Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem

Virtual Partner Interaction (VPI): Exploring Novel Behaviors via Coordination Dynamics

Inspired by the dynamic clamp of cellular neuroscience, this paper introduces VPI—Virtual Partner Interaction—a coupled dynamical system for studying real time interaction between a human and a machine. In this proof of concept study, human subjects coordinate hand movements with a virtual partner, an avatar of a hand whose movements are driven by a computerized version of the Haken-Kelso-Bunz (HKB) equations that have been shown to govern basic forms of human coordination. As a surrogate system for human social coordination, VPI allows one to examine regions of the parameter space not typically explored during live interactions. A number of novel behaviors never previously observed are uncovered and accounted for. Having its basis in an empirically derived theory of human coordination, VPI offers a principled approach to human-machine interaction and opens up new ways to understand how humans interact with human-like machines including identification of underlying neural mechanisms

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

Dissimilarity-Based Correlation of Movements and Events on Circular Scales of Space and Time

© 2020, Springer Nature Switzerland AG. Circular scales appear in many applications related to a comparative analysis of the timing of events, wind directions, animals and vehicle movement directions, etc. The paper introduces a new non-statistical correlation function on circular scales based on a recently proposed approach to constructing correlation functions (association measures) using (dis)similarity measures on the set with an involutive operation. An involutive negation and a dissimilarity function satisfying required properties on a circular set are introduced and used for constructing the new correlation function. This correlation function can measure correlation both between two grades of circular scale and between sets of measurements of two circular variables