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

Which morphological abnormalities better define the elongation of transverse aortic arch: a magnetic resonance angiography study

Background: The aim of the study is to investigate the relation between morphological abnormalities that might indicate elongation of transverse aortic arch (ETA) and various aortic and thoracic measurements, and to determine which morphological criteria define the elongated transverse arch better.Materials and methods: Patients under 40 years of age who underwent contrast enhanced thoracic magnetic resonance angiography were included in the study. Images were evaluated for the presence of morphological arch abnormalities such as late take off (LTO) of left subclavian artery (LSA), flattening of the arch, and kinking at the posterior or anterior contour of the lesser curvature. Various aortic and thoracic measurements, including the distance between the orifices of the left common carotid artery (LCCA) and LSA, were made. Statistical relation between morphological abnormalities and these measurements was analysed. The effect of morphological abnormalities and their combinations on the distance between LCCA and LSA orifices was evaluated by linear regression analysis.Results: Ninety three cases were included in the study. All morphological abnormalities and most of their combinations show statistically significant relation with longer LCCA to LSA distance. The parameters that most affected this distance were combination of flattening with LTO of LSA, anterior kinking and combination of anterior kinking with both flattening and LTO, respectively.Conclusions: Our study showed that the finding which best defines ETA is the combination of LTO and arch flattening. Therefore, we recommend using this combination in the diagnosis of ETA instead of the classical diagnostic criteria including combination of LTO and posterior kinking

FARKLI TUTKALLARIN KAYIN ve SARIÇAM AĞAÇLARINDAKİ YAPIŞMA DİRENÇLERİNİN BELİRLENMESİ

Bu çalışmada, poliüretan esaslı Pu-Mon ve Pu-Ma, polivinilasetat esaslı PVAc-MA22, PVAc-MA35 ve PVAc-MA50 ile yapıştırılmış Doğu kayını (Fagus orientalis L.) ve sarıçam (Pinus Sylvestris L.) odunlarının yapışma direnci, TS EN 205 esaslarına göre belirlenmiştir. Deney sonuçlarına göre, en yüksek yapışma direnci Pu-Ma (16.01 N/mm2) ve PVAc-MA35 (15.12 N/mm2) ile yapıştırılmış kayın numunelerinde, en düşük yapışma direnci ise Pu-Mon (7.98 N/mm2) ve PVAc-MA35 (7.67 N/mm2) ile yapıştırılmış sarıçam numunelerinde tespit edilmiştir. 

Level curvature distribution in a model of two uncoupled chaotic subsystems

We study distributions of eigenvalue curvatures for a block diagonal random matrix perturbed by a full random matrix. The most natural physical realization of this model is a quantum chaotic system with some inherent symmetry, such that its energy levels form two independent subsequences, subject to a generic perturbation which does not respect the symmetry. We describe analytically a crossover in the form of a curvature distribution with a tunable parameter namely the ratio of inter/intra subsystem coupling strengths. We find that the peak value of the curvature distribution is much more sensitive to the changes in this parameter than the power law tail behaviour. This observation may help to clarify some qualitative features of the curvature distributions observed experimentally in acoustic resonances of quartz blocks

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

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

Terahertz communications for 5G and beyond

A brief discussion about the exclusive properties and applications of terahertz technology is provided in this chapter. The frequency spectrum terahertz (THz) is also discussed. The applications of terahertz in the field of sensors and terahertz for communications are covered. State-of-the-art literature starting from the early to the latest research conducted is provided and analyzed in terms of the performance of terahertz systems. Terahertz, known as Tera waves or T-waves rather than submillimeter wave, has approximately a fraction of a wavelength less than 30 μm. T-wave is heavily used in sensing and imaging applications, and has no ionization hazards and is an excellent candidate frequency band to defeat the multipaths interference problems for pulse communications. The lower quantum energy of T-waves identifies its potential applications toward near-field imaging, telecommunications, spectroscopy, and sensing, including medical diagnoses and security screening. Identification of DNA signatures including complex real-time molecular dynamics through dielectric resonance is a good example of terahertz spectroscopy instruments nowadays. This concluding chapter will not only address the practical applications of terahertz communications, but also identify the research challenges that lie ahead in terms of terahertz antenna desig