相关论文: Numerical Calculations Using Maple: Why & How?
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
We present the CAPD::DynSys library for rigorous numerical analysis of dynamical systems. The basic interface is described together with several interesting case studies illustrating how it can be used for computer-assisted proofs in…
PLUMED is an open-source software package that is widely used for analyzing and enhancing molecular dynamics simulations that works in conjunction with most available molecular dynamics softwares. While the computational cost of PLUMED…
It is the aim of this work to identify and illustrate the potential and weaknesses of the computer algebra system Maple in the area of the Calculus of Variations: a classical area of mathematics that studies the methods for finding maximum…
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, characterizing spike patterns in the resulting data, and linking…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
Starting from the basic level of mathematica here we illustrate how to use a mathematica notebook and write a program in the notebook. Next, we investigate elaborately the way of linking of external programs with mathematica, so-called the…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The Python colorspace package provides a toolbox for mapping between different color spaces which can then be used to generate a wide range of perceptually-based color palettes for qualitative or quantitative (sequential or diverging)…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
We develop the Mechanic package, which is a new numerical framework for dynamical astronomy. The aim of our software is to help in massive numerical simulations by efficient task management and unified data storage. The code is built on top…
Coordination protocols help programmers of distributed systems reason about the effects of transactions on the state of the system, but they're not cheap. Coordination protocols may involve multiple rounds of communication, which can hurt…
A unified mathematical language for medicine and science will be presented. Using this language, models for DNA replication, protein synthesis, chemical reactions, neurons and a cardiac cycle of a heart have been built. Models for Turing…
We present the Populus toolkit for exploring the dynamics of mass action systems under different assumptions.
Information technologies for studying physical-mathematical disciplines on base of mathematical modeling in the computer algebra system Maple are described.