Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

A philosophical context for methods to estimate origin-destination trip matrices using link counts.

This paper creates a philosophical structure for classifying methods which estimate origin-destination matrices using link counts. It is claimed that the motivation for doing so is to help real-life transport planners use matrix estimation methods effectively, especially in terms of trading-off observational data with prior subjective input (typically referred to as 'professional judgement'). The paper lists a number of applications that require such methods, differentiating between relatively simple and highly complex applications. It is argued that a sound philosophical perspective is particularly important for estimating trip matrices in the latter type of application. As a result of this argument, a classification structure is built up through using concepts of realism, subjectivity, empiricism and rationalism. Emphasis is put on the fact that, in typical transport planning applications, none of these concepts is useful in its extreme form. The structure is then used to make a review of methods for estimating trip matrices using link counts, covering material published over the past 30 years. The paper concludes by making recommendations, both philosophical and methodological, concerning both practical applications and further research

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

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

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

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

Intrarenal Resistance Index as a Prognostic Parameter in Patients with Liver Cirrhosis Compared with Other Hepatic Scoring Systems

Background and Aims: Patients with advanced liver cirrhosis who develop renal dysfunction have a poor prognosis. Elevated intrarenal resistance indices (RIs) due to renal vascular constriction have been described before in cirrhotic patients. In the current study, we prospectively investigated the course of intrarenal RIs and compared their prognostic impact with those of the Model for End-Stage Liver Disease (MELD) and the Child-Pugh scores. Methods: Sixty-three patients with liver cirrhosis underwent a baseline visit which included a sonographic examination and laboratory tests. Forty-four patients were prospectively monitored. The end points were death or survival at the day of the follow-up visit. Results: In 28 patients, a follow-up visit was performed after 22 8 months (group 1). Sixteen patients died during follow-up after 12 8 months (group 2). Group 2 patients showed a significantly higher baseline RI (0.76 +/- 0.05) than group 1 patients (RI = 0.72 +/- 0.06; p < 0.05). As shown by receiver operating characteristic analysis, the RI and the MELD score achieved similar sensitivity and specificity {[}area under the curve (AUC): 0.722; 95% confidence interval (95% CI): 0.575-0.873 vs. AUC: 0.724; 95% CI: 0.575-0.873, z = 0.029, n.s.] in predicting survival and were superior to the Child-Pugh score (AUC: 0.677; 96% Cl: 0.518-0.837). Conclusion: The RI is not inferior in sensitivity and specificity to the MELD score. Cirrhotic patients with elevated RIs have impaired short- and long-term survival. The RI may help identify high-risk patients that require special therapeutic care. Copyright (C) 2012 S. Karger AG, Base

The frequency of endometriosis in the general and selected populations: A systematic review

Background: In this article, we have reviewed available data on the frequency of endometriosis considering separately the incidence and the prevalence of the disease using data from papers published from 2000 to June 2019. Study design: Systematic review and meta-analysis. PubMed and EMBASE were searched for observational studies reporting data on the incidence or prevalence rates or ratios for the following pre-speci\ufb01ed populations: general population, infertile women, women reporting pelvic pain, women who underwent pelvic surgical procedures unrelated with endometriosis. Results: A total of 42 papers were included in this review. Considering the 11 studies that have analysed the prevalence of endometriosis in the general population, the reported prevalence ranged from 0.8% to 28.6% with an overall estimated of 4.4% (95% CI 3.6\u20135.2). When we considered separately the estimates reported in each study according to geographic area, the pooled estimate was lower in the European studies (1.4%), increased to 5.7% in the US studies and was 15.4% in the Asian ones. The pooled estimated prevalence of endometriosis was 33.5% (95% CI 24.3\u201342.8, Figure 2(c)) in women who underwent surgery for benign gynaecological conditions, 23.8% (95% CI 16.1\u201331.5, Figure 2(d)) in infertile women, and 49.7 % (95% CI 14.4\u201385.0) in women with chronic pelvic pain. Conclusion: This review offers an overview of the available data on the frequency of endometriosis in the general population and in selected population, in particular among infertile women and women with chronic pelvic pain