Lattice model for rapidly folding protein-like heteropolymers.

Protein folding is a relatively fast process considering the astronomical number of conformations in which a protein could find itself. Within the framework of a lattice model, we show that one can design rapidly folding sequences by assigning the strongest attractive couplings to the contacts present in a target native state. Our protein design can be extended to situations with both attractive and repulsive contacts. Frustration is minimized by ensuring that all the native contacts are again strongly attractive. Strikingly, this ensures the inevitability of folding and accelerates the folding process by an order of magnitude. The evolutionary implications of our findings are discussed.

The SEIQS stochastic epidemic model with external source of infection

This paper deals with a stochastic epidemic model for computer viruses with latent and quarantine periods, and two sources of infection: internal and external. All sojourn times are considered random variables which are assumed to be independent and exponentially distributed. For this model extinction and hazard times are analyzed, giving results for their Laplace transforms and moments. The transient behavior is considered by studying the number of times that computers are susceptible, exposed, infectious and quarantined during a period of time (0, t] and results for their joint and marginal distributions, moments and cross moments are presented. In order to give light this analysis, some numerical examples are showed.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Semiparametric smooth-coefficient stochastic frontier model

This paper proposes a semiparametric smooth-coefficient (SPSC) stochastic production frontier model where regression coefficients are unknown smooth functions of environmental factors (ZZ). Technical inefficiency is specified in the form of a parametric scaling function which also depends on the ZZ variables. Thus, in our SPSC model the ZZ variables affect productivity directly via the technology parameters as well as through inefficiency. A residual-based bootstrap test of the relevance of the environmental factors in the SPSC model is suggested. An empirical application is also used to illustrate the technique.

Bayesian precalibration of a large stochastic microsimulation model

Calibration of stochastic traffic microsimulation models is a challenging task. This paper proposes a fast iterative probabilistic precalibration framework and demonstrates how it can be successfully applied to a real-world traffic simulation model of a section of the M40 motorway and its surrounding area in the U.K. The efficiency of the method stems from the use of emulators of the stochastic microsimulator, which provides fast surrogates of the traffic model. The use of emulators minimizes the number of microsimulator runs required, and the emulators' probabilistic construction allows for the consideration of the extra uncertainty introduced by the approximation. It is shown that automatic precalibration of this real-world microsimulator, using turn-count observational data, is possible, considering all parameters at once, and that this precalibrated microsimulator improves on the fit to observations compared with the traditional expertly tuned microsimulation. © 2000-2011 IEEE.

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

An irregular lattice model to simulate crack paths in bonded granular assemblies

Peer reviewed

An irregular lattice model to simulate crack paths in bonded granular assemblies

Peer reviewed

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.

Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]