Intersection Graph of a Module

Let $V$ be a left $R$-module where $R$ is a (not necessarily commutative) ring with unit. The intersection graph \cG(V) of proper $R$-submodules of $V$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper $R$-submodules of $V,$ and there is an edge between two distinct vertices $U$ and $W$ if and only if $U\cap W\neq 0.$ We study these graphs to relate the combinatorial properties of \cG(V) to the algebraic properties of the $R$-module $V.$ We study connectedness, domination, finiteness, coloring, and planarity for \cG (V). For instance, we find the domination number of \cG (V). We also find the chromatic number of \cG(V) in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs in \cG (V) determining the structure of $V$ for which \cG(V) is planar

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201

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

Wheel Hub Fatigue Performance under Non-constant Rotational Loading and Comparison to Eurocycle Test

AbstractWheel Eurocycle (EC) loading condition could be adapted to hub as a result of similar loading characteristics on vehicle. A correlation is constructed between road load data (RLD) for specified vehicles and EC test spectrum. To provide correlation between EC and RLD, test speed, axial and lateral loads at EC are converted to cyclic loading condition and relevant loading scenarios are generated. Rotational effect is taken into account. Pseudo-damage results of RLD and EC spectra are compared and expected fatigue lifetime for hub is presented

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

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

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