Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit

Modeling of Community- and Hospital-acquired Methicillin-resistant Staphylococcus Aureus Transmission in Hospital Settings

In this paper we developed both deterministicand stochastic models of community- and hospital-acquired methicillin-resistant staphylococcus aureus transmission (MRSA) to quantify their interactions in a hospital settings. The disease-free equilibrium of the model is locally-asymptotically stable whenever the associated reproduction number is less than unity. The disease persists in the community whenever the reproduction number is greater than unity. Although our stochastic model evolves on an unbounded state space, we show it is positive recurrent. The result obtained from the sensitivity analysis using the deterministic model indicates that the dominant parameters are the hand washing compliance rate, the health-care workers decolonization rate, environmental contamination rate, the admission rates into the hospital, isolation rate of patients with CA-MRSA and isolation rate of patients with HA-MRSA, the transmission probabilities of CA- and HA-MRSA  per contact with health-care workers and transmission probability of health-care workers  per contact with patients. Numerical simulations of the deterministic model obtained from using the dominate parameters as combination of control strategies such as low-, moderate and high-effectiveness control strategies show that disease prevalence among the hospital patients and the bacterial in the hospital environment can be controlled by moderate- and high-effectiveness control strategies. However, for health-care workers the disease prevalence can only be effectively controlled by the high-effectiveness control strategy

Stochastic integration based on simple, symmetric random walks

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, it gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not c\`adl\`ag in general.Comment: 16 pages, some typos correcte

Excision of a strong Markov process

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47651/1/440_2004_Article_BF00532853.pd

Patterns in random walks and Brownian motion

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.Comment: 31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_

Whole genome analysis of a schistosomiasis-transmitting freshwater snail

Biomphalaria snails are instrumental in transmission of the human blood fluke Schistosoma mansoni. With the World Health Organization's goal to eliminate schistosomiasis as a global health problem by 2025, there is now renewed emphasis on snail control. Here, we characterize the genome of Biomphalaria glabrata, a lophotrochozoan protostome, and provide timely and important information on snail biology. We describe aspects of phero-perception, stress responses, immune function and regulation of gene expression that support the persistence of B. glabrata in the field and may define this species as a suitable snail host for S. mansoni. We identify several potential targets for developing novel control measures aimed at reducing snail-mediated transmission of schistosomiasis

Fine-Scale Mapping of the 5q11.2 Breast Cancer Locus Reveals at Least Three Independent Risk Variants Regulating MAP3K1

Peer reviewe

MicroRNA Related Polymorphisms and Breast Cancer Risk

Peer reviewe