Additive clustering provides a conceptually simple and potentially powerful approach to modeling the similarity relationships between stimuli. The ability of additive clustering models to accommodate similarity data, however, typically arises through the incorporation of large numbers of parameterized clusters. Accordingly, for the purposes of both model generation and model comparison, it is n...

Inspired by the PNNI protocol of the ATM Forum, this work focuses on the problem of node aggregation within peer groups and link aggregation between peer groups. It is assumed that the (large) network is already divided into peer groups. The objective is to maximally condense topology information subject to a given accuracy constraint. The QoS measures can be reduced into three distinct classes...

We study the connection between the additive structure of a finite set A ⊂ Z and the measure of large values of a trigonometric sum.

We develope a construction of an L-fuzzy valued measure by extending a measure defined on a σ-algebra of crisp sets to an L-fuzzy valued TM-countably additive measure defined on a TMclan of L-fuzzy sets in the case when operations for L-fuzzy sets and L-fuzzy real numbers are based on the minimum t-norm TM. Keywords— L-fuzzy set, L-fuzzy real number, L-fuzzy valued measure.

Entropy is a key measure in studies related to information theory and its many applications. Campbell for the first time recognized that the exponential of the Shannon’s entropy is just the size of the sample space, when distribution is uniform. Here is the idea to study exponentials of Shannon’s and those other entropy generalizations that involve logarithmic function for a probability distrib...

where d×x denotes a Haar measure on G. Up to constants, for (additive) Haar measure dx on A, d×x = dx/|detx|. For brevity, write |x| for |detx| when possible. [0.1] Convergence The integral defining us converges absolutely in Re(s) > n− 1: Recall the Iwasawa decomposition G = P ·K with P the parabolic subgroup of upper-triangular matrices. Since K is open in G, Haar measure on G restricted to K...

Additive trees have proved to be a valuable alternative to multidimensional scaling for representing proximity data [Sattath & Tversky, 1977]. Especially when the stimuli are conceptual rather than perceptual, an additive tree representation can be very useful [cf. Pruzansky, Tversky, & Carroll, 1982]. A tree is a connected graph where every pair of nodes is connected by a unique path. In an ad...

We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the s...

A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are intervalvalued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of intervalvalued non-additive measures, have been extensively applied in the mathematical representation of the vario...

Calculation of watermarking capacities of private Laplacian watermarking systems with the magnitude-error distortion measure under fixed attacks is addressed. First, in the case of an additive Laplacian attack, a nice closed-form formula for the watermarking capacities is derived, which involves only the distortion level and the parameter of the Laplacian attack. Second, in the case of an arbit...