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The genetic code is the function from the set of codons to the set of amino acids by which a DNA sequence encodes proteins. Since the codons also influence the shape of the DNA molecule itself, the same sequence that encodes a protein also…
Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…
Recent observations have revealed that dust is widespread and abundant in galaxies up to $z\,{\backsimeq}\,8$, significantly influencing their appearance and spectral properties. In the early Universe, dust is thought to form primarily in…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
Identity-by-descent (IBD) is a fundamental concept in genetics with many applications. In a common definition, two haplotypes are said to contain an IBD segment if they share a segment that is inherited from a recent shared common ancestor…
We introduce an approach to integrate segmentation information within a convolutional neural network (CNN). This counter-acts the tendency of CNNs to smooth information across regions and increases their spatial precision. To obtain…
Data duplication during pretraining can degrade generalization and lead to memorization, motivating aggressive deduplication pipelines. However, at web scale, it is unclear what constitutes a ``duplicate'': beyond surface-form matches,…
For a model of DNA denaturation, exponents describing the distributions of denaturated loops and unzipped end-segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions…
The physical sizes of supernova remnants (SNRs) in a number of nearby galaxies follow an approximately linear cumulative distribution, contrary to what is expected for decelerating shock fronts. This has been attributed to selection…
The study of core-collapse supernova remnants (SNRs) presents a fascinating puzzle, with intricate morphologies and a non-uniform distribution of stellar debris. Particularly, young remnants (aged less than 5000 years) hold immense value as…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in…
The distribution of bases spacing in human genome was investigated. An analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution…
We consider the task of detecting regulatory elements in the human genome directly from raw DNA. Past work has focused on small snippets of DNA, making it difficult to model long-distance dependencies that arise from DNA's 3-dimensional…
We present an analysis of the impact of spiral density waves (DWs) on the radial and surface density distributions of supernovae (SNe) in host galaxies with different arm classes. We use a well-defined sample of 269 relatively nearby,…
Convolutional Neural Networks (CNN) have been pivotal to the success of many state-of-the-art classification problems, in a wide variety of domains (for e.g. vision, speech, graphs and medical imaging). A commonality within those domains is…
We present an analysis of the height distributions of the different types of supernovae (SNe) from the plane of their host galaxies. We use a well-defined sample of 102 nearby SNe appeared inside high-inclined (i > 85 deg), morphologically…
The amount and type of self-entanglement of DNA filaments is significantly affected by spatial confinement, which is ubiquitous in biological systems. Motivated by recent advancements in single DNA molecule experiments based on nanofluidic…
We build networks of genetic similarity in which the nodes are organisms sampled from biological populations. The procedure is illustrated by constructing networks from genetic data of a marine clonal plant. An important feature in the…
In sparse coding it is common to tile an image into nonoverlapping patches, and then use a dictionary to create a sparse representation of each tile independently. In this situation, the overcompleteness of the dictionary is the number of…