Reconfiguration of Dominating Sets

We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions $s$ and $t$ such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of $k$, we consider properties of $D_k(G)$, the graph consisting of a vertex for each dominating set of size at most $k$ and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that $D_{\Gamma(G)+1}(G)$ is not necessarily connected, for $\Gamma(G)$ the maximum cardinality of a minimal dominating set in $G$. The result holds even when graphs are constrained to be planar, of bounded tree-width, or $b$-partite for $b \ge 3$. Moreover, we construct an infinite family of graphs such that $D_{\gamma(G)+1}(G)$ has exponential diameter, for $\gamma(G)$ the minimum size of a dominating set. On the positive side, we show that $D_{n-m}(G)$ is connected and of linear diameter for any graph $G$ on $n$ vertices having at least $m+1$ independent edges.Comment: 12 pages, 4 figure

Quiver theories, soliton spectra and Picard-Lefschetz transformations

Quiver theories arising on D3-branes at orbifold and del Pezzo singularities are studied using mirror symmetry. We show that the quivers for the orbifold theories are given by the soliton spectrum of massive 2d N=2 theory with weighted projective spaces as target. For the theories obtained from the del Pezzo singularities we show that the geometry of the mirror manifold gives quiver theories related to each other by Picard-Lefschetz transformations, a subset of which are simple Seiberg duals. We also address how one indeed derives Seiberg duality on the matter content from such geometrical transitions and how one could go beyond and obtain certain ``fractional Seiberg duals.'' Moreover, from the mirror geometry for the del Pezzos arise certain Diophantine equations which classify all quivers related by Picard-Lefschetz. Some of these Diophantine equations can also be obtained from the classification results of Cecotti-Vafa for the 2d N=2 theories.Comment: 34 pages, 11 figure

Dibaryons from Exceptional Collections

We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription identifies the R-charge R and all baryonic U(1) charges Q_I with divisors in the del Pezzo surface without any Weyl group ambiguity. As one application of the correspondence, we identify the cubic anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N superconformal gauge theories. Examples can be given for all del Pezzo surfaces using three- and four-block exceptional collections. Markov-type equations enforce consistency among anomaly equations for three-block collections.Comment: 47 pages, 11 figures, corrected ref

Interleukin-6 Receptor Antagonists in Critically Ill Patients with Covid-19.

BACKGROUND: The efficacy of interleukin-6 receptor antagonists in critically ill patients with coronavirus disease 2019 (Covid-19) is unclear. METHODS: We evaluated tocilizumab and sarilumab in an ongoing international, multifactorial, adaptive platform trial. Adult patients with Covid-19, within 24 hours after starting organ support in the intensive care unit (ICU), were randomly assigned to receive tocilizumab (8 mg per kilogram of body weight), sarilumab (400 mg), or standard care (control). The primary outcome was respiratory and cardiovascular organ support-free days, on an ordinal scale combining in-hospital death (assigned a value of -1) and days free of organ support to day 21. The trial uses a Bayesian statistical model with predefined criteria for superiority, efficacy, equivalence, or futility. An odds ratio greater than 1 represented improved survival, more organ support-free days, or both. RESULTS: Both tocilizumab and sarilumab met the predefined criteria for efficacy. At that time, 353 patients had been assigned to tocilizumab, 48 to sarilumab, and 402 to control. The median number of organ support-free days was 10 (interquartile range, -1 to 16) in the tocilizumab group, 11 (interquartile range, 0 to 16) in the sarilumab group, and 0 (interquartile range, -1 to 15) in the control group. The median adjusted cumulative odds ratios were 1.64 (95% credible interval, 1.25 to 2.14) for tocilizumab and 1.76 (95% credible interval, 1.17 to 2.91) for sarilumab as compared with control, yielding posterior probabilities of superiority to control of more than 99.9% and of 99.5%, respectively. An analysis of 90-day survival showed improved survival in the pooled interleukin-6 receptor antagonist groups, yielding a hazard ratio for the comparison with the control group of 1.61 (95% credible interval, 1.25 to 2.08) and a posterior probability of superiority of more than 99.9%. All secondary analyses supported efficacy of these interleukin-6 receptor antagonists. CONCLUSIONS: In critically ill patients with Covid-19 receiving organ support in ICUs, treatment with the interleukin-6 receptor antagonists tocilizumab and sarilumab improved outcomes, including survival. (REMAP-CAP ClinicalTrials.gov number, NCT02735707.)

Impairment of the ER/mitochondria compartment in human cardiomyocytes with PLN p.Arg14del mutation

The phospholamban (PLN) p.Arg14del mutation causes dilated cardiomyopathy, with the molecular disease mechanisms incompletely understood. Patient dermal fibroblasts were reprogrammed to hiPSC, isogenic controls were established by CRISPR/Cas9, and cardiomyocytes were differentiated. Mutant cardiomyocytes revealed significantly prolonged Ca(2+) transient decay time, Ca(2+)‐load dependent irregular beating pattern, and lower force. Proteomic analysis revealed less endoplasmic reticulum (ER) and ribosomal and mitochondrial proteins. Electron microscopy showed dilation of the ER and large lipid droplets in close association with mitochondria. Follow‐up experiments confirmed impairment of the ER/mitochondria compartment. PLN p.Arg14del end‐stage heart failure samples revealed perinuclear aggregates positive for ER marker proteins and oxidative stress in comparison with ischemic heart failure and non‐failing donor heart samples. Transduction of PLN p.Arg14del EHTs with the Ca(2+)‐binding proteins GCaMP6f or parvalbumin improved the disease phenotype. This study identified impairment of the ER/mitochondria compartment without SR dysfunction as a novel disease mechanism underlying PLN p.Arg14del cardiomyopathy. The pathology was improved by Ca(2+)‐scavenging, suggesting impaired local Ca(2+) cycling as an important disease culprit

Size Doesn't Matter: Towards a More Inclusive Philosophy of Biology

notes: As the primary author, O’Malley drafted the paper, and gathered and analysed data (scientific papers and talks). Conceptual analysis was conducted by both authors.publication-status: Publishedtypes: ArticlePhilosophers of biology, along with everyone else, generally perceive life to fall into two broad categories, the microbes and macrobes, and then pay most of their attention to the latter. ‘Macrobe’ is the word we propose for larger life forms, and we use it as part of an argument for microbial equality. We suggest that taking more notice of microbes – the dominant life form on the planet, both now and throughout evolutionary history – will transform some of the philosophy of biology’s standard ideas on ontology, evolution, taxonomy and biodiversity. We set out a number of recent developments in microbiology – including biofilm formation, chemotaxis, quorum sensing and gene transfer – that highlight microbial capacities for cooperation and communication and break down conventional thinking that microbes are solely or primarily single-celled organisms. These insights also bring new perspectives to the levels of selection debate, as well as to discussions of the evolution and nature of multicellularity, and to neo-Darwinian understandings of evolutionary mechanisms. We show how these revisions lead to further complications for microbial classification and the philosophies of systematics and biodiversity. Incorporating microbial insights into the philosophy of biology will challenge many of its assumptions, but also give greater scope and depth to its investigations

Evidence for Parapatric Speciation in the Mormyrid Fish, Pollimyrus castelnaui (Boulenger, 1911), from the Okavango–Upper Zambezi River Systems: P. marianne sp. nov., Defined by Electric Organ Discharges, Morphology and Genetics

We report on parapatric speciation in the mormyrid fish,Pollimyrus castelnaui (Boulenger, 1911), from the Okavango and the Upper Zambezi River systems. We recognise samples from the Zambezi River as a distinct species, P. marianne, displaying an eastern phenotype of electric organ discharge (EOD) waveform (Type 3) that is distinct from the western EOD phenotype (Type 1) observed in P. castelnaui samples from the neighbouring Okavango. Samples from the geographically intermediate Kwando/Linyanti River (a tributary of the Zambezi that is also intermittently connected to the Okavango) presented a more variable third EOD phenotype (Type 2). In 13 out of 14 morphological characters studied, the Zambezi River samples differed significantly from P. castelnaui. Morphologically and in EOD characters, the Kwando/Linyanti fish are distinct from both P. castelnaui and P. marianne. Sequence analysis of the mitochondrial cytochrome b gene unambiguously reveals that specimens from the Zambezi River System form a well supported taxon which clearly differs from P. castelnaui from the Okavango (1.5–2.5% sequence divergence).Within specimens from theKwando–Zambezi System some geographic differentiation can be detected (nucleotide substitutions up to 0.6%); but groups cannot be resolved with certainty. Significant allozyme differences were found between the Okavango and all other EOD types from the Upper Zambezi System, and, within the Zambezi System, between the Kwando (Type 2) and Zambezi (Type 3) individuals. The low Wright’s fixation index values, the lack of fixed allele differences, and small genetic distances provide little evidence for speciation between groups within the Zambezi System, but moderate to great fixation index values and significant allele frequency differences were observed between the Okavango and the other fishes. It is concluded that within the Zambezi System, differentiation between Kwando/Linyanti and Zambezi populations (as revealed by morphology and EOD waveform comparisons) is so recent that substantial genetic (allozyme and mitochondrial sequence) differences could not have evolved, or were not detected

The global trend in plant twining direction

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