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The origin of macroscopic complexity is traced in a wide range of systems (imunology, ecology, finance, marketing, etc) to the discrete and auto-catalytic (i.e. multiplicative) character of their elementary components. Even in the simplest…
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
Electric circuits manipulate electric charge and magnetic flux via a small set of discrete components to implement useful functionality over continuous time-varying signals represented by currents and voltages. Much of the same…
In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed…
Nature has found one method of organizing living matter, but maybe other options exist -- not yet discovered -- on how to create life. To study the life "as it could be" is the objective of an interdisciplinary field called Artificial Life…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the…
We give a self-contained introduction to the theory of directed graphs, leading up to the relationship between the Perron-Frobenius eigenvectors of a graph and its autocatalytic sets. Then we discuss a particular dynamical system on a fixed…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
Autocatalysis is thought to have played an important role in the earliest stages of the origin of life. An autocatalytic cycle (AC) is a set of reactions that results in stoichiometric increase in its constituent chemicals. When the…
This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure,…
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…
High-throughput data acquisition in synthetic biology leads to an abundance of data that need to be processed and aggregated into useful biological models. Building dynamical models based on this wealth of data is of paramount importance to…
A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self-organizes into an…
Automated Fact-Checking (AFC) is the automated verification of claim accuracy. AFC is crucial in discerning truth from misinformation, especially given the huge amounts of content are generated online daily. Current research focuses on…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the…
Specifying the intended behaviour of autonomous systems is becoming increasingly important but is fraught with many challenges. This technical report provides an overview of existing work on specifications of autonomous systems and places a…