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

An Enhanced Factor Analysis of Performance Degradation Assessment on Slurry Pump Impellers

Slurry pumps, such as oil sand pumps, are widely used in industry to convert electrical energy to slurry potential and kinetic energy. Because of adverse working conditions, slurry pump impellers are prone to suffer wear, which may result in slurry pump breakdowns. To prevent any unexpected breakdowns, slurry pump impeller performance degradation assessment should be immediately conducted to monitor the current health condition and to ensure the safety and reliability of slurry pumps. In this paper, to provide an alternative to the impeller health indicator, an enhanced factor analysis based impeller indicator (EFABII) is proposed. Firstly, a low-pass filter is employed to improve the signal to noise ratios of slurry pump vibration signals. Secondly, redundant statistical features are extracted from the filtered vibration signals. To reduce the redundancy of the statistic features, the enhanced factor analysis is performed to generate new statistical features. Moreover, the statistic features can be automatically grouped and developed a new indicator called EFABII. Data collected from industrial oil sand pumps are used to validate the effectiveness of the proposed method. The results show that the proposed method is able to track the current health condition of slurry pump impellers

Principal Components of Superhigh-Dimensional Statistical Features and Support Vector Machine for Improving Identification Accuracies of Different Gear Crack Levels under Different Working Conditions

Gears are widely used in gearbox to transmit power from one shaft to another. Gear crack is one of the most frequent gear fault modes found in industry. Identification of different gear crack levels is beneficial in preventing any unexpected machine breakdown and reducing economic loss because gear crack leads to gear tooth breakage. In this paper, an intelligent fault diagnosis method for identification of different gear crack levels under different working conditions is proposed. First, superhigh-dimensional statistical features are extracted from continuous wavelet transform at different scales. The number of the statistical features extracted by using the proposed method is 920 so that the extracted statistical features are superhigh dimensional. To reduce the dimensionality of the extracted statistical features and generate new significant low-dimensional statistical features, a simple and effective method called principal component analysis is used. To further improve identification accuracies of different gear crack levels under different working conditions, support vector machine is employed. Three experiments are investigated to show the superiority of the proposed method. Comparisons with other existing gear crack level identification methods are conducted. The results show that the proposed method has the highest identification accuracies among all existing methods

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