Let X1 t1 , X 2 t2 , · · · ,X N tN be N independent Lévy processes in IR d with their respective Lévy exponents Ψj, j = 1, 2, · · · , N . The random field Xt = X 1 t1 +X 2 t2 + · · ·+X N tN , t = (t1, t2, · · · , tN ) ∈ IR N + is called the additive Lévy process. Let λd denote Lebesgue measure in IR . Define E1 + E2 = {x+ y : x ∈ E1, y ∈ E2} for any two sets E1, E2 of IR . The following theorem...

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

We prove the following theorems: 1. If X has strong measure zero and if Y has strong first category, then their algebraic sum has property s0. 2. If X has Hurewicz’s covering property, then it has strong measure zero if, and only if, its algebraic sum with any first category set is a first category set. 3. If X has strong measure zero and Hurewicz’s covering property then its algebraic sum with...

This paper focusses on the investigation of a pattern recognition method based on the fuzzy integral. Until now this method has used a general fuzzy measure, which is characterized by exponential complexity. Naturally this led to some difficulties in practical applications of this pattern recognition method. In this paper, a heuristic algorithm for the identification of the 2-additive fuzzy mea...

Based on the monogamy of entanglement, we develop the technique of quantum conditioning to build an additive entanglement measure: the conditional entanglement of mutual information. Its operational meaning is elaborated to be the minimal net "flow of qubits" in the process of partial state merging. The result and conclusion can also be generalized to multipartite entanglement cases.

We propose an additive "semantic measure" theory based on the model of a perception based fuzzy truthoods in analogy to probability measure. Probability measure, which is the subject of the probability theory, is a special case of the fuzzy measure in the Dempster-Shafer theory when the focal sets are singletons. In the literature, the fuzzy measure is considered an extension of the probability...

This paper explains the empirical phenomenon of persistent “fifty-fifty”probability judgments through a model of Bayesian updating under ambiguity. To this purpose I characterize an announced probability judgment as a Bayesian estimate given as the solution to a Choquet expected utility maximization problem with respect to a neo-additive capacity that has been updated in accordance with the Gen...

Reverse phase protein arrays (RPPA) measure the relative expression levels of a protein in many samples simultaneously. Observed signal from these arrays is a combination of true signal, additive background, and multiplicative spatial effects. Background subtraction alone is not sufficient to remove all nonbiological trends from the data. We developed a surface adjustment that uses information ...

AIMS This study was undertaken to determine whether simultaneous administration of both alcohol and nicotine systemically would result in an additive dopamine release in the nucleus accumbens (NACC). Moreover, to also investigate whether nicotinic receptors may be mediating these effects of alcohol and nicotine, the effects of mecamylamine, a nicotinic receptor antagonist was also evaluated. ...

In this study, a duration{based measure is formulated for assigning con dence scores to phonetic time{alignments produced by an automatic speech segmentation system. For speech corrupted by additive noise or telephone channel environments, the proposed con dence measure is shown to provide a reliable means by which gross segmentation errors can be automatically detected and marked for human han...