K. G. Subramanian

Normal Forms of Spiking Neural P Systems With Anti-Spikes

Spiking neural P systems with anti-spikes (ASN P systems, for short) are a variant of spiking neural P systems, which were inspired by inhibitory impulses/spikes or inhibitory synapses. In this work, we consider normal forms of ASN P systems. Specifically, we prove that ASN P systems with pure spiking rules of categories (a, a) and (a, a̅) without forgetting rules are universal as number generating devices. In an ASN P system with spiking rules of categories (a, a̅) and (a̅, a) without forgetting rules, the neurons change spikes to anti-spikes or change anti-spikes to spikes; such systems are proved to be universal. We also prove that ASN P systems with inhibitory synapses using pure spiking rules of category (a, a) and forgetting rules are universal. These results answer an open problem and improve a corresponding result from [IJCCC, IV(3), 2009, 273-282].

Pure 2D picture grammars and languages

A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids.

Pure 2D picture grammars (P2DPG) and P2DPG with regular control

In this note a new model of grammatical picture generation is introduced. The model is based on the notion of pure context-free grammars of formal string language theory. The resulting model, called Pure 2D context-free grammar (CFG), generates rectangular picture arrays of symbols. The generative power of this model in comparison to certain other related models is examined. Also we associate a regular control language with a Pure 2D CFG and notice that the generative power increases. Certain closure properties are obtained.

P systems and picture languages

Array-rewriting P systems were introduced in [2] linking the two areas of membrane computing and picture grammars. Subsequently a variety of P systems with array objects and different kinds of rewriting has been introduced. Here we discuss a few prominent systems among these, point out their features and indicate possible problems for future study.

Recognizing occluded faces by exploiting psychophysically inspired similarity maps

The presence of occlusions in facial images is inevitable in unconstrained scenarios. However recognizing occluded faces remains a partially solved problem in computer vision. In this contribution we propose a novel Bayesian technique inspired by psychophysical mechanisms relevant to face recognition to address the facial occlusion problem. For some individuals certain facial regions, e.g. features comprising of some of the upper face, might be more discriminative than the rest of the features in the face. For others, it might be the features over the mid face and some of the lower face that are important. The proposed approach in this paper, will allow for such a psychophysical analysis to be factored into the recognition process. We have discovered and modeled similarity mappings that exist in facial domains by means of Bayesian Networks. The model can efficiently learn and exploit these mappings from the facial domain and hence capable of tackling uncertainties caused by occlusions. The proposed technique shows improved recognition rates over state of the art techniques.

A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

Functions that are analytic in the unit disk and satisfy the differential equation are considered, where is subordinated to a normalized convex univalent function . These functions are given by a double integral operator of the form with subordinated to . The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function .

Contextual array grammars and array P systems

Contextual array grammars, with selectors not having empty cells, are considered. A P system model, called contextual array P system, that makes use of array objects and contextual array rules, is introduced and its generative power for the description of picture arrays is examined. A main result of the paper is that there is a proper infinite hierarchy with respect to the classes of languages described by contextual array P systems. Such a hierarchy holds as well in the case when the selector is also endowed with the #−sensing ability.

A P System Model for Contextual Array Languages

A P system model, called Contextual array P system, that makes use of array objects and contextual array rules, is introduced and its generative power in the description of picture arrays is examined, by comparing it with certain other array generating devices.

A P system model with pure context-free rules for picture array generation

Syntactic models constitute one of the main areas of mathematical studies on picture array generation. A number of 2D grammar models have been proposed motivated by a variety of applications. A P system is a biologically motivated new computing model, proposed by Paun in the area of membrane computing. It is a rich framework for dealing with different problems, including the problem of handling picture array generation. In this paper, the generative power of the array-rewriting P system with pure 2D context-free rules is investigated by comparing it with other 2D grammar models, thus bringing out the suitability of this P system model for picture array generation.

Convolution Properties of Classes of Analytic and Meromorphic Functions

General classes of analytic functions defined by convolution with a fixed analytic function are introduced. Convolution properties of these classes which include the classical classes of starlike, convex, close-to-convex, and quasiconvex analytic functions are investigated. These classes are shown to be closed under convolution with prestarlike functions and the Bernardi-Libera integral operator. Similar results are also obtained for the classes consisting of meromorphic functions in the punctured unit disk.