Linear-time algorithms for scattering number and Hamilton-connectivity of interval graphs.

We prove that for all inline image an interval graph is inline image-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an inline image time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known inline image time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in inline image time

Cluster Approximation for the Farey Fraction Spin Chain

We consider the Farey fraction spin chain in an external field $h$. Utilising ideas from dynamical systems, the free energy of the model is derived by means of an effective cluster energy approximation. This approximation is valid for divergent cluster sizes, and hence appropriate for the discussion of the magnetizing transition. We calculate the phase boundaries and the scaling of the free energy. At $h=0$ we reproduce the rigorously known asymptotic temperature dependence of the free energy. For $h \ne 0$, our results are largely consistent with those found previously using mean field theory and renormalization group arguments.Comment: 17 pages, 3 figure

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field $h$. Using ideas from dynamical systems and functional analysis, we show that the free energy $f$ in the vicinity of the second-order phase transition is given, exactly, by $$f \sim \frac t{\log t}-\frac1{2} \frac{h^2}t \quad \text{for} \quad h^2\ll t \ll 1 .$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_c})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, $\lambda_G$. It follows that $\lambda_G$ determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment

Coupling a model of human thermoregulation with computational fluid dynamics for predicting human-environment interaction

This paper describes the methods developed to couple a commercial CFD program with a multi-segmented model of human thermal comfort and physiology. A CFD model is able to predict detailed temperatures and velocities of airflow around a human body, whilst a thermal comfort model is able to predict the response of a human to the environment surrounding it. By coupling the two models and exchanging information about the heat transfer at the body surface the coupled system can potentially predict the response of a human body to detailed local environmental conditions. This paper presents a method of exchanging data, using shared files, to provide a means of dynamically exchanging simulation data with the IESD-Fiala model during the CFD solution process. Additional code is used to set boundary conditions for the CFD simulation at the body surface as determined by the IESD-Fiala model and to return information about local environmental conditions adjacent to the body surface as determined by the CFD simulation. The coupled system is used to model a human subject in a naturally ventilated environment. The resulting ventilation flow pattern agrees well with other numerical and experimental work

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

Instability of misoprostol tablets stored outside the blister: a potential serious concern for clinical outcome in medical abortion

Misoprostol (Cytotec) is recognised to be effective for many gynaecological indications including termination of pregnancy, management of miscarriage and postpartum haemorrhage. Although not licensed for such indications, it has been used for these purposes by millions of women throughout the world. Misoprostol tablets are most often packaged as multiple tablets within an aluminium strip, each within an individual alveolus. When an alveolus is opened, tablets will be exposed to atmospheric conditions

On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

Effect of ethanolic extract of Justicia secunda (blood root) leaves on reproductive organs and hormones in female Wistar rats

Background: Several environmental chemicals are suspected to be responsible for adverse health effects on the reproductive system. Poisonous plants grow in most communities found on range lands and pastures. One major effect on consumption of these plants is on reproduction which includes birth defect, abortion and interference with Oogenesis, spermatogenesis, libido and estrous cycle. Justicia secunda (blood root) as the name implies is known for its anti-anemic properties.Methods: Animals were grouped into 6 groups with 6 rats in each group. They were housed in metal cages at room temperature and had access to commercial standard rodent pellets and clean water. Group 1 (control 0.00 mg/kg.) was given distilled water, groups 2-6 were given 99% ethanolic extract of Justicia secunda leaves orally at dose levels of 300, 400, 400, 450 and 450 mg/day, respectively for 42 days.Results: The result of this study indicates that ethanolic extract of Justicia secunda (blood root) was able to increase the level of FSH significantly at medium dose group. Significant increase in oestrogen level observed in this study.Conclusions: ethanolic extract of Justicia secunda (blood root) leaves is likely to cause an increase in the secreting ability of cells of the anterior pituitary gland producing FSH or cells of the hypothalamus producing gonadotrophin releasing hormones. The plant is likely to contain steroids

Unc13A and Unc13B contribute to the decoding of distinct sensory information in Drosophila

The physical distance between presynaptic Ca2+ channels and the Ca2+ sensors triggering the release of neurotransmitter-containing vesicles regulates short-term plasticity (STP). While STP is highly diversified across synapse types, the computational and behavioral relevance of this diversity remains unclear. In the Drosophila brain, at nanoscale level, we can distinguish distinct coupling distances between Ca2+ channels and the (m)unc13 family priming factors, Unc13A and Unc13B. Importantly, coupling distance defines release components with distinct STP characteristics. Here, we show that while Unc13A and Unc13B both contribute to synaptic signalling, they play distinct roles in neural decoding of olfactory information at excitatory projection neuron (ePN) output synapses. Unc13A clusters closer to Ca2+ channels than Unc13B, specifically promoting fast phasic signal transfer. Reduction of Unc13A in ePNs attenuates responses to both aversive and appetitive stimuli, while reduction of Unc13B provokes a general shift towards appetitive values. Collectively, we provide direct genetic evidence that release components of distinct nanoscopic coupling distances differentially control STP to play distinct roles in neural decoding of sensory information