PhD
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/50
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Some Studies of Two-Population Neural Field Model(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Zeeshan Afzal; CIIT/FA13-PMATH-009/LHR; Dr. Muhammad Yousaf Bhatti; LHR TP 5949We investigate the appearance and disappearance of localized activity states, so called bumps in Wilson-Cowan type two population neural field model under the influence of transient spatio-temporal external input with smooth α-type and piecewise-type temporal functions. This two-population model is composed of two coupled nonlinear differential equations derived for the dynamics of spatially localized populations of both excitatory and inhibitory model neurons. The model with no external input corresponds to atmost two bump pair solutions. Such a system can be interpreted as a minimal cortical model for short term working memory, that is the ability of the brain to actively hold stimulus-related information for some seconds in short term memory and discards once it becomes irrele- vant Initially, if there is no activity in the system, persistent activity state can be evoked by switching on a suitable transient excitatory external input. This activity remains stable even though external input is switched off. The effect of external input on appearance and disappearance of bumps for different spatial, smooth α-type and piecewise-type temporal functions of external input is investigated and found that certain parameters play a key role in the generation of persistent activity states in the network e.g. relative inhibition time constant, total duration and the amplitude of external input. It is found that the minimum values of the amplitude and active time to evoke the activity in the network is smaller than those observed in showing that the present choice of temporal functions in the external in- put is more effective and more close to natural behavior.Item Topological In Variants Of Graphs(Library Information Services, COMSATS University, Lahore Campus, 2017) Imran Nadeem,; FA13-PMATH-003; Dr. Hani Shaker, Assistant Profesor [Supervisor]Chemical graph theory provides useful tools such as molecular descriptors to develop strong intrinsic relationship between the physicochemical features of chemical com pounds and their molecular graphs. The study of molecular descriptors provides a the oretical basis for the fabrication of chemical materials and is helpful in making up for the lack of chemical experiments. There are two prominent types of molecular descrip tors; the topological indices and counting polynomials. Further, topological indices can be categorized in two major classes: one class is based on degree and the other class is based on distance. In this thesis, we present the study of certain topological indices belonging to degree- and distance-based classes and counting polynomials for some well-known nanostructures. We also present a comparative study between dif ferent topological indices belonging to degree- and distance-based classes for general graphs. In addition, we study the para-line transformation of graphs and obtain the gen eral expressions of certain topological indices for this transformation. We achieve the lower and upper bounds of certain distance-based topological indices for the para-line transformation of graphs