On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.

On the asymptotic enumeration of accessible automata

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments. (C) 2007 Elsevier B.V. All rights reserved.

Modeling the kinetics of the coalescence of water droplets in crude oil emulsions subject to an electric field, with the cellular automata technique

In this study, the concept of cellular automata is applied in an innovative way to simulate the separation of phases in a water/oil emulsion. The velocity of the water droplets is calculated by the balance of forces acting on a pair of droplets in a group, and cellular automata is used to simulate the whole group of droplets. Thus, it is possible to solve the problem stochastically and to show the sequence of collisions of droplets and coalescence phenomena. This methodology enables the calculation of the amount of water that can be separated from the emulsion under different operating conditions, thus enabling the process to be optimized. Comparisons between the results obtained from the developed model and the operational performance of an actual desalting unit are carried out. The accuracy observed shows that the developed model is a good representation of the actual process. (C) 2010 Published by Elsevier Ltd.

Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases

There are several ways of controlling the propagation of a contagious disease. For instance, to reduce the spreading of an airborne infection, individuals can be encouraged to remain in their homes and/or to wear face masks outside their domiciles. However, when a limited amount of masks is available, who should use them: the susceptible subjects, the infective persons or both populations? Here we employ susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations and probabilistic cellular automata in order to investigate how the deletion of links in the random complex network representing the social contacts among individuals affects the dynamics of a contagious disease. The inspiration for this study comes from recent discussions about the impact of measures usually recommended by health public organizations for preventing the propagation of the swine influenza A (H1N1) virus. Our answer to this question can be valid for other eco-epidemiological systems. (C) 2010 Elsevier BM. All rights reserved.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density

We investigate the sensitivity of the composite cellular automaton of H. Fuks [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density classification performance of the resulting probabilistic cellular automaton (PCA) numerically. We conclude that the composite PCA performs the density classification task reliably only up to very small levels of noise. In particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an imperfect classifier, for any level of noise. While the original composite CA is nonergodic, analyses of relaxation times indicate that its noisy version is an ergodic automaton, with the relaxation times decaying algebraically over an extended range of parameters with an exponent very close (possibly equal) to the mean-field value.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.

A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.

Small-World Effect in Epidemics Using Cellular Automata

The spread of an infectious disease in a population involves interactions leading to an epidemic outbreak through a network of contacts. Extending on Watts and Strogatz (1998) who showed that short-distance connections create a small-world effect, a model combining short-and long-distance probabilistic and regularly updated contacts helps considering spatial heterogeneity. The method is based on cellular automata. The presence of long-distance connections accelerates the small-world effect, as if the world shrank in proportion of their total number.

Equine chorionic gonadotropin and gonadotropin-releasing hormone enhance fertility in a norgestomet-based, timed artificial insemination protocol in suckled Nelore (Bos indicus) cows

Two experiments were conducted to investigate the effects of equine chorionic gonadotropin (eCG) at progestin removal and gonadotropin-releasing hormone (GnRH) at timed artificial insemination (TA!) on ovarian follicular dynamics (Experiment 1) and pregnancy rates (Experiment 2) in suckled Nelore (Bos indicus) cows. Both experiments were 2 x 2 factorials (eCG or No eCG, and GnRH or No GnRH), with identical treatments. In Experiment 1, 50 anestrous cows, 134.5 +/- 2.3 d postpartum, received a 3 mg norgestomet ear implant se, plus 3 mg norgestomet and 5 mg estradiol valerate im on Day 0. The implant was removed on Day 9, with TAI 54 h later. Cows received 400 IU eCG or no further treatment on Day 9 and GnRH (100 mu g gonadorelin) or no further treatment at TAI. Treatment with eCG increased the growth rate of the largest follicle from Days 9 to 11 (means +/- SEM, 1.53 +/- 0.1 vs. 0.48 +/- 0.1 mm/d; P < 0.0001), its diameter on Day 11(11.4 +/- 0.6 vs. 9.3 +/- 0.7 mm; P = 0.03), as well as ovulation rate (80.8% vs. 50.0%, P = 0.02), whereas GnRH improved the synchrony of ovulation (72.0 +/- 1.1 VS. 71.1 +/- 2.0 h). In Experiment 2 (n = 599 cows, 40 to 120 d postpartum), pregnancy rates differed (P = 0.004) among groups (27.6%, 40.1%, 47.7%, and 55.7% for Control. GnRH, eCG, and eCG + GnRH groups). Both eCG and GnRH improved pregnancy rates (51.7% vs. 318%, P = 0.002; and 48.0% vs 37.6%, P = 0.02, respectively), although their effects were not additive (no significant interaction). In conclusion, eCG at norgestomet implant removal increased the growth rate of the largest follicle (LF) from implant removal to TAI, the diameter of the LF at TAI, and rates of ovulation and pregnancy rates. Furthermore, GnRH at TAI improved the synchrony of ovulations and pregnancy rates in postpartum Nelore cows treated with a norgestomet-based TAI protocol. (C) 2010 Elsevier Inc. All rights reserved.

Effects of gonadotropin-releasing hormone at initiation of the 5-d timed artificial insemination (AI) program and timing of induction of ovulation relative to AI on ovarian dynamics and fertility of dairy heifers

Two experiments evaluated the effects of the first GnRH injection of the 5-d timed artificial insemination (AI) program on ovarian responses and pregnancy per AT (P/AI), and the effect of timing of the final GnRH to induce ovulation relative to AT on P/AI. In experiment 1, 605 Holstein heifers were synchronized for their second insemination and assigned randomly to receive GnRH on study d 0 (n = 298) or to remain as untreated controls (n = 307). Ovaries were scanned on study d 0 and 5. All heifers received a controlled internal drug-release (CIDR) insert containing progesterone on d 0, a single injection of PGF(2 alpha),, and removal of the CIDR on d 5, and GnRH concurrent with timed AT on d 8. Blood was analyzed for progesterone at AI. Pregnancy was diagnosed on d 32 and 60 after AI. Ovulation on study d 0 was greater for GnRH than control (35.4 vs. 10.6%). Presence of a new corpus luteum (CL) at PGF(2 alpha),, injection was greater for GnRH than for control (43.1 vs. 20.8%), although the proportion of heifers with a CL at PGF(2 alpha) did not differ between treatments and averaged 87.1%. Progesterone on the day of AT was greater for GaRH than control (0.50 +/- 0.07 vs. 0.28 +/- 0.07 ng/mL). The proportion of heifers at AI with progesterone <0.5 ng/mL was less for GURH than for control (73.8 vs. 88.2%). The proportion of heifers in estrus at AI did not differ between treatments and averaged 66.8%. Pregnancy per AI was not affected by treatment at d 32 or 60 (GnRH = 52.5 and 49.8% vs. control = 54.1 and 50.0%), and pregnancy loss averaged 6.0%. Responses to GnRH were not influenced by ovarian status on study d 0. In experiment 2, 1,295 heifers were synchronized for their first insemination and assigned randomly to receive a CIDR on d 0, PGF(2 alpha) and removal of the CIDR on d 5, and either GnRH 56 h after PGF(2 alpha) and AI 16 h later (OVS56, n = 644) or GnRH concurrent with AI 72 h after PGF(2 alpha) (COS72; n = 651). Estrus at AI was greater for COS72 than for OVS56 (61.4 vs. 47.5). Treatment did not affect P/AI on d 32 in heifers displaying signs of estrus at AI, but COS72 improved P/AI compared with OVS56 (55.0 vs. 47.6%) in those not in estrus at AI. Similarly, P/AI on d 60 did not differ between treatments for heifers displaying estrus, but COS72 improved P/AI compared with OVS56 (53.0 vs. 44.7%) in those not in estrus at AI. Administration of GnRH on the first day of the 5-d timed AI program resulted in low ovulation rate and no improvement in P/AI when heifers received a single PGF(2 alpha) injection 5 d later. Moreover, extending the proestrus by delaying the finAI GnRH from 56 to 72 h concurrent with AI benefited fertility of dairy heifers that did not display signs of estrus at insemination following the 5-d timed AI protocol.

Effects of equine chorionic gonadotropin and type of ovulatory stimulus in a timed-AI protocol on reproductive responses in dairy cows

The objectives were to evaluate the effects of equine chorionic gonadotropin (eCG) supplementation (with or without eCG) and type of ovulatory stimulus (GnRH or ECP) on ovarian follicular dynamics, luteal function, and pregnancies per AI (P/AI) in Holstein cows receiving timed artificial insemination (TAI). On Day 0, 742 cows in a total of 782 breedings, received 2 mg of estradiol benzoate (EB) and one intravaginal progesterone (P4) insert (CIDR). On Day 8, the CIDR was removed, and all cows were given PGF2 alpha and assigned to one of four treatments in a 2 x 2 factorial arrangement: (1) CG: GnRH 48 h later; (2) CE: ECP; (3) EG: eCG + GnRH 48 It later; (4) EE: eCG + ECP. There were significant interactions for eCG x ovulatory stimulus and eCG x BCS. Cows in the CG group were less likely (28.9% vs. 33.8%; P < 0.05) to become pregnant compared with those in the EG group (odds ratio [OR] = 0.28). There were no differences in P/AI between CE and EE cows (30.9% vs. 29.1%; OR = 0.85; P = 0.56), respectively. Thinner cows not receiving eCG had lower P/AI than thinner cows receiving eCG (15.2% vs. 38.0%; OR = 0.20; P < 0.01). Treatment with eCG tended to increase serum progestesterone concentrations during the diestrus following synchronized ovulation (P < 0.10). However, the treatment used to induce ovulation did not affect CL volume or serum progesterone concentrations. In conclusion, both ECP and GnRH yielded comparable P/AI. However, eCG treatment at CIDR removal increased pregnancy rate in cows induced to ovulate with GnRH and in cows with lower BCS. (C) 2009 Elsevier Inc. All rights reserved.

An extinction-survival-type phase transition in the probabilistic cellular automaton p182-q200

We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram`s enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction-survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

A new classification of foods based on the extent and purpose of their processing

This paper describes a new food classification which assigns foodstuffs according to the extent and purpose of the industrial processing applied to them. Three main groups are defined: unprocessed or minimally processed foods (group 1), processed culinary and food industry ingredients (group 2), and ultra-processed food products (group 3). The use of this classification is illustrated by applying it to data collected in the Brazilian Household Budget Survey which was conducted in 2002/2003 through a probabilistic sample of 48,470 Brazilian households. The average daily food availability was 1,792 kcal/person being 42.5% from group 1 (mostly rice and beans and meat and milk), 37.5% from group 2 (mostly vegetable oils, sugar, and flours), and 20% from group 3 (mostly breads, biscuits, sweets, soft drinks, and sausages). The share of group 3 foods increased with income, and represented almost one third of all calories in higher income households. The impact of the replacement of group 1 foods and group 2 ingredients by group 3 products on the overall quality of the diet, eating patterns and health is discussed.