25,285 research outputs found
A polynomial kernel for Block Graph Deletion
In the Block Graph Deletion problem, we are given a graph on vertices
and a positive integer , and the objective is to check whether it is
possible to delete at most vertices from to make it a block graph,
i.e., a graph in which each block is a clique. In this paper, we obtain a
kernel with vertices for the Block Graph Deletion problem.
This is a first step to investigate polynomial kernels for deletion problems
into non-trivial classes of graphs of bounded rank-width, but unbounded
tree-width. Our result also implies that Chordal Vertex Deletion admits a
polynomial-size kernel on diamond-free graphs. For the kernelization and its
analysis, we introduce the notion of `complete degree' of a vertex. We believe
that the underlying idea can be potentially applied to other problems. We also
prove that the Block Graph Deletion problem can be solved in time .Comment: 22 pages, 2 figures, An extended abstract appeared in IPEC201
The Potential Role of Aerobic Exercise-Induced Pentraxin 3 on Obesity-Related Inflammation and Metabolic Dysregulation
Obesity is defined as the excess accumulation of intra-abdominal body fat, resulting in a state of chronic, low-grade proinflammation that can directly contribute to the development of insulin resistance. Pentraxin 3 (PTX3) is an acute-phase protein that is expressed by a variety of tissue and cell sources and provides an anti-inflammatory property to downregulate the production of proinflammatory cytokines, in particular interleukin-1 beta and tumor necrosis factor alpha. Although PTX3 may therapeutically aid in altering the proinflammatory milieu in obese individuals, and despite elevated expression of PTX3 mRNA observed in adipose tissue, the circulating level of PTX3 is reduced with obesity. Interestingly, aerobic activity has been demonstrated to elevate PTX3 levels. Therefore, the purpose of this review is to discuss the therapeutic potential of PTX3 to positively regulate obesity-related inflammation and discuss the proposition for utilizing aerobic exercise as a nonpharmacological anti-inflammatory treatment strategy to enhance circulating PTX3 concentrations in obese individuals
Microscopic structure and dynamics of air/water interface by computer simulations-comparison with sum-frequency generation experiments
The air/water interface was simulated and the mode amplitudes and their ratios of the effective nonlinear sum-frequency generation (SFG) susceptibilities (A_(eff)'s) were calculated for the ssp, ppp, and sps polarization combinations and compared with experiments. By designating “surface-sensitive” free OH bonds on the water surface, many aspects of the SFG measurements were calculated and compared with those inferred from experiment. We calculate an average tilt angle close to the SFG observed value of 35, an average surface density of free OH bonds close to the experimental value of about 2.8 × 10^(18) m^(−2), computed ratios of A_(eff)'s that are very similar to those from the SFG experiment, and their absolute values that are in reasonable agreement with experiment. A one-parameter model was used to calculate these properties. The method utilizes results available from independent IR and Raman experiments to obtain some of the needed quantities, rather than calculating them ab initio. The present results provide microscopic information on water structure useful to applications such as in our recent theory of on-water heterogeneous catalysis
Strong electron correlations in cobalt valence tautomers
We have examined cobalt based valence tautomer molecules such as
Co(SQ)(phen) using density functional theory (DFT) and variational
configuration interaction (VCI) approaches based upon a model Hamiltonian. Our
DFT results extend earlier work by finding a reduced total energy gap (order
0.6 eV) between high temperature and low temperature states when we fully relax
the coordinates (relative to experimental ones). Futhermore we demonstrate that
the charge transfer picture based upon formal valence arguments succeeds
qualitatively while failing quantitatively due to strong covalency between the
Co 3 orbitals and ligand orbitals. With the VCI approach, we argue that
the high temperature, high spin phase is strongly mixed valent, with about 30 %
admixture of Co(III) into the predominantly Co(II) ground state. We confirm
this mixed valence through a fit to the XANES spectra. Moreover, the strong
electron correlations of the mixed valent phase provide an energy lowering of
about 0.2-0.3 eV of the high temperature phase relative to the low temperature
one. Finally, we use the domain model to account for the extraordinarily large
entropy and enthalpy values associated with the transition.Comment: 10 pages, 4 figures, submitted to J. Chem. Phy
An FPT algorithm and a polynomial kernel for Linear Rankwidth-1 Vertex Deletion
Linear rankwidth is a linearized variant of rankwidth, introduced by Oum and
Seymour [Approximating clique-width and branch-width. J. Combin. Theory Ser. B,
96(4):514--528, 2006]. Motivated from recent development on graph modification
problems regarding classes of graphs of bounded treewidth or pathwidth, we
study the Linear Rankwidth-1 Vertex Deletion problem (shortly, LRW1-Vertex
Deletion). In the LRW1-Vertex Deletion problem, given an -vertex graph
and a positive integer , we want to decide whether there is a set of at most
vertices whose removal turns into a graph of linear rankwidth at most
and find such a vertex set if one exists. While the meta-theorem of
Courcelle, Makowsky, and Rotics implies that LRW1-Vertex Deletion can be solved
in time for some function , it is not clear whether this
problem allows a running time with a modest exponential function.
We first establish that LRW1-Vertex Deletion can be solved in time . The major obstacle to this end is how to handle a long
induced cycle as an obstruction. To fix this issue, we define necklace graphs
and investigate their structural properties. Later, we reduce the polynomial
factor by refining the trivial branching step based on a cliquewidth expression
of a graph, and obtain an algorithm that runs in time . We also prove that the running time cannot be improved to under the Exponential Time Hypothesis assumption. Lastly,
we show that the LRW1-Vertex Deletion problem admits a polynomial kernel.Comment: 29 pages, 9 figures, An extended abstract appeared in IPEC201
Symmetry breaking: A tool to unveil the topology of chaotic scattering with three degrees of freedom
We shall use symmetry breaking as a tool to attack the problem of identifying
the topology of chaotic scatteruing with more then two degrees of freedom.
specifically we discuss the structure of the homoclinic/heteroclinic tangle and
the connection between the chaotic invariant set, the scattering functions and
the singularities in the cross section for a class of scattering systems with
one open and two closed degrees of freedom.Comment: 13 pages and 8 figure
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