Exponential sums and rigid cohomology

In this article, we prove a comparison theorem between the Dwork cohomology introduced by Adolphson and Sperber and the rigid cohomology. As a corollary, we can calculate the rigid cohomology of Dwork isocrystal on torus.     

The Universality of an Absolutely Convergent Series on Short Intervals

Siberian Mathematical Journal - Under consideration is a Dirichlet series depending on a parameter and absolutely convergent in the right half of the critical strip. We prove that...     

Prediction of drug-target interaction by integrating diverse heterogeneous information source with multiple kernel learning and clustering methods

BackgroundIdentification of potential drug-target interaction pairs is very important for pharmaceutical innovation and drug discovery. Numerous machine learning-based and network-based algorithms have been developed for predicting drug-target interactions. However, large-scale pharmacological, genomic and chemical datum emerged recently provide new opportunity for further heightening the accuracy of drug-target interactions prediction.ResultsIn this work, based on the assumption that similar drugs tend to interact with similar proteins and vice versa, we developed a novel computational method (namely MKLC-BiRW) to predict new drug-target interactions. MKLC-BiRW integrates diverse drug-related and target-related heterogeneous information source by using the multiple kernel learning and clustering methods to generate the drug and target similarity matrices, in which the low similarity elements are set to zero to build the drug and target similarity correction networks. By incorporating these drug and target similarity correction networks with known drug-target interaction bipartite graph, MKLC-BiRW constructs the heterogeneous network on which Bi-random walk algorithm is adopted to infer the potential drug-target interactions.ConclusionsCompared with other existing state-of-the-art methods, MKLC-BiRW achieves the best performance in terms of AUC and AUPR. MKLC-BiRW can effectively predict the potential drug-target interactions.     

On exact solutions for time-fractional Korteweg-de Vries and Korteweg-de Vries-Burger’s equations using homotopy analysis transform method

In this paper we consider the homotopy analysis transform method (HATM) to solve the time fractional order Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger’s (KdVB) equations. The HATM is a combination of the Laplace decomposition method (LDM) and the homotopy analysis method (HAM). The fractional derivatives are defined in the Caputo sense. This method gives the solution in the form of a rapidly convergent series with h-curves are used to determine the intervals of convergent. Averaged residual errors are used to find the optimal values of h. It is found that the optimal h accelerates the convergence of the HATM, with the rate of convergence depending on the parameters in the KdV and KdVB equations. The HATM solutions are compared with exact solutions and excellent agreement is found.     

Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.