Spectra of Modular and Small-World Matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing short-cuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz type singular behaviour of the spectral density in a localised region of small $|\lambda|$ values. In the case of modular networks, we can identify contributions local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localised states in the band-gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalisation results.Comment: 18 pages, 5 figure

On the critical level-curvature distribution

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.Comment: 4 pages, 3 figure

An evolving network model with community structure

Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analysed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo

Multiband optical variability of 3C 279 on diverse time-scales

We have monitored the flat spectrum radio quasar, 3C 279, in the optical B, V, R, and I passbands from 2018 February to 2018 July for 24 nights, with a total of 716 frames, to study flux, colour, and spectral variability on diverse time-scales. 3C 279 was observed using seven different telescopes: two in India, two in Argentina, two in Bulgaria, and one in Turkey to understand the nature of the source in optical regime. The source was found to be active during the whole monitoring period and displayed significant flux variations in B, V, R, and I passbands. Variability amplitudes on intraday basis varied from 5.20 to 17.9 per cent. A close inspection of variability patterns during our observation cycle reveals simultaneity among optical emissions from all passbands. During the complete monitoring period, progressive increase in the amplitude of variability with frequency was detected for our target. The amplitudes of variability in B, V, R, and I passbands have been estimated to be 177 per cent, 172 per cent, 171 per cent, and 158 per cent, respectively. Using the structure function technique, we found intraday time-scales ranging from ∼23 min to about 115 min. We also studied colour–magnitude relationship and found indications of mild bluer-when-brighter trend on shorter time-scales. Spectral indices ranged from 2.3 to 3.0 with no clear trend on long-term basis. We have also generated spectral energy distributions for 3C 279 in optical B, V, R, and I passbands for 17 nights. Finally, possible emission mechanisms causing variability in blazars are discussed briefly.Fil: Agarwal, Aditi. Indian Institute of Astrophysics; IndiaFil: Cellone, Sergio Aldo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Complejo Astronómico "El Leoncito". Universidad Nacional de Córdoba. Complejo Astronómico "El Leoncito". Universidad Nacional de la Plata. Complejo Astronómico "El Leoncito". Universidad Nacional de San Juan. Complejo Astronómico "El Leoncito"; ArgentinaFil: Andruchow, Ileana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Mammana, Luis Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Complejo Astronómico "El Leoncito". Universidad Nacional de Córdoba. Complejo Astronómico "El Leoncito". Universidad Nacional de la Plata. Complejo Astronómico "El Leoncito". Universidad Nacional de San Juan. Complejo Astronómico "El Leoncito"; ArgentinaFil: Singh, Mridweeka. Aryabhatta Research Institute of Observational Sciences; IndiaFil: Anupama, G. C.. Indian Institute of Astrophysics; IndiaFil: Mihov, B.. Bulgarian Academy of Sciences; BulgariaFil: Raj, Ashish. Indian Institute of Astrophysics; IndiaFil: Slavcheva Mihova, L.. Bulgarian Academy of Sciences; BulgariaFil: Özdönmez, Aykut. Tübİtak National Observatory; TurquíaFil: Ege, Ergün. Istanbul University; Turquí

2,3,6,7-Tetra­bromo-9-butyl-9H-carbazole

In he title compound, C16H13Br4N, the carbazole skeleton is nearly planar [maximum deviation = 0.026 (4) Å] and makes a dihedral angle of 73.8 (4)° with the butyl chain. The butyl chain adopts a trans conformation. In the crystal, mol­ecules are linked by π–π stacking inter­actions [centroid–centroid distance = 3.559 (2) Å]

Vascular Wall-Resident CD44+ Multipotent Stem Cells Give Rise to Pericytes and Smooth Muscle Cells and Contribute to New Vessel Maturation

Here, we identify CD44(+)CD90(+)CD73(+)CD34(−)CD45(−) cells within the adult human arterial adventitia with properties of multipotency which were named vascular wall-resident multipotent stem cells (VW-MPSCs). VW-MPSCs exhibit typical mesenchymal stem cell characteristics including cell surface markers in immunostaining and flow cytometric analyses, and differentiation into adipocytes, chondrocytes and osteocytes under culture conditions. Particularly, TGFß1 stimulation up-regulates smooth muscle cell markers in VW-MPSCs. Using fluorescent cell labelling and co-localisation studies we show that VW-MPSCs differentiate to pericytes/smooth muscle cells which cover the wall of newly formed endothelial capillary-like structures in vitro. Co-implantation of EGFP-labelled VW-MPSCs and human umbilical vein endothelial cells into SCID mice subcutaneously via Matrigel results in new vessels formation which were covered by pericyte- or smooth muscle-like cells generated from implanted VW-MPSCs. Our results suggest that VW-MPSCs are of relevance for vascular morphogenesis, repair and self-renewal of vascular wall cells and for local capacity of neovascularization in disease processes

Paying for parking : improving stated-preference surveys

This article describes an experiment which introduced random ranges into the variables used for the design of a stated preference survey and its effects on willingness to pay for parking. User behaviour at the time of parking was modelled to determine their willingness to pay in order to get to their final destination more quickly. Calculating willingness to pay is fundamental during the social and economic assessment of projects. It is important to correctly model how car parks and their users interact in order to get values which represent reality as closely as possible. Willingness to pay is calculated using a stated preference survey and by calibrating multinomial logit models, taking variable tastes into account. It is shown that a value with a low variability can be obtained for willingness to pay by correctly establishing the context of the choice and randomly changing the variables around an average value

An approach for the identification of targets specific to bone metastasis using cancer genes interactome and gene ontology analysis

Metastasis is one of the most enigmatic aspects of cancer pathogenesis and is a major cause of cancer-associated mortality. Secondary bone cancer (SBC) is a complex disease caused by metastasis of tumor cells from their primary site and is characterized by intricate interplay of molecular interactions. Identification of targets for multifactorial diseases such as SBC, the most frequent complication of breast and prostate cancers, is a challenge. Towards achieving our aim of identification of targets specific to SBC, we constructed a 'Cancer Genes Network', a representative protein interactome of cancer genes. Using graph theoretical methods, we obtained a set of key genes that are relevant for generic mechanisms of cancers and have a role in biological essentiality. We also compiled a curated dataset of 391 SBC genes from published literature which serves as a basis of ontological correlates of secondary bone cancer. Building on these results, we implement a strategy based on generic cancer genes, SBC genes and gene ontology enrichment method, to obtain a set of targets that are specific to bone metastasis. Through this study, we present an approach for probing one of the major complications in cancers, namely, metastasis. The results on genes that play generic roles in cancer phenotype, obtained by network analysis of 'Cancer Genes Network', have broader implications in understanding the role of molecular regulators in mechanisms of cancers. Specifically, our study provides a set of potential targets that are of ontological and regulatory relevance to secondary bone cancer.Comment: 54 pages (19 pages main text; 11 Figures; 26 pages of supplementary information). Revised after critical reviews. Accepted for Publication in PLoS ON