Global existence and time decay estimate of solutions to the Keller–Segel system

We consider the chemotaxis‐Navier–Stokes system 1.1-1.4 (Keller–Segel system) in the whole space, which describes the motion of oxygen‐driven bacteria, eukaryotes, in a fluid. We proved the global existence and time decay estimate of solutions to the Cauchy problem 1.1-1.2 in with the small initial data. Moreover, when the fluid motion is described by the Stokes equations, we established the global weak solutions to 1.3-1.4 in with the potential function ? is small and the initial density n₀(x) has finite mass.     

A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation

The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.     

Bayesian Estimation and Statistical Analysis of Risk Measurements

The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.     

Code2vect: An efficient heterogenous data classifier and nonlinear regression technique

The aim of this paper is to present a new classification and regression algorithm based on Artificial Intelligence. The main feature of this algorithm, which will be called Code2Vect, is the nature of the data to treat: qualitative or quantitative and continuous or discrete. Contrary to other artificial intelligence techniques based on the “Big-Data,” this new approach will enable working with a reduced amount of data, within the so-called “Smart Data” paradigm. Moreover, the main purpose of this algorithm is to enable the representation of high-dimensional data and more specifically grouping and visualizing this data according to a given target. For that purpose, the data will be projected into a vectorial space equipped with an appropriate metric, able to group data according to their affinity (with respect to a given output of interest). Furthermore, another application of this algorithm lies on its prediction capability. As it occurs with most common data-mining techniques such as regression trees, by giving an input the output will be inferred, in this case considering the nature of the data formerly described. In order to illustrate its potentialities, two different applications will be addressed, one concerning the representation of high-dimensional and categorical data and another featuring the prediction capabilities of the algorithm.     

Identifying mutated driver pathways in cancer by integrating multi-omics data

Since the driver pathway in cancer plays a crucial role in the formation and progression of cancer, it is very imperative to identify driver pathways, which will offer important information for precision medicine or personalized medicine. In this paper, an improved maximum weight submatrix problem model is proposed by integrating such three kinds of omics data as somatic mutations, copy number variations, and gene expressions. The model tries to adjust coverage and mutual exclusivity with the average weight of genes in a pathway, and simultaneously considers the correlation among genes, so that the pathway having high coverage but moderate mutual exclusivity can be identified. By introducing a kind of short chromosome code and a greedy based recombination operator, a parthenogenetic algorithm PGA-MWS is presented to solve the model. Experimental comparisons among algorithms GA, MOGA, iMCMC and PGA-MWS were performed on biological and simulated data sets. The experimental results show that, compared with the other three algorithms, the PGA-MWS one based on the improved model can identify the gene sets with high coverage but moderate mutual exclusivity and scales well. Many of the identified gene sets are involved in known signaling pathways, most of the implicated genes are oncogenes or tumor suppressors previously reported in literatures. The experimental results indicate that the proposed approach may become a useful complementary tool for detecting cancer pathways.     

Anisotropy Effects and Observational Data on the Constraints of Evolution Dark Energy Models

We investigate cosmological dark energy models where the accelerated expansion of the universe is driven by a field with an anisotropic universe. The constraints on the parameters are obtained by maximum likelihood analysis using observational of 194 Type Ia supernovae(SNIa) and the most recent joint light-curve analysis(JLA) sample. In particular we reconstruct the dark energy equation of state parameter w(z) and the deceleration parameter q(z). We find that the best fit dynamical w(z) obtained from the 194 SNIa dataset does not cross the phantom divide line w(z) =-1 and remains above and close to w(z)≈-0.92 line for the whole redshift range 0 ≤ z ≤ 1.75 showing no evidence for phantom behavior. By applying the anisotropy effect on the ΛCDM model, the joint analysis indicates that ?_(σ0)= 0.0163 ± 0.03,with 194 SNIa, ?_(σ0)=-0.0032 ± 0.032 with 238 the SiFTO sample of JLA and ?_(σ0)= 0.011 ± 0.0117 with 1048 the SALT2 sample of Pantheon at 1σ′confidence interval. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models with JLA SNe datasets. Furthermore, we use two statistical tests such as the usual χ_(min)~2/dof and p-test to compare two dark energy models with ΛCDM model. Finally we show that the presence of anisotropy is confirmed in mentioned models via SNIa dataset.