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We propose a new sixth-order finite volume scheme to solve the bidimensional linear steady-state Stokes problem on staggered unstructured meshes and complex geometries. The method is based on several classes of polynomial reconstructions to accurately evaluate the diffusive fluxes, the pressure gradient, and the velocity divergence. The main difficulty is to handle the div-grad duality to avoid numerical locking and oscillations. A new preconditioning technique based on the construction of a pseudo-inverse matrix is also proposed to dramatically reduce the computational effort. Several numerical simulations are carried out to highlight the performance of the new method. [ABSTRACT FROM AUTHOR]

We are interested in monotonicity and symmetry properties for nonnegative solutions of elliptic equations defined in geodesic balls of the hyperbolic space H n , which is the simplest example of manifold with negative curvature. More precisely, let B be a geodesic ball in H n and let u ∈ W 1 , p ( B ) ∩ L ∞ ( B ) be a sufficiently regular solution of Δ p u + f ( u ) = 0 in B with boundary condition u = 0 , where Δ p is the p -Laplace–Beltrami operator with p > 2 . Then we prove local or global symmetry results for nonnegative solutions according to the assumptions about the zeros of the nonlinearity f ( s ) , which is merely continuous. [ABSTRACT FROM AUTHOR]

• Conjugate heat transfer problems in arbitrary smooth curved domains. • Very high-order accurate finite volume scheme with polyhedral meshes. • Explicit matrix formulation replacing the standard residual operator formulation. • Error convergence analysis emphasising at least the sixth-order of convergence. • Substantial computational gains for the execution time and memory usage. The conjugate heat transfer problem is found in many engineering applications and comprises the heat transfer between solids and fluids in contact. The discretization method of these problems must guarantee that the interface conditions are properly satisfied, which is an additional difficulty when designing a numerical scheme with very high-order of convergence. The three-dimensional case with arbitrary curved domains is particularly challenging to treat, as the standard approaches to preserve the optimal convergence order become cumbersome with the use of curved meshes and non-linear transformations. Moreover, the implementation aspects of very high-order of convergence methods are critical for the three-dimensional case, as the computational cost of conventional algorithms often grows exponentially with the problem dimension. A very high-order accurate finite volume scheme with general polyhedral meshes is proposed in this work, which is able to solve three-dimensional conjugate heat transfer problems in arbitrary curved domains. The implementation of the proposed method is addressed and optimized calculations are derived to provide the same approximate solution at a significantly reduced computational cost. The provided set of numerical benchmarks, addressing several situations of the conjugate heat transfer problem, allows confirming that the optimal convergence order is effectively achieved. The results obtained also show that the proposed method overcomes the main shortcomings of the standard curved mesh approaches, while preserving the accuracy and the convergence order with the sole use of polyhedral meshes. A computational benchmark proves that substantial performance improvements are obtained from the proposed optimization, which represents a significant advance towards less demanding and more efficient numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we describe methods for using oxygen-15 water (H2O15) positron emission tomography (PET) to explore the functional neuroanatomy of cognition in awake, non-human primates. The discussion is based on a recent study designed to identify regions in the monkey brain associated with perceiving auditory stimuli, and species-specific calls, in particular [Gil-da-Costa et al., Proc. Natl. Acad. Sci. USA 101 (2004) 17516–17521]. Details are provided concerning critical aspects of the experimental paradigm, including pre-scanning habituation sessions to acclimate the animals to the PET scanner environment, and details of a pilot study to determine the auditory stimulus parameters necessary to produce robust activity in brain regions known to process auditory information (belt and parabelt regions of monkey auditory cortex). Methods for acquiring and analyzing PET data to identify significant regions of brain activity in single animals are also presented. [Copyright &y& Elsevier]

Metastatic spread in breast cancer patients is the major driver of cancer-related deaths. A unique subset of cells disseminated from pre-invasive or primary tumor lesions are recognized as the main seeds for metastatic outgrowth. Disseminated cancer cells (DCCs) can migrate to distant organs and settle in a dormant state for a prolonged period until they emerge to overt metastases. Understanding the biology of breast cancer cells dissemination, dormancy and reactivation to form overt metastases has become an important focus. In this review, we discuss the recent advancements of molecular pathways involving breast cancer cell dissemination, role of chemokine-chemokine receptor networks in DCCs migration, DCCs phenotypic heterogeneity and unique genes signatures in tumor dormancy, microenvironmental regulation and specific niches that favors DCCs homing and dormancy. In addition, we also discuss recent findings relating to the role of immune response on DCC dissemination and dormancy. With recent advances in the field of immunotherapy/targeted therapy and its beneficial effects in cancer treatment, this review will focus on their impact on DCCs, reversal of stemness, tumor dormancy and metastatic relapse. [ABSTRACT FROM AUTHOR]