arithmetic problems for the SMT-LIB benchmark collection. The problems come from an automated proof procedure of Gerhold-Kauers, which is well suited for solution by SMT. The problems of this type have not been tackled by SMT-solvers before. We describe the proof technique and give one new such proof to illustrate it. We then describe the dataset and the results of benchmarking. The benchmarks on the new dataset are quite different to the existing ones. The benchmarking also brings forward some interesting debate on the use/inclusion of rational functions and algebraic numbers in the SMT-LIB. © 2023 CEUR-WS. All rights reserved.

关键词： Rational functions

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Numerical Analysis of a Functional Equation for the Stochastic Optimal Control Problem 15

Numerical Analysis of a Functional Equation for the Stochast...

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15th International Conference Management of Large-Scale System Development, MLSD 2022

作者： Chernov, Aleksey Zhukova, Aleksandra MIPT-School of Applied Mathematics and Computer Science Moscow Institute of Physics and Technology Moscow Russia Frc Csc Ras Dept. of Mathematical Modelling of Economic Systems Moscow Russia

This work presents the approach to solving the functional equation of non-local type that appears in the study of a stochastic optimal control problem. This experience demonstrates the challenges and possible solution... 详细信息

ISBN: (数字)9781665497015

ISBN: (纸本)9781665497015

关键词： Numerical methods

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Impact of saturation on evaporation-driven density instabilities in porous media: mathematical and numerical analysis

arXiv

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arXiv 2025年

作者： Bringedal, C. Kiemle, S. van Duijn, C.J. Helmig, R. Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Science Bergen Norway Institute for Modelling Hydraulic and Environmental Systems University of Stuttgart Stuttgart Germany Department of Mechanical Engineering Eindhoven University of Technology Eindhoven Netherlands

Evaporation from a porous medium partially saturated with saline water, causes the salinity (salt concentration) to increase near the top of the porous medium as water leaves while salt stays behind. As the density of the water increases with increased salt concentration, the evaporation leads to a gravitational unstable setting, where density instabilities can form. Whether density instabilities form, depends on a large range of parameters like the evaporation rate and intrinsic permeability of the porous medium, but also on the water saturation. As water saturation decreases, the storage, convection and diffusion of salt also decrease, which all influence the onset of instabilities. By performing a linear stability analysis on the governing equations, we give criteria for onset of instabilities. Numerical simulations give information about the further development of these instabilities. With this knowledge we can predict whether and when density instabilities occur, and how they will influence the further development of salt concentration in the porous medium. © 2025, CC BY.

关键词： Stability criteria

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LEARNING SURROGATE EQUATIONS FOR THE ANALYSIS OF AN AGENT-BASED CANCER MODEL

arXiv

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arXiv 2025年

作者： Burrage, Kevin Burrage, Pamela Kreikemeyer, Justin N. Uhrmacher, Adelinde M. Weerasinghe, Hasitha N. School of Mathematical Sciences Queensland University of Technology BrisbaneQLD Australia Department of Computer Science University of Oxford United Kingdom Modelling and Simulation Institute for Visual and Analytic Computing Faculty of Informatics and Electrical Engineering University of Rostock Rostock Germany

In this paper, we adapt a two species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction with a third species – namely immune cells. We run six different scenarios to explore the competition between cancer and immune cells and the initial concentration of the immune cells on cancer dynamics. We then use coupled equation learning to construct a population-based reaction model for each scenario. We show how they can be unified into a single surrogate population-based reaction model, whose underlying three coupled ordinary differential equations are much easier to analyse than the original agent-based model. As an example, by finding the single steady state of the cancer concentration, we are able to find a linear relationship between this concentration and the initial concentration of the immune cells. This then enables us to estimate suitable values for the competition and initial concentration to reduce the cancer substantially without performing additional complex and expensive simulations from an agent-based stochastic model. The work shows the importance of performing equation learning from agent-based stochastic data for gaining key insights about the behaviour of complex cellular dynamics. © 2025, CC BY.

关键词： Lung cancer

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REAF: ROI Extraction and Adaptive Fusion for Breast Cancer Diagnosis in Ultrasound Images

REAF: ROI Extraction and Adaptive Fusion for Breast Cancer D...

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2023 IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2023

作者： Zhang, Ziyang Lim, Jia Wei Zheng, Yuanxun Chen, Bozhao Chen, Dongxin Lin, Yi North China University of Techonology Brunel London School Beijing China Brunel University London Centre for Mathematical and Statistical Modelling Kingston Lane Uxbridge United Kingdom The Norinco Group Aviation Ammunition Research Institute Harbin China China Southern Power Grid Digital Grid Group Co. Ltd Guangzhou China Harbin Institute of Technology School of Computer Science and Technology Harbin China

ISBN: (纸本)9798350337488

Breast cancer leads to the top cause of death among women worldwide. Early detection of breast cancer is the most effective way to reduce the risk of death and increase the likelihood of survival. Breast ultrasound imaging is an essential test for early detection but its accurate evaluation is difficult due to the limited number of experienced sonographers. So the computer-aided system for breast cancer diagnosis on ultrasound images is vitally necessary. Recent breast cancer diagnosis methods are mostly developed by improving or transferring visual deep models to breast cancer diagnosis. These methods ignored the characteristics of breast cancer on ultrasound images. Some methods fuse the pre-defined region of interest (ROI) to adapt the characteristics of ultrasound images but cannot diagnose those samples whose ROIs are not defined. In this paper, we propose a novel framework, ROI Extraction and Adaptive Fusion (REAF), for breast cancer diagnosis on ultrasound images. To make the framework be applied to the samples without pre-defined ROIs as well as incorporate the characteristics of breast cancer on ultrasound images, the proposed REAF firstly extracts the ROI of breast tumor areas as a confidence degree map. Then we propose an adaptive fusion method to fuse the extracted ROI into the downstream diagnostic model. In addition, we propose a pair augmentation method to increase the variety of samples for enhancing the generalization of the proposed REAF. The experimental results demonstrate that the REAF surpasses state-of-the-art visual classification models and breast cancer methods. For the evaluation of the REAF, the AUC reaches 95.52%, the accuracy reaches 88.97%, the specificity reaches 92.86%, the precision reaches 89.43%, the recall reaches 86.82% and the f1-score reaches 88.05%. © 2023 IEEE.

关键词： Adaptive Fusion Breast cancer diagnosis Convolutional Neural Networks Ultrasound Images

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mathematical Model of Asset and Liability Management in the Presence of Normative and Internal Constraints

Mathematical Model of Asset and Liability Management in the ...

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International Conference on Control Systems, mathematical modelling, Automation and Energy Efficiency (SUMMA)

作者： Aleksandra Zhukova Anna Flerova Aleksey Chernov Nikolay Pilnik Dept. of Mathematical Modelling of Economic Systems FRC CSC of RAS MIPT Moscow Russian Federation Dept. of Mathematical Modelling of Economic Systems FRC CSC RAS Moscow Russian Federation MIPT-School of Applied Mathematics and Computer Science Moscow Institute of Physics and Technology Moscow Russian Federation

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A Road Map of Prompt Engineering for ChatGPT in Healthcare: A Perspective Study

A Road Map of Prompt Engineering for ChatGPT in Healthcare: ...

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34th Medical Informatics Europe Conference, MIE 2024

作者： Abhari, Shahabeddin Fatahi, Somayeh Saragadam, Ashish Chumachenko, Dmytro Pelegrini Morita, Plinio School of Public Health Sciences University of Waterloo WaterlooON Canada Department of Computer Science University of Saskatchewan SaskatoonSK Canada Department of Mathematical Modelling and Artificial Intelligence National Aerospace University "Kharkiv Aviation Institute" Kharkiv Ukraine Department of Systems Design Engineering University of Waterloo WaterlooON Canada Research Institute for Aging University of Waterloo WaterlooON Canada Centre for Digital Therapeutics Techna Institute University Health Network TorontoON Canada Institute of Health Policy Management and Evaluation Dalla Lana School of Public Health University of Toronto TorontoON Canada

ISBN: (纸本)9781643685335

Generative AI models, such as ChatGPT, have significantly impacted healthcare through the strategic use of prompts to enhance precision, relevance, and ethical standards. This perspective explores the application of prompt engineering to tailor outputs specifically for healthcare stakeholders: patients, providers, policymakers, and researchers. A nine-stage process for prompt engineering in healthcare is proposed, encompassing identifying applications, understanding stakeholder needs, designing tailored prompts, iterative testing and refinement, ethical considerations, collaborative feedback, documentation, training, and continuous updates. A literature review focused on "Generative AI" or "ChatGPT," prompts, and healthcare informed this study, identifying key prompts through qualitative analysis and expert input. This systematic approach ensures that AI-generated prompts align with stakeholder requirements, offering valuable insights into symptoms, treatments, and prevention, thereby supporting informed decision-making among patients. © 2024 The Authors.

关键词： Decision making

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On stable and quasi-chaotic regimes in a one-dimensional unimodal mapping obtained by modeling the dynamics of a biological population 12

On stable and quasi-chaotic regimes in a one-dimensional uni...

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12th International Conference on mathematical Modeling in Physical sciences, IC-MSQUARE 2023

作者： Polyanovsky, V.O. Kamenev, I.G. Laboratory of system biology and computational genetics Vavilov Institute of General Genetics RAS Gubkin Street 3 Moscow119991 Russia Department of Mathematical Modelling of Economic Systems Federal Research Center 'Computer Science and Control RAS Vavilov Street 44-2 Moscow119333 Russia Department of Fundamental Sciences-11 Bauman Moscow State Technical University 2nd Baumanskaya Street 5-1 Moscow05005 Russia

The paper considers the properties of the difference equation describing the dynamics of the animal population, obtained earlier in the framework of studies of tundra communities. We have considered a special case in which the model is represented by a one-parameter difference equation that defines a one-dimensional unimodal mapping of a segment into itself, similar to the well-known triangular (tent) mapping, supplemented by a region with a constant value. A change in the mapping parameter generates a bifurcation scenario, in which stability zones arise, characterized by orbits of a constant period, interspersed with zones with more complicated, "quasi-chaotic" regimes. Based on the properties of the n-iterated triangular mapping, a necessary and sufficient condition for the localization of cyclic orbits in the considered type of unimodal mappings is formulated, which makes it possible to identify stability regions for any given period n. On the basis of this condition an algorithm for detecting stability zones is proposed. The main subject of the study is the fractal properties of the set, which is the complement of the obtained set of stability regions to the entire domain of mapping definition. The dynamics of the DH (n) value is obtained, the limit of which at n → ∞ is equal to the fractal dimension dH. It is shown that in the studied range of n (2 ≤ n ≤ 22), the DH (n) H T = 0, which means that the complement of the set of stability regions consists of isolated points. © 2024 institute of Physics Publishing. All rights reserved.

关键词： Mapping

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SMT-Solving Induction Proofs of Inequalities

arXiv

引用

arXiv 2023年

MSC Codes 68W30This paper accompanies a new dataset of non-linear real arithmetic problems for the SMT-LIB benchmark collection. The problems come from an automated proof procedure of Gerhold–Kauers, which is well suited for solution by SMT. The problems of this type have not been tackled by SMT-solvers before. We describe the proof technique and give one new such proof to illustrate it. We then describe the dataset and the results of benchmarking. The benchmarks on the new dataset are quite different to the existing ones. The benchmarking also brings forward some interesting debate on the use/inclusion of rational functions and algebraic numbers in the SMT-LIB. © 2023, CC BY.

关键词： Rational functions

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