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Reaction system is a computing model inspired by the biochemical interaction taking place within the living cells. Various extended or modified frameworks motivated by biological, physical, or purely mathematically considerations have been…
Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model…
In this paper we define a notion of automatic randomness tests (ART) which capture measure theoretic typicalness of infinite binary sequences within the framework of automata theory. An individual ART is found to be equivalent to a…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology,…
For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
In this thesis we present a mathematical model describing the population dynamics of molecules in an artificial chemistry where large molecules can be produced by successive ligation of pairs of smaller molecules. The chemistry contains a…
Life is commonly described as a self-organized, far-from-equilibrium process that maintains internal order by consuming free energy and exporting entropy. This thermodynamic view underlies diverse theoretical frameworks -- from autopoiesis…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Random Boolean networks (RBNs) are models of genetic regulatory networks. It is useful to describe RBNs as self-organizing systems to study how changes in the nodes and connections affect the global network dynamics. This article reviews…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
Coupled chemical interactions in a well-mixed solution are commonly formalized as chemical reaction networks (CRNs). However, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs…
Autopilot is a system designed to guide a vehicle without aid. Due to increase in flight hours and complexity of modern day flight it has become imperative to equip the aircrafts with autopilot. Thus reliability and consistency of an…
This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high…
There is an abundance of complex dynamic systems that are critical to our daily lives and our society but that are hardly understood, and even with today's possibilities to sense and collect large amounts of experimental data, they are so…
We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a…
Self-projective sets are natural fractal sets which describe the action of a semigroup of matrices on projective space. In recent years there has been growing interest in studying the dimension theory of self-projective sets, as well as…
This article aims to describe and explain the theoretical foundations of concurrent and set concurrent algorithms, considering an asynchronous shared memory system where any number of processes can crash. Verification of concurrent…