Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Empirical Tests Of Optimal Cognitive Distance

This article provides empirical tests of the hypothesis of ‘optimal cognitive distance’, proposed by Nooteboom (1999, 2000), in two distinct empirical settings. Variety of cognition, needed for learning, has two dimensions: the number of agents with different cognition, and differences in cognition between them (cognitive distance). The hypothesis is that in interfirm relationships optimal learning entails a trade-off between the advantage of increased cognitive distance for a higher novelty value of a partner’s knowledge, and the disadvantage of less mutual understanding. If the value of learning is the mathematical product of novelty value and understandability, it has an inverse-U shaped relation with cognitive distance, with an optimum level that yields maximal value of learning. With auxiliary hypotheses, the hypothesis is tested on interfirm agreements between pharmaceutical companies and biotech companies, as well as on interfirm agreements in ICT industries.innovation;organizational learning;ICT;biotechnology;alliances

RoboJam: A Musical Mixture Density Network for Collaborative Touchscreen Interaction

RoboJam is a machine-learning system for generating music that assists users of a touchscreen music app by performing responses to their short improvisations. This system uses a recurrent artificial neural network to generate sequences of touchscreen interactions and absolute timings, rather than high-level musical notes. To accomplish this, RoboJam's network uses a mixture density layer to predict appropriate touch interaction locations in space and time. In this paper, we describe the design and implementation of RoboJam's network and how it has been integrated into a touchscreen music app. A preliminary evaluation analyses the system in terms of training, musical generation and user interaction

Spacelike hypersurfaces in standard static spacetimes

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices, we prove that every complete CMC hypersurface having either bounded hyperbolic angle or bounded height is maximal. Our conclusions follow from general mean curvature estimates for spacelike hypersurfaces. In case where the spacetime is a Lorentzian product with spatial factor of nonnegative Ricci curvature and sectional curvatures bounded below, we also show that a complete maximal hypersurface not intersecting a spacelike slice is itself a slice. This result is obtained from a gradient estimate for parametric maximal hypersurfaces.Comment: 50 page