Related papers: Automatic discovery of structural rules of permuta…

The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite…

The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to…

We present a principled approach to uncover the structure of visual data by solving a novel deep learning task coined visual permutation learning. The goal of this task is to find the permutation that recovers the structure of data from…

Recent research has examined algorithms to minimize robots' resource footprints. The class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods for reducing their space…

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this…

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…

We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially…

This work presents a new meta-heuristic approach to select the structure of polynomial NARX models for regression and classification problems. The method takes into account the complexity of the model and the contribution of each term to…

We study aspects of the enumeration of permutation classes, sets of permutations closed downwards under the subpermutation order. First, we consider monotone grid classes of permutations. We present procedures for calculating the generating…

We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-machines generate, and how these systems of…

Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…

This note contributes to the structure theory of abstract rigidity matroids in general dimension. In the spirit of classical matroid theory, we prove several cryptomorphic characterizations of abstract rigidity matroids (in terms of…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

We present a new approach to the problem of enumerating permutations of length n that avoid a fixed consecutive pattern of length m. We use this idea to give explicit upper and lower bounds on the number of permutations avoiding a pattern…

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

We argue that the selective inclusion of data points based on latent objectives is common in practical situations, such as music sequences. Since this selection process often distorts statistical analysis, previous work primarily views it…

Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure,…