The Hopf algebra structure of the Z3_3-graded quantum supergroup GLq,j(1∣1)_{q,j}(1|1)

In this work, we give some features of the Z$_3$-graded quantum supergroup

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

A bronze mirror with Aphrodite and Eros from Nicomedia in Bithynia (northwestern Turkey)

The Archeological and Ethnographical Museum of Kocaeli has in its collection a small, disc–shaped bronze mirror decorated with a relief scene, whose protagonist is the goddess Aphrodite. The scene shows Aphrodite seated left of centre on a rock. She is accompanied by two figures, a female who stands on a pedestal in front of her and her young son, Eros, who is behind her. This formerly unpublished object was found in Nicomedia in Bithynia, and has been dated to the fourth century BC. This paper will give a detailed presentation of the mirror relief scene, focus on its art–historical contextualisation and argue a first century BC. date for this object

External Sampling

36th International Colloquium, ICALP 2009, Rhodes, Greece, July 5-12, 2009, Proceedings, Part IWe initiate the study of sublinear-time algorithms in the external memory model [1]. In this model, the data is stored in blocks of a certain size B, and the algorithm is charged a unit cost for each block access. This model is well-studied, since it reflects the computational issues occurring when the (massive) input is stored on a disk. Since each block access operates on B data elements in parallel, many problems have external memory algorithms whose number of block accesses is only a small fraction (e.g. 1/B) of their main memory complexity. However, to the best of our knowledge, no such reduction in complexity is known for any sublinear-time algorithm. One plausible explanation is that the vast majority of sublinear-time algorithms use random sampling and thus exhibit no locality of reference. This state of affairs is quite unfortunate, since both sublinear-time algorithms and the external memory model are important approaches to dealing with massive data sets, and ideally they should be combined to achieve best performance. In this paper we show that such combination is indeed possible. In particular, we consider three well-studied problems: testing of distinctness, uniformity and identity of an empirical distribution induced by data. For these problems we show random-sampling-based algorithms whose number of block accesses is up to a factor of 1/√B smaller than the main memory complexity of those problems. We also show that this improvement is optimal for those problems. Since these problems are natural primitives for a number of sampling-based algorithms for other problems, our tools improve the external memory complexity of other problems as well.David & Lucile Packard Foundation (Fellowship)Center for Massive Data Algorithmics (MADALGO)Marie Curie (International Reintegration Grant 231077)National Science Foundation (U.S.) (Grant 0514771)National Science Foundation (U.S.) (Grant 0728645)National Science Foundation (U.S.) (Grant 0732334)Symantec Research Labs (Research Fellowship

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

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 network biology approach to prostate cancer

There is a need to identify genetic mediators of solid-tumor cancers, such as prostate cancer, where invasion and distant metastases determine the clinical outcome of the disease. Whole-genome expression profiling offers promise in this regard, but can be complicated by the challenge of identifying the genes affected by a condition from the hundreds to thousands of genes that exhibit changes in expression. Here, we show that reverse-engineered gene networks can be combined with expression profiles to compute the likelihood that genes and associated pathways are mediators of a disease. We apply our method to non-recurrent primary and metastatic prostate cancer data, and identify the androgen receptor gene (AR) among the top genetic mediators and the AR pathway as a highly enriched pathway for metastatic prostate cancer. These results were not obtained on the basis of expression change alone. We further demonstrate that the AR gene, in the context of the network, can be used as a marker to detect the aggressiveness of primary prostate cancers. This work shows that a network biology approach can be used advantageously to identify the genetic mediators and mediating pathways associated with a disease