Stochastic processes

We consider a particle performing a stochastic motion on a one-dimensional lattice with jump widths distributed according to a power-law with exponent μ + 1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x) ∼ x^-α and we find that as long as μ < α there is a finite probability that the walker will never be trapped, no matter how long the process is. This analytical result, valid on infinite chains, is corroborated by numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.

Purpose. Conduct a social network analysis of the health and non–health related organizations that participate in Bogotá's Ciclovía Recreativa (Ciclovía). Design. Cross-sectional study. Setting. Ciclovía is a multisectoral community-based mass program in which streets are temporarily closed to motorized transport, allowing exclusive access to individuals for leisure activities and physical activity. Subjects. Twenty-five organizations that participate in the Ciclovía. Measures. Seven variables were examined by using network analytic methods: relationship, link attributes (integration, contact, and importance), and node attributes (leadership, years in the program, and the sector of the organization). Analysis. The network analytic methods were based on a visual descriptive analysis and an exponential random graph model. Results. Analysis shows that the most central organizations in the network were outside of the Health sector and include Sports and Recreation, Government, and S...

One concern with current techniques of UV reactor validation is that they provide only a measure of the mean UV fluence. In this research, the actual fluence distribution of a UV reactor is measured through the use of photochemically active fluorescent microspheres. ...

A wireless network consisting of large number of small sensors with low-power transceivers. These devices rely on battery power so that; improvement in the energy of these networks becomes important. Wireless sensor network (WSN) require various power management protocols to reduce the power consumption. In this paper we study that different number of clustering algorithm leads to different network performance on the energy balancing, energy consumption and network lifetime. We propose a Multi-hop Hierarchical Stable Election Protocol (MHSEP) for wireless sensor networks to enhance the network lifetime and avoid the formation of energy holes. Classical clustering protocols assume that all the nodes in a system are equipped with the equal amount of energy and as a result, network cannot take full advantage of the presence of node heterogeneity in system. Our proposed protocol is a heterogeneous-aware protocol to increase the time-interval before the death of first node (we refer to a...

In this paper we consider several parametric assumptions for the instantaneous covariance structure of the LIBOR market model, whose role in the modern interest-rate derivatives theory is becoming more and more central. We examine the impact of each different parameterization on the evolution of the term structure of volatilities in time, on terminal correlations and on the joint calibration to the caps and swaptions markets. We present a number of cases of calibration in the Euro market. In particular, we consider calibration via a parameterization establishing a controllable one to one correspondence between instantaneous covariance parameters and swaptions volatilities, and assess the benefits of smoothing the input swaption matrix before calibrating.

Penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions. The penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood, such that smooth images are favored. Attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself. The previously introduced median root prior (MRP) favors locally monotonic images. MRP preserves sharp edges while reducing locally nonmonotonic noise at the same time. Quantitative properties of MRP are good, because differences in the neighboring pixel values are not penalized as such. The median is used as an estimate for a penalty reference, against which the pixel value is compared when setting the penalty. In order to generalize the class of MRP-type of priors, the standard median was replaced by other order statistic operations, the L and finite-impluse-response median hybrid (FMH) filters. They allow for smoother appearance as they apply linear weighting together with robust nonlinear operations. The images reconstructed using the new MRP-L and MRP-FMH priors are visually more conventional. Good quantitative properties of MRP are not significantly altered by the new priors.

The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy, while a solution of the stochastic optimal power control is obtained through

The pharmacokinetics of cyclosporin (CsA) are unusual because of several heterogeneous features which include the presence of more than one conformer, considerable accumulation in erythrocytes and lipoproteins, extensive plasma protein binding, distribution into deep tissues, biliary secretion and hepatic clearance involving a large number of metabolites. In this study, a stochastic compartmental model was developed to describe the heterogeneous elimination kinetics of CsA. This new approach relies on a probabilistic transfer model with a gamma distributed probability intensity coefficient for drug elimination. For comparative purposes both the stochastic model and compartmental deterministic models were fitted to real post infusion data from patients receiving CsA as a 2-hr intravenous infusion. The criteria for selecting the best model showed that the stochastic model, although simpler than the compartmental deterministic models, is more flexible and gives a better fit to the kine...

Our previous research effort has resulted in a stochastic model that provides an excellent fit to our experimental data on proliferation and differentiation of oligodendrocyte type-2 astrocyte progenitor cells at the clonal level. However, methods for estimation of model parameters and their statistical properties still remain far away from complete exploration. The main technical difficulty is that no explicit analytic expression for the joint distribution of the number of progenitor cells and oligodendrocytes, and consequently for the corresponding likelihood function, is available. In the present paper, we overcome this difficulty by using computer-intensive simulation techniques for estimation of the likelihood function. Since the output of our simulation model is essentially random, stochastic optimization methods are necessary to maximize the estimated likelihood function. We use the Kiefer–Wolfowitz procedure for this purpose. Given sufficient computing resources, the proposed estimation techniques significantly extend the spectrum of problems that become approachable. In particular, these techniques can be applied to more complex branching models of multi-type cell systems with dependent evolutions of different types of cells.

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs.