90 research outputs found

    Mathematical analysis of a model of river channel formation.

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    The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin

    Actin Nemaline Myopathy Mouse Reproduces Disease, Suggests Other Actin Disease Phenotypes and Provides Cautionary Note on Muscle Transgene Expression

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    Mutations in the skeletal muscle α-actin gene (ACTA1) cause congenital myopathies including nemaline myopathy, actin aggregate myopathy and rod-core disease. The majority of patients with ACTA1 mutations have severe hypotonia and do not survive beyond the age of one. A transgenic mouse model was generated expressing an autosomal dominant mutant (D286G) of ACTA1 (identified in a severe nemaline myopathy patient) fused with EGFP. Nemaline bodies were observed in multiple skeletal muscles, with serial sections showing these correlated to aggregates of the mutant skeletal muscle α-actin-EGFP. Isolated extensor digitorum longus and soleus muscles were significantly weaker than wild-type (WT) muscle at 4 weeks of age, coinciding with the peak in structural lesions. These 4 week-old mice were ∼30% less active on voluntary running wheels than WT mice. The α-actin-EGFP protein clearly demonstrated that the transgene was expressed equally in all myosin heavy chain (MHC) fibre types during the early postnatal period, but subsequently became largely confined to MHCIIB fibres. Ringbinden fibres, internal nuclei and myofibrillar myopathy pathologies, not typical features in nemaline myopathy or patients with ACTA1 mutations, were frequently observed. Ringbinden were found in fast fibre predominant muscles of adult mice and were exclusively MHCIIB-positive fibres. Thus, this mouse model presents a reliable model for the investigation of the pathobiology of nemaline body formation and muscle weakness and for evaluation of potential therapeutic interventions. The occurrence of core-like regions, internal nuclei and ringbinden will allow analysis of the mechanisms underlying these lesions. The occurrence of ringbinden and features of myofibrillar myopathy in this mouse model of ACTA1 disease suggests that patients with these pathologies and no genetic explanation should be screened for ACTA1 mutations

    Online learning algorithm for zero-sum games with integral reinforcement learning

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    In this paper we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous-time zero sum game solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data based approach to the solution of the Hamilton-Jacobi-Isaacs equation and it does not require explicit knowledge on the system’s drift dynamics. A novel adaptive control algorithm is given that is based on policy iteration and implemented using an actor/ disturbance/critic structure having three adaptive approximator structures. All three approximation networks are adapted simultaneously. A persistence of excitation condition is required to guarantee convergence of the critic to the actual optimal value function. Novel adaptive control tuning algorithms are given for critic, disturbance and actor networks. The convergence to the Nash solution of the game is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result
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