Math

Browse all posts in the Math category.

37 to 42 of 82

27JUN 2023
Math
Null controllability for population dynamics with age, size structuring and diffusion
Null controllability for population dynamics with age, size structuring and diffusion 1. Motivation and description of age, size structured model 1.1. Motivation Knowing the mechanisms of tumor growth can be useful for developing treatments. To mathematically describe its evolution from a global point of view, we can use a so-called “diffusion” equation. Diffusion equations are […]
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03MAY 2023
Math
Breaking the symmetry with Robin boundary conditions
Breaking the symmetry with Robin boundary conditions Introduction Establishing symmetry properties of solutions to differential equations is a very important task in mathematical analysis, both from the theoretical point of view and for applications. Indeed, partial differential equations arise in modeling many phenomena in physics, mechanics, and so on. A first question that arises quite […]
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01APR 2023
Math
Convolutional autoencoders for very low-dimensional parametrizations of nonlinear fluid flow
Convolutional autoencoders for very low-dimensional parametrizations of nonlinear fluid flow 1. Introduction The control of large-dimensional nonlinear dynamical systems is a challenging task because of the 1. system’s size that means a high demand in computational resources 2. and the nonlinearity that adds model inherent complexity to be resolved by the controller. As long as […]
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13MAR 2023
Math
Torsional Rigidity: Classical and new results
Torsional Rigidity: Classical and new results Torsional rigidity is a key quantity to characterize how a beam responds to applied forces. The higher the torsional rigidity, the harder it is to deform the beam. A natural question arises: which shape for the beam’s cross section yields the highest torsional rigidity? The answer was conjectured to […]
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20DEC 2022
Hub
Federated Learning: Protect your data and privacy
Federated Learning: Protect your data and privacy Code: A basic PyTorch implementation of the FedAvg algorithm (GitHub) Federated Learning is becoming an increasingly popular topic in machine learning. But what is it, and why do we need it? To explain what the excitement is all about, this post outlines the basics of Federated Learning and […]
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14DEC 2022
Math
Breaking the curse of dimensionality with Barron spaces
Breaking the curse of dimensionality with Barron spaces 1 Introduction Recent advances in computational hardware have enabled the implementation of the set of algorithmic methods known as Deep Learning, whose development nevertheless dates back several decades. In this way, they have emerged in the latest years as the main tool in many practical Machine Learning […]
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