The evolution of the cover time

The cover time of a graph is a celebrated example of a parameter that is easy to approximate using a randomized algorithm, but for which no constant factor deterministic polynomial time approximation is known. A breakthrough due to Kahn, Kim, Lovasz and Vu yielded a (log log n)^2 polynomial time approximation. We refine this upper bound, and show that the resulting bound is sharp and explicitly computable in random graphs. Cooper and Frieze showed that the cover time of the largest component of the Erdos-Renyi random graph G(n,c/n) in the supercritical regime with c>1 fixed, is asymptotic to f(c) n \log^2 n, where f(c) tends to 1 as c tends to 1. However, our new bound implies that the cover time for the critical Erdos-Renyi random graph G(n,1/n) has order n, and shows how the cover time evolves from the critical window to the supercritical phase. Our general estimate also yields the order of the cover time for a variety of other concrete graphs, including critical percolation clusters on the Hamming hypercube {0,1}^n, on high-girth expanders, and on tori Z_n^d for fixed large d. For the graphs we consider, our results show that the blanket time, introduced by Winkler and Zuckerman, is within a constant factor of the cover time. Finally, we prove that for any connected graph, adding an edge can increase the cover time by at most a factor of 4.Comment: 14 pages, to appear in CP

Flow cytometric methodology for the detection of de novo human T-cell leukemia virus -1 infection in vitro: a tool to study novel infection inhibitors

Methodology to detect and study de novo human T-cell leukemia virus (HTLV)-1 infection is required to further our knowledge of the viruses’ mechanisms of infection and to study potential therapeutic interventions. Whilst methodology currently exists, utilisation of an anti- Tax antibody to detect de novo Tax expression in permissive cells labelled with cell tracker allowing for the detection by flow cytometry of new infection after co-culture with donor cell lines productively infected with HTLV-1 is an alternative strategy. Using this methodology, we have been able to detect de novo infection of the T cell line HUT78 following co-culture with the productively infected HTLV-1 donor cell line MT-2 and to confirm that infection can be effectively blocked with well characterised infection inhibitors. This methodology will benefit experimental studies examining HTLV infection in vitro and may aid identification of therapeutic agents that block this process

Chaotic Evolution in Quantum Mechanics

A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure

Extrapolation of DEM simulations to large time scale. Application to the mixing of powder in a conical screw mixer

International audienceThe paper proposes an original algorithm which allows a long time scale extrapolation of DEM results at a very low computational cost. This algorithm can be adapted to any periodic processes. In this study, it is applied to the mixing process of powders within a conical screw mixer. The results are then compared with long time DEM simulations. It appears that this method is able to predict the DEM results with a very good accuracy

Quantum Branching Programs and Space-Bounded Nonuniform Quantum Complexity

In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the paper, simulations between quantum branching programs and nonuniform quantum Turing machines are presented which allow to transfer lower and upper bound results between the two models. In the second part of the paper, different variants of quantum OBDDs are compared with their deterministic and randomized counterparts. In the third part, quantum branching programs are considered where the performed unitary operation may depend on the result of a previous measurement. For this model a simulation of randomized OBDDs and exponential lower bounds are presented.Comment: 45 pages, 3 Postscript figures. Proofs rearranged, typos correcte

On Stellar Coronae and Solar Active Regions

Based on Yohkoh Soft X-Ray Telescope (SXT) observations of the Sun near peak activity level obtained on 1992 January 6, we search for coronal structures that have emission measure distributions EM(T ) that match the observed stellar coronal emission measure distributions derived for the intermediate-activity stars v Eri (K2 V) and m Boo A (G8 V) from Extreme Ultraviolet Explorer spectro- scopic observations. We —nd that the temperatures of the peaks of the observed stellar distributions EM(T ), as well as their slopes in the temperature range are very similar to those 6.0 ( log T ( 6.5, obtained for the brightest of the solar active regions in the 1992 January 6 SXT images. The observed slopes correspond approximately to EM P T b with b D 4, which is much steeper than predicted by static, uniformly heated loop models. Plasma densities in the coronae of v Eri and m Boo A are also observed to be essentially the same as the plasma densities typical of solar active regions. These data provide the best observational support yet obtained for the hypothesis that solar-like stars up to the activity levels of v Eri (K2 V) and m Boo A are dominated by active regions similar to, though possibly considerably larger than, those observed on the Sun. The surface —lling factor of bright active regions needed to explain the observed stellar emission measures is approximately unity. We speculate on the scenario in which small-scale ii nano—ares ˇˇ dominate the heating of active regions up to activity levels similar to those of v Eri (K2 V) and m Boo A. At higher activity levels still, the interactions of the active regions themselves may lead to increasing —aring on larger scales that is responsible for heating plasma to the observed coronal temperatures of on very active stars. Observations of X-ray and T Z 107 K EUV light curves using more sensitive instruments than are currently available, together with determi- nations of plasma densities over the full range of coronal temperatures (106¨107 K and higher), will be important to con—rm —are heating hypotheses and to elicit further details concerning coronal structures at solar-like active region temperatures and the temperatures that characterize the most (T ( 5 ) 106 K) active stars (T Z 107 K). Subject headings: stars: coronaestars: individual (v Eridani, m Bootis) ¨ Sun: corona ¨ Sun: X-rays, gamma raysX-rays: star

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure

The explosion mechanism of core-collapse supernovae: progress in supernova theory and experiments

The explosion of core-collapse supernova depends on a sequence of events taking place in less than a second in a region of a few hundred kilometers at the center of a supergiant star, after the stellar core approaches the Chandrasekhar mass and collapses into a proto-neutron star, and before a shock wave is launched across the stellar envelope. Theoretical efforts to understand stellar death focus on the mechanism which transforms the collapse into an explosion. Progress in understanding this mechanism is reviewed with particular attention to its asymmetric character. We highlight a series of successful studies connecting observations of supernova remnants and pulsars properties to the theory of core-collapse using numerical simulations. The encouraging results from first principles models in axisymmetric simulations is tempered by new puzzles in 3D. The diversity of explosion paths and the dependence on the pre-collapse stellar structure is stressed, as well as the need to gain a better understanding of hydrodynamical and MHD instabilities such as SASI and neutrino-driven convection. The shallow water analogy of shock dynamics is presented as a comparative system where buoyancy effects are absent. This dynamical system can be studied numerically and also experimentally with a water fountain. The potential of this complementary research tool for supernova theory is analyzed. We also review its potential for public outreach in science museums.Comment: 19 pages, 6 figures, invited review accepted for publication in PAS