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In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the…

Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…

The mechanism and driving forces of chromosome segregation in the bacterial cell cycle of E. coli is one of the least understood events in its life cycle. Using principles of entropic repulsion between polymer loops confined in a cylinder,…

We consider a distributed detection system with communication constraints, where several nodes are arranged in an arbitrary tree topology, under the assumption of conditionally independent observations. We propose a cyclic design procedure…

Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…

The interplay of topological constraints and persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three dimensional lattice model. We ask if the results are consistent with…

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform…

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings,…

Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like…

Manifold alignment is a type of data fusion technique that creates a shared low-dimensional representation of data collected from multiple domains, enabling cross-domain learning and improved performance in downstream tasks. This paper…

Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…

We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…

We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of…

New machine learning based algorithms have been developed and tested for Monte Carlo integration based on generative Boosted Decision Trees and Deep Neural Networks. Both of these algorithms exhibit substantial improvements compared to…

Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group method could handle the system in…