Related papers: Minimum length RNA folding trajectories

In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

We consider the design of sublinear space and query complexity algorithms for estimating the cost of a minimum spanning tree (MST) and the cost of a minimum traveling salesman (TSP) tour in a metric on $n$ points. We first consider the…

To find a shortest path between two nodes $s_0$ and $s_1$ in a given graph, a classical approach is to start a Breadth-First Search (BFS) from $s_0$ and run it until the search discovers $s_1$. Alternatively, one can start two Breadth-First…

Several algorithms for RNA inverse folding have been used to design synthetic riboswitches, ribozymes and thermoswitches, whose activity has been experimentally validated. The RNAiFold software is unique among approaches for inverse folding…

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be…

Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…

The shortest distance between the first $n$ iterates of a typical point can be quantified with a log rule for some dynamical systems admitting Gibbs measures. We show this in two settings. For topologically mixing Markov shifts with at most…

The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization…

Understanding the principles of protein folding is a cornerstone of computational biology, with implications for drug design, bioengineering, and the understanding of fundamental biological processes. Lattice protein folding models offer a…

In 2012, Pflug and Pichler proved, under regularity assumptions, that the value function in Multistage Stochastic Programming (MSP) is Lipschitz continuous w.r.t. the Nested Distance, which is a distance between scenario trees (or discrete…

We investigate the dependence of the approximation capacity of deep residual networks on its depth in a continuous dynamical systems setting. This can be formulated as the general problem of quantifying the minimal time-horizon required to…

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…

The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that…

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This…

Tree rearrangements such as Nearest Neighbor Interchange (NNI) and Subtree Prune and Regraft (SPR) are commonly used to explore phylogenetic treespace. Computing distances based on them, however, is often intractable, so the efficiently…

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating…

Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…

Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict studies in…