Global existence for a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition

In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different well-posedness results are shown, depending on the smoothness properties of the involved bulk and surface free energies

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network revealsirregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior. We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine-tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained, and can approximate several possible sources of noise, e.g. random channel gating or synaptic bombardment. The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).Comment: REVTeX4-1, 18 pages, 9 figure

Limiting problems for a nonstandard viscous Cahn--Hilliard system with dynamic boundary conditions

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp.105--118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the Laplace-Beltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases

Distributed optimal control of a nonstandard system of phase field equations

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.Comment: Key words: distributed optimal control, nonlinear phase field systems, first-order necessary optimality condition

The demography of the lizard Tropidurus torquatus (Squamata, Tropiduridae) in a highly seasonal Neotropical savanna

The demography of a population of Tropidurus torquatus was studied from March 1996 until December 1998, in the Cerrado biome of the Central Brazil, using the method of capture and recapture. Population size, number of incoming individuals in the population, and age structure varied seasonally, reflecting the reproductive cycle of the species. The instantaneous rate of population increase did not differ from zero throughout the study. In general, the permanence rate of juveniles and adults were low, indicating a large turnover of individuals in the population, with a maximum life expectancy of three years. The sex-ratio among adults was biased toward females. Since no bias was observed among juveniles and there was no difference in adults permanence between sexes, we suggestet that the biased adult sex-ratio resulted from a lower permanence of males during a short ontogenetic period, when secondary sexual characteristics develop. When compared to T. itambere, the studied population of T. torquatus attained a higher density and a greater female bias in the sex-ratio. In general, the studied population presented characteristics that, according to life history theory, should be associated with early age at maturity and polyginy: short life expectancy, high population turnover, and female biased sex-ratios

Probability of Trypanosoma cruzi transmission by Triatoma infestans (Hemiptera: Reduviidae) to the opossum Didelphis albiventris (Marsupialia: Didelphidae)

The probability of Trypanosoma cruzi transmission to opossums by independent events of predation and fecal contamination during feeding ("biting") with positive Triatoma infestans was estimated. Negative female opossums were challenged for 23 hr with 10 infected third and fourth instars of T. infestans, and tests for positivity for T. cruzi by xenodiagnosis were performed at 30, 60, and 90 days. From these data, seven probability parameters were estimated by maximum likelihood, and likelihood ratio statistics confidence intervals were calculated. Simultaneous estimation of p1 (probability that a "bite" will infect an opossum), p3 (probability that a bug that has been eaten by an opossum will infect it), and p6 (probability that the opossum will become infected if faced with an infected triatomine), resulted in p̂1 = 0.06, p̂3 = 0.075, and p̂6 = 0.059. On average, each opossum should be exposed to an average of 700 encounters with bugs during its life, resulting in about eight potentially infective contacts, to produce the 35% opossum prevalence found in the field.Facultad de Ciencias Naturales y Muse

Validation of the Italian version of the Revised Prenatal Coping Inventory (NuPCI) and its correlations with pregnancy-specific stress

Background: Pregnancy is a period of happiness but also of physical and psychological changes that can lead to distress. Functional coping strategies can reduce the pregnancy specific-stress. This study aimed to assess the psychometric properties of the Revised Prenatal Coping Inventory (NuPCI) in an Italian sample and to investigate how coping strategies were associated with pregnancy-specific stress. Methods: In this cross-sectional study, low-risk pregnant women (N = 211) were assessed with NuPCI, NuPDQ (Revised-Prenatal Distress Questionnaire), Brief-COPE (Coping Orientation to the Problems Experienced), and STAI (State-Trait Anxiety Inventory). The reliability of NuPCI was evaluated by assessing its internal consistency and factor structure (with a Confirmatory Factor Analysis, CFA). The concurrent validity between NuPCI and Brief-COPE and NuPDQ and STAI was investigated. Lastly, the relationship between NuPCI and NuPDQ was analyzed, as well as the ability of these scales to predict Apgar score at birth. Results: Internal consistency of NuPCI scales was good for Planning-Preparation (\u251C=0.84) and Spiritual-Positive Coping (\u251C=0.81) scales, acceptable for Avoidance (\u251C=0.76) scale. Moreover, the original three-factor structure was confirmed using a CFA with 29 of the 32 items (\u3c72374 = 618.06; RMSEA = 0.056, 95% confidence interval: [0.048, 0.063]); CFI = 0.920; and TLI = 0.913). Statistically significant correlations between NuPCI scales and Brief-COPE subscales ranged between r = + 0.217 and r = + 0.624; also, NuPDQ score was positively correlated with STAI scales (State scale: r = + 0.539; Trait scale: r = + 0.462). Concurrent validity was confirmed reporting that NuPDQ score was predicted by NuPCI scores (R2 = 0.423, p < 0.001), positively by Avoidance (\u3b2=+0.572) and Planning-Preparation (\u3b2=+0.215) and negatively by Spiritual-Positive Coping (\u3b2=-0.132). Finally, considering the stress, the effect of the Avoidance and Spiritual-Positive Coping scores respectively in decreasing (+ 155%) and increasing (+ 16%) the Apgar score became stronger. Conclusions: Italian NuPCI has sound psychometric properties and it is a useful coping measure. NuPDQ showed also a good validity. Our results may suggest a significant role for coping strategies, particularly in modulating the condition of the newborn at birth

Probability of Trypanosoma cruzi transmission by Triatoma infestans (Hemiptera: Reduviidae) to the opossum Didelphis albiventris (Marsupialia: Didelphidae)

The probability of Trypanosoma cruzi transmission to opossums by independent events of predation and fecal contamination during feeding ("biting") with positive Triatoma infestans was estimated. Negative female opossums were challenged for 23 hr with 10 infected third and fourth instars of T. infestans, and tests for positivity for T. cruzi by xenodiagnosis were performed at 30, 60, and 90 days. From these data, seven probability parameters were estimated by maximum likelihood, and likelihood ratio statistics confidence intervals were calculated. Simultaneous estimation of p1 (probability that a "bite" will infect an opossum), p3 (probability that a bug that has been eaten by an opossum will infect it), and p6 (probability that the opossum will become infected if faced with an infected triatomine), resulted in p̂1 = 0.06, p̂3 = 0.075, and p̂6 = 0.059. On average, each opossum should be exposed to an average of 700 encounters with bugs during its life, resulting in about eight potentially infective contacts, to produce the 35% opossum prevalence found in the field.Facultad de Ciencias Naturales y Muse

Role of infarct scar dimensions, border zone repolarization properties and anisotropy in the origin and maintenance of cardiac reentry

Cardiac ventricular tachycardia (VT) is a life-threatening arrhythmia consisting of a well organized structure of reentrant electrical excitation pathways. Understanding the generation and maintenance of the reentrant mechanisms, which lead to the onset of VT induced by premature beats in presence of infarct scar, is one of the most important issues in current electrocardiology. We investigate, by means of numerical simulations, the role of infarct scar dimension, repolarization properties and anisotropic fiber structure of scar tissue border zone (BZ) in the genesis of VT. The simulations are based on the Bidomain model, a reaction-diffusion system of Partial Differential Equations, discretized by finite elements in space and implicit-explicit finite differences in time. The computational domain adopted is an idealized left ventricle affected by an infarct scar extending transmurally. We consider two different scenarios: i) the scar region extends along the entire transmural wall thickness, from endocardium to epicardium, with the exception of a BZ region shaped as a central sub-epicardial channel (CBZ); ii) the scar region extends transmurally along the ventricular wall, from endocardium to a sub-epicardial surface, and is surrounded by a BZ region (EBZ). In CBZ simulations, the results have shown that: i) the scar extent is a crucial element for the genesis of reentry; ii) the repolarization properties of the CBZ, in particular the reduction of IKs and IKr currents, play an important role in the genesis of reentrant VT. In EBZ simulations, since the possible reentrant pathway is not assigned a-priori, we investigate in depth where the entry and exit sites of the cycle of reentry are located and how the functional channel of reentry develops. The results have shown that: i) the interplay between the epicardial anisotropic fiber structure and the EBZ shape strongly affects the propensity that an endocardial premature stimulus generates a cycle of reentry; ii) reentrant pathways always develop along the epicardial fiber direction; iii) very thin EBZs rather than thick EBZs facilitate the onset of cycles of reentry; iv) the sustainability of cycles of reentry depends on the endocardial stimulation site and on the interplay between the epicardial breakthrough site, local fiber direction and BZ rim