Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑N n=1 f(n)Xn ∑N n=1 f(n) = EX a.s.

We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random a...

The position of the hinge point of mitral annulus (MA) is important for segmentation, modeling and multimodalities registration of cardiac structures. The main difficulties in identifying the hinge point of MA are the inherent noisy, low resolution of echocardiography, and so on. This work aims to automatically detect the hinge point of MA by combining local context feature with additive suppor...

Let f(n) be a strongly additive complex valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑ N n=1 f(n)Xn ∑ N n=1 f(n) a.s. = EX.

We present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typically arise in finite element discretizations. An example of the additive Schwarz method applied to nonsymmetric but definite matrices is presented for which the abstract assumptions are verified. A variable precondit...

Rates of convergence of limit theorems are established for a class of random processes called here quasi-additive smooth Euclidean functionals. Examples include the objective functions of the traveling salesman problem, the Steiner tree problem, the minimumspanning tree problem, the minimumweight matching problem, and a variant of the minimum spanning tree problem with power weighted edges.

This paper examines GMM and ML estimation of econometric models and the theory of Hausman tests with sampling weights. Weighted conditional GMM can be more e$cient than weighted conditional MLE, an ine$cient alternative to full information MLE under choice-based sampling, unless regressions have homoscedastic additive disturbances or sampling weights are independent of exogenous variables. GMM ...

We propose to extend the aggregation scheme of Saaty’s AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the consistency case....

We derive a formula for the result of the additive mixture of two colours, in double-cone space. We use NakaRushton law to combine the luminance, circular weighted averaging to combine the hue and two rules of thumb to get the resulting chromatic saturation.

Let G = (V;E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe an ~ O(minfn3=2m1=2; n7=3g) time algorithmAPASP2 for computing all distances in G with an additive one-sided error...