121 research outputs found
Covering Grassmannian Codes: Bounds and Constructions
Grassmannian is the set of all -dimensional subspaces
of the vector space Recently, Etzion and Zhang introduced a
new notion called covering Grassmannian code which can be used in network
coding solutions for generalized combination networks. An
- covering Grassmannian code is a
subset of such that every set of codewords of
spans a subspace of dimension at least in
In this paper, we derive new upper and lower bounds on the
size of covering Grassmannian codes. These bounds improve and extend the
parameter range of known bounds.Comment: 17 page
Packing and covering balls in graphs excluding a minor
We prove that for every integer there exists a constant such
that for every -minor-free graph , and every set of balls in ,
the minimum size of a set of vertices of intersecting all the balls of
is at most times the maximum number of vertex-disjoint balls in . This
was conjectured by Chepoi, Estellon, and Vax\`es in 2007 in the special case of
planar graphs and of balls having the same radius.Comment: v3: final versio
3D IC optimal layout design. A parallel and distributed topological approach
The task of 3D ICs layout design involves the assembly of millions of
components taking into account many different requirements and constraints such
as topological, wiring or manufacturability ones. It is a NP-hard problem that
requires new non-deterministic and heuristic algorithms. Considering the time
complexity, the commonly applied Fiduccia-Mattheyses partitioning algorithm is
superior to any other local search method. Nevertheless, it can often miss to
reach a quasi-optimal solution in 3D spaces. The presented approach uses an
original 3D layout graph partitioning heuristics implemented with use of the
extremal optimization method. The goal is to minimize the total wire-length in
the chip. In order to improve the time complexity a parallel and distributed
Java implementation is applied. Inside one Java Virtual Machine separate
optimization algorithms are executed by independent threads. The work may also
be shared among different machines by means of The Java Remote Method
Invocation system.Comment: 26 pages, 9 figure
European Journal of Combinatorics Index, Volume 27
BACKGROUND: Diabetes is an inflammatory condition associated with iron abnormalities and increased oxidative damage. We aimed to investigate how diabetes affects the interrelationships between these pathogenic mechanisms. METHODS: Glycaemic control, serum iron, proteins involved in iron homeostasis, global antioxidant capacity and levels of antioxidants and peroxidation products were measured in 39 type 1 and 67 type 2 diabetic patients and 100 control subjects. RESULTS: Although serum iron was lower in diabetes, serum ferritin was elevated in type 2 diabetes (p = 0.02). This increase was not related to inflammation (C-reactive protein) but inversely correlated with soluble transferrin receptors (r = - 0.38, p = 0.002). Haptoglobin was higher in both type 1 and type 2 diabetes (p < 0.001) and haemopexin was higher in type 2 diabetes (p < 0.001). The relation between C-reactive protein and haemopexin was lost in type 2 diabetes (r = 0.15, p = 0.27 vs r = 0.63, p < 0.001 in type 1 diabetes and r = 0.36, p = 0.001 in controls). Haemopexin levels were independently determined by triacylglycerol (R(2) = 0.43) and the diabetic state (R(2) = 0.13). Regarding oxidative stress status, lower antioxidant concentrations were found for retinol and uric acid in type 1 diabetes, alpha-tocopherol and ascorbate in type 2 diabetes and protein thiols in both types. These decreases were partially explained by metabolic-, inflammatory- and iron alterations. An additional independent effect of the diabetic state on the oxidative stress status could be identified (R(2) = 0.5-0.14). CONCLUSIONS: Circulating proteins, body iron stores, inflammation, oxidative stress and their interrelationships are abnormal in patients with diabetes and differ between type 1 and type 2 diabetes</p
Density version of the Ramsey problem and the directed Ramsey problem
We discuss a variant of the Ramsey and the directed Ramsey problem. First,
consider a complete graph on vertices and a two-coloring of the edges such
that every edge is colored with at least one color and the number of bicolored
edges is given. The aim is to find the maximal size of a
monochromatic clique which is guaranteed by such a coloring. Analogously, in
the second problem we consider semicomplete digraph on vertices such that
the number of bi-oriented edges is given. The aim is to bound the
size of the maximal transitive subtournament that is guaranteed by such a
digraph.
Applying probabilistic and analytic tools and constructive methods we show
that if , (), then where only depend on , while if then . The latter case is
strongly connected to Tur\'an-type extremal graph theory.Comment: 17 pages. Further lower bound added in case $|E_{RB}|=|E_{bi}| =
p{n\choose 2}
Independence numbers of Johnson-type graphs
We consider a family of distance graphs in and find its
independent numbers in some cases.
Define graph in the following way: the vertex set consists
of all vectors from with nonzero coordinates; edges connect
the pairs of vertices with scalar product . We find the independence number
of for in the cases and ;
these cases for are solved completely. Also the independence number is
found for negative odd and
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