Multiple sclerosis：integration of modeling with biology,clinical and imaging measures to provide better monitoring of disease progression and prediction of outcome

Multiple Sclerosis（MS） is a major cause of neurological disability in adults and has an annual cost of approximately $28 billion in the United States. MS is a very complex disorder as demyelination can happen in a variety of locations throughout the brain; therefore, this disease is never the same in two patients making it very hard to predict disease progression. A modeling approach which combines clinical, biological and imaging measures to help treat and fight this disorder is needed. In this paper, I will outline MS as a very heterogeneous disorder, review some potential solutions from the literature, demonstrate the need for a biomarker and will discuss how computational modeling combined with biological, clinical and imaging data can help link disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism.

Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.

CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM

In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.

CONVERGENCE RATE OF MULTIPLE FRACTIONAL STRATONOVICH TYPE INTEGRAL FOR HURST PARAMETER LESS THAN 1/2

In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn＋1（[0, T ]n） is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of interpolation approximation of fractional Brownian motion BtH with Hurst parameter H 1/2. The limit process is the multiple Stratonovich integral of the function f . In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is 2H in the mean square sense, where is the norm of the partition generating the approximations.

Some Important Properties of Multiple G-Ito Integral in the G-Expectation Space

In the G-expectation space, we propose the multiple Itô?integral, which is driven by multi-dimensional G-Brownian motion. We prove the recursive relationship of multiple G-Itô?integrals by G-Itôformula and mathematical induction, and we obtain some computational formulas for a kind of multiple G-Itô?integrals.

ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.

Nonlinear control for global stabilization of multiple-integrator system by bounded controls

The global stabilization problem of the multiple-integrator system by bounded controls is considered. A nonlinear feedback law consisting of nested saturation functions is proposed. This type of nonlinear feedback law that is a modification and generalization of the result given in [1] needs only [（n ＋ 1）/2] （n is the dimensions of the system） saturation elements, which is fewer than that which the other nonlinear laws need. Furthermore, the poles of the closedloop system can be placed on any location on the left real axis when none of the saturation elements in the control laws is saturated. This type of nonlinear control law exhibits a simpler structure and can significantly improve the transient performances of the closed-loop system, and is very superior to the other existing methods. Simulation on a fourth-order system is used to validate the proposed method.

ON MULTIPLE WIENER INTEGRAL EXPANSIONS FOR D'-VALUED NONLINEAR RANDOM FUNCTIONALS

In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integral kernels such that the nonlinear functional can be expanded by series of multiple Wiener integrals of the integral kernels with respect to the Wiener D'-process.

The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications

By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.

APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE FOURIER INTEGRALS AND FOURIER SERIES ON SET OF FULL MEASURE

In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.

An Extended Multiple Hardy-Hilbert's Integral Inequality

In this paper, by introducing the norm ｜｜x｜｜ （x ∈ Rn）, a multiple Hardy- Hilbert＇s integral inequality with the best constant factor and it＇s equivalent form are given.

ON THE LOCALIZATION AND CONVERGENCE OF MULTIPLE FOURIER INTEGRAL BY BOCHNER-RIESZ MEANS

In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).

COMPLEX WIENER-ITO CHAOS DECOMPOSITION REVISITED

In this article, some proper ties of complex Wiener-Ito multiple integrals and complex Ornstein-Uhlenbeck opera tors and semigroups are obtained. Those include Stroock's formula, Hu-Meyer formula, Clark-Ocone formula, and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of complex Wiener-Ito multiple integrals are given.

FRACTIONAL 2D-STOCHASTIC CURRENTS

Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.

MAURER-CARTAN EQUATION OF A_∞-ALGEBRAS

The axioms of A ∞ algebras can be written as Maurer Cartan equation.Infi nitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F product.

Multiple Integral Inequalities for Schur Convex Functions on Symmetric and Convex Bodies

In this paper,by making use of Divergence theorem for multiple integrals,we establish some integral inequalities for Schur convex functions defined on bodies B⊂R^(n)that are symmetric,convex and have nonempty interiors.Examples for three dimensional balls are also provided.

Moderate Deviations for Parameter Estimation in the Fractional Ornstein–Uhlenbeck Processes with Periodic Mean

In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.

DISCRETIZATION OF JUMP STOCHASTIC DIFFERENTIAL EQUATIONS IN TERMS OF MULTIPLE STOCHASTIC INTEGRALS

In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.

Semicontinuity of Multiple Integrals on W^(k, p)(Ω, R^m)(k≥1)

This paper shows that W1,P-quasiconvexity is a necessary and sufficient condition of swlsc （sw*lsc） for multiple integrals with a Caratheodory function as the variational function, bounded by 0≤f（x,u,ξ）≤g（x,u）（|ξ|P+1）, （if 1≤p≤+∞）, where g（x, u） is also a Caratheodory function, or 0≤f（x,u,ξ）≤+∞, （if p=+∞）. The result for Wk,p-quasiconvexity is also shown.

3D image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging

We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays （PDFAs） with elemental images in computational integral imaging. The multiple PDFAs, whose spatial periods correspond to object＇s depths with the elemental image array （EIA）, can generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method. To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects and present the results.