The Design of the Black Patch

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Multidimensional dependency measures

The problem of dependency between two random variables has been studied throughly in the literature. Many dependency measures have been proposed according to concepts such as concordance, quadrant dependency, etc. More recently, the development of the Theory of Copulas has had a great impact in the study of dependence of random variables specially in the case of continuous random variables. In the case of the multivariate setting, the study of the strong mixing conditions has lead to interesting results that extend some results like the central limit theorem to the case of dependent random variables.In this paper, we study the behavior of a multidimensional extension of two well-known dependency measures, finding their basic properties as well as several examples. The main difference between these measures and others previously proposed is that these ones are based on the definition of independence among n random elements or variables, therefore they provide a nice way to measure dependency.The main purpose of this paper is to present a sample version of one of these measures, find its properties, and based on this sample version to propose a test of independence of multivariate observations. We include several references of applications in Statistics.     

脉冲摄动微分系统的有界性

通过利用变分Lyapunov函数方法, 该文主要研究了脉冲摄动微分系统关于两个测度的有界性. 与以前结果相比, 不难发现变分Lyapunov函数方法是Lyapunov函数方法的推广 .     

Convolution products of nonidentical distributions on a topological semigroup

In this paper we present a number of sufficient conditions on a sequence of probability measuresµ _n on a locally compact (second countable) Hausdorff topological semigroupS that guarantee the weak convergence of the sequence of convolution productsµ _k,n µ _{k + 1} *···*µ _n (k), asn, for allk0.     

Zeros of the densities of infinitely divisible measures on R n

Let be an infinitely divisible probability measure onR ⁿ without Gaussian component and let be its Lévy measure. Suppose that is absolutely continuous with respect to the Lebesgue measure . We investigate the structure of the set ⁿ of admissible translates of . This yields a unified presentation of previously known results. We also show that if(S)>0 then is equivalent to , under the assumption that supp =R ⁿ , whereS is the closure of the semigroup generated by the support of .The research of this author is supported by KBN Grant.The research of this author is supported by AFSOR Grant No. 90-0168, and the University of Tennessee Science Alliance, a State of Tennessee Center of Excellence.     

Rearrangements of the Haar System that Preserve BMO

Let D denote the collection of dyadic intervals in the unitinterval. Let be a rearrangement of the dyadic intervals. Westudy the induced operator where h_I is the L normalized Haar function. We find geometricconditions on which are necessary and sufficient for T to bebounded on BMO. We also characterize the rearrangements of theL^p normalized Haar system in L^p. 1991 Mathematics Subject Classification:42C20, 43A17, 47B38.     

Trace operators,Feynman distributions,and multiparameter white noise

Within the framework of white noise analysis on the probability space = ^* R ^d R ^M , the recent work by Johnson and Kallianpur on the Hu-Meyer formula, traces, and natural extensions is generalized to the multiparameter case:d>1. Besides providing a more general setting for these topics, the paper gives an alternative definition for the traces, a distributional version of the natural extension, and a generalized Kallianpur-Feynman distribution. The development illustrates how traces and natural extensions are intimately related to Wick products and the change of covariance formula from quantum field theory, as well as to the projective tensor product of Hilbert spaces from functional analysis.     

Oscillating singularities on cantor sets: A grand-canonical multifractal formalism

The singular behavior of functions is generally characterized by their Hölder exponent. However, we show that this exponent poorly characterizes oscillating singularities. We thus introduce a second exponent that accounts for the oscillations of a singular behavior and we give a characterization of this exponent using the wavelet transform. We then elaborate on a grand-canonical multifractal formalism that describes statistically the fluctuations of both the Hölder and the oscillation exponents. We prove that this formalism allows us to recover the generalized singularity spectrum of a large class of fractal functions involving oscillating singularities.     

A journey through the hazards of possible errors in the analysis of trace elements in body fluids and tissues

Accuracy of the analysis results of trace elements in body fluids and tissues needs to be ascertained during every step of the procedure, starting with the choice of sample, followed by appropriate sampling, analytical methodology and quality assurance, to end with the evaluation of the data. The characterisation of the reference group is important because it is fundamental in the decision making step. Appropriate sampling ensures that the concentration of the trace element in the collected sample is exactly the same as was originally present in the individual. Besides, sample manipulation should not alter the concentrations. The analytical technique chosen is supposed to offer sufficient specificity and sensitivity, and to allow the determination of the trace element with a signal exceeding the quantification limit of detection. Quality assurance through the analysis of similar levels in certified reference materials is a very valuable asset to prove the validity of the detection and to eliminate possible errors which may jeopardize the accuracy and reliability of the data.