Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Counting arithmetical structures on paths and cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag(d)-A)r = 0, where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag(d)-A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients C(2n-1,n-1), and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

LPS Responsiveness and Neutrophil Chemotaxis In Vivo Require PMN MMP-8 Activity

We identify matrix metalloproteinase (MMP)-8, the polymorphonuclear (PMN) leukocyte collagenase, as a critical mediator initiating lipopolysaccharide (LPS)-responsiveness in vivo. PMN infiltration towards LPS is abrogated in Mmp8-null mice. MMP-8 cleaves LPS-induced CXC chemokine (LIX) at Ser(4)∼Val(5) and Lys(79)∼Arg(80). LIX bioactivity is increased upon N-terminal cleavage, enhancing intracellular calcium mobilization and chemotaxis upon binding its cognate receptor, CXCR2. As there is no difference in PMN chemotaxis in Mmp8-null mice compared with wild-type mice towards synthetic analogues of MMP-8-cleaved LIX, MMP-8 is not essential for extravasation or cell migration in collagenous matrices in vivo. However, with biochemical redundancy between MMPs 1, 2, 9, and 13, which also cleave LIX at position 4∼5, it was surprising to observe such a markedly reduced PMN infiltration towards LPS and LIX in Mmp8-/- mice. This lack of physiological redundancy in vivo identifies MMP-8 as a key mediator in the regulation of innate immunity. Comparable results were found with CXCL8/IL-8 and CXCL5/ENA-78, the human orthologues of LIX. MMP-8 cleaves CXCL8 at Arg(5)-Ser(6) and at Val(7)-Leu(8) in CXCL5 to activate respective chemokines. Hence, rather than collagen, these PMN chemoattractants are important MMP-8 substrates in vivo; PMN-derived MMP-8 cleaves and activates LIX to execute an in cis PMN-controlled feed-forward mechanism to orchestrate the initial inflammatory response and promote LPS responsiveness in tissue

Excavaciones en el conjunto megalítico de la Peña Oviedo (Camaleño, Cantabria)

La excavación del conjunto megalítico de la Peña Oviedo, pretende ser el inicio de un estudio más amplio que aborde de manera global el fenómeno megalítico en las cue.ncas altas de los ríos Deva y Nansa. El total desconocimiento que se tenía hasta esta década, no ya del fenómeno megalítico, sino incluso de su existencia en estos valles montañosos del Occidente de Cantabria hace necesario un estudio que ponga de manifiesto sus características y las relaciones con las áreas vecinas.The excavation of the megalithic complex of the Peña Oviedo, pretends to be the beginning of a larger study that approaches the megalithic phenomenon in the global River basins of the Deva and Nansa rivers. The total lack of knowledge of the megalithic phenomenon, but not even of its existence in these mountain valleys of western Cantabria, requires a study that reveals its characteristics and relations with neighboring areas

Suppression of autophagy impedes glioblastoma development and induces senescence

The function of macroautophagy/autophagy during tumor initiation or in established tumors can be highly distinct and context-dependent. To investigate the role of autophagy in gliomagenesis, we utilized a KRAS-driven glioblastoma mouse model in which autophagy is specifically disrupted via RNAi against Atg7, Atg13 or Ulk1. Inhibition of autophagy strongly reduced glioblastoma development, demonstrating its critical role in promoting tumor formation. Further supporting this finding is the observation that tumors originating from Atg7-shRNA injections escaped the knockdown effect and thereby still underwent functional autophagy. In vitro, autophagy inhibition suppressed the capacity of KRAS-expressing glial cells to form oncogenic colonies or to survive low serum conditions. Molecular analyses revealed that autophagy-inhibited glial cells were unable to maintain active growth signaling under growth-restrictive conditions and were prone to undergo senescence. Overall, these results demonstrate that autophagy is crucial for glioma initiation and growth, and is a promising therapeutic target for glioblastoma treatment

Tree leaves of Salix babylonica extract as a natural anthelmintic for small-ruminant farms in a semiarid region in Mexico

Introduction In Mexico, sheep and goats are important resources of cash income, savings, food (meat and milk), wool, fertilizer, and employment of family members, particularly in populations with a low income and where poverty prevails. However, parasitic diseases caused by gastrointestinal nematodes remains as one of the major constraints in sheep and goat production systems in Mexico and in most developing countries (Mejı´a-Herna´ndez et al. 2014; Cedillo et al. 2015). Nematodes in such humid and sub-humid tropical areas can cause poor growth, production losses, and even mortality in young animals (Ancheta et al. 2004). Globally, small ruminant producers depend on synthetic anthelmintics to achieve control of gastrointestinal nematodes and parasites. However, administration of chemical anthelmintic drugs has been proved to increase the development of parasite resistance towards these treatments (Jabbar et al. 2006; Shaik et al. 2006), and to raise concerns regarding the presence of pharmacological residues in animal products (McKellar 1997). Moreover, chemical treatments are costly when used regularly to prevent helminth parasites in livestock (Jabbar et al. 2006). Consequently, there is an increasing interest in screening phytogenic extracts and medicinal plants as alternatives to the expensive traditional drugs (Olmedo- Jua´rezThe study aimed to test the potential anthelmintic activity of Salix babylonica (SB) extract for the control of gastrointestinal and pulmonary parasites in sheep and goats under field conditions. A representative sample of 20 % of all animals reared in 8 sheep and 7 goat farms was used in the study. Animals from each farm were randomly selected for a total number of 93 sheep and 75 goats. Animals suffered a natural gastrointestinal nematode infection and had never been treated with chemical anthelmintic drug

Genetic Predisposition to Chronic Lymphocytic Leukemia Is Mediated by a BMF Super-Enhancer Polymorphism

SummaryChronic lymphocytic leukemia (CLL) is an adult B cell malignancy. Genome-wide association studies show that variation at 15q15.1 influences CLL risk. We deciphered the causal variant at 15q15.1 and the mechanism by which it influences tumorigenesis. We imputed all possible genotypes across the locus and then mapped highly associated SNPs to areas of chromatin accessibility, evolutionary conservation, and transcription factor binding. SNP rs539846 C>A, the most highly associated variant (p = 1.42 × 10−13, odds ratio = 1.35), localizes to a super-enhancer defined by extensive histone H3 lysine 27 acetylation in intron 3 of B cell lymphoma 2 (BCL2)-modifying factor (BMF). The rs539846-A risk allele alters a conserved RELA-binding motif, disrupts RELA binding, and is associated with decreased BMF expression in CLL. These findings are consistent with rs539846 influencing CLL susceptibility through differential RELA binding, with direct modulation of BMF expression impacting on anti-apoptotic BCL2, a hallmark of oncogenic dependency in CLL