Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Time representation in reinforcement learning models of the basal ganglia

Reinforcement learning (RL) models have been influential in understanding many aspects of basal ganglia function, from reward prediction to action selection. Time plays an important role in these models, but there is still no theoretical consensus about what kind of time representation is used by the basal ganglia. We review several theoretical accounts and their supporting evidence. We then discuss the relationship between RL models and the timing mechanisms that have been attributed to the basal ganglia. We hypothesize that a single computational system may underlie both RL and interval timing—the perception of duration in the range of seconds to hours. This hypothesis, which extends earlier models by incorporating a time-sensitive action selection mechanism, may have important implications for understanding disorders like Parkinson's disease in which both decision making and timing are impaired

Strong solutions of the thin film equation in spherical geometry

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile

Potential impact of midwives in preventing and reducing maternal and neonatal mortality and stillbirths: a Lives Saved Tool modelling study.

Background Strengthening the capacity of midwives to deliver high-quality maternal and newborn health services has been highlighted as a priority by global health organisations. To support low-income and middle-income countries (LMICs) in their decisions about investments in health, we aimed to estimate the potential impact of midwives on reducing maternal and neonatal deaths and stillbirths under several intervention coverage scenarios. Methods For this modelling study, we used the Lives Saved Tool to estimate the number of deaths that would be averted by 2035, if coverage of health interventions that can be delivered by professional midwives were scaled up in 88 countries that account for the vast majority of the world's maternal and neonatal deaths and stillbirths. We used four scenarios to assess the effects of increasing the coverage of midwife-delivered interventions by a modest amount (10% every 5 years), a substantial amount (25% every 5 years), and the amount needed to reach universal coverage of these interventions (ie, to 95%); and the effects of coverage attrition (a 2% decrease every 5 years). We grouped countries in three equal-sized groups according to their Human Development Index. Group A included the 30 countries with the lowest HDI, group B included 29 low-to-medium HDI countries, and group C included 29 medium-to-high HDI countries. Findings We estimated that, relative to current coverage, a substantial increase in coverage of midwife-delivered interventions could avert 41% of maternal deaths, 39% of neonatal deaths, and 26% of stillbirths, equating to 2·2 million deaths averted per year by 2035. Even a modest increase in coverage of midwife-delivered interventions could avert 22% of maternal deaths, 23% of neonatal deaths, and 14% of stillbirths, equating to 1·3 million deaths averted per year by 2035. Relative to current coverage, universal coverage of midwife-delivered interventions would avert 67% of maternal deaths, 64% of neonatal deaths, and 65% of stillbirths, allowing 4·3 million lives to be saved annually by 2035. These deaths averted would be particularly concentrated in the group B countries, which currently account for a large proportion of the world's population and have high mortality rates compared with group C. Interpretation Midwives can help to substantially reduce maternal and neonatal mortality and stillbirths in LMICs. However, to realise this potential, midwives need to have skills and competencies in line with recommendations from the International Confederation of Midwives, to be part of a team of sufficient size and skill, and to work in an enabling environment. Our study highlights the potential of midwives but there are many challenges to the achievement of this potential. If increased coverage of midwife-delivered interventions can be achieved, health systems will be better able to provide effective coverage of essential sexual, reproductive, maternal, newborn, and adolescent health interventions

Existence of weak solutions for the generalized Navier-Stokes equations with damping

In this work we consider the generalized Navier-Stokes equations with the presence of a damping term in the momentum equation. The problem studied here derives from the set of equations which govern isothermal flows of incompressible and homogeneous non-Newtonian fluids. For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any and any sigma > 1, where q is the exponent of the diffusion term and sigma is the exponent which characterizes the damping term.MCTES, Portugal [SFRH/BSAB/1058/2010]; FCT, Portugal [PTDC/MAT/110613/2010]info:eu-repo/semantics/publishedVersio

SOLVABILITY OF HIGHER-ORDER BVPS IN THE HALF-LINE WITH UNBOUNDED NONLINEARITIES

This work presents suficient conditions for the existence of unbounded solutions of a Sturm-Liouville type boundary value problem on the half-line. One-sided Nagumo condition plays a special role because it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on fixed point theory and lower and upper solutions method. An example is given to show the applicability of our results