Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art

Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero boundary condition at infinity, in any dimension. We focus on even potentials that are positive definite or positive tempered distributions.Comment: Communications in Partial Differential Equations (2010

Correlation functions and momentum distribution of one-dimensional Bose systems

The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.Comment: 4 pages, 5 figure

Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with respect to the truth of logical formulae rather than the signs of polynomials; and CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint. We here consider how best to formulate problems for input to this algorithm. We focus on a choice (not relevant for other CAD algorithms) about the order in which constraints are presented. We develop new heuristics to help make this choice and thus allow the best use of the algorithm in practice. We also consider other choices of problem formulation for CAD, as discussed in CICM 2013, revisiting these in the context of the new algorithm

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

It's not only about technology, it's about people: interpersonal skills as a part of the IT education.

Proceedings of: Second World Summit on the Knowledge Society (WSKS 2009), Chania, Crete, Greece, September 16-18, 2009.The importance of what have been termed the "soft skills" for the professional development of IT professionals is beyond any doubt. Taking account of this circumstance, the objective of the current research may be phrased as two separate questions. In the first place, determining the importance which IT related degree students place on these types of competencies for their professional future. In the second place, the importance which the development of the mentioned competencies has been given during their studies. The realization of an empirical study has fulfilled the two objectives described. The results demonstrate, on the one side, the moderate relevance which students assign to interpersonal competencies, especially emotional competencies, in contrast to the international curricular recommendations and studies concerning labor markets. On the other hand, the results indicate the scarce emphasis which lecturers have placed on the development of such competencies.Publicad

A workshop on ‘Dietary Sweetness—Is It an Issue?’

This report summarises a workshop convened by ILSI Europe on 3 and 4 April 2017 to discuss the issue of dietary sweetness. The objectives were to understand the roles of sweetness in the diet, establish whether exposure to sweetness affects diet quality and energy intake, and consider whether sweetness per se affects health. Although there may be evidence for tracking of intake of some sweet components of the diet through childhood, evidence for tracking of whole diet sweetness, or through other stages of maturity are lacking. The evidence to date does not support adverse effects of sweetness on diet quality or energy intake, except where sweet food choices increase intake of free sugars. There is some evidence for improvements in diet quality and reduced energy intake where sweetness without calories replaces sweetness with calories. There is a need to understand the physiological and metabolic relevance of sweet taste receptors on the tongue, in the gut and elsewhere in the body, as well as possible differentiation in the effects of sustained consumption of individual sweeteners. Despite a plethora of studies, there is no consistent evidence for an association of sweetness sensitivity/preference with obesity or type 2 diabetes. A multifaceted integrated approach, characterising nutritive and sensory aspects of the whole diet or dietary patterns, may be more valuable in providing contextual insight. The outcomes of the workshop could be used as a scientific basis to inform the expert community and create more useful dialogue among health care professionals