The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Tactile-STAR: A Novel Tactile STimulator And Recorder System for Evaluating and Improving Tactile Perception

Many neurological diseases impair the motor and somatosensory systems. While several different technologies are used in clinical practice to assess and improve motor functions, somatosensation is evaluated subjectively with qualitative clinical scales. Treatment of somatosensory deficits has received limited attention. To bridge the gap between the assessment and training of motor vs. somatosensory abilities, we designed, developed, and tested a novel, low-cost, two-component (bimanual) mechatronic system targeting tactile somatosensation: the Tactile-STAR—a tactile stimulator and recorder. The stimulator is an actuated pantograph structure driven by two servomotors, with an end-effector covered by a rubber material that can apply two different types of skin stimulation: brush and stretch. The stimulator has a modular design, and can be used to test the tactile perception in different parts of the body such as the hand, arm, leg, big toe, etc. The recorder is a passive pantograph that can measure hand motion using two potentiometers. The recorder can serve multiple purposes: participants can move its handle to match the direction and amplitude of the tactile stimulator, or they can use it as a master manipulator to control the tactile stimulator as a slave. Our ultimate goal is to assess and affect tactile acuity and somatosensory deficits. To demonstrate the feasibility of our novel system, we tested the Tactile-STAR with 16 healthy individuals and with three stroke survivors using the skin-brush stimulation. We verified that the system enables the mapping of tactile perception on the hand in both populations. We also tested the extent to which 30 min of training in healthy individuals led to an improvement of tactile perception. The results provide a first demonstration of the ability of this new system to characterize tactile perception in healthy individuals, as well as a quantification of the magnitude and pattern of tactile impairment in a small cohort of stroke survivors. The finding that short-term training with Tactile-STARcan improve the acuity of tactile perception in healthy individuals suggests that Tactile-STAR may have utility as a therapeutic intervention for somatosensory deficits

Shape Recognition: A Landmark-Based Approach

Shape recognition has applications in computer vision tasks such as industrial automated inspection and automatic target recognition. When objects are occluded, many recognition methods that use global information will fail. To recognize partially occluded objects, we represent each object by a Set of landmarks. The landmarks of an object are points of interest which have important shape attributes and are usually obtained from the object boundary. In this study, we use high curvature points along an object boundary as the landmarks of the object. Given a scene consisting of partially occluded objects, the hypothesis of a model object in the scene is verified by matching the landmarks of an object with those in the scene. A measure of similarity between two landmarks, one from a model and the other from a scene, is needed to perform this matching. One such local shape measure is the sphericity of a triangular transformation mapping the model landmark and its two neighboring landmarks to the scene landmark and its two neighboring landmarks. Sphericity is in general defined for a diffeomorphism. Its invariant properties under a group of transformation, namely, translation, rotation, and scaling are derived. The sphericity of a triangular transformation is shown to be a robust local shape measure in the sense that minor distortion in the landmarks does not significantly alter its value. To match landmarks between a model and a scene, a table of compatibility, where each entry of the table is the sphericity value derived from the mapping of a model landmark to a scene landmark, is constructed. A hopping dynamic programming procedure which switches between a forward and a backward dynamic programming procedure is applied to guide the landmark matching through the compatibility table. The location of the model in the scene is estimated with a least squares fit among the matched landmarks. A heuristic measure is then computed to decide if the model is in the scene