On the black-box complexity of Sperner's Lemma

We present several results on the complexity of various forms of Sperner's Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an $O(\sqrt{n})$ deterministic query algorithm for the black-box version of the problem {\bf 2D-SPERNER}, a well studied member of Papadimitriou's complexity class PPAD. This upper bound matches the $\Omega(\sqrt{n})$ deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an $\Omega(\sqrt[4]{n})$ lower bound for its probabilistic, and an $\Omega(\sqrt[8]{n})$ lower bound for its quantum query complexity, showing that all these measures are polynomially related.Comment: 16 pages with 1 figur

Hydrodynamics and sediment transport. Fundamental aspects related to sustainable management of sandy coasts: aim and scope of the research project

The main scientific objectives of this research proposal can be summarised in the question why certain sandy coasts are dynamically stable and others are not. The following tools will be used to search for the answer:•Literature study•Building of a framework to model sediment transport in the near shore zone•Incorporation of the influence of complex spectra in the formulation of sediment transport influenced by currents and waves• Synergy of understanding of the physical processes (theoretical basis), numerical and physical modelling• Qualitative confrontation with available in situ measurementsSince we are convinced that the planned research activities are of international value, not only in terms of scientific merits but also from the point of view of sustainable coastal development, the following objectives form also part of this proposal:•Collaboration with other research teams in Europe who deal with this topic, for example by participating in experiments in the framework of TMR-LSF•Writing and submitting of a problem oriented and interdisciplinary research proposal to the E.U.•Dissimination of the results through conferences and by publication in international journal

High quality ultrafast transmission electron microscopy using resonant microwave cavities

Ultrashort, low-emittance electron pulses can be created at a high repetition rate by using a TM$_{110}$ deflection cavity to sweep a continuous beam across an aperture. These pulses can be used for time-resolved electron microscopy with atomic spatial and temporal resolution at relatively large average currents. In order to demonstrate this, a cavity has been inserted in a transmission electron microscope, and picosecond pulses have been created. No significant increase of either emittance or energy spread has been measured for these pulses. At a peak current of $814\pm2$ pA, the root-mean-square transverse normalized emittance of the electron pulses is $\varepsilon_{n,x}=(2.7\pm0.1)\cdot 10^{-12}$ m rad in the direction parallel to the streak of the cavity, and $\varepsilon_{n,y}=(2.5\pm0.1)\cdot 10^{-12}$ m rad in the perpendicular direction for pulses with a pulse length of 1.1-1.3 ps. Under the same conditions, the emittance of the continuous beam is $\varepsilon_{n,x}=\varepsilon_{n,y}=(2.5\pm0.1)\cdot 10^{-12}$ m rad. Furthermore, for both the pulsed and the continuous beam a full width at half maximum energy spread of $0.95\pm0.05$ eV has been measured

Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians

The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1 Q_1^2+\Omega_2 Q_2^2)/2 +C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4 +(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for only four sets of values of the constants. Only one of these, identical to the traveling wave reduction of the Manakov system, has been explicitly integrated (Wojciechowski, 1985), while the three others are not yet integrated in the generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building a birational transformation to two fourth order first degree equations in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painlev\'e property. This transformation involves the stationary reduction of various partial differential equations (PDEs). The result is the same as for the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases, a general solution which is meromorphic and hyperelliptic with genus two. As a consequence, no additional autonomous term can be added to either the cubic or the quartic Hamiltonians without destroying the Painlev\'e integrability (completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200

Integrated research on sand suppletion as a coastal defence system: application to the Flemish East Coast

An integrated technical research explores a complete synergy of physical scale modelling, numerical simulations and field records in order to validate the potential use of sand suppletion as a coastal defence for the Flemish East coast. Detailed analysis of the rich field data forms an optimum reflective mirror to put the respective design and calculation tools in both a comparative and evaluating framework. Combining all available instruments in an interactive modelling approach leads to an optimum design and a more economic application of beach nourishment techniques in this area

Combining situated Cognitive Engineering with a novel testing method in a case study comparing two infusion pump interfaces

We validated the usability of a new infusion pump interface designed with a situated Cognitive Engineering approach by comparing it to a reference interface using a novel testing method employing repeated measurements and process measures, in addition to traditional outcome measures. The sample consisted of 25 nurses who performed eight critical tasks three times. Performance measures consisted of number and type of errors, deviations from a pre-established normative path solution, task completion times, number of keystrokes, mental effort and preferences in use. Results showed that interaction with the new interface resulted in 18% fewer errors, 90% fewer normative path deviations, 42% lower task completion times, 40% fewer keystrokes, 39% lower mental effort and 76% more subjective preferences in use. These outcomes suggest that within the scope of this case study, combining the situated Cognitive Engineering approach with a novel testing method addresses various shortcomings of earlier testing methods

On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.Comment: 12 pages, 3 figures, NATO ARW, 15-19 september 2002, Elb