The Abel-Zeilberger Algorithm

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.Comment: 18 page

Higgs Boson Search Sensitivity in the H→WWH \to WW Dilepton Decay Mode at s=7\sqrt s = 7 and 10 TeV

Prospects for discovery of the standard model Higgs boson are examined at center of mass energies of $7$ and $10$ TeV at the CERN Large Hadron Collider. We perform a simulation of the signal and principal backgrounds for Higgs boson production and decay in the $W^+ W^-$ dilepton mode, finding good agreement with the ATLAS and CMS collaboration estimates of signal significance at 14 TeV for Higgs boson masses near $m_H = 160$~GeV. At the lower energy of $7$~TeV, using the same analysis cuts as these collaborations, we compute expected signal sensitivities of about $2$ standard deviations ($\sigma$'s) at $m_H = 160$~GeV in the ATLAS case, and about 3.6~$\sigma$ in the CMS case for $1$~fb$^{-1}$ of integrated luminosity. Integrated luminosities of 8~$\rm{fb}^{-1}$ and 3~$\rm{fb}^{-1}$ are needed in the ATLAS case at $7$ and $10$~TeV, respectively, for $5~\sigma$ level discovery. In the CMS case, the numbers are 2~$\rm{fb}^{-1}$ and 1~$\rm{fb}^{-1}$ at $7$ and $10$~TeV. Our different stated expectations for the two experiments arise from the more restrictive analysis cuts in the CMS case. Recast as exclusion limits, our results show that with $1~{\rm fb}^{-1}$ of integrated luminosity at 7~TeV, the LHC may be able to exclude $m_H$ values in the range 160 to 180~GeV provided no signal is seen.Comment: 29 pages, 8 figures. New results on estimated discovery reach for both CMS and ATLAS, as well as exclusion limits, along with comparisons with Tevatron possibilities. References added

DehazeNet: An end-to-end system for single image haze removal

© 1992-2012 IEEE. Single image haze removal is a challenging ill-posed problem. Existing methods use various constraints/priors to get plausible dehazing solutions. The key to achieve haze removal is to estimate a medium transmission map for an input hazy image. In this paper, we propose a trainable end-to-end system called DehazeNet, for medium transmission estimation. DehazeNet takes a hazy image as input, and outputs its medium transmission map that is subsequently used to recover a haze-free image via atmospheric scattering model. DehazeNet adopts convolutional neural network-based deep architecture, whose layers are specially designed to embody the established assumptions/priors in image dehazing. Specifically, the layers of Maxout units are used for feature extraction, which can generate almost all haze-relevant features. We also propose a novel nonlinear activation function in DehazeNet, called bilateral rectified linear unit, which is able to improve the quality of recovered haze-free image. We establish connections between the components of the proposed DehazeNet and those used in existing methods. Experiments on benchmark images show that DehazeNet achieves superior performance over existing methods, yet keeps efficient and easy to use

Two-stage analysis strategy for identifying the IgM quantitative trait locus

Genetic association studies offer an opportunity to find genetic variants underlying complex human diseases. Various tests have been developed to improve their power. However, none of these tests is uniformly best and it is usually unclear at the outset what test is best for a specific dataset. For example, Hotelling's T2 test is best for normally distributed data, but it can lose considerable power when normality is not met. To achieve satisfactory power in most cases, without compromising the overall significance level, we propose to adopt a two-stage adaptive analysis strategy – several statistics are compared on a portion of the samples at the first stage and the most powerful statistic is then used for the remaining samples. We evaluated this procedure by mapping the quantitative trait locus of IgM with the simulated data in Genetic Analysis Workshop 15 Problem 3. The results show that the gain in power of the two-stage adaptive analysis procedure could be considerable when the initial choice of test statistic is wrong, whereas the loss is relatively small in the case that the optimal test chosen initially is correct

Bilinear effect in complex systems

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. Bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.Comment: 5 pages, 5 figure

Applying Deep Learning To Airbnb Search

The application to search ranking is one of the biggest machine learning success stories at Airbnb. Much of the initial gains were driven by a gradient boosted decision tree model. The gains, however, plateaued over time. This paper discusses the work done in applying neural networks in an attempt to break out of that plateau. We present our perspective not with the intention of pushing the frontier of new modeling techniques. Instead, ours is a story of the elements we found useful in applying neural networks to a real life product. Deep learning was steep learning for us. To other teams embarking on similar journeys, we hope an account of our struggles and triumphs will provide some useful pointers. Bon voyage!Comment: 8 page

Comparison of microsatellites, single-nucleotide polymorphisms (SNPs) and composite markers derived from SNPs in linkage analysis

There is growing evidence that a map of dense single-nucleotide polymorphisms (SNPs) can outperform a map of sparse microsatellites for linkage analysis. There is also argument as to whether a clustered SNP map can outperform an evenly spaced SNP map. Using Genetic Analysis Workshop 14 simulated data, we compared for linkage analysis microsatellites, SNPs, and composite markers derived from SNPs. We encoded the composite markers in a two-step approach, in which the maximum identity length contrast method was employed to allow for recombination between loci. A SNP map 2.3 times as dense as a microsatellite map (~2.9 cM compared to ~6.7 cM apart) provided slightly less information content (~0.83 compared to ~0.89). Most inheritance information could be extracted when the SNPs were spaced < 1 cM apart. Comparing the linkage results on using SNPs or composite markers derived from them based on both 3 cM and 0.3 cM resolution maps, we showed that the inter-SNP distance should be kept small (< 1 cM), and that for multipoint linkage analysis the original markers and the derived composite markers had similar power; but for single point linkage analysis the resulting composite markers lead to more power. Considering all factors, such as information content, flexibility of analysis method, map errors, and genotyping errors, a map of clustered SNPs can be an efficient design for a genome-wide linkage scan

Linkage studies of catechol-O-methyltransferase (COMT) and dopamine-beta-hydroxylase (DBH) cDNA expression levels

The COMT and DBH genes are physically located at chromosomes 22q11 and 9q34, respectively, and both COMT and DBH are involved in catecholamine metabolism and are strong candidates for certain psychiatric and neurological disorders. Although the genetic determinants for both enzymes' activities have been widely studied, their genetic involvement on gene mRNA expression levels remains unclear. In this study we performed quantitative linkage analysis of COMT and DBH cDNA expression levels, identifying transcriptional regulatory regions for both genes. Multiple Haseman-Elston regression was used to detect both additive and interactive effects between two loci. We found that the master transcriptional regulatory region 20q13 had an additive effect on the COMT expression level. We also found that chromosome 19p13 showed both additive and interactive effects with 9q34 on DBH expression level. Furthermore, a potential interaction between COMT and DBH was indicated

Safety and efficacy of etomidate and propofol anesthesia in elderly patients undergoing gastroscopy: A double-blind randomized clinical study

The aim of the present study is to compare the safety, efficacy and cost effectiveness of anesthetic regimens by compound, using etomidate and propofol in elderly patients undergoing gastroscopy. A total of 200 volunteers (65–79 years of age) scheduled for gastroscopy under anesthesia were randomly divided into the following groups: P, propofol (1.5–2.0 mg/kg); E, etomidate (0.15-0.2 mg/kg); P+E, propofol (0.75–1 mg/kg) followed by etomidate (0.075-0.1 mg/kg); and E+P, etomidate (0.075-0.01 mg/kg) followed by propofol (0.75–1 mg/kg). Vital signs and bispectral index were monitored at different time points. Complications, induction and examination time, anesthesia duration, and recovery and discharge time were recorded. At the end of the procedure, the satisfaction of patients, endoscopists and the anesthetist were evaluated. The recovery (6.1±1.2 h) and discharge times (24.8±2.8 h) in group E were significantly longer compared with groups P, P+E and E+P (P<0.05). The occurrence of injection pain in group P+E was significantly higher compared with the other three groups (P<0.05). In addition, the incidence of myoclonus and post-operative nausea and vomiting were significantly higher in group P+E compared with the other three groups (P<0.05). There was no statistical difference among the four groups with regards to the patients' immediate, post-procedure satisfaction (P>0.05). Furthermore, there was no difference in the satisfaction of anesthesia, as evaluated by the anesthetist and endoscopist, among the four groups (P>0.05). The present study demonstrates that anesthesia for gastroscopy in elderly patients can be safely and effectively accomplished using a drug regimen that combines propofol with etomidate. The combined use of propofol and etomidate has unique characteristics which improve hemodynamic stability, cause minimal respiratory depression and less side effects, provide rapid return to full activity and result in high levels of satisfaction

Disruption of mesoderm formation during cardiac differentiation due to developmental exposure to 13-cis-retinoic acid.

13-cis-retinoic acid (isotretinoin, INN) is an oral pharmaceutical drug used for the treatment of skin acne, and is also a known teratogen. In this study, the molecular mechanisms underlying INN-induced developmental toxicity during early cardiac differentiation were investigated using both human induced pluripotent stem cells (hiPSCs) and human embryonic stem cells (hESCs). Pre-exposure of hiPSCs and hESCs to a sublethal concentration of INN did not influence cell proliferation and pluripotency. However, mesodermal differentiation was disrupted when INN was included in the medium during differentiation. Transcriptomic profiling by RNA-seq revealed that INN exposure leads to aberrant expression of genes involved in several signaling pathways that control early mesoderm differentiation, such as TGF-beta signaling. In addition, genome-wide chromatin accessibility profiling by ATAC-seq suggested that INN-exposure leads to enhanced DNA-binding of specific transcription factors (TFs), including HNF1B, SOX10 and NFIC, often in close spatial proximity to genes that are dysregulated in response to INN treatment. Altogether, these results identify potential molecular mechanisms underlying INN-induced perturbation during mesodermal differentiation in the context of cardiac development. This study further highlights the utility of human stem cells as an alternative system for investigating congenital diseases of newborns that arise as a result of maternal drug exposure during pregnancy