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Video
Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (19271, founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals, as time elapsed after infection. During the 70s, many mathematical studies were developed when equations are structured by age, size, more generally a physiological trait. The renewal, growth-fragmentation are the more standard equations. The talk will present structured equations, show that a universal generalized relative entropy structure is available in the linear case, which imposes relaxation to a steady state under non-degeneracy conditions. In the nonlinear cases, it might be that periodic solutions occur, which can be interpreted in biological terms, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance (called Fortet-Mourier distance) also gives a general non-expansion property of solutions.
Event date: 19/1/2023
Speaker: Prof. Benoît Perthame (Sorbonne University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics and Biology
- Keywords:
- Biomathematics Equations
- Resource Type:
- Video
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e-journal
In this journal platform, you can find the articles which published under the Creative Commons Attribution-NonCommercial 4.0 International License. The journal covers a various disciplines, including:
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- Chemistry Management Environmental sciences Physics Industrial management Mathematics Social Sciences Engineering Humanities Computer science Biology
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- e-journal
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e-journal
Maxwell Scientific Publication Corp. operates as an independent science and technology publisher with a global reputation for quality products and services to contribute to the advancement of research knowledge. In this journal platform, you can find the articles which published under the open license. The journal including the disciplines:
Agricultural Sciences
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- Food industry trade Economics Social sciences Statistics Science Agriculture Technology Food science Fisheries Industrial management Mathematics Periodicals Life sciences Dairying Engineering Environmental sciences Aquatic sciences Information technology Medicine
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- e-journal
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In this journal platform, you can find the articles which published under the open license. The journal including the disciplines:
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In this journal platform, you can find the articles which published under the open license. The journal including the disciplines:
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Estonian Academy Publishers issues seven open access scientific journals, peer-reviewed, indexed and abstracted in international review publications and databases. All journals have an international Editorial board. Publications of the Estonian Academy Publishers cover almost all important areas of contemporary science. Our journals are peer reviewed and recognized by the Estonian Research Council and the Estonian Committee of Science Compentence as journals meeting international scientific standards.
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- Mathematics and Statistics, Chemistry, Archeology, Environmental Sciences, Biology, Physics, and Foreign Language Learning
- Keywords:
- Chemistry Uralic languages Social sciences Science History Technology Archaeology Physics Mathematics Geology Periodicals Ecology Humanities Engineering Europe -- Baltic Sea Region
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Courseware
This course is intended for both mathematics and biology undergrads with a basic mathematics background, and consists of an introduction to modeling biological problems using continuous ODE methods (rather than discrete methods as used in 113A). We describe the basic qualitative behavior of dynamical systems in the context of a simple population model and, as time allows, introduce other types of models such as chemical reactions inside the cell or excitable systems leading to oscillations and neuronal signals. Certain topics from linear algebra that are needed for this course are presented as well, so a linear algebra prerequisite is not necessary.
- Subjects:
- Mathematics and Statistics and Biology
- Keywords:
- Biology -- Mathematical models
- Resource Type:
- Courseware
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Courseware
Provides students with the basic tools for analyzing experimental data, properly interpreting statistical reports in the literature, and reasoning under uncertain situations. Topics organized around three key theories: Probability, statistical, and the linear model. Probability theory covers axioms of probability, discrete and continuous probability models, law of large numbers, and the Central Limit Theorem. Statistical theory covers estimation, likelihood theory, Bayesian methods, bootstrap and other Monte Carlo methods, as well as hypothesis testing, confidence intervals, elementary design of experiments principles and goodness-of-fit. The linear model theory covers the simple regression model and the analysis of variance. Places equal emphasis on theory, data analyses, and simulation studies.
- Subjects:
- Mathematics and Statistics and Biology
- Keywords:
- Cognitive science Statistics
- Resource Type:
- Courseware
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Courseware
With the growing availability and lowering costs of genotyping and personal genome sequencing, the focus has shifted from the ability to obtain the sequence to the ability to make sense of the resulting information. This course is aimed at exploring the computational challenges associated with interpreting how sequence differences between individuals lead to phenotypic differences in gene expression, disease predisposition, or response to treatment.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Biology
- Keywords:
- Genomes Genomics
- Resource Type:
- Courseware