Related papers: A Markov Chain Sampler for Plane Curves

Sampling-based path planning is a widely used method in robotics, particularly in high-dimensional state space. Among the whole process of the path planning, collision detection is the most time-consuming operation. In this paper, we…

A number of problems in a variety of fields are characterised by target distributions with a multimodal structure in which the presence of several isolated local maxima dramatically reduces the efficiency of Markov Chain Monte Carlo…

Two isomorphic graphs can have inequivalent spatial embeddings in 3-space. In this way, an isomorphism class of graphs contains many spatial graph types. A common way to measure the complexity of a spatial graph type is to count the minimum…

In the classical knot theory there is a well-known notion of descending diagram. From an arbitrary diagram one can easily obtain, by some crossing changes, a descending diagram which is a diagram of the unknot or unlink. In this paper the…

With sufficient time, double edge-swap Markov chain Monte Carlo (MCMC) methods are able to sample uniformly at random from many different and important graph spaces. For instance, for a fixed degree sequence, MCMC methods can sample any…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great…

We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from (a x b x c) to ((a-1) x (b+1) x c) or ((a+1) x (b-1) x c). Algorithmic realization of…

In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…

Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box…

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use…

We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…

We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…

Knotted molecules occur naturally and are designed by scientists to gain special biological and material properties. Understanding and utilizing knotting require efficient methods to recognize and generate knotted structures, which are…

Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

This paper considers the task of connecting points on a piece of paper by drawing a curve between each pair of them. Under mild assumptions, we prove that many pairwise disjoint curves are unavoidable if either of the following rules is…

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…

To solve the problems in measuring coefficient of skewness related to extreme value, irregular distance from the middle point and distance between two consecutive numbers, "Rank skewness" a new measure of the coefficient of skewness has…