Laplacian energy of graphs and digraphs.

Spectral graph theory (Algebraic graph theory) which emerged in 1950s and 1960s is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues and eigenvectors of matrices associated to the graph. The major source of research in spectral graph theory has been the study of relationship between the structural and spectral properties of graphs. Another source has research in quantum chemistry. Just as astronomers study stellar spectra to determine the make-up of distant stars, one of the main goals in spectral graph theory is to deduce the principal properties and structure of a graph from its graph spectrum (or from a short list of easily computable invariants). The spectral approach for general graphs is a step in this direction.Digital copy of Thesis.University of Kashmir

Spectral properties of geometric-arithmetic index

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reflected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA(1) from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices. Moreover, using this matrix, we define a GA Laplacian matrix which determines the geometric-arithmetic index of a graph and satisfies properties similar to the ones of the classical Laplacian matrix. (C) 2015 Elsevier Inc. All rights reserved.This research was supported in part by a Grant from Ministerio de Economía y Competitividad (MTM 2013-46374-P), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México

Upper bounds on the Laplacian spread of graphs

The Laplacian spread of a graph $G$ is defined as the difference between the largest and the second smallest eigenvalue of the Laplacian matrix of $G$. In this work, an upper bound for this graph invariant, that depends on first Zagreb index, is given. Moreover, another upper bound is obtained and expressed as a function of the nonzero coefficients of the Laplacian characteristic polynomial of a graph

Granice za Kirhofov indeks grafa

A longitudinal study conducted with the aim to study the effects of certain ergonomic programs on the prevention and reduction of the risks of musculoskeletal disorders in primary-school-age children rests on a sample of 76 examinees, pupils from Niš primary schools, aged 10 (±6 months). The basic sample was divided into three subsamples. The first subsample, EG1, comprising 28 pupils of both genders, represented the first experimental group. The second subsample, EG2, consisting of 22 pupils of both genders, represented the second experimental group, and the third subsample, KG, which consisted of 26 pupils of both genders, represented the control group. Both experimental groups (EG1 and EG2) underwent special four-month programs based on the education of children regarding ergonomic risks and their prevention, while the control group KG, attended only regular physical education classes. In addition, all three groups were subjected to a survey based on the Nordic questionnaire and body map, in order to determine the level of discomfort and pain when sitting or being in certain positions. Furthermore, all three groups were subjected to anthropometric measurements, and their postural status was established by an ultrasonic device (Spinal mouse). This was followed by taking anthropo-technical measurements of the school chairs and benches from the classrooms in which the pupils resided. Two measurements of the examinees were conducted -one at the beginning and the other at the end of the experimental period. The examinees from the experimental groups EG1 and EG2 underwent a special training program on ergonomic risks after which they were distributed a number of posters, leaflets and pamphlets on proper body posture and proper way of sitting. These groups had a chance to see a special cartoon on ergonomic risks and proper body posture, which was followed by an ergonomic quiz they were asked to do. The difference between the experimental groups EG1 and EG2 was reflected in the way of implementation of the two programs. Among other exercises, the experimental group EG1, had exercises with stability (pilates) balls during their physical education classes, while the experimental group EG2 practiced the program "School on the Move" (during the classes, the children could, when and if they would feel like it, move freely or do stretching or any other exercises). Group EG1 was shown the practical application of the ergonomic backpack which was complemented by weighing the school bags they carry every day. The obtained data were statistically analyzed and presented in several tables. Following the set objectives, tasks and research hypotheses, the conclusions were drawn which indicate the positive effects of the experimental programs and the negative impact of school furniture on the postural status of the examinees. A proposal was made to change the size and shape of school furniture, which should be adjusted to the examinees’ anthropometric measures. According to the obtained results, the experimental group EG1, working with stability balls, had statistically more significant results than the experimental group EG2 and the control group KG. The experimental group EG2, which applied the concept of "School on the move", had statistically more significant results in comparison to the control group KG. As for the children’s postural status, the different programs and approaches applied with experimental groups (EG1 and EG2) and the control group KG point to the fact that there were statistically significant effects with the examinees of the experimental groups in terms of body posture. The Nordic test, used in the final measurement with the experimental group EG1 revealed good statistical significance in reducing discomfort and pain in the neck area, while the experimental group EG2 confirmed statistical significance in reducing pain and discomfort during prolonged sitting. This research has its practical and theoretical value. First of all, there is a great need to pay attention to children in growth, because there is a high risk of developing musculoskeletal disorders in the spine region, as well as of other hypertension diseases, hypokinesia, obesity, cardiac and vascular disorders. This study could serve as a pilot research for a larger and more complex scientific research in the field of prevention of musculoskeletal and other changes

Biochemical and molecular characterisation of purine transporters of Trypanosoma brucei brucei

This thesis describes the elucidation and comparison of substrate recognition relationships for the H2 nucleobase transporter of T. b. brucei and the main nucleobase transporter of human erythrocytes. Using standard transport kinetics, application of the Cheng-Prusoff equation and a derivation of the Nernst equation, it was possible to determine the Gibbs free energy (DG°) for the interactions of purine analogues with each transporter, which allowed predictions about the nature of the interactions that are essential for uptake. A range of unusual tricyclic and "fleximer" purine analogues was also assayed for ability to interact with the various purine transporters in T. b. burcei and human erythrocytes. This provided further insights into the extent that the substrate-binding pocket can accommodate unusual and large substrates. Some of the purine analogues used for the substrate-recognition study also displayed limited trypanocidal activity in vitro. More importantly, these results provide a foundation for the design and development of purine nucleobase analogues with anti-trypanosomal action that are efficiently and selectively accumulated by the parasite. One of the main aims of the project was to clone and characterise nucleobase transporters from T. b. brucei. The initial functional complementation strategy in nucleobase-transport deficient trypanosomes proved unsuccessful due to the presence of an additional, previously uncharacterised purine transporter in the trypanosome selection background and other technical obstacles. Homology searching of the T. b. brucei genome database led to the identification of a sequence with substantial similarity to the Adenosine Transporter 1 (TbAT1) gene previously shown to be responsible for the P2 nucleoside transport activity. The AT-like sequence was cloned, functionally expressed in heterologous systems (Saccharomyces cerevisiae and Xenopus oocytes), and characterised as the high-affinity Nucleobase Transporter 1 (TbNBT1). This also marked the first time a nucleobase-specific transporter had been cloned and characterised from any protozoan

Activation of beta2-adrenergic receptors alleviates neuropathic pain hypersensitivity in mice: focus on spinal glial cells

Chronic pain affects roughly one-fifth of the world’s population, and many patients do not respond to current therapies or conventional analgesics. Thus, studying the molecular mechanisms underlying neuropathic pain is crucial in identifying novel molecular targets that can be used to develop effective pain relief therapies. Previous studies have thus far focused on α2-adrenergic receptors (α2-ARs) and neuronal excitability, among others. However, recent research suggests that astrocytes and microglia, which express adrenergic receptors, contribute significantly to neuropathic pain. In particular, microglia have been found to express elevated levels of Gs-coupled β2-AR and they are responsive to norepinephrine application. Additionally, systemic administration of β2-AR agonists, such as Formoterol, has anti-inflammatory and anti-nociceptive properties in neuropathic pain, but the underlying processes are poorly understood. Therefore, this thesis work focuses on investigating glial noradrenergic signaling via β2-AR, specifically on microglia and its contribution to the modulation of neuropathic pain in mice. In the present study, activation of the β2-ARs through Formoterol induced a decrease of anti-inflammatory cytokine levels in primary isolated microglia and reversed nerve injury-induced morphological alterations in spinal dorsal horn microglia. Systemic administration of Formoterol inhibited evoked behaviors as well as aversive components related to neuropathic pain and reduced chronically-established neuropathic pain. The analgesic effects of Formoterol were mainly mediated by microglia, as demonstrated by employing the conditional knock-out mouse line lacking the β2-AR specifically in microglia. Remarkably, the effect of Formoterol on neuropathic pain-related behavior and microgliosis was lost in mice with the microglia-specific deletion of β2-ARs. In addition, microglia phenotype showed a sex-dependency in the late phase of neuropathic pain, which was not observed in response to β2-AR stimulation. Notably, Formoterol also reduced astrogliosis in the late stage of neuropathic pain independently of β2-AR signaling in microglia. Collectively, this work highlights the impact of microglial β2-AR stimulation in mediating the inhibition of pro-inflammatory signaling in the spinal cord during the initial phase of neuropathic pain. These results emphasize the importance of exploring microglial β2-AR agonists in alleviating neuropathic pain and elucidating the underlying mechanisms

Rational Drug Design for Neglected Diseases: Implementation of Computational Methods to Construct Predictive Devices and Examine Mechanisms

Over a billion individuals worldwide suffer from neglected diseases. This equates to approximately one-sixth of the human population. These infections are often endemic in remote tropical regions of impoverished populations where vectors can flourish and infected individuals cannot be effectively treated due to a lack of hospitals, medical equipment, drugs, and trained personnel. The few drugs that have been approved for the treatments of such illnesses are not widely used because they are riddled with inadequate implications of cost, safety, drug availability, administration, and resistance. Hence, there exists an eminent need for the design and development of improved new therapeutics. Influential world-renowned scientists in the Consortium for Parasitic Drug Development (CPDD) have preformed extensive biological testing for compounds active against parasites that cause neglected diseases. These data were acquired through several collaborations and found applicable to computational studies that examine quantitative structure-activity relationships through the development of predictive models and explore structural relationships through docking. Both of these in silico tools can contribute to an understanding of compound structural importance for specific targets. The compilation of manuscripts presented in this dissertation focus on three neglected diseases: trypanosomiasis, Chagas disease, and leishmaniasis. These diseases are caused by kinetoplastid parasites Trypanosoma brucei, Trypanosoma cruzi, and Leishmania spp., respectively. Statistically significant predictive devices were developed for the inhibition of the: (1) T. brucei P2 nucleoside transporter, (2) T. cruzi parasite at two temperatures, and (3) two species of Leishmania. From these studies compound structural importance was assessed for the targeting of each parasitic system. Since these three parasites are all from the Order Kinetoplastida and the kinetoplast DNA has been determined a viable target, compound interactions with DNA were explored to gain insight into binding modes of known and novel compounds