相关论文: The degree distribution in bipartite planar maps: …

The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…

We address the enumeration of q-coloured planar maps counted bythe number of edges and the number of monochromatic edges. We prove that the associated generating function is differentially algebraic,that is, satisfies a non-trivial…

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…

This article studies the sequence of iterative degrees of a birational map of the plane. This sequence is known either to be bounded or to have a linear, quadratic or exponential growth. The classification elements of infinite order with a…

We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…

We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply,…

In the open map approach to bisimilarity, the paths and their runs in a given state-based system are the first-class citizens, and bisimilarity becomes a derived notion. While open maps were successfully used to model bisimilarity in…

We show that the edges of any planar graph of maximum degree at most $9$ can be partitioned into $4$ linear forests and a matching. Combined with known results, this implies that the edges of any planar graph $G$ of odd maximum degree…

Spanning trees of complete bipartite graphs exhibit a rich interaction between degree sequences and graph structure. In this paper, we obtain lower bounds on the number of isomorphism classes of spanning trees in $K_{a,b}, 2 \leq a \leq b$…

Let S and T be vectors of positive integers with the same sum. We study the uniform distribution on the space of simple bipartite graphs with degree sequence S in one part and T in the other; equivalently, binary matrices with row sums S…

This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights…

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…

Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have…

The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…

Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…

In this article bipartite planar graphs St_r are investigated, r the number of their plane regions. Bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to such graphs are discussed. We prove that…

We consider special cases of the two tree degree sequences problem. We show that if two tree degree sequences do not have common leaves then they always have edge-disjoint caterpillar realizations. By using a probabilistic method, we prove…

We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost…

Let B_{2t} be a bipartite planar graph with an even number of regions. We are able to find bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to the graph. We also will investigate the minimal…