applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [8] proved that there exists a unique compact set K = K(I), called the attractor of the IFS I, such that K = ⋃m j=1 φj(K). Moreover, for any given probability vector p = (p1, . . . , pm), i.e. pj > 0 for all j and ∑m j=1 pj = 1, there exists a unique compactly supported proba...

A modified type of iterated function system (IFS) has recently been shown to generate images qualitatively similar to “classical” chaotic attractors. Here, we use time-delay embedding reconstructions of time-series from this system to generate three-dimentional projections of IFS attractors. These reconstructions may be used to access the topological structure of the periodic orbits embedded wi...

We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in R with arbitrary dimension H. Each IFS defines a probability distribution on R , so that the fractal inverse problem can b...

Following their early success in the utilisation of IFS to describe fractals, Barnsley and Demko mounted an investigation of the applicability of the IFS scheme for the description of arbitrary shapes. Central to the (general) IFS has became what they refer to as the collage theorem: the notion that if a figure can be "lazy tiled" with sufficient accuracy by smaller copies of itself at various ...

The most popular \fractal-based" algorithms for both the representation as well as compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces, e.g. IFS with probabilities (IFSP), Iterated Fuzzy Set Systems (IFZS), Fractal Transforms (FT), the Bath Fractal Transform (BFT) and IFS with grey-level maps (IFSM). (FT and...

conclusions current study revealed that a. flavus was the most common isolated pathogen. moreover, a. fumigatus was the second common isolated pathogen in patients with ifs. additionally, the hospital construction was an important environmental risk factor for acquisition of infection in patients with hematological malignancy. the most common season for ifs incidence was summer. additionally, t...

We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in R d , and the " IFS " refers to such a finite system of transformations, or functions. The iteration limits are pairs (X, µ) where X is a compact subset of R d , (the support of µ) and the mea...

Iterative Flattening Search (IFS) is a meta-heuristic strategy for solving multi-capacity scheduling problems. Given an initial solution, IFS iteratively applies: (1) a relaxationstep, in which a subset of scheduling decisions are randomly retracted from the current solution; and (2) a flattening-step, in which a new solution is incrementally recomputed from this partial schedule. Whenever a be...