Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise

Stochastic fractional differential systems are important and useful in the mathematics, physics, and engineering fields. However, the determination of their probabilistic responses is difficult due to their non-Markovian property. The recently developed globally-evolving-based generalized density evolution equation (GE-GDEE), which is a unified partial differential equation (PDE) governing the transient probability density function (PDF) of a generic path-continuous process, including non-Markovian ones, provides a feasible tool to solve this problem. In the paper, the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established. In particular, it is proved that in the GE-GDEE corresponding to the state-quantities of interest, the intrinsic drift coefficient is a time-varying linear function, and can be analytically determined. In this sense, an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original high-dimensional linear fractional differential system can be constructed such that their transient PDFs are identical. Specifically, for a multi-dimensional linear fractional differential system, if only one or two quantities are of interest, GE-GDEE is only in one or two dimensions, and the surrogate system would be a one- or two-dimensional linear integer-order system. Several examples are studied to assess the merit of the proposed method. Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems, the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian, and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems

A New Approach for Capturing the Probability Density Function of the Maximum Value of a Markov Process

In the present paper a method to determine the probability distribution of the maximum value process (MVP) of a Markov process is proposed. In this method, an augmented vector process of a physical process and its MVP is constructed. The joint probability density function is then calculated by the path integral solution (PIS), and further the probability density function of the MVP can be obtained as the marginal probability density. A numerical example is shown to validate the proposed method.Financial supports from the National Natural Science Foundation of China (NSFC Grant Nos. 11672209, 51538010 and the National Distinguished Youth Fund of NSFC with Grant No.51725804), the NSFC-DFG joint program (11761131014) and the International Joint Research Program of Shanghai Municipal Government (Grant No. 18160712800) are highly appreciated

A Study of Machine Learning Models in Epidemic Surveillance: Using the Query Logs of Search Engines

Epidemics inevitably result in a large number of deaths and always cause considerable social and economic damage. Epidemic surveillance has thus become an important healthcare research issue. In 2009, Ginsberg et al. observed that the query logs of search engines can be used to estimate the status of epidemics in a timely manner. In this paper, we model epidemic surveillance as a classification problem and employ query statistics from Google to classify the status of a dengue fever epidemic. The query logs of twenty-three dengue-related keywords serve as observations for machine learning and testing, and a number of machine learning models are investigated to evaluate their surveillance performance. Evaluations based on a 5-year real world dataset demonstrate that search engine query logs can be used to construct accurate epidemic status classifiers. Moreover, the learned classifiers generally outperform conventional regression approaches. We also apply various machine learning models, including generative, discriminative, sequential, and non-sequential classification models, to demonstrate their applicability to epidemic surveillance

SjTPdb: integrated transcriptome and proteome database and analysis platform for Schistosoma japonicum

<p>Abstract</p> <p>Background</p> <p><it>Schistosoma japonicum </it>is one of the three major blood fluke species, the etiological agents of schistosomiasis which remains a serious public health problem with an estimated 200 million people infected in 76 countries. In recent years, enormous amounts of both transcriptomic and proteomic data of schistosomes have become available, providing information on gene expression profiles for developmental stages and tissues of <it>S. japonicum</it>. Here, we establish a public searchable database, termed SjTPdb, with integrated transcriptomic and proteomic data of <it>S. japonicum</it>, to enable more efficient access and utility of these data and to facilitate the study of schistosome biology, physiology and evolution.</p> <p>Description</p> <p>All the available ESTs, EST clusters, and the proteomic dataset of <it>S. japonicum </it>are deposited in SjTPdb. The core of the database is the 8,420 <it>S. japonicum </it>proteins translated from the EST clusters, which are well annotated for sequence similarity, structural features, functional ontology, genomic variations and expression patterns across developmental stages and tissues including the tegument and eggshell of this flatworm. The data can be queried by simple text search, BLAST search, search based on developmental stage of the life cycle, and an integrated search for more specific information. A PHP-based web interface allows users to browse and query SjTPdb, and moreover to switch to external databases by the following embedded links.</p> <p>Conclusion</p> <p>SjTPdb is the first schistosome database with detailed annotations for schistosome proteins. It is also the first integrated database of both transcriptome and proteome of <it>S. japonicum</it>, providing a comprehensive data resource and research platform to facilitate functional genomics of schistosome. SjTPdb is available from URL: <url>http://function.chgc.sh.cn/sj-proteome/index.htm</url>.</p