491 research outputs found
Maximum Independent Sets in Subcubic Graphs: New Results
The maximum independent set problem is known to be NP-hard in the class of
subcubic graphs, i.e. graphs of vertex degree at most 3. We present a
polynomial-time solution in a subclass of subcubic graphs generalizing several
previously known results
Precise Localization of the Soft Gamma Repeater SGR 1627-41 and the Anomalous X-ray Pulsar AXP 1E1841-045 with Chandra
We present precise localizations of AXP 1E1841-045 and SGR 1627-41 with
Chandra. We obtained new infrared observations of SGR 1627-41 and reanalyzed
archival observations of AXP 1E1841-045 in order to refine their positions and
search for infrared counterparts. A faint source is detected inside the error
circle of AXP 1E1841-045. In the case of SGR 1627-41, several sources are
located within the error radius of the X-ray position and we discuss the
likelihood of one of them being the counterpart. We compare the properties of
our candidates to those of other known AXP and SGR counterparts. We find that
the counterpart candidates for SGR 1627-41 and SGR 1806-20 would have to be
intrinsically much brighter than AXPs to have detectable counterparts with the
observational limits currently available for these sources. To confirm the
reported counterpart of SGR 1806-20, we obtained new IR observations during the
July 2003 burst activation of the source. No brightening of the suggested
counterpart is detected, implying that the counterpart of SGR 1806-20 remains
yet to be identified.Comment: 29 pages, 4 figures, accepted for publication in Ap
Tree decompositions with small cost
The f-cost of a tree decomposition ({Xi | i e I}, T = (I;F))
for a function f : N -> R+ is defined as EieI f(|Xi|). This measure
associates with the running time or memory use of some algorithms
that use the tree decomposition. In this paper we investigate the
problem to find tree decompositions of minimum f-cost.
A function f : N -> R+ is fast, if for every i e N: f(i+1) => 2*f(i).
We show that for fast functions f, every graph G has a tree decomposition
of minimum f-cost that corresponds to a minimal triangulation
of G; if f is not fast, this does not hold. We give polynomial time
algorithms for the problem, assuming f is a fast function, for graphs
that has a polynomial number of minimal separators, for graphs of
treewidth at most two, and for cographs, and show that the problem
is NP-hard for bipartite graphs and for cobipartite graphs.
We also discuss results for a weighted variant of the problem derived
of an application from probabilistic networks
Independent Set Reconfiguration in Cographs
We study the following independent set reconfiguration problem, called
TAR-Reachability: given two independent sets and of a graph , both
of size at least , is it possible to transform into by adding and
removing vertices one-by-one, while maintaining an independent set of size at
least throughout? This problem is known to be PSPACE-hard in general. For
the case that is a cograph (i.e. -free graph) on vertices, we show
that it can be solved in time , and that the length of a shortest
reconfiguration sequence from to is bounded by , if such a
sequence exists.
More generally, we show that if is a graph class for which (i)
TAR-Reachability can be solved efficiently, (ii) maximum independent sets can
be computed efficiently, and which satisfies a certain additional property,
then the problem can be solved efficiently for any graph that can be obtained
from a collection of graphs in using disjoint union and complete join
operations. Chordal graphs are given as an example of such a class
Synthesis and Pharmacology of Halogenated δ-Opiod Selective [\u3csub\u3eD\u3c/sub\u3eAla\u3csup\u3e2\u3c/sup\u3e] Deltorphin II Peptide Analogs
Deltorphins are naturally occurring peptides produced by the skin of the giant monkey frog (Phyllomedusa bicolor). They are δ-opioid receptor-selective agonists. Herein, we report the design and synthesis of a peptide, Tyr-d-Ala-(pI)Phe-Glu-Ile-Ile-Gly-NH2 3 (GATE3-8), based on the [d-Ala2]deltorphin II template, which is δ-selective in in vitro radioligand binding assays over the μ- and κ-opioid receptors. It is a full agonist in [35S]GTPγS functional assays and analgesic when administered supraspinally to mice. Analgesia of 3 (GATE3-8) is blocked by the selective δ receptor antagonist naltrindole, indicating that the analgesic action of 3 is mediated by the δ-opioid receptor. We have established a radioligand in which 125I is incorporated into 3 (GATE3-8). The radioligand has a KD of 0.1 nM in Chinese hamster ovary (CHO) cells expressing the δ receptor. Additionally, a series of peptides based on 3 (GATE3-8) was synthesized by incorporating various halogens in the para position on the aromatic ring of Phe3. The peptides were characterized for binding affinity at the μ-, δ-, and κ-opioid receptors, which showed a linear correlation between binding affinity and the size of the halogen substituent. These peptides may be interesting tools for probing δ-opioid receptor pharmacology
On the complexity of color-avoiding site and bond percolation
The mathematical analysis of robustness and error-tolerance of complex
networks has been in the center of research interest. On the other hand, little
work has been done when the attack-tolerance of the vertices or edges are not
independent but certain classes of vertices or edges share a mutual
vulnerability. In this study, we consider a graph and we assign colors to the
vertices or edges, where the color-classes correspond to the shared
vulnerabilities. An important problem is to find robustly connected vertex
sets: nodes that remain connected to each other by paths providing any type of
error (i.e. erasing any vertices or edges of the given color). This is also
known as color-avoiding percolation. In this paper, we study various possible
modeling approaches of shared vulnerabilities, we analyze the computational
complexity of finding the robustly (color-avoiding) connected components. We
find that the presented approaches differ significantly regarding their
complexity.Comment: 14 page
Retention of Supraspinal Delta-like Analgesia and Loss of Morphine Tolerance in δ Opioid Receptor Knockout Mice
AbstractGene targeting was used to delete exon 2 of mouse DOR-1, which encodes the δ opioid receptor. Essentially all 3H-[D-Pen2,D-Pen5]enkephalin (3H-DPDPE) and 3H-[D-Ala2,D-Glu4]deltorphin (3H-deltorphin-2) binding is absent from mutant mice, demonstrating that DOR-1 encodes both δ1 and δ2 receptor subtypes. Homozygous mutant mice display markedly reduced spinal δ analgesia, but peptide δ agonists retain supraspinal analgesic potency that is only partially antagonized by naltrindole. Retained DPDPE analgesia is also demonstrated upon formalin testing, while the nonpeptide δ agonist BW373U69 exhibits enhanced activity in DOR-1 mutant mice. Together, these findings suggest the existence of a second delta-like analgesic system. FinallyDOR-1 mutant mice do not develop analgesic tolerance to morphine, genetically demonstrating a central role for DOR-1 in this process
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
We formulate, and in some cases prove, three statements concerning the purity
or, more generally the naturality of the resolution of various rings one can
attach to a generic curve of genus g and a torsion point of order l in its
Jacobian. These statements can be viewed an analogues of Green's Conjecture and
we verify them computationally for bounded genus. We then compute the
cohomology class of the corresponding non-vanishing locus in the moduli space
R_{g,l} of twisted level l curves of genus g and use this to derive results
about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3}
is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is
greater than or equal to 19. In the last section we explain probabilistically
the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the
statement of Prop 2.
Maximum Independent Sets in Subcubic Graphs: New Results
International audienceWe consider the complexity of the classical Independent Set problem on classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. It is well-known that a necessary condition for Independent Set to be tractable in such a class (unless P=NP) is that the set of forbidden induced subgraphs includes a subdivided star S k,k,k , for some k. Here, S k,k,k is the graph obtained by taking three paths of length k and identifying one of their endpoints. It is an interesting open question whether this condition is also sufficient: is Independent Set tractable on all hereditary classes of subcu-bic graphs that exclude some S k,k,k ? A positive answer to this question would provide a complete classification of the complexity of Independent Set on all classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. The best currently known result of this type is tractability for S2,2,2-free graphs. In this paper we generalize this result by showing that the problem remains tractable on S 2,k,k-free graphs, for any fixed k. Along the way, we show that subcubic Independent Set is tractable for graphs excluding a type of graph we call an "apple with a long stem", generalizing known results for apple-free graphs
Register Allocation After Classical SSA Elimination is NP-Complete
Abstract. Chaitin proved that register allocation is equivalent to graph coloring and hence NP-complete. Recently, Bouchez, Brisk, and Hack have proved independently that the interference graph of a program in static single assignment (SSA) form is chordal and therefore colorable in linear time. Can we use the result of Bouchez et al. to do register allocation in polynomial time by first transforming the program to SSA form, then performing register allocation, and finally doing the classical SSA elimination that replaces φ-functions with copy instructions? In this paper we show that the answer is no, unless P = NP: register allocation after classical SSA elimination is NP-complete. Chaitin’s proof technique does not work for programs after classical SSA elimination; instead we use a reduction from the graph coloring problem for circular arc graphs.
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