The simplest model of this form is for the graph bisection problem. This is the problem of partitioning the vertices of a graph into two equal-sized sets while minimizing the number of edges bridging the sets. To create an instance of the planted bisection problem, we first choose a paritition of the vertices into equal-sized sets V 1 and V 2. When then choose probabilities p > q, and place edg...

Business process models extracted from real event data via process mining are often visually complex and hard to interpret, cannot easily display all of the relevant process data in one view, and are of unknown quality. It is therefore difficult to present a meaningful comparison of two mined process models, for example to confirm business changes have had a significant effect. We propose a fra...

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

In this paper we view interleaved Gabidulin codes and describe how to correct errors up to a rank equal to the amount of redundancy of the code with high probability. We give a detailed proof for our estimation of the probability of correct decoding. In a second part, we view the application to variants of the GPT cryptosystem. For GGPT this leads to an efficient attack on the remaining secure ...

The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically. ∗ First appeared in J. Stat. Physics 98, Nos. 1/2, pp. 131–244, 2000

The lattice of the set partitions of [n] ordered by refinement is studied. Suppose r partitions p1, . . . , pr are chosen independently and uniformly at random. The probability that the coarsest refinement of all pi ’s is the finest partition {1}, . . . , {n} is shown to approach 0 for r = 2, and 1 for r ≥ 3. The probability that the finest coarsening of all pi ’s is the one-block partition is ...

We give an algorithm that, with high probability, recovers a planted k-partition in a random graph, where edges within vertex classes occur with probability p and edges between vertex classes occur with probability r ≥ p + c √ p log n/n. The algorithm can handle vertex classes of different sizes and, for fixed k, runs in linear time. We also give variants of the algorithm for partitioning matri...

Let T be a given tree. Each vertex of T is either a supply vertex or a demand vertex, and is assigned a positive number, called the supply or demand. Each demand vertex v must be supplied an amount of “power,” equal to the demand of v, from exactly one supply vertex through edges in T . Each edge is assigned a positive number called the capacity. One wishes to partition T into subtrees by delet...