Related papers: Algebraic double cut and join -- A group-theoretic…
In medicine, visualizing chromosomes is important for medical diagnostics, drug development, and biomedical research. Unfortunately, chromosomes often overlap and it is necessary to identify and distinguish between the overlapping…
The three dimensional structure of DNA in the nucleus (chromatin) plays an important role in many cellular processes. Recent experimental advances have led to high-throughput methods of capturing information about chromatin conformation on…
Though performed almost effortlessly by humans, segmenting 2D gray-scale or color images into respective regions of interest (e.g.~background, objects, or portions of objects) constitutes one of the greatest challenges in science and…
The string splicing was introduced by Tom Head which stands as an abstract model for the DNA recombination under the influence of restriction enzymes. The complex chemical process of three dimensional molecules in three dimensional space…
In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk (coupling two or more pathways) or inhibiting molecular…
In 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to the class of digraphs and generalized several results for vertex colorings in digraphs. Although, as a consequence of these results, a digraph can be obtained by…
Multiple genome alignment remains a challenging problem. Effects of recombination including rearrangement, segmental duplication, gain, and loss can create a mosaic pattern of homology even among closely related organisms. We describe a…
Deep convolutional neural networks (CNNs) have emerged as a new paradigm for Mammogram diagnosis. Contemporary CNN-based computer-aided-diagnosis (CAD) for breast cancer directly extract latent features from input mammogram image and ignore…
The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well…
The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian…
In this paper, we propose a deep evolutionary learning (DEL) process that integrates fragment-based deep generative model and multi-objective evolutionary computation for molecular design. Our approach enables (1) evolutionary operations in…
Previous divide-and-conquer segmentation analyses of DNA sequences do not provide a satisfactory stopping criterion for the recursion. This paper proposes that segmentation be considered as a model selection process. Using the tools in…
We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping…
Deep graph clustering, which aims to reveal the underlying graph structure and divide the nodes into different groups, has attracted intensive attention in recent years. However, we observe that, in the process of node encoding, existing…
This paper explores convolutional generative networks as an alternative to iterative reconstruction algorithms in medical image reconstruction. The task of medical image reconstruction involves mapping of projection main data collected from…
The fall of prices of the high-throughput genome sequencing changes the landscape of modern genomics. A number of large scale projects aimed at sequencing many human genomes are in progress. Genome sequencing also becomes an important aid…
A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…
We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum…