2,065 research outputs found
Escape from the boundary in Markov population processes
Density dependent Markov population processes in large populations of size
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 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 , and
the length of time taken until all populations have sizes comparable to
then becomes infinite as . Under suitable assumptions, we show
that in the early stages of development, up to the time when all populations
have sizes at least , for , 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 equipped with a
metric. In typical examples, 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.
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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
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 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 in terms of the nth power
of an operator . By analyzing the spectrum of , 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
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