Related papers: Dispersed Dyck paths revisited
This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.
Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.
We introduce weighted succession rules and parametric production matrices - simple extensions of the standard ECO method succession rules and production matrices. The purpose is to enumerate combinatorial objects with respect to several…
We consider the Busemann process in planar directed first passage percolation. We extend existing techniques to establish the existence of the process in our setting and determine its distribution in a number of integrable models. As…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete…
This is a survey of the exciting recent progress made in understanding the complexity of distributed subgraph finding problems. It overviews the results and techniques for assorted variants of subgraph finding problems in various models of…
The problem of identifying the k-shortest paths (KSPs for short) in a dynamic road network is essential to many location-based services. Road networks are dynamic in the sense that the weights of the edges in the corresponding graph…
Originally proposed by Duffy et al., Diffusion is a variant of chip-firing in which chips from flow from places of high concentration to places of low concentration. In the variant, Perturbation Diffusion, the first step involves a…
We consider an ensemble of $N$ discrete nonintersecting paths starting from equidistant points and ending at consecutive integers. Our first result is an explicit formula for the correlation kernel that allows us to analyze the process as…
We interpret walks in the first quadrant with steps {(1,1),(1,0),(-1,0), (-1,-1)} as a generalization of Dyck words with two sets of letters. Using this language, we give a formal expression for the number of walks in the steps above…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
We suggest a new hardcore Poisson-type distribution for Young diagrams with the row lengths from some finite list. A discrete variant of the time-ordered Mat\'{e}rn II process in 1D is employed. This approach is related to that based on the…
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…
A constrained diffusive random walk of n steps and a random flight in Rd, which can be expressed in the same terms, were investigated independently in recent papers. The n steps of the walk are identically and independently distributed…
A new package, DISPred, is described. The package can be used to calculate ep deep inelastic scattering cross sections at Born level in Electroweak theory and at both leading and next-to-leading order in QCD.
A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to…
Given an undirected $n$-vertex graph and $k$ pairs of terminal vertices $(s_1,t_1), \ldots, (s_k,t_k)$, the $k$-Disjoint Shortest Paths ($k$-DSP)-problem asks whether there are $k$ pairwise vertex-disjoint paths $P_1,\ldots, P_k$ such that…
We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, strengthening an analogous result in the random setting by…