Functional centrality in graphs

In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node. Closed walks are appropriately weighted according to the topological features that we need to measure

Holograms of Conformal Chern-Simons Gravity

We show that conformal Chern-Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor, even when the former is restricted to asymptotic Anti-deSitter behavior. For constant or fixed Weyl factor our results agree with a suitable scaling limit of topologically massive gravity results. For varying Weyl factor we find an enhancement of the asymptotic symmetry group, the details of which depend on certain choices. We focus on a particular example where an affine u(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a free chiral boson in the dual conformal field theory.Comment: 5

Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces

We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under free, periodic, and a combination of free and periodic boundary conditions. Results are also obtained for a simple quartic net embedded on two non-orientable surfaces, a Moebius strip and the Klein bottle. Our results are based on the use of a formula expressing the spanning tree generating function in terms of the eigenvalues of an associated tree matrix. An elementary derivation of this formula is given.Comment: latex, 9 pages, no figures, to appear in Lett. Appl. Mat

The Nullity of Bicyclic Signed Graphs

Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5

Quantum transport on small-world networks: A continuous-time quantum walk approach

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks and we evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that the limiting value of the transition probability is reached very quickly; second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request

Analysis of the ectopic osteogenic potential of adipose-derived mesenchymal stem cells in mice based on the relative gene expression of osteogenic markers

Osnovni cilj disertacije je da se uporedi i analizira osteogeni potencijal sveže izolovanih mezenhimskih matičnih ćelija belog masnog tkiva (ADSC) i in vitro osteoindukovanih ADSC na modelu ektopične implantacije kod Balb/c miševa. ADSC su nakon izolacije okarakterisane imunocitohemijskom analizom. Osteogena diferencijacija ADSC ispitana je analizom relativne ekspresije gena osteriksa (Sp7), osteokalcina (Bglap), alfa 1 lanca kolagena tipa I (Col1a1) i alkalne fosfataze (Alpl), vizuelizacijom fosfata i analizom ekspresije osteopontina. Miševima su subkutano implantirani implantati sastavljeni od sveže izolovanih ADSC, mineralnog koštanog matriksa (BMM) i plazme obogaćene trombocitima (PRP) (SPN grupa), osteoindukovanih ADSC, BMM i PRP (OPN grupa), PRP i BMM (PN kontrola) i samo od BMM (N kontrola). Osteogeneza u implantatima je ispitana analizom relativne ekspresije Sp7, Bglap, Col1a1 i Alpl, histomorfološkom, histomorfometrijskom i imunohistohemijskom analizom. Nađena je pozitivna CD29 i negativna CD14 ekspresija kod ćelija, što je karakteristika ADSC. Nakon petnaestodnevne osteoindukcije ADSC, zabeležena je najjača ekspresija markera osteogene diferencijacije. Najviša ekspresija gena markera osteogeneze, prisustvo ćelija nalik osteoblastima i osteoklastima, resorpcija BMM, visok procenat infiltriranog tkiva i prisustvo tkiva nalik osteoidu, ukazuju na napredovanje osteogeneze u OPN grupi nakon osme nedelje. U SPN grupi, nađeni su izraženi znaci inicijacije osteogeneze posle druge nedelje, a od četvrte ekspresija gena i ostalih markera opada što ukazuje na slabljenje osteogeneze.Rezultati doprinose razumevanju osteogenog potencijala različito pripremljenih ADSC što treba imati u vidu pri izboru načina i uslova za njihovu primenu u tretmanu koštanih defekata.The main subject of this doctoral dissertation was to compare and evaluate the osteogenic potential of freshly isolated, non-treated adipose-derived mesenchymal stem cells (ADSCs) and the potential of in vitro osteoinduced ADSCs in the ectopic boneforming model in Balb/c mice. The ADSCs were characterized after isolation by immunocytochemical analysis. Osteogenic differentiation of ADSCs was evaluated using relative gene expression analysis of osterix (Sp7), osteocalcin (Bglap), collagen type I alpha 1 chain (Col1a1) and alkaline phosphatase (Alpl), along with an assay for detection of phosphate deposits and an immunoexpression analysis of osteopontin. The implants composed of freshly isolated ADSCs, bone mineral matrix (BMM) and platelet-rich plasma (PRP) (SPN group), osteoinduced ADSCs, BMM and PRP (OPN group), BMM and PRP (PN control) and BMM-only (N control), were implanted subcutaneously in mice. The implants were analyzed using relative gene expression analysis of Sp7, Bglap, Col1a1 and Alpl, histochemical, histomorfometrical and immunohistochemical analyses. Positive immunoexpression of CD29 and negative of CD14 was found in the cells, which is a characteristic of ADSCs. After fifteen days of osteoinduction of ADSCs, the expression of the markers of osteogenic differentiation was the highest. The highest level of the bone-related gene expression, the presence of osteoblast-like and osteoclast-like cells, the resorption of BMM, a high percentage of infiltrated tissue and the presence of osteoid-like tissue, all suggest the progress of the osteogenesis in OPN implants after eight weeks. Strongly expressed signs of the initiation of osteogenesis were found in SPN implants after two weeks, but from the fourth week the expression of bone-related genes, as well as other analyzed markers decreased. The obtained results represent a contribution to the understanding of differences in the osteogenic potential of differently prepared ADSCs which is very important because of their utilization for the treatment of bone defects

Random matrix analysis of complex networks

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random, scale-free and small-world networks. These distributions follow Gaussian orthogonal ensemble statistic of RMT. To probe long-range correlations in the eigenvalues we study spectral rigidity via $\Delta_3$ statistic of RMT as well. It follows RMT prediction of linear behavior in semi-logarithmic scale with slope being $\sim 1/\pi^2$. Random and scale-free networks follow RMT prediction for very large scale. Small-world network follows it for sufficiently large scale, but much less than the random and scale-free networks.Comment: accepted in Phys. Rev. E (replaced with the final version

Quantitative structure-activity relationship of some 1-benzylbenzimidazole derivatives as antifungal agents

In the present study, the antifungal activity of some 1-benzylbenzimidazole derivatives against yeast Saccharomyces cerevisiae was investigated. The tested benzimidazoles displayed in vitro antifungal activity and minimum inhibitory concentration (MIC) was determined for all the compounds. Quantitative structure-activity relationship (QSAR) has been used to study the relationships between the antifungal activity and lipophilicity parameter, logP, calculated by using CS Chem-Office Software version 7.0. The results are discussed on the basis of statistical data. The best QSAR model for prediction of antifungal activity of the investigated series of benzimidazoles was developed. High agreement between experimental and predicted inhibitory values was obtained. The results of this study indicate that the lipophilicity parameter has a significant effect on antifungal activity of this class of compounds, which simplify design of new biologically active molecules

Spectral analysis of deformed random networks

We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are introduced, the spacing distribution shows a transition from the Poisson statistics to the Gaussian orthogonal ensemble statistics of random matrix theory. The eigenvalue density distribution shows a transition to the Wigner's semicircular behavior for a completely deformed network. The range for which spectral rigidity, measured by the Dyson-Mehta $\Delta_3$ statistics, follows the Gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure. The spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure, whereas the density distribution and the $\Delta_3$ statistics remain identical to the undeformed network. On the other hand the $\Delta_3$ statistics is useful for the larger deformation strengths. Finally, we analyze the spectrum of a protein-protein interaction network for Helicobacter, and compare the spectral behavior with those of the model networks.Comment: accepted for publication in Phys. Rev. E (replaced with the final version

Alloy formation by mg under-potential deposition on al from nitrate melts

Magnesium was underpotentially deposited on aluminium electrodes from magnesium nitrate-ammonium nitrate melts at temperatures ranging from 390 to 500 K. The electrochemical techniques used were linear sweep voltammetry and potential step. Electrodes were studied by scanning electron microscopy (SEM), energy dispersive spectrometry (EDS), energy dispersive X-ray spectroscopy (EDX) and X-ray diffraction (XRD). It was found that reduction processes of nitrate, nitrite and water (when present), in the underpotential range studied, took part simultaneously with magnesium underpotential deposition. Consequently, magnesium UPD reduction and stripping voltammetry peaks were not pronounced and well defined. Nevertheless, EDS, EDX and XRD measurements showed evidence of Mg2Al3, MgAl2 and Al12Mg17 alloys formed by underpotential deposition of magnesium onto aluminium substrate