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These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…

Analysis of PDEs · Mathematics 2010-12-23 Kay Jachmann , Jens Wirth

Even though a few initial works have shown on small sets of data some level of bias in the performance of fingerprint recognition technology with respect to certain demographic groups, there is still not sufficient evidence to understand…

Computer Vision and Pattern Recognition · Computer Science 2024-10-07 Javier Galbally , Aleksandrs Cepilovs , Ramon Blanco-Gonzalo , Gillian Ormiston , Oscar Miguel-Hurtado , Istvan Sz. Racz

Human kinematics is of fundamental importance for rehabilitation and assistive robotic systems that physically interact with human. The wrist plays an essential role for dexterous human-robot interaction, but its conventional kinematic…

Robotics · Computer Science 2020-02-17 Ningbo Yu , Chang Xu

Several families of continual learning techniques have been proposed to alleviate catastrophic interference in deep neural network training on non-stationary data. However, a comprehensive comparison and analysis of limitations remains…

Machine Learning · Computer Science 2021-12-14 Timm Hess , Martin Mundt , Iuliia Pliushch , Visvanathan Ramesh

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…

We present magnetic fingerprints; an input technique for mobile touchscreen devices that uses a small magnet attached to a user's fingernail in order to differentiate between a normal touch and a magnetic touch. The polarity of the magnet…

Human-Computer Interaction · Computer Science 2015-01-15 Halim Cagri Ates , Ilias Apostolopoulos , Eelke Folmer

The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing

This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…

Neural and Evolutionary Computing · Computer Science 2020-05-29 Andrei Ivanov , Uwe Iben , Anna Golovkina

The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…

Quantum Physics · Physics 2007-05-23 E. C. G. Sudarshan

Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…

Quantum Physics · Physics 2013-11-19 P. Schindler , M. Müller , D. Nigg , J. T. Barreiro , E. A. Martinez , M. Hennrich , T. Monz , S. Diehl , P. Zoller , R. Blatt

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase…

Quantitative Methods · Quantitative Biology 2015-07-31 Adam L. MacLean , Heather A. Harrington , Michael P. H. Stumpf , Helen M. Byrne

This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…

chao-dyn · Physics 2008-02-03 Allen Back , John Guckenheimer , Mark Myers

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…

Adaptation and Self-Organizing Systems · Physics 2012-10-19 Anirban Banerjee , Jürgen Jost

An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…

Classical Analysis and ODEs · Mathematics 2007-05-23 V. A. Savva , V. I. Zelenkov , A. S. Mazurenko

Blood system functions are very diverse and important for most processes in human organism. One of its primary functions is matter transport among different parts of the organism including tissue supplying with oxygen, carbon dioxide…

Biological Physics · Physics 2007-12-31 A. S. Kholodov , S. S. Simakov , Y. A. Kholodov , A. A. Nadolsky , A. N. Shushlebin

Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…

Dynamical Systems · Mathematics 2025-11-05 Harry Dankowicz , Jan Sieber

The optimal fingerprint method serves as a potent approach for detecting and attributing climate change. However, its experimental validation encounters challenges due to the intricate nature of climate systems. Here, we experimentally…

Atmospheric and Oceanic Physics · Physics 2025-05-13 Jinbo Hu , Hong Yuan , Letian Chen , Nan Zhao , C. P. Sun

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…

Mathematical Physics · Physics 2022-06-20 Evan Patterson , Andrew Baas , Timothy Hosgood , James Fairbanks

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with a…

Materials Science · Physics 2020-04-10 Pablo M. Piaggi , Michele Parrinello