A certain class of starlike functions

This paper presents a new class of functions analytic in the open unit disc, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well known classes. The paper deals with several ideas and techniques used in geometric function theory. The order of starlikeness in the class of convex functions of negative order is also considered here.     

On the distribution function of the complexity of finite sequences

Investigations of complexity of sequences lead to important applications such as effective data compression, testing of randomness, discriminating between information sources and many others. In this paper we establish formulae describing the distribution functions of random variables representing the complexity of finite sequences introduced by Lempel and Ziv in 1976. It is known that this quantity can be used as an estimator of entropy. We show that the distribution functions depend affinely on the probabilities of the so-called “exact” sequences.     

Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity

A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language (e.g., common nouns, verbs, adjectives, adverbs, modifiers). Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect to atomic and identity formulae as a special case. The systems admit a proof-theoretic semantics which does not only apply to logically compound but also to atomic and identity formulae—as well as to their components. The potential of the defined systems for a meticulous first-order analysis of natural inferences whose validity crucially depends on expressions of some of the aforementioned categories is demonstrated.     

Neural Network Based Algorithm for Dynamic System Optimization

A class of artificial neural networks with a two‐layer feedback topology to solve nonlinear discrete dynamic optimization problems is developed. Generalized recurrent neuron models are introduced. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. A comparative analysis of the computational requirements is made. The analysis shows advantages of this approach as compared to the standard dynamic programming algorithm. The technique has been applied to several important optimization problems, such as shortest path and control optimal problems.     

A multicriteria approach to two-level hierarchy scheduling in grids

In this paper we address a multicriteria scheduling problem for computational Grid systems. We focus on the two-level hierarchical Grid scheduling problem, in which at the first level (the Grid level) a Grid broker makes scheduling decisions and allocates jobs to Grid nodes. Jobs are then sent to the Grid nodes, where local schedulers generate local schedules for each node accordingly. A general approach is presented taking into account preferences of all the stakeholders of Grid scheduling (end-users, Grid administrators, and local resource providers) and assuming a lack of knowledge about job time characteristics. A single-stakeholder, single-criterion version of the approach has been compared experimentally with the existing approaches.     

Space-time image sequence analysis: object tunnels and occlusion volumes.

We address the issue of image sequence analysis jointly in space and time. While typical approaches to such an analysis consider two image frames at a time, we propose to perform this analysis jointly over multiple frames. We concentrate on spatiotemporal segmentation of image sequences and on analysis of occlusion effects therein. The segmentation process is three-dimensional (3-D); we search for a volume carved out by each moving object in the image sequence domain, or "object tunnel," a new space-time concept. We pose the problem in variational framework by using only motion information (no intensity edges). The resulting formulation can be viewed as volume competition, a 3-D generalization of region competition. We parameterize the unknown surface to be estimated, but rather than using an active-surface approach, we embed it into a higher dimensional function and apply the level-set methodology. We first develop simple models for the detection of moving objects over static background; no motion models are needed. Then, in order to improve segmentation accuracy, we incorporate motion models for objects and background. We further extend the method by including explicit models for occluded and newly exposed areas that lead to "occlusion volumes," another new space-time concept. Since, in this case, multiple volumes are sought, we apply a multiphase variant of the level-set method. We present various experimental results for synthetic and natural image sequences.