In this paper, we study the essential dimension of classes of central simple algebras with involutions of index less or equal to 4. Using structural theorems for simple algebras with involutions, we obtain the essential dimension of projective and symplectic groups of small degree.

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between both walks and study limit theorems and absorption problems for correlated random walks by our PQRS method, which was used in our analysis of quantum walks.

Food webs (i.e., networks of species and their feeding interactions) share multiple structural features across ecosystems. The factors explaining such similarities are still debated, and the role played by most organismal traits and their intraspecific variation is unknown. Here, we assess how variation in traits controlling predator-prey interactions (e.g., body size) affects food web structur...

Differences between individual human genomes, or between human and cancer genomes, range in scale from single nucleotide variants (SNVs) through intermediate and large-scale duplications, deletions, and rearrangements of genomic segments. The latter class, called structural variants (SVs), have received considerable attention in the past several years as they are a previously under appreciated ...

In this article we introduce a notion of normalized angle for Lorentzian pre-length spaces. This concept allows us to prove some equivalences the definition timelike curvature bounds from below Specifically, establish comparison theorems known as local version Toponogov theorem and Alexandrov convexity property. Finally, an application obtain first variation Formula non-negatively curved global...

There is growing appreciation that the human genome contains significant numbers of structural rearrangements, such as insertions, deletions, inversions, and large tandem repeats. Recent studies have defined approximately 5% of the human genome as structurally variant in the normal population, involving more than 800 independent genes. We present a detailed review of the various structural rear...

Despite the known relevance of genomic structural variants to pathogen behavior, cancer, development, and evolution, certain repeat based structural variants may evade detection by existing high-throughput techniques. Here, we present ruler arrays, a technique to detect genomic structural variants including insertions and deletions (indels), duplications, and translocations. A ruler array explo...

MOTIVATION Structural variation including deletions, duplications and rearrangements of DNA sequence are an important contributor to genome variation in many organisms. In human, many structural variants are found in complex and highly repetitive regions of the genome making their identification difficult. A new sequencing technology called strobe sequencing generates strobe reads containing mu...

We present a natural language generator that produces a range of medical reports on the clinical histories of cancer patients, and discuss the problem of conceptual restatement in generating various textual views of the same conceptual content. We focus on two features of our system: the demand for “loose paraphrases” between the various reports on a given patient, with a high degree of semanti...