Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.Comment: to appear in Quarterly of Applied Mathematic

A path integral leading to higher-order Lagrangians

We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.Comment: 6 page

A Survey on the Application of Evolutionary Algorithms for Mobile Multihop Ad Hoc Network Optimization Problems

Evolutionary algorithms are metaheuristic algorithms that provide quasioptimal solutions in a reasonable time. They have been applied to many optimization problems in a high number of scientific areas. In this survey paper, we focus on the application of evolutionary algorithms to solve optimization problems related to a type of complex network likemobilemultihop ad hoc networks. Since its origin, mobile multihop ad hoc network has evolved causing new types of multihop networks to appear such as vehicular ad hoc networks and delay tolerant networks, leading to the solution of new issues and optimization problems. In this survey, we review the main work presented for each type of mobile multihop ad hoc network and we also present some innovative ideas and open challenges to guide further research in this topic

Normalization Techniques for Statistical Inference from Magnetic Resonance Imaging

While computed tomography and other imaging techniques are measured in absolute units with physical meaning, magnetic resonance images are expressed in arbitrary units that are difficult to interpret and differ between study visits and subjects. Much work in the image processing literature on intensity normalization has focused on histogram matching and other histogram mapping techniques, with little emphasis on normalizing images to have biologically interpretable units. Furthermore, there are no formalized principles or goals for the crucial comparability of image intensities within and across subjects. To address this, we propose a set of criteria necessary for the normalization of images. We further propose simple and robust biologically motivated normalization techniques for multisequence brain imaging that have the same interpretation across acquisitions and satisfy the proposed criteria. We compare the performance of different normalization methods in thousands of images of patients with Alzheimer\u27s Disease, hundreds of patients with multiple sclerosis, and hundreds of healthy subjects obtained in several different studies at dozens of imaging centers

Canonical Quantization of Noncommutative Field Theory

A simple method to canonically quantize noncommutative field theories is proposed. As a result, the elementary excitations of a (2n+1)-dimensional scalar field theory are shown to be bilocal objects living in an (n+1)-dimensional space-time. Feynman rules for their scattering are derived canonically. They agree, upon suitable redefinitions, with the rules obtained via star-product methods. The IR/UV connection is interpreted within this framework.Comment: 8 pages, 1 figur

Disruption of thalamic functional connectivity is a neural correlate of dexmedetomidine-induced unconsciousness

Understanding the neural basis of consciousness is fundamental to neuroscience research. Disruptions in cortico-cortical connectivity have been suggested as a primary mechanism of unconsciousness. By using a novel combination of positron emission tomography and functional magnetic resonance imaging, we studied anesthesia-induced unconsciousness and recovery using the α2-agonist dexmedetomidine. During unconsciousness, cerebral metabolic rate of glucose and cerebral blood flow were preferentially decreased in the thalamus, the Default Mode Network (DMN), and the bilateral Frontoparietal Networks (FPNs). Cortico-cortical functional connectivity within the DMN and FPNs was preserved. However, DMN thalamo-cortical functional connectivity was disrupted. Recovery from this state was associated with sustained reduction in cerebral blood flow and restored DMN thalamo-cortical functional connectivity. We report that loss of thalamo-cortical functional connectivity is sufficient to produce unconsciousness. DOI: http://dx.doi.org/10.7554/eLife.04499.00

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

Coleman-Gurtin type equations with dynamic boundary conditions

We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory which includes the usual heat equation subject to a dynamic boundary condition as a special case. We investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of [11]. Additionally, we do not assume that the interior and the boundary share the same memory kernel.Comment: 27 pages; to appear in Physica D: Nonlinear Phenomen