Springer correspondences for dihedral groups

Recent work by a number of people has shown that complex reflection groups give rise to many representation-theoretic structures (e.g., generic degrees and families of characters), as though they were Weyl groups of algebraic groups. Conjecturally, these structures are actually describing the representation theory of as-yet undescribed objects called ''spetses'', of which reductive algebraic groups ought to be a special case. In this paper, we carry out the Lusztig--Shoji algorithm for calculating Green functions for the dihedral groups. With a suitable set-up, the output of this algorithm turns out to satisfy all the integrality and positivity conditions that hold in the Weyl group case, so we may think of it as describing the geometry of the ''unipotent variety'' associated to a spets. From this, we determine the possible ''Springer correspondences'', and we show that, as is true for algebraic groups, each special piece is rationally smooth, as is the full unipotent variety.Comment: 21 page

Improving Workplace Expertise to Meet Increasing Customer Requirements: The Impact of Training

This article focuses upon the training of engineers at a factory producing integrated circuits. Inadequate use of statistical process techniques by the engineers meant that the production process was not being optimised in the context of increasing customer requirements. A training needs analysis was undertaken and a training programme was developed, implemented and evaluated. The results of this programme are presented and conclusions drawn

Greek Olive Oil: How Can Its International Market Potential Be Realized?

Trade issues affecting virgin olive oil originating in Greece are examined. A gravity model is estimated to determine the factors affecting trade in olive oil. The results provided by the gravity model yield information that is central to determining the strengths and weaknesses of the sector, as well as the opportunities and threats that exist. Finally, some proposals and suggestions are developed for increasing the international competitiveness of the Greek olive oil industry and endowing it with essential quality and safety assurances.competitiveness, gravity model, olive oil, quality, trade flows, Agricultural and Food Policy, International Development, International Relations/Trade,

Parameter estimation for macroscopic pedestrian dynamics models from microscopic data

In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -- microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in- and outflow conditions, for varying numbers of individual trajectories and for differing channel geometries

Enhancing retinal images by nonlinear registration

Being able to image the human retina in high resolution opens a new era in many important fields, such as pharmacological research for retinal diseases, researches in human cognition, nervous system, metabolism and blood stream, to name a few. In this paper, we propose to share the knowledge acquired in the fields of optics and imaging in solar astrophysics in order to improve the retinal imaging at very high spatial resolution in the perspective to perform a medical diagnosis. The main purpose would be to assist health care practitioners by enhancing retinal images and detect abnormal features. We apply a nonlinear registration method using local correlation tracking to increase the field of view and follow structure evolutions using correlation techniques borrowed from solar astronomy technique expertise. Another purpose is to define the tracer of movements after analyzing local correlations to follow the proper motions of an image from one moment to another, such as changes in optical flows that would be of high interest in a medical diagnosis.Comment: 21 pages, 7 figures, submitted to Optics Communication

Evolution of trade flows for sheep milk cheese: an empirical model for Greece

This research examines Feta cheese trade flows, having as raw material sheep milk. The findings of the implementation of the gravity model demonstrate the significance of trade flows for Greek Feta worldwide. It will be a very useful instrument for examining the trading potential of Feta cheese, on the condition that there will be a positive outcome on the judicial and political level for the product in the WTO negotiations. The findings of the gravity model will be very helpful for an analysis which follows, in order to show off the strengths and weaknesses of the sector, as well as the opportunities and threats the market creates. Finally, there is a list of proposals suggestions which focus on increasing the competitiveness of the sector and on armouring it with all the essential quality and safety reassurances. This is done in order to avoid, in the future, attempts from competitors to jeopardize once more all this effort that has been done up till now. These proposals form an action plan which provides viable solutions to the quality and safety issue, as well as an aggressive marketing plan for gaining market shares in both EU and non-EU countries, utilizing the competitive advantage the product gains, as PDO.Trade flows, quality, competitiveness, International Relations/Trade, Livestock Production/Industries,