Reach Energy of Digraphs

A Digraph D consists of two finite sets ), where  denotes the vertex set and denotes the arc set. For vertices  if there exists a directed path from  to  then  is said to be reachable from  and vice versa. The Reachability matrix of D is the  matrix , where  if  is reachable from and  otherwise. The eigen values corresponding to the reachability matrix are called reach eigen values. The reach energy of a digraph is defined by where  is the eigen value of the reachability matrix. In this paper we introduce the reach spectrum of a digraph and study its properties and bounds. Moreover, we compute reachspectrum for some digraphs

Fuzzy Semi-S-irresolute Continuous Mappings in Šostak’s Fuzzy Topological Spaces

In this paper, the concepts of fuzzy semi-S-irresolute open map, fuzzy semi-S-irresolute closed map and fuzzy semi-S-irresolute homeomorphism to the fuzzy topological spaces in Šostak’s sense are introduced and studied. Some of their characteristic properties are considered. Also a comparison between these new types of functions are established by giving examples

Altered Immune Responses in Rhesus Macaques Co-Infected with SIV and Plasmodium cynomolgi: An Animal Model for Coincident AIDS and Relapsing Malaria

BACKGROUND:Dual epidemics of the malaria parasite Plasmodium and HIV-1 in sub-Saharan Africa and Asia present a significant risk for co-infection in these overlapping endemic regions. Recent studies of HIV/Plasmodium falciparum co-infection have reported significant interactions of these pathogens, including more rapid CD4+ T cell loss, increased viral load, increased immunosuppression, and increased episodes of clinical malaria. Here, we describe a novel rhesus macaque model for co-infection that supports and expands upon findings in human co-infection studies and can be used to identify interactions between these two pathogens. METHODOLOGY/PRINCIPAL FINDINGS:Five rhesus macaques were infected with P. cynomolgi and, following three parasite relapses, with SIV. Compared to macaques infected with SIV alone, co-infected animals had, as a group, decreased survival time and more rapid declines in markers for SIV progression, including peripheral CD4+ T cells and CD4+/CD8+ T cell ratios. The naïve CD4+ T cell pool of the co-infected animals was depleted more rapidly than animals infected with SIV alone. The co-infected animals also failed to generate proliferative responses to parasitemia by CD4+ and CD8+ T cells as well as B cells while also having a less robust anti-parasite and altered anti-SIV antibody response. CONCLUSIONS/SIGNIFICANCE:These data suggest that infection with both SIV and Plasmodium enhances SIV-induced disease progression and impairs the anti-Plasmodium immune response. These data support findings in HIV/Plasmodium co-infection studies. This animal model can be used to further define impacts of lentivirus and Plasmodium co-infection and guide public health and therapeutic interventions

Hypergraphs and Rough Sets with Their Applications in Decision-Making Problems

In this work, authors introduce a novel rough set called hypergraph rough set using the minimal soft description. A relation [Formula: see text] on the set of all hypergraph rough sets T is defined and theoretically proved that [Formula: see text] is a lattice. The uniqueness of this study is highlighted by combining the hypergraphs and rough set theory. The developed concepts are illustrated through a real-life example which aims at finding the satisfaction level of employees in an organization. A comparative analysis authenticates the accuracy of the newly framed concept over the existing rough set theory. </jats:p

An Analysis of Organizational Behaviour using k-Approximation Spaces

Rough set theory and Soft set theory are the two mathematical concepts that plays a vital role in decision making problems. In complex systems, the objects are equipped with various set of attributes and that will add the complexity in making decision. In this paper, we introduce k-approximation space and covering based k-soft approximation space that leads us to define k-rough set and covering based k-soft rough set. The significance of these two concepts are illustrated and compared in analyzing the Organizational behaviour of the employees in an Organization

Fuzzy Graph Cellular Automaton and Its Applications in Parking Recommendations

The scope of this paper is to make the best use of cellular automaton. It is important that they can simulate not just a discrete model but also used to solve practical problems. To stimulate the research in this field, we define Fuzzy Graph Cellular Automaton (FGCA) and classify the fuzzy rule matrix according to the rules of the cellular automaton. We also provide the details of the generations of FGCA. To cover the defined concept, the parking recommendations have been figured out to show the effective performance of the research. In this proposed model, the fuzzy neighbourhood function represents the possible cell to which the vehicle can moved so that an efficient parking management can be maintained. By using fuzzy graph cellular automaton in parking recommendations, the results are more accurate than the other models. A comparative analysis is also done. In parking recommendations, the possibility of the available parking space can be predicted appropriately using the defined concepts. The results are simulated with [Formula: see text] coding in MATlab. </jats:p