Fast global null controllability for a viscous Burgers' equation despite the presence of a boundary layer

In this work, we are interested in the small time global null controllability for the viscous Burgers' equation y_t - y_xx + y y_x = u(t) on the line segment [0,1]. The second-hand side is a scalar control playing a role similar to that of a pressure. We set y(t,1) = 0 and restrict ourselves to using only two controls (namely the interior one u(t) and the boundary one y(t,0)). In this setting, we show that small time global null controllability still holds by taking advantage of both hyperbolic and parabolic behaviors of our system. We use the Cole-Hopf transform and Fourier series to derive precise estimates for the creation and the dissipation of a boundary layer

Throughput-Optimal Random Access with Order-Optimal Delay

In this paper, we consider CSMA policies for scheduling of multihop wireless networks with one-hop traffic. The main contribution of this paper is to propose Unlocking CSMA (U-CSMA) policy that enables to obtain high throughput with low (average) packet delay for large wireless networks. In particular, the delay under U-CSMA policy becomes order-optimal. For one-hop traffic, delay is defined to be order-optimal if it is O(1), i.e., it stays bounded, as the network-size increases to infinity. Using mean field theory techniques, we analytically show that for torus (grid-like) interference topologies with one-hop traffic, to achieve a network load of $\rho$, the delay under U-CSMA policy becomes $O(1/(1-\rho)^{3})$ as the network-size increases, and hence, delay becomes order optimal. We conduct simulations for general random geometric interference topologies under U-CSMA policy combined with congestion control to maximize a network-wide utility. These simulations confirm that order optimality holds, and that we can use U-CSMA policy jointly with congestion control to operate close to the optimal utility with a low packet delay in arbitrarily large random geometric topologies. To the best of our knowledge, it is for the first time that a simple distributed scheduling policy is proposed that in addition to throughput/utility-optimality exhibits delay order-optimality.Comment: 44 page

Is There a Metaphysics of Consciousness Without a Phenomenology of Consciousness? Some Thoughts Derived from Husserl's Philosophical Phenomenology

The paper first addresses Husserl's conception of philosophical phenomenology, metaphysics, and the relation between them, in order to explain why, on Husserl's view, there is no metaphysics of consciousness without a phenomenology of consciousness. In doing so, it recalls some of the methodological tenets of Husserl's phenomenology, pointing out that phenomenology is an eidetic or a priori science which has first of all to do with mere ideal possibilities of consciousness and its correlates; metaphysics of consciousness, on the other hand, has to do with its reality or actuality, requiring an eidetic foundation in order to become scientifically valuable. Presuming that, if consciousness is to be the subject-matter of a metaphysics which is not simply speculative or based on prejudice, it is crucial to get the phenomenology of consciousness right, the paper then engages in a detailed descriptive-eidetic analysis of mental acts of re-presenting something and tries to argue that their structures, involving components of non-actual experiencing, pose a serious problem for a materialistic or physicalistic metaphysics of consciousness. The paper ends with a brief comment on Husserl's broader view of metaphysics, having to do with the irrationality of the transcendental fact, i.e. the constitution of the factual world and the factual life of the min