Related papers: Framework of two-dimensional functional walks
This paper examines the relationship between gestures' function and form in design collaboration. It adopts a cognitive design research viewpoint. The analysis is restricted to gesticulations and emblems. The data analysed come from an…
Ideas of Kn\"odel and B\"ohm-Hornik about walks in certain graphs, resembling the classical symmetric random walk on the integers, are combined. All the relevant generating functions (although occasionally quite involved) are made fully…
The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs are…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
Recent years have seen a proliferation of new digital products for the efficient management of indoor spaces, with important applications like emergency management, virtual property showcasing and interior design. These products rely on…
We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which this is based. The framework has no need for coin…
We present short review of two methods for obtaining functional equations for Feynman integrals. Application of these methods for finding functional equations for one- and two- loop integrals is described in detail. It is shown that with…
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…
We explain an array of basic functional analysis puzzles on the way to general spectral flow formulae and indicate a direction of future topological research for dealing with these puzzles.
Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…
Polya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional…
We give a survey and unified treatment of functional integral representations for both simple random walk and some self-avoiding walk models, including models with strict self-avoidance, with weak self-avoidance, and a model of walks and…
We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on $\mathbb{Z}^2$ defined by a fixed step set that is a subset of the non-zero vectors with coordinates 0, 1 or $-1$. We concern ourselves with…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, {global and local} walkers. The global walker chooses a local walker at every step, then the chosen local walker moves a…
In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with…