Related papers: Mathematic principles underlying genetic structure…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
I propose here a new concept of information based on two relevant aspects of its expression. The first related to the undeniable fact that the expression of information modifies the physical state of its receiver. The second to the…
A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently,…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…
The fields of computing and biology have begun to cross paths in new ways. In this paper a review of the current research in biological computing is presented. Fundamental concepts are introduced and these foundational elements are explored…
Stochastic networks represent very important subject of research because they have been found in almost all branches of modern science, including also sociology and economy. We provide a information theory point of view, mostly based on its…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
Genomics methods have uncovered patterns in a range of biological systems, but obscure important aspects of cell behavior: the shape, relative locations of, movement of, and interactions between cells in space. Spatial technologies that…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
Everyone can see that over the last 150 years, theoretical ecology has become considerably more mathematical. But what is the nature of this phenomenon? Are mathematics applied, as in the use of statistical tests, for example, or are they…
Graphs are central to the chemical sciences, providing a natural language to describe molecules, proteins, reactions, and industrial processes. They capture interactions and structures that underpin materials, biology, and medicine. This…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
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…
Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…