On Strichartz estimates for many-body Schr\"odinger equation in the periodic setting

In this paper, we prove Strichartz estimates for many body Schr\"odinger equations in the periodic setting, specifically on tori $\mathbb{T}^d$, where $d\geq 3$. The results hold for both rational and irrational tori, and for small interacting potentials in a certain sense. Our work is based on the standard Strichartz estimate for Schr\"odinger operators on periodic domains, as developed in Bourgain-Demeter \cite{BD}. As a comparison, this result can be regarded as a periodic analogue of Hong \cite{hong2017strichartz} though we do not use the same perturbation method. We also note that the perturbation method fails due to the derivative loss property of the periodic Strichartz estimate.Comment: 14 pages. Comments are welcom

PSSP-RFE: Accurate Prediction of Protein Structural Class by Recursive Feature Extraction from PSI-BLAST Profile, Physical-Chemical Property and Functional Annotations

Protein structure prediction is critical to functional annotation of the massively accumulated biological sequences, which prompts an imperative need for the development of high-throughput technologies. As a first and key step in protein structure prediction, protein structural class prediction becomes an increasingly challenging task. Amongst most homological-based approaches, the accuracies of protein structural class prediction are sufficiently high for high similarity datasets, but still far from being satisfactory for low similarity datasets, i.e., below 40% in pairwise sequence similarity. Therefore, we present a novel method for accurate and reliable protein structural class prediction for both high and low similarity datasets. This method is based on Support Vector Machine (SVM) in conjunction with integrated features from position-specific score matrix (PSSM), PROFEAT and Gene Ontology (GO). A feature selection approach, SVM-RFE, is also used to rank the integrated feature vectors through recursively removing the feature with the lowest ranking score. The definitive top features selected by SVM-RFE are input into the SVM engines to predict the structural class of a query protein. To validate our method, jackknife tests were applied to seven widely used benchmark datasets, reaching overall accuracies between 84.61% and 99.79%, which are significantly higher than those achieved by state-of-the-art tools. These results suggest that our method could serve as an accurate and cost-effective alternative to existing methods in protein structural classification, especially for low similarity datasets

Spatio-temporal propagation of COVID-19 pandemics

The new coronavirus known as COVID-19 is spread world-wide since December 2019. Without any vaccination or medicine, the means of controlling it are limited to quarantine and social distancing. Here we study the spatio-temporal propagation of the first wave of the COVID-19 virus in China and compare it to other global locations. We provide a comprehensive picture of the spatial propagation from Hubei to other provinces in China in terms of distance, population size, and human mobility and their scaling relations. Since strict quarantine has been usually applied between cities, more insight about the temporal evolution of the disease can be obtained by analyzing the epidemic within cities, especially the time evolution of the infection, death, and recovery rates which affected by policies. We study and compare the infection rate in different cities in China and provinces in Italy and find that the disease spread is characterized by a two-stages process. At early times, at order of few days, the infection rate is close to a constant probably due to the lack of means to detect infected individuals before infection symptoms are observed. Then at later times it decays approximately exponentially due to quarantines. The time evolution of the death and recovery rates also distinguish between these two stages and reflect the health system situation which could be overloaded

Controlling the balance between remote, pinhole, and van der Waals epitaxy of Heusler films on graphene/sapphire

Remote epitaxy on monolayer graphene is promising for synthesis of highly lattice mismatched materials, exfoliation of free-standing membranes, and re-use of expensive substrates. However, clear experimental evidence of a remote mechanism remains elusive. In many cases, due to contaminants at the transferred graphene/substrate interface, alternative mechanisms such as pinhole-seeded lateral epitaxy or van der Waals epitaxy can explain the resulting exfoliatable single-crystalline films. Here, we find that growth of the Heusler compound GdPtSb on clean graphene on sapphire substrates produces a 30 degree rotated epitaxial superstructure that cannot be explained by pinhole or van der Waals epitaxy. With decreasing growth temperature the volume fraction of this 30 degree domain increases compared to the direct epitaxial 0 degree domain, which we attribute to slower surface diffusion at low temperature that favors remote epitaxy, compared to faster surface diffusion at high temperature that favors pinhole epitaxy. We further show that careful graphene/substrate annealing ($T\sim 700 ^\circ C$) and consideration of the film/substrate vs film/graphene lattice mismatch are required to obtain epitaxy to the underlying substrate for a variety of other Heusler films, including LaPtSb and GdAuGe. The 30 degree rotated superstructure provides a possible experimental fingerprint of remote epitaxy since it is inconsistent with the leading alternative mechanisms

Towards pathway-centric cancer therapies via pharmacogenomic profiling analysis of ERK signalling pathway

Background: Genomic heterogeneity in human cancers complicates gene-centric personalized medicine. Malignant tumors often share a core group of pathways that are perturbed by diverse genetic mutations. Therefore, one possible solution to overcome the heterogeneity challenge is a shift from gene-centric to pathway-centric therapies. Pathway-centric perspectives, which underscore the need to understand key pathways and their critical properties, could address the complexity of cancer heterogeneity better than gene-centric approaches to aid cancer drug discovery and therapy. Methods: We used large-scale pharmacogenomic profiling data provided by the Cancer Genome Project of the Wellcome Trust Sanger Institute and the Cancer Cell Line Encyclopedia. In a systematic in silico investigation of ERK signalling pathway components and topological structures determines their influences on pathway activity and targeted therapies. Mann–Whitney U test was used to identify gene alterations associated with drug sensitivity with p values and Benjamini–Hochberg correction for multiple hypotheses testing. Results: The analysis demonstrated that genetic alterations were crucial to activation of effector pathway and subsequent tumorigenesis, however drug sensitivity suffered from both drug effector and non-effector pathways, which were determined by not only underlying genomic alterations, but also interplay and topological relationship of components in pathway, suggesting that the combinatorial targets of key nodes in perturbed pathways may yield better treatment outcome. Furthermore, we proposed a model to provide a more comprehensive insight and understanding of pathway-centric cancer therapies. Conclusions: Our study provides a holistic view of factors influencing drug sensitivity and sheds light on pathway-centric cancer therapies. Electronic supplementary material The online version of this article (doi:10.1186/s40169-015-0066-1) contains supplementary material, which is available to authorized users

Association analysis of dopaminergic degeneration and the neutrophil-to-lymphocyte ratio in Parkinson’s disease

IntroductionPeripheral inflammatory responses are suggested to play a major role in the pathophysiology of Parkinson’s disease (PD). The neutrophil-to-lymphocyte ratio (NLR), a new recognized biomarker, can reflect peripheral inflammation in PD. However, the association between the NLR and dopaminergic degeneration in PD remains unclear.MethodsIn this retrospective study, 101 enrolled PD patients were categorized into early-stage and advanced-stage PD based on the Hoehn and Yahr (HY) scale. We evaluated the clinical characteristics, peripheral immune profile, and 11C-CFT striatal dopamine transporter (DAT) binding levels. Linear regression analyses were employed to assess the associations between NLR and striatal DAT levels at different stages in PD patients.ResultsCovariate-controlled regression analysis revealed that higher NLR was significantly associated with lower DAT levels in the caudate (β = −0.27, p = 0.003) and the putamen (β = −0.27, p = 0.011). Moreover, in the early-stage PD subgroup, a similar association was observed (caudate: β = −0.37, p = 0.013; putamen: β = −0.45, p = 0.005). The lymphocytes count was correlated positively with the striatal DAT levels in the Spearman correlation analysis whether in total patients (caudate: ρ = 0.25, p = 0.013; putamen: ρ = 0.22, p = 0.026) or in the early-stage subgroup (caudate: ρ = 0.31, p = 0.023, putamen: ρ = 0.34, p = 0.011).ConclusionDopaminergic degeneration is associated with peripheral inflammation in PD. The NLR, a widely used inflammatory marker, may have the potential to reflect the degree of dopaminergic degeneration in individuals with early-stage PD