相关论文: Characterization of circular D0L systems

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…

The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial…

This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-counting function N(T), for radius T, is finite for all T is…

Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play a central role, and the schedule of entities update is a priori unknown. This article presents…

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not…

We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…

In 1970, Donald Ornstein proved a landmark result in dynamical systems, viz., two Bernoulli systems with the same entropy are isomorphic except for a measure 0 set. Keane and Smorodinsky gave a finitary proof of this result. They also…

In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because…

A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along with several results for infinite classes of cyclic codes with $t=2$ and $t=3$. From these, a theoretically justification of…

Sequence rotation consists of a circular shift of the sequence's elements by a given number of positions. We present the four classic algorithms to rotate a sequence; the loop invariants underlying their correctness; detailed correctness…

Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs…

Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…

We present a circular and cut-free proof system for the hybrid mu-calculus and prove its soundness and completeness. The system uses names for fixpoint unfoldings, like the circular proof system for the mu-calculus previously developed by…

In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed…

We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…

The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…

Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, acto-myosin filaments and microtubule bundles are active…

We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.

In this paper, we introduce the notion of circular orderability for quandles. We show that the set all right (respectively left) circular orderings of a quandle is a compact topological space. We also show that the space of right…