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The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…
An efficient algorithm is developed that identifies all independencies implied by the topology of a Bayesian network. Its correctness and maximality stems from the soundness and completeness of d-separation with respect to probability…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…
Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first one, it is a first return map for a circle rotation onto a union of finite number of circle arcs, and by the second one, it…
We propose a minimal multi-agent model for the collective dynamics of opinion formation in the society, by modifying kinetic exchange dynamics studied in the context of income, money or wealth distributions in a society. This model has an…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Every rotationless outer automorphism of a finite rank free group is represented by a particularly useful relative train track map called a CT. The main result of this paper is that the constructions of CTs can be made algorithmic. A key…
We propose a minimal model for the collective dynamics of opinion formation in the society, by modifying kinetic exchange dynamics studied in the context of income, money or wealth distributions in a society. This model has an intriguing…
Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The…
We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems. Using the algorithm, we obtain the set of all possible greedy solutions and…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the…
We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…