Optimal two-level conjoint designs for large numbers of attributes.

In this paper, we propose a simple strategy to construct D-, A-, G- and V-optimal two-level multi-attribute designs for rating-based conjoint studies. Our approach combines orthogonal designs and balanced or partially balanced incomplete block designs. In order not to overload respondents with complicated tasks, the designs hold one or more attributes at a constant level. The designs are variance-balanced meaning that they yield an equal amount of information on each of the part-worths. Some examples are provided to illustrate the method.Balanced and partially balanced incomplete block designs; D-,A-,G- and V-optimality; Orthogonal designs; Two-level conjoint designs; Strategy; Design; Studies; Order; Yield; Information;

Improved methods for the travelling salesperson problem with hotel selection

In this talk, a new formulation and a new metaheuristic solution procedure for the travelling salesperson problem with hotel selection (TSPHS) is presented. The metaheuristic is a multi-start procedure that outperforms existing heuristics on all benchmark instances. We also provide a number of new optimal solutions found by a commercial solver extended with a dedicated cutting plane procedure, as well as new best known solutions for most benchmark instances

A fundamental measure theory for the sticky hard sphere fluid

We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of weighted densities and an exact result from scaled particle theory (SPT). It is demonstrated that the excess free energy density of the inhomogeneous SHS fluid $\Phi_{\text{SHS}}$ is uniquely defined when (a) it is solely a function of the weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A {\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c) it yields any given direct correlation function (DCF) from the class of generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J. Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very good agreement with simulation data. In particular, this FMT yields the correct contact value of the density profiles with no adjustable parameters. Rather than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT produces them. Interestingly, although equivalent to Kierlik and Rosinberg's FMT in the case of hard spheres, the set of weighted densities used for Rosenfeld's original FMT is insufficient for constructing a DFT which yields the SHS DCF.Comment: 11 pages, 3 figure

DD-optimal saturated designs: a simulation study

In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric structure of the design and we compare them with the classical $D$-efficiency criterion. We perform a simulation study. In all the test cases we observe that designs with high values of $D$-efficiency have also high values of the new objective functions.Comment: 8 pages. Preliminary version submitted to the 7th IWS Proceeding

Role of beam propagation in Goos-H\"{a}nchen and Imbert-Fedorov shifts

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence, for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-H\"{a}nchen and Imbert-Fedorov shifts when the incident beam is focussed.Comment: 3 pages, 1 figure, submitted to Opt. Let

Scarred Resonances and Steady Probability Distribution in a Chaotic Microcavity

We investigate scarred resonances of a stadium-shaped chaotic microcavity. It is shown that two components with different chirality of the scarring pattern are slightly rotated in opposite ways from the underlying unstable periodic orbit, when the incident angles of the scarring pattern are close to the critical angle for total internal reflection. In addition, the correspondence of emission pattern with the scarring pattern disappears when the incident angles are much larger than the critical angle. The steady probability distribution gives a consistent explanation about these interesting phenomena and makes it possible to expect the emission pattern in the latter case.Comment: 4 pages, 5 figure

A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology

This paper reports on a study that investigated the pedagogical practices and beliefs of pre-service and beginning teachers in integrating technology into the teaching of secondary school mathematics. A case study documents how one teachers modes of working with technology changed over time and across different school contexts, and identifies relationships between a range of personal and contextual factors that influenced the development of his identity as a teacher. This analysis views teachers learning as increasing participation in sociocultural practices, and uses Valsiners concepts of the Zone of Proximal Development, Zone of Free Movement, and Zone of Promoted Action to offer a dynamic way of theorising teacher learning as identity formation

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field

Using fundamental measure density functional theory we investigate paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thicknesses. An external magnetic field induces uniaxial alignment and acts on the platelets with a strength that is taken to scale with the platelet area. At particle diameter ratio lambda=1.5 the system displays paranematic-nematic coexistence. For lambda=2, demixing into two nematic states with different compositions also occurs, between an upper critical point and a paranematic-nematic-nematic triple point. Increasing the field strength leads to shrinking of the coexistence regions. At high enough field strength a closed loop of immiscibility is induced and phase coexistence vanishes at a double critical point above which the system is homogeneously nematic. For lambda=2.5, besides paranematic-nematic coexistence, there is nematic-nematic coexistence which persists and hence does not end in a critical point. The partial orientational order parameters along the binodals vary strongly with composition and connect smoothly for each species when closed loops of immiscibility are present in the corresponding phase diagram.Comment: 9 pages, to appear in J.Phys:Condensed Matte