| 1. |
- Aaghabali, M., et al.
(författare)
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Upper bounds on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges
- 2015
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Ingår i: European journal of combinatorics (Print). - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 45, s. 132-144
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Tidskriftsartikel (refereegranskat)abstract
- We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on 2n vertices. The upper bound is sharp for even n. For odd n we state a conjecture on a sharp upper bound.
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| 2. |
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| 3. |
- Svensson, Per-Arne, 1969, et al.
(författare)
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Copper induces the expression of cholesterogenic genes in human macrophages.
- 2003
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Ingår i: Atherosclerosis. - 0021-9150. ; 169:1, s. 71-6
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Tidskriftsartikel (refereegranskat)abstract
- Accumulation of lipids and cholesterol by macrophages and subsequent transformation into foam cells are key features in development of atherosclerosis. Serum copper concentrations have been shown to be associated with cardiovascular disease. However, the mechanism behind the proatherogenic effect of copper is not clear. We used DNA microarrays to define the changes in gene expression profile in response to copper exposure of human macrophages. Expression monitoring by DNA microarray revealed 91 genes that were regulated. Copper increased the expression of seven cholesterogenic genes (3-hydroxy-3-methylglutaryl coenzyme A (HMG CoA) synthase, IPP isomerase, squalene synthase, squalene epoxidase, methyl sterol oxidase, H105e3 mRNA and sterol-C5-desaturase) and low-density lipoprotein receptor (LDL-R), and decreased the expression of CD36 and lipid binding proteins. The expression of LDL-R and HMG CoA reductase was also investigated using real time PCR. The expression of both of these genes was increased after copper treatment of macrophages (P<0.01 and P<0.01, respectively). We conclude that copper activates cholesterogenic genes in macrophages, which may provide a mechanism for the association between copper and atherosclerosis. The effect of copper on cholesterogenic genes may also have implications for liver steatosis in early stages of Wilson's disease.
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| 4. |
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| 5. |
- Friedland, S., et al.
(författare)
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On the number of matching in regular graphs
- 2008
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Ingår i: The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 15:1
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Tidskriftsartikel (refereegranskat)abstract
- For the set of graphs with a given degree sequence, consisting of any number of 2's and 1's, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of m-matchings. We find the expected value of the number of m-matchings of r-regular bipartite graphs on 2n veritces with respect to the two standard measures. We state and discuss the conjectured upper and lower bounds for m-matchings in r-regular bipartite graphs on 2n vertices, and their asymptotic versions for infinite r-regular bipartite graphs. We prove these conjectures for 2-regular bipartite graphs and for m-matchings with m <= 4.
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| 8. |
- Friedland, S., et al.
(författare)
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On the Validations of the Asymptotic Matching Conjectures
- 2008
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Ingår i: Journal of statistical physics. - : Springer. - 0022-4715 .- 1572-9613. ; 133:3, s. 513-533
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p is an element of[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.
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| 9. |
- Friedland, S., et al.
(författare)
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The 1-vertex transfer matrix and accurate estimation of channel capacity
- 2010
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Ingår i: IEEE Transactions on Information Theory. - : IEEE. - 0018-9448 .- 1557-9654. ; 57:8, s. 3692-3699
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Tidskriftsartikel (refereegranskat)abstract
- The notion of a 1-vertex transfer matrix for multidimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method is applied to estimate the first 15 digits of the entropy of the 2-D (0, 1) run length limited channel. A large-scale computation of eigenvalues for the (0, 1) run length limited channel in 2-D and 3-D have been carried out. This was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with. This in turn leads to improvements on the best previous lower and upper bounds for these channels.
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