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1.
In complex biological systems, entities that are conceptually distinct but empirically related—such as sunlight and plant growth or antigene and immune response—are being explicitly linked through the identification of highly specific uninterrupted interaction sequences that take place between their macromolecular system components. These uninterrupted sequences of causation include common elements that are shared by the empirically related but conceptually distinct entities. Through the identification of specific shared elements, “conceptual continuity” is established between these entities. Examples are introduced to suggest that in sociopolitical systems, an analogous conceptual continuity can be established between distinct sociopolitical entities. The identification of specific shared elements, essential for the well being of each of the entities, can play a significant role in resolving conflicts between those separated by seemingly insurmountable obstacles such as race or religion or ideology. © 2006 Wiley Periodicals, Inc. Complexity 11:20–24, 2006  相似文献   
2.
As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk  相似文献   
3.
Summary We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces.  相似文献   
4.
For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.  相似文献   
5.
We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.  相似文献   
6.
GIRSANOV’STHEOREMONABSTRACTWIENERSPACESZHANGYINNANAbstractLet(E,H,μ)beanabstractWienerspaceinthesenseofL.Gros.Itisprovedth...  相似文献   
7.
Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x k ): (ϕk(|x k |)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψk), we characterize the continuity of the superposition operators P f from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type. This research was supported by Estonian Science Foundation Grant 5376.  相似文献   
8.
We consider a large class of partially hyperbolic systems containing, among others, affine maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms. If the rate of mixing is sufficiently high, the system satisfies many classical limit theorems of probability theory.

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9.
Let Um be an m×m Haar unitary matrix and U[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U[m,n] as m/nλ and n→∞. The rate function and the limit distribution are given explicitly. U[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.  相似文献   
10.
A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.  相似文献   
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