Cycle Bases of Reduced Powers of Graphs

We define what appears to be a new construction. Given a graph G and a positive integer k, the reduced kth power of G, denoted G(k), is the configuration space in which k indistinguishable tokens are placed on the vertices of G, so that any vertex can hold up to k tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex. We present propositions related to the structural properties of reduced graph powers and, most significantly, provide a construction of minimum cycle bases of G(k). The minimum cycle basis construction is an interesting combinatorial problem that is also useful in applications involving configuration spaces. For example, if G is the state-transition graph of a Markov chain model of a stochastic automaton, the reduced power G(k) is the state-transition graph for k identical (but not necessarily independent) automata. We show how the minimum cycle basis construction of G(k) may be used to confirm that state-dependent coupling of automata does not violate the principle of microscopic reversibility, as required in physical and chemical applications

Eulerian 2-Complexes

It is shown that Euler's theorem for graphs can be generalized for 2-complexes. Two notions that generalize cycle and Eulerian tour are introduced (``circlet'' and ``Eulerian cover''), and we show that for a strongly-connected, pure 2-complex, the following are equivalent: (i) each edge meets a positive even number of 2-cells (faces), (ii) the complex can be decomposed as the face-disjoint union of circlets, and (iii) the complex has an Eulerian cover. A number of examples are provided.Comment: 13 pages, 15 figure

A new view of hypercube genus

Beineke, Harary and Ringel discovered a formula for the minimum genus of a torus in which the $n$-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this surface as a union of certain faces in the hypercube's 2-skeleton. For odd dimension $n$, the entire 2-skeleton decomposes into $(n-1)/2$ copies of the surface, and the intersection of any two copies is the hypercube graph.Comment: 8 pages, 6 figure

Euler's Theorem for Regular CW-Complexes

For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and traversability.Comment: 15 pages, 3 figures, to appear in Combinatorica, 202

On Cartesian skeletons of graphs,

Abstract Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a notion of a Cartesian skeleton which transfers their multiplication properties to the Cartesian product. The present article introduces simplified definitions of Cartesian skeletons for the direct and strong products, and provides new, fast and transparent algorithms for their construction. Since the complexity of the prime factorization of the direct and the strong product is determined by the complexity of the construction of the Cartesian skeleton, the new algorithms also improve the complexity of the prime factorizations of graphs with respect to the direct and the strong product. We indicate how these simplifications fit into the existing literature

Arteriolosclerosis that affects multiple brain regions is linked to hippocampal sclerosis of ageing

Hippocampal sclerosis of ageing is a prevalent brain disease that afflicts older persons and has been linked with cerebrovascular pathology. Arteriolosclerosis is a subtype of cerebrovascular pathology characterized by concentrically thickened arterioles. Here we report data from multiple large autopsy series (University of Kentucky Alzheimer's Disease Centre, Nun Study, and National Alzheimer's Coordinating Centre) showing a specific association between hippocampal sclerosis of ageing pathology and arteriolosclerosis. The present analyses incorporate 226 cases of autopsy-proven hippocampal sclerosis of ageing and 1792 controls. Case-control comparisons were performed including digital pathological assessments for detailed analyses of blood vessel morphology. We found no evidence of associations between hippocampal sclerosis of ageing pathology and lacunar infarcts, large infarcts, Circle of Willis atherosclerosis, or cerebral amyloid angiopathy. Individuals with hippocampal sclerosis of ageing pathology did not show increased rates of clinically documented hypertension, diabetes, or other cardiac risk factors. The correlation between arteriolosclerosis and hippocampal sclerosis of ageing pathology was strong in multiple brain regions outside of the hippocampus. For example, the presence of arteriolosclerosis in the frontal cortex (Brodmann area 9) was strongly associated with hippocampal sclerosis of ageing pathology (P 5 0.001). This enables informative evaluation of anatomical regions outside of the hippocampus. To assess the morphology of brain microvasculature far more rigorously than what is possible using semi-quantitative pathological scoring, we applied digital pathological (Aperio ScanScope) methods on a subsample of frontal cortex sections from hippocampal sclerosis of ageing (n = 15) and control (n = 42) cases. Following technical studies to optimize immunostaining methods for small blood vessel visualization, our analyses focused on sections immunostained for smooth muscle actin (a marker of arterioles) and CD34 (an endothelial marker), with separate analyses on grey and white matter. A total of 43 834 smooth muscle actin-positive vascular profiles and 603 798 CD34-positive vascular profiles were evaluated. In frontal cortex of cases with hippocampal sclerosis of ageing, smooth muscle actin-immunoreactive arterioles had thicker walls (P 5 0.05), larger perimeters (P 5 0.03), and larger vessel areas (P 5 0.03) than controls. Unlike the arterioles, CD34-immunoreactive capillaries had dimensions that were unchanged in cases with hippocampal sclerosis of ageing versus controls. Arteriolosclerosis appears specific to hippocampal sclerosis of ageing brains, because brains with Alzheimer's disease pathology did not show the same morphological alterations. We conclude that there may be a pathogenetic change in aged human brain arterioles that impacts multiple brain areas and contributes to hippocampal sclerosis of ageing

A Key Role for Neurotensin in Chronic-Stress-Induced Anxiety-Like Behavior in Rats

Accepted ManuscriptChronic stress is a major cause of anxiety disorders that can be reliably modeled preclinically, providing insight into alternative therapeutic targets for this mental health illness. Neuropeptides have been targeted in the past to no avail possibly due to our lack of understanding of their role in pathological models. In this study we use a rat model of chronic stress-induced anxiety-like behaviors and hypothesized that neuropeptidergic modulation of synaptic transmission would be altered in the bed nucleus of the stria terminalis (BNST), a brain region suspected to contribute to anxiety disorders. We use brain slice neurophysiology and behavioral pharmacology to compare the role of locally released endogenous neuropeptides on synaptic transmission in the oval (ov) BNST of non-stressed (NS) or chronic unpredictably stressed (CUS) rats. We found that in NS rats, post-synaptic depolarization induced the release of vesicular neurotensin (NT) and corticotropin-releasing factor (CRF) that co-acted to increase ovBNST inhibitory synaptic transmission in 59% of recorded neurons. CUS bolstered this potentiation (100% of recorded neurons) through an enhanced contribution of NT over CRF. In contrast, locally released opioid neuropeptides decreased ovBNST excitatory synaptic transmission in all recorded neurons, regardless of stress. Consistent with CUS-induced enhanced modulatory effects of NT, blockade of ovBNST NT receptors completely abolished stress-induced anxiety-like behaviors in the elevated plus maze paradigm. The role of NT has been largely unexplored in stress and our findings highlight its potential contribution to an important behavioral consequence of chronic stress, that is, exaggerated avoidance of open space in rats.CPN was funded by CIHR Vanier Graduate Scholarship (338319); APVS was funded by Fundação para a Ciência e Tecnologia (SFRH/BPD/52078/2013); ERH was funded by CIHR Postdoctoral Fellowship (MFE-123712); SA was funded by a Queen Elizabeth II Graduate Scholarship in Science and Technology; ÉCD was funded by the Canadian Institute of Health Research (MOP-25953)info:eu-repo/semantics/publishedVersio

Geochemical and Strontium Isotope Characterization of Produced Waters from Marcellus Shale Natural Gas Extraction

Extraction of natural gas by hydraulic fracturing of the Middle Devonian Marcellus Shale, a major gas-bearing unit in the Appalachian Basin, results in significant quantities of produced water containing high total dissolved solids (TDS). We carried out a strontium (Sr) isotope investigation to determine the utility of Sr isotopes in identifying and quantifying the interaction of Marcellus Formation produced waters with other waters in the Appalachian Basin in the event of an accidental release, and to provide information about the source of the dissolved solids. Strontium isotopic ratios of Marcellus produced waters collected over a geographic range of ∼375 km from southwestern to northeastern Pennsylvania define a relatively narrow set of values (εSr SW = +13.8 to +41.6, where εSr SW is the deviation of the 87Sr/86Sr ratio from that of seawater in parts per 104); this isotopic range falls above that of Middle Devonian seawater, and is distinct from most western Pennsylvania acid mine drainage and Upper Devonian Venango Group oil and gas brines. The uniformity of the isotope ratios suggests a basin-wide source of dissolved solids with a component that is more radiogenic than seawater. Mixing models indicate that Sr isotope ratios can be used to sensitively differentiate between Marcellus Formation produced water and other potential sources of TDS into ground or surface waters

Graph Exponentiation and Neighborhood Reconstruction

Any graph G admits a neighborhood multiset (G) = {NG(x) | x ∈ V (G)} whose elements are precisely the open neighborhoods of G. We say G is neighborhood reconstructible if it can be reconstructed from (G), that is, if G ≅ H whenever (G) = (H) for some other graph H. This note characterizes neighborhood reconstructible graphs as those graphs G that obey the exponential cancellation GK2 ≅ HK2 ⇒ G ≅= H