相关论文: Coding rotations on intervals

A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…

In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.

I discuss the notions of traditional vector length, and suggest defining a complex vector length for complex vectors, as opposed to the traditional Hermitian real length. The advantages of this are shown in the development of rotations…

This paper explores features of an idealized mathematical machine (algorithm) that would be capable of reconstructing the gravitational nature (the multipolar structure or spacetime metric) of a compact object, by observing gravitational…

We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…

The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…

Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…

Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few…

Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…

We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit…

This paper is the extended version of On the Complexity of Infinite Advice Strings (ICALP 2018). We investigate a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a…

A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…

We study infinite words coding an orbit under an exchange of three intervals which have full complexity $\C(n)=2n+1$ for all $n\in\N$ (non-degenerate 3iet words). In terms of parameters of the interval exchange and the starting point of the…

We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…

For a continuous map on a topological graph containing a loop $S$ it is possible to define the degree (with respect to the loop $S$) and, for a map of degree $1$, rotation numbers. We study the rotation set of these maps and the periods of…

We introduce the notion of expandability in the context of automaton semigroups and groups: a word is k-expandable if one can append a suffix to it such that the size of the orbit under the action of the automaton increases by at least k.…

In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, the rotation number does not vary continuously. Each map where one of these discontinuities occurs is itself discontinuous and we can…

Let $\mathfrak{g}$ be an untwisted affine Lie algebra with associated Weyl group $W_a$. To any level 0 weight $\gamma$ we associate a weighted graph $\Gamma_\gamma$ that encodes the orbit of $\gamma$ under the action $W_a$. We show that the…

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…

We examine the itinerary of $0\in S^{1}=\R/\Z$ under the rotation by $\alpha\in\R\bs\Q$. The motivating question is: if we are given only the itinerary of 0 relative to $I\subset S^{1}$, a finite union of closed intervals, can we recover…