Related papers: A steepest descent calculation of RNA pseudoknots
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
Spiking neural networks (SNNs) have closer dynamics to the brain than current deep neural networks. Their low power consumption and sample efficiency make these networks interesting. Recently, several deep convolutional spiking neural…
In this paper we study canonical $\gamma$-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A $\gamma$-structure is composed by specific building…
Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. To tackle…
We investigate theoretically the translocation of structured RNA/DNA molecules through narrow pores which allow single but not double strands to pass. The unzipping of basepaired regions within the molecules presents significant kinetic…
We show that computing the minimum rank of a sign pattern matrix is NP hard. Our proof is based on a simple but useful connection between minimum ranks of sign pattern matrices and the stretchability problem for pseudolines arrangements. In…
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality…
Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented through graph theory, using edges to model strands of DNA joined at junctions, represented by vertices. Because guided…
In the study of grain-surface chemistry in the interstellar medium, there exists much uncertainty regarding the reaction mechanisms with few constraints on the abundances of grain-surface molecules. Bayesian inference can be performed to…
The representation of knots by petal diagrams (Adams et al. 2012) naturally defines a sequence of distributions on the set of knots. In this article we establish some basic properties of this randomized knot model. We prove that in the…
We give some new advances in the research of the maximum number of triangles that we may obtain in a simple arrangements of n lines or pseudo-lines.
The Human Genome Project has led to an exponential increase in data related to the sequence, structure, and function of biomolecules. Bioinformatics is an interdisciplinary research field that primarily uses computational methods to analyze…
Accurate RNA structure modeling remains difficult because RNA backbones are highly flexible, non-canonical interactions are prevalent, and experimentally determined 3D structures are comparatively scarce. We introduce \emph{RiboSphere}, a…
We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two…
The structure of the light proton and neutron rich nuclei is studied in a microscopic multicluster model using the stochastic variational method. This approach enables us to describe the weakly bound nature of these nuclei in a consistent…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
We introduce a computational topology-based approach with unsupervised machine-learning algorithms to estimate the database size and content of RNA-like graph topologies. Specifically, we apply graph theory enumeration to generate all…
In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…
This document is a contribution to the proceedings of the MathemAmplitudes 2019 conference held in December 2019 in Padova, Italy. A key step in modern high energy physics scattering amplitudes computation is to express the latter in terms…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…