Related papers: Rapid growth sequences
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
Spider silks are remarkable materials characterized by superb mechanical properties such as strength, extensibility and lightweightedness. Yet, to date, limited models are available to fully explore sequence-property relationships for…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
A widely studied model for generating sequences is to ``evolve'' them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally ``far apart'' in terms of variational distance.
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…
We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic…
Sequential pattern discovery is a well-studied field in data mining. Episodes are sequential patterns describing events that often occur in the vicinity of each other. Episodes can impose restrictions to the order of the events, which makes…
The purpose of this note is to verify that the results attained in [6] admit an extension to the multidimensional setting. Namely, for subsets of the two dimensional torus we find the sharp growth rate of the step(s) of a generalized…
In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with…
In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of…
The aim of this work is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite time.
We extend the recent latent recurrent modeling to sequential input streams. By interleaving fast, recurrent latent updates with self-organizational ability between slow observation updates, our method facilitates the learning of stable…
Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…
We present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one-, two- and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families…
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…
Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating phylogenetic parameters for a fixed number of species as we increase the number of characters. However, as sequences are often of fixed length…