Related papers: Algebraic double cut and join -- A group-theoretic…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…
We propose a new compression scheme for genomic data given as sequence fragments called reads. The scheme uses a reference genome at the decoder side only, freeing the encoder from the burdens of storing references and performing…
We propose a 3D convolutional neural network to simultaneously segment and detect cell nuclei in confocal microscopy images. Mirroring the co-dependency of these tasks, our proposed model consists of two serial components: the first part…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
The perceptual-based grouping process produces a hierarchical and compositional image representation that helps both human and machine vision systems recognize heterogeneous visual concepts. Examples can be found in the classical…
De novo genome assembly, i.e., rebuilding the sequence of an unknown genome from redundant and erroneous short sequences, is a key but computationally intensive step in many genomics pipelines. The exponential growth of genomic data is…
Medical image segmentation is a crucial method for assisting professionals in diagnosing various diseases through medical imaging. However, various factors such as noise, blurriness, and low contrast often hinder the accurate diagnosis of…
It is crucial to provide real-time performance in many applications, such as interactive and exploratory data analysis. In these settings, users often need to view subsets of query results quickly. It is challenging to deliver such results…
In mammalian cells, repair centers for DNA double-strand breaks (DSBs) have been identified. However, previous researches predominantly rely on methods that induce specific DSBs by cutting particular DNA sequences. The clustering and its…
We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…
This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…
Cellular Electron Cryo-Tomography (CECT) is a powerful imaging technique for the 3D visualization of cellular structure and organization at submolecular resolution. It enables analyzing the native structures of macromolecular complexes and…
Deep convolutional neural networks (CNNs) have been intensively used for multi-class segmentation of data from different modalities and achieved state-of-the-art performances. However, a common problem when dealing with large, high…
In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…
When applying automatic analysis of fluorescence or histopathological images of cells, it is necessary to partition, or de-clump, partially overlapping cell nuclei. In this work, I describe a method of partitioning partially overlapping…
Over the past two decades, machine analysis of medical imaging has advanced rapidly, opening up significant potential for several important medical applications. As complicated diseases increase and the number of cases rises, the role of…
Deep neural network is a powerful tool for many tasks. Understanding why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past years. In the literature of…