Continuity - based and discontinuity - based segmentation in transparent and spatially segregated global motion

The mechanisms underlying the parsing of a spatial distribution of velocity vectors into two adjacent (spatially segregated) or overlapping (transparent) motion surfaces were examined using random dot kinematograms. Parsing might occur using either of two principles. Surfaces might be defined on the basis of similarity of motion vectors and then sharp perceptual boundaries drawn between different surfaces (continuity-based segmentation). Alternatively, detection of a high gradient of direction or speed separating the motion surfaces might drive the process (discontinuity-based segmentation). To establish which method is used, we examined the effect of blurring the motion direction gradient. In the case of a sharp direction gradient, each dot had one of two directions differing by 135°. With a shallow gradient, most dots had one of two directions but the directions of the remainder spanned the range between one motion-defined surface and the other. In the spatial segregation case the gradient defined a central boundary separating two regions. In the transparent version the dots were randomly positioned. In both cases all dots moved with the same speed and existed for only two frames before being randomly replaced. The ability of observers to parse the motion distribution was measured in terms of their ability to discriminate the direction of one of the two surfaces. Performance was hardly affected by spreading the gradient over at least 25% of the dots (corresponding to a 1° strip in the segregation case). We conclude that detection of sharp velocity gradients is not necessary for distinguishing different motion surfaces.

On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

Gateaux complex differentiability and continuity

As is known, there are everywhere discontinuous infinitely Frechet differentiable functions on the real locally convex spaces D(R) and V(R) of finitely supported infinitely differentiable functions and, respectively, of generalized functions. In this paper the relationship between the complex differentiability and continuity of a function on a complex locally convex space is considered. We describe a class of complex locally convex spaces, which includes the complex space V(R), such that every Gateaux complex-differentiable function on a space of this class is continuous. We also describe another class of locally convex spaces, which includes the complex space D(R), such that on every space of this class there is an everywhere discontinuous infinitely Frechet complex-differentiable function whose derivatives are continuous.

On the continuity of the support of masa-bimodules

We anounce results on the continuity of the map sending a masa-bimodule to its support. The proofs of the results will be published elsewhere.

Continuity and Change in the European Union’s Approach to Enlargement::Turkey and Central and Eastern Europe compared

Existing studies of European Union (EU) enlargement provide few answers to questions concerning continuity and change in the dynamics of the process. This article identifies a number of conditioning factors that have shaped the EU’s approach to eastern enlargement and traces elements of continuity and change in the EU’s handling of Turkey’s membership aspirations. The article focuses on three established factors – member state preferences, supranational activism and EU capacity – and two less prominent factors – public opinion and narrative frame

History of Child Welfare and Protection Social Work in Northern Ireland: Finding Continuity amongst Discontinuity in Case Files from 1950-1968

This article reports on research carried out on 200 child welfare files from the largest welfare authority in Northern Ireland from 1950-1968. The literature review provides a commentary on some of the major debates surrounding child welfare and protection social work from the perspective of its historical development. The report of the research which follows offers an insight into one core, and less well-known period of child welfare history in Northern Ireland between the two Children and Young Persons Acts (1950 & 1968). Using a method of discourse analysis influenced by Michel Foucault, a detailed description of the nature of practice is offered. This paper is offered as a work in progress, with further work being planned for dissemination of more detailed analysis of the method and outcomes. The research seeks to ask a few core questions based on problems identified in the present with our current understandings of child welfare and protection histories. While recognising the limitations of this study and the need for broader analysis of the wider context surrounding child welfare practice at the moment, it is argued that some salient conclusions can be drawn about continuity and discontinuity in practice which are of interest to practitioners and students of child welfare social work.