Related papers: myPhysmatics: Connected Mathematical Models in Phy…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
Mixed-effect models are flexible tools for researchers in a myriad of fields, but that flexibility comes at the cost of complexity and if users are not careful in how their model is specified, they could be making faulty inferences from…
The ability to explain decisions made by machine learning models remains one of the most significant hurdles towards widespread adoption of AI in highly sensitive areas such as medicine, cybersecurity or autonomous driving. Great interest…
More than hundred years ago the 'classic physics' was it in its full power, with just a few unexplained phenomena; which however led to a revolution and the development of the 'modern physics'. Today the computing is in a similar position:…
Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction…
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…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
Knitting turns yarn, a 1D material, into a 2D fabric that is flexible, durable [1], and can be patterned to adopt a wide range of 3D geometries [2]. Like other mechanical metamaterials [3], the elasticity of knitted fabrics is an emergent…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
A scientometric analysis has been performed on selected physics journals to estimate the presence of simulation and modeling in physics literature in the past fifty years. Correlations between the observed trends and several social and…
The Theory of Functional Connections (TFC) is most often used for constraints over the field of real numbers. However, previous works have shown that it actually extends to arbitrary fields. The evidence for these claims is restricting…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…