Consonant Random Sets: Structure and Properties

Abstract. In this paper, we investigate consonant random sets from the point of view of lattice theory. We introduce a new definition of consonancy and study its relationship with possibility measures as upper probabilities. This allows us to improve a number of results from the literature. Finally, we study the suitability of consonant random sets as models of the imprecise observation of random variables

Maxitive Integral of Real-Valued Functions

The paper pursues the definition of a maxitive integral on all real-valued functions (i.e., the integral of the pointwise maximum of two functions must be the maximum of their integrals). This definition is not determined by maxitivity alone: additional requirements on the integral are necessary. The paper studies the consequences of additional requirements of invariance with respect to affine transformations of the real line. © Springer International Publishing Switzerland 2014

Quantitative approximation by shift invariant multivariate sublinear-shilkret operators

A very general multivariate positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized Shilkret operators are presented fulfilling all the above properties, the higher order of multivariate approximation of these operators is also considered. It follows [3]

Quantitative approximation by shift invariant univariate sublinear-shilkret operators

A very general positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another general positive sublinear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Additionally, two examples of very general specialized operators are presented fulfilling all the above properties, the higher order of approximation of these operators is also considered. It follows [3]

Quantitative approximation by shift invariant multivariate sublinear-shilkret operators

A very general multivariate positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized Shilkret operators are presented fulfilling all the above properties, the higher order of multivariate approximation of these operators is also considered. It follows [3]

Use of DNA Fingerprinting To Investigate a Multiyear, Multistate Tuberculosis Outbreak

In 1998–1999, the Baltimore TB control program detected a cluster of 21 tuberculosis (TB) cases. Patients reported frequent travel to various East Coast cities. An investigation was conducted to determine whether transmission of the same Mycobacterium tuberculosis strain was occurring in these other localities. A collaborative investigation among federal, state, and local TB controllers included TB record reviews, interviews of patients, and restriction fragment length polymorphism (RFLP) analysis of selected M. tuberculosis isolates from diagnosed TB patients in several cities in 1996–2001. A national TB genotyping database was searched for RFLP patterns that matched the outbreak pattern. Eighteen additional outbreak-related cases were detected outside of Baltimore—the earliest diagnosed in New Jersey in 1996, and the most recent in New York City in late 2001. The outbreak demonstrates the need for strategies to detect links among patients diagnosed with TB across multiple TB control jurisdictions