389 research outputs found
Vertex-primitive groups and graphs of order twice the product of two distinct odd primes
A non-Cayley number is an integer n for which there exists a vertex-transitive graph on n vertices which is not a Cayley graph. In this paper, we complete the determination of the non-Cayley numbers of the form 2pq, where p, q are distinct odd primes. Earlier work of Miller and the second author had dealt with all such numbers corresponding to vertex-transitive graphs admitting an imprimitive subgroup of automorphisms. This paper deals with the primitive case. First the primitive permutation groups of degree 2pq are classified. This depends on the finite simple group classification. Then each of these groups G is examined to determine whether there are any non-Cayley graphs which admit G as a vertex-primitive subgroup of automorphisms, and admit no imprimitive subgroups. The outcome is that 2pq is a non-Cayley number, where
Automatically generating streamlined constraint models with ESSENCE and CONJURE
Streamlined constraint reasoning is the addition of uninferred constraints to a constraint model to reduce the search space, while retaining at least one solution. Previously, effective streamlined models have been constructed by hand, requiring an expert to examine closely solutions to small instances of a problem class and identify regularities. We present a system that automatically generates many conjectured regularities for a given Essence specification of a problem class by examining the domains of decision variables present in the problem specification. These conjectures are evaluated independently and in conjunction with one another on a set of instances from the specified class via an automated modelling tool-chain comprising of Conjure, Savile Row and Minion. Once the system has identified effective conjectures they are used to generate streamlined models that allow instances of much larger scale to be solved. Our results demonstrate good models can be identified for problems in combinatorial design, Ramsey theory, graph theory and group theory - often resulting in order of magnitude speed-ups.Postprin
Ramified rectilinear polygons: coordinatization by dendrons
Simple rectilinear polygons (i.e. rectilinear polygons without holes or
cutpoints) can be regarded as finite rectangular cell complexes coordinatized
by two finite dendrons. The intrinsic -metric is thus inherited from the
product of the two finite dendrons via an isometric embedding. The rectangular
cell complexes that share this same embedding property are called ramified
rectilinear polygons. The links of vertices in these cell complexes may be
arbitrary bipartite graphs, in contrast to simple rectilinear polygons where
the links of points are either 4-cycles or paths of length at most 3. Ramified
rectilinear polygons are particular instances of rectangular complexes obtained
from cube-free median graphs, or equivalently simply connected rectangular
complexes with triangle-free links. The underlying graphs of finite ramified
rectilinear polygons can be recognized among graphs in linear time by a
Lexicographic Breadth-First-Search. Whereas the symmetry of a simple
rectilinear polygon is very restricted (with automorphism group being a
subgroup of the dihedral group ), ramified rectilinear polygons are
universal: every finite group is the automorphism group of some ramified
rectilinear polygon.Comment: 27 pages, 6 figure
Stress and epilepsy: fact or fiction, and what can we do about it?
People with epilepsy report that stress is their most common trigger for seizures and some believe it caused their epilepsy in the first place. The extensive preclinical, epidemiological and clinical studies examining the link between stress and epilepsy have given confusing results; the clinical studies in particular are fraught with confounders. However stress is clearly bad for health, and we now have substantial preclinical evidence suggesting that chronic stress worsens epilepsy; in selected cases it may even be a causal factor for epilepsy. Healthcare professionals working with people with epilepsy should pay more attention to stress in clinical practice. This review includes some practical advice and guidance for stress screening and management
Tpl2 kinase regulates T cell interferon-γ production and host resistance to Toxoplasma gondii
Tpl2 (Tumor progression locus 2), also known as Cot/MAP3K8, is a hematopoietically expressed serine-threonine kinase. Tpl2 is known to have critical functions in innate immunity in regulating tumor necrosis factor–α, Toll-like receptor, and G protein–coupled receptor signaling; however, our understanding of its physiological role in T cells is limited. We investigated the potential roles of Tpl2 in T cells and found that it was induced by interleukin-12 in human and mouse T cells in a Stat4-dependent manner. Deficiency of Tpl2 was associated with impaired interferon (IFN)-γ production. Accordingly, Tpl2−/− mice had impaired host defense against Toxoplasma gondii with reduced parasite clearance and decreased IFN-γ production. Furthermore, reconstitution of Rag2−/− mice with Tpl2-deficient T cells followed by T. gondii infection recapitulated the IFN-γ defect seen in the Tpl2-deficient mice, confirming a T cell–intrinsic defect. CD4+ T cells isolated from Tpl2−/− mice showed poor induction of T-bet and failure to up-regulate Stat4 protein, which is associated with impaired TCR-dependent extracellular signal-regulated kinase activation. These data underscore the role of Tpl2 as a regulator of T helper cell lineage decisions and demonstrate that Tpl2 has an important functional role in the regulation of Th1 responses
Dental age assessment in 6- to 14-year old German children: comparison of Cameriere and Demirjian methods
Anthrax Lethal Toxin Disrupts Intestinal Barrier Function and Causes Systemic Infections with Enteric Bacteria
A variety of intestinal pathogens have virulence factors that target mitogen activated protein kinase (MAPK) signaling pathways, including Bacillus anthracis. Anthrax lethal toxin (LT) has specific proteolytic activity against the upstream regulators of MAPKs, the MAPK kinases (MKKs). Using a murine model of intoxication, we show that LT causes the dose-dependent disruption of intestinal epithelial integrity, characterized by mucosal erosion, ulceration, and bleeding. This pathology correlates with an LT-dependent blockade of intestinal crypt cell proliferation, accompanied by marked apoptosis in the villus tips. C57BL/6J mice treated with intravenous LT nearly uniformly develop systemic infections with commensal enteric organisms within 72 hours of administration. LT-dependent intestinal pathology depends upon its proteolytic activity and is partially attenuated by co-administration of broad spectrum antibiotics, indicating that it is both a cause and an effect of infection. These findings indicate that targeting of MAPK signaling pathways by anthrax LT compromises the structural integrity of the mucosal layer, serving to undermine the effectiveness of the intestinal barrier. Combined with the well-described immunosuppressive effects of LT, this disruption of the intestinal barrier provides a potential mechanism for host invasion via the enteric route, a common portal of entry during the natural infection cycle of Bacillus anthracis
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