Optimal clustering of a pair of irregular objects

Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects

Analytical Solution for the Deformation of a Cylinder under Tidal Gravitational Forces

Quite a few future high precision space missions for testing Special and General Relativity will use optical resonators which are used for laser frequency stabilization. These devices are used for carrying out tests of the isotropy of light (Michelson-Morley experiment) and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary. Therefore in this article we investigate the modeling of optical resonators in a space environment. Usually for simulation issues the Finite Element Method (FEM) is applied in order to investigate the influence of disturbances on the resonator measurements. However, for a careful control of the numerical quality of FEM simulations a comparison with an analytical solution of a simplified resonator model is beneficial. In this article we present an analytical solution for the problem of an elastic, isotropic, homogeneous free-flying cylinder in space under the influence of a tidal gravitational force. The solution is gained by solving the linear equations of elasticity for special boundary conditions. The applicability of using FEM codes for these simulations shall be verified through the comparison of the analytical solution with the results gained within the FEM code.Comment: 23 pages, 3 figure

Emergent Concepts on Knowledge Intensive Processes

An approach to refine and revise the general framework of KiP (Knowledge Intensive Process) is presented. The specific case of collaborative KiP is studied and the prominent role of collaborative KiPs in the general context of Business Processes is revealed. The approach is based on Formal Concept Analysis.Junta de Andalucía TIC-606

A bayesian meta-analysis of multiple treatment comparisons of systemic regimens for advanced pancreatic cancer

© 2014 Chan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Background: For advanced pancreatic cancer, many regimens have been compared with gemcitabine (G) as the standard arm in randomized controlled trials. Few regimens have been directly compared with each other in randomized controlled trials and the relative efficacy and safety among them remains unclear

BKM Lie superalgebras from counting twisted CHL dyons

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun. Math. Phy

The Mid-Infrared Instrument for the James Webb Space Telescope, III: MIRIM, The MIRI Imager

In this article, we describe the MIRI Imager module (MIRIM), which provides broad-band imaging in the 5 - 27 microns wavelength range for the James Webb Space Telescope. The imager has a 0"11 pixel scale and a total unobstructed view of 74"x113". The remainder of its nominal 113"x113" field is occupied by the coronagraphs and the low resolution spectrometer. We present the instrument optical and mechanical design. We show that the test data, as measured during the test campaigns undertaken at CEA-Saclay, at the Rutherford Appleton Laboratory, and at the NASA Goddard Space Flight Center, indicate that the instrument complies with its design requirements and goals. We also discuss the operational requirements (multiple dithers and exposures) needed for optimal scientific utilization of the MIRIM.Comment: 29 pages, 9 figure

Evaluating predictive pharmacogenetic signatures of adverse events in colorectal cancer patients treated with fluoropyrimidines

The potential clinical utility of genetic markers associated with response to fluoropyrimidine treatment in colorectal cancer patients remains controversial despite extensive study. Our aim was to test the clinical validity of both novel and previously identified markers of adverse events in a broad clinical setting. We have conducted an observational pharmacogenetic study of early adverse events in a cohort study of 254 colorectal cancer patients treated with 5-fluorouracil or capecitabine. Sixteen variants of nine key folate (pharmacodynamic) and drug metabolising (pharmacokinetic) enzymes have been analysed as individual markers and/or signatures of markers. We found a significant association between TYMP S471L (rs11479) and early dose modifications and/or severe adverse events (adjusted OR = 2.02 [1.03; 4.00], p = 0.042, adjusted OR = 2.70 [1.23; 5.92], p = 0.01 respectively). There was also a significant association between these phenotypes and a signature of DPYD mutations (Adjusted OR = 3.96 [1.17; 13.33], p = 0.03, adjusted OR = 6.76 [1.99; 22.96], p = 0.002 respectively). We did not identify any significant associations between the individual candidate pharmacodynamic markers and toxicity. If a predictive test for early adverse events analysed the TYMP and DPYD variants as a signature, the sensitivity would be 45.5 %, with a positive predictive value of just 33.9 % and thus poor clinical validity. Most studies to date have been under-powered to consider multiple pharmacokinetic and pharmacodynamic variants simultaneously but this and similar individualised data sets could be pooled in meta-analyses to resolve uncertainties about the potential clinical utility of these markers