Escape from the boundary in Markov population processes

Density dependent Markov population processes in large populations of size $N$ were shown by Kurtz (1970, 1971) to be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, and to exhibit stochastic fluctuations about this deterministic solution on the scale $\sqrt N$ that can be approximated by a diffusion process. Here, motivated by an example from evolutionary biology, we are concerned with describing how such a process leaves an absorbing boundary. Initially, one or more of the populations is of size much smaller than $N$, and the length of time taken until all populations have sizes comparable to $N$ then becomes infinite as $N \to \infty$. Under suitable assumptions, we show that in the early stages of development, up to the time when all populations have sizes at least $N^{1-\alpha}$, for $1/3 < \alpha < 1$, the process can be accurately approximated in total variation by a Markov branching process. Thereafter, the process is well approximated by the deterministic solution starting from the original initial point, but with a random time delay. Analogous behaviour is also established for a Markov process approaching an equilibrium on a boundary, where one or more of the populations become extinct.Comment: 50 page

Approximating the ground state of gapped quantum spin systems

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on X^c, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue

Bio-self-healing of cementitious mortar incubated within clay soil

The use of bacteria-based self-healing concrete for sub-structures in ground conditions is an area of increasing interest for enhancing the durability and longevity of infrastructure. In line with this objective, the present study investigates the bio-self-healing performance when a cementitious material is embedded in clay soil with varying chemical exposures and water-saturation regimes. Laboratory experiments were conducted on pre-cracked mortar specimens with Bacillus Subtilis encapsulated in perlite. The specimens were then incubated in the soil with different pH and sulphate levels, representing three exposure classes (based on Eurocodes). The crack healing ratio was evaluated through visual inspection and capillary-water absorption - before and after soil incubation. Findings showed that all inoculated specimens exhibited healing ratios noticeably larger than the control specimens, which mainly experienced small autogenous healing. Of note, the best healing performance was observed when the soil was fully-saturated and pH-neutral. From the design perspective of bio-concrete, this study emphasises the consideration of groundwater regime as well as acidity and sulphate of the ground. This material may be downloaded for personal use only. Any other use requires prior permission of the American Society of Civil Engineers

Monitoring the bio-self-healing performance of cement mortar incubated within soil and water using electrical resistivity

In research on self-healing concrete, the restorative performance can be evaluated by a wide range of techniques. However, most of these techniques can be challenging to apply to concrete samples embedded in soil without causing a significant disturbance to the test (as they require removing the samples from the soil, washing off any residue, and examining and returning them). To provide a solution to this issue, we investigated the potential application of an in-situ, non-destructive method utilising electrical resistivity (embedded electrodes). The study was conducted on bio-mortar specimens incubated within saturated soil and water for 11 weeks. The bio-specimens were cast by adding expanded perlite impregnated with Bacillus subtilis and nutrients to the fresh mix. Standard cement mortar (without bacterial agents) was also tested to serve as control specimens. Additional testing (capillary rise and absolute porosity) was conducted under typical conditions to provide context for interpreting the changes in electrical resistivity in relation to the healing process. The bio-mortar showed greater improvements in electrical resistivity (accompanied by a reduction in crack area, water absorption and absolute porosity) than the control mortar. The study demonstrated that the electrical resistivity technique could potentially monitor the self-healing performance of concrete embedded in soil without disturbing the concrete-soil system

Juridical Analyst Supervision Function of the Notary Supervisory Board in the City of Baubau

Notaries as public officials who carry out the profession in providing legal services to the public, need to get protection and guarantees in order to achieve legal certainty. This study aims: (1) To determine the implementation of notary supervision conducted by the Notary Regional Supervisory Board in the City of Baubau (2) To determine the factors that influence the implementation of notary supervision by the Regional Notary Supervisory Board of the City of Baubau. This study uses an Empirical Juridical approach that seeks to link prevailing legal norms with reality in society, the authors conduct research with analytical descriptive research that is to reveal the real problem or situation, to reveal the facts of the research so as to provide an objective picture. The results of the study show that (1) The implementation of notary supervision by the Notary Supervisory Board in the City of Baubau by making efforts to guide, supervise the notary, that supervision as a preventive and curative activity, preventive activities carried out are activities that include authority administrative, regulate procedural procedures and notary protocols, while curative regulates the taking of suspected violations. (2) Factors influencing the implementation of notary supervision by the Regional Supervisory Board of Baubau City, namely in carrying out their functions and duties, human resources are not yet maximal, supporting infrastructures are still limited, budgets are still very minimal, coordination between management is still low. weak, lack of legal awareness from several notaries, especially administrative order

Translated Poisson approximation to equilibrium distributions of Markov population processes

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in Kolmogorov distance, is of the smallest order that is compatible with their having integer support. Here, an approximation in the much stronger total variation norm is established, without any loss in the asymptotic order of accuracy; the approximating distribution is a translated Poisson distribution having the same variance and (almost) the same mean. Our arguments are based on the Stein-Chen method and Dynkin's formula.Comment: 18 page

Anaemia and its associated factors among pregnant women in Koko, Kebbi State, Nigeria

Background: Anaemia in pregnancy remains a common problem affecting women in northern Nigeria. It is associated with several adverse consequences.Objective: The aim of this study was to determine the prevalence of anaemia and its associated factors among pregnant women in Koko/Besse local government area of Kebbi state,Northwest Nigeria.Methodology: A cross-sectional study was conducted among women using a standardized questionnaire for data collection. Haematocrit level was determined using the centrifuge technique. Data was analysed descriptively in Statistical Package for Social Sciences (SPSS).Results: The prevalence of anaemia among our respondents was 23.5%.There were higher prevalence rates among those married in monogamous families, who did not attend antenatal care, unemployed, and those who were non-compliant with their prescribed antenatal care haematinics.Conclusion: The prevalence of anaemia in pregnancy even though high, was relatively lower than findings from other studies in the sub-region.A well developed and implemented public health intervention is likely to further reduce this prevalence.Keywords: Anaemia, pregnancy, prevalence, associated factors, Koko, Kebb

Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

On the Boolean dimension of a graph and other related parameters

We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star decomposition. We relate the Boolean dimension with the inversion index of a tournament.Comment: 13 pages, 2 figure