On the Leibniz rule and Laplace transform for fractional derivatives

Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and Laplace transform. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann-Liouville derivative is doubtful for n-th continuously differentiable function. By the aid of this series representation, the exact formula of Caputo Leibniz rule and the explanation of Riemann-Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results

Cross-Modal Attention Effects in the Vestibular Cortex during Attentive Tracking of Moving Objects

The midposterior fundus of the Sylvian fissure in the human brain is central to the cortical processing of vestibular cues. At least two vestibular areas are located at this site: the parietoinsular vestibular cortex (PIVC) and the posterior insular cortex (PIC). It is now well established that activity in sensory systems is subject to cross-modal attention effects. Attending to a stimulus in one sensory modality enhances activity in the corresponding cortical sensory system, but simultaneously suppresses activity in other sensory systems. Here, we wanted to probe whether such cross-modal attention effects also target the vestibular system. To this end, weused a visual multiple-object tracking task. By parametrically varying the number of tracked targets, we could measure the effect of attentional load on the PIVC and the PIC while holding the perceptual load constant. Participants performed the tracking task during functional magnetic resonance imaging. Results show that, compared with passive viewing of object motion, activity during object tracking was suppressed in the PIVC and enhanced in the PIC. Greater attentional load, induced by increasing the number of tracked targets, was associated with a corresponding increase in the suppression of activity in the PIVC. Activity in the anterior part of the PIC decreased with increasing load, whereas load effects were absent in the posterior PIC. Results of a control experiment show that attention-induced suppression in the PIVC is stronger than any suppression evoked by the visual stimulus per se. Overall, our results suggest that attention has a cross-modal modulatory effect on the vestibular cortex during visual object tracking

Clonal Deletion Prunes but Does Not Eliminate Self-Specific αβ CD8+ T Lymphocytes

SummaryIt has long been thought that clonal deletion efficiently removes almost all self-specific T cells from the peripheral repertoire. We found that self-peptide MHC-specific CD8+ T cells in the blood of healthy humans were present in frequencies similar to those specific for non-self antigens. For the Y chromosome-encoded SMCY antigen, self-specific T cells exhibited only a 3-fold lower average frequency in males versus females and were anergic with respect to peptide activation, although this inhibition could be overcome by a stronger stimulus. We conclude that clonal deletion prunes but does not eliminate self-specific T cells and suggest that to do so would create holes in the repertoire that pathogens could readily exploit. In support of this hypothesis, we detected T cells specific for all 20 amino acid variants at the p5 position of a hepatitis C virus epitope in a random group of blood donors

Mutation mapping and identification by whole-genome sequencing

Genetic mapping of mutations in model systems has facilitated the identification of genes contributing to fundamental biological processes including human diseases. However, this approach has historically required the prior characterization of informative markers. Here we report a fast and cost-effective method for genetic mapping using next-generation sequencing that combines single nucleotide polymorphism discovery, mutation localization, and potential identification of causal sequence variants. In contrast to prior approaches, we have developed a hidden Markov model to narrowly define the mutation area by inferring recombination breakpoints of chromosomes in the mutant pool. In addition, we created an interactive online software resource to facilitate automated analysis of sequencing data and demonstrate its utility in the zebrafish and mouse models. Our novel methodology and online tools will make next-generation sequencing an easily applicable resource for mutation mapping in all model systems.Harvard Stem Cell Institute (Junior Faculty Grant)National Institutes of Health (U.S.) (Grant 1R01DK090311)National Institutes of Health (U.S.) (Grant 5R01MH084676

Guiding the Design of Synthetic DNA-Binding Molecules with Massively Parallel Sequencing

Genomic applications of DNA-binding molecules require an unbiased knowledge of their high affinity sites. We report the high-throughput analysis of pyrrole-imidazole polyamide DNA-binding specificity in a 10^(12)-member DNA sequence library using affinity purification coupled with massively parallel sequencing. We find that even within this broad context, the canonical pairing rules are remarkably predictive of polyamide DNA-binding specificity. However, this approach also allows identification of unanticipated high affinity DNA-binding sites in the reverse orientation for polyamides containing β/Im pairs. These insights allow the redesign of hairpin polyamides with different turn units capable of distinguishing 5′-WCGCGW-3′ from 5′-WGCGCW-3′. Overall, this study displays the power of high-throughput methods to aid the optimal targeting of sequence-specific minor groove binding molecules, an essential underpinning for biological and nanotechnological applications

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment