372 research outputs found
Intersection Graph of a Module
Let be a left -module where is a (not necessarily commutative)
ring with unit. The intersection graph \cG(V) of proper -submodules of
is an undirected graph without loops and multiple edges defined as follows: the
vertex set is the set of all proper -submodules of and there is an edge
between two distinct vertices and if and only if We
study these graphs to relate the combinatorial properties of \cG(V) to the
algebraic properties of the -module 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 for which \cG(V) is planar
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 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
for large level-curvatures 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
Locally Decodable Codes for Edit Distance
Abstract. Locally decodable codes (LDC) [1,5] are error correcting codes that allow decoding (any) individual symbol of the message, by reading only few symbols of the codeword. Consider an application such as storage solutions for large data, where errors may occur in the disks (or some disks may just crush). In such an application, it is often de-sirable to recover only small portions of the data (have random access). Thus, in such applications, using LDC provides enormous efficiency gains over standard error correcting codes (ECCs), that need to read the en-tire encoded message to learn even a single bit of information. Typically, LDC’s, as well as standard ECC’s decode the encoded messaged if upto some bounded fraction of the symbols had been modified. This corre-sponds to decoding strings of bounded Hamming distance from a valid codeword. An often more realistic metric is the edit distance, measur-ing the shortest sequence of insertions and deletions (indel.) of symbols leading from one word to another. For example, (few) indel. modifica
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
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
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
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