Neutrix Calculus and Finite Quantum Field Theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a Letter to the Edito

Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers

This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more accessible to physicists than the specialized mathematical literature. There are also some new results: On the practical side we give important empirical properties of large quasi-random point sets, especially the exact quadratic discrepancies; on the theoretical side, there is the exact distribution of quadratic discrepancy for random point sets.Comment: 51 pages. Full paper, including all figures also available at: ftp://ftp.nikhef.nl/pub/preprints/96-017.ps.gz Accepted for publication in Comp.Phys.Comm. Fixed some typos, corrected formula 108,figure 11 and table

The paradox of soft singularity crossing and its resolution by distributional cosmological quantitities

A cosmological model of a flat Friedmann universe filled with a mixture of anti-Chaplygin gas and dust-like matter exhibits a future soft singularity, where the pressure of the anti-Chaplygin gas diverges (while its energy density is finite). Despite infinite tidal forces the geodesics pass through the singularity. Due to the dust component, the Hubble parameter has a non-zero value at the encounter with the singularity, therefore the dust implies further expansion. With continued expansion however, the energy density and the pressure of the anti-Chaplygin gas would become ill-defined, hence from the point of view of the anti-Chaplygin gas only a contraction is allowed. Paradoxically, the universe in this cosmological model would have to expand and contract simultaneously. This obviosly could not happen. We solve the paradox by redefining the anti-Chaplygin gas in a distributional sense. Then a contraction could follow the expansion phase at the singularity at the price of a jump in the Hubble parameter. Although such an abrupt change is not common in any cosmological evolution, we explicitly show that the set of Friedmann, Raychaudhuri and continuity equations are all obeyed both at the singularity and in its vicinity. We also prove that the Israel junction conditions are obeyed through the singular spatial hypersurface. In particular we enounce and prove a more general form of the Lanczos equation.Comment: 12 pages; to be published in Phys.Rev.

Continuum Surface Energy from a Lattice Model

We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with general binary interactions in two dimensions. A new bond counting approach is used, which reduces the problem to the lattice point problem of number theory. The main contribution is an explicit formula for the surface energy density as a function of the deformation gradient and boundary normal. The result is valid for a large class of domains, including faceted (polygonal) shapes and regions with piecewise smooth boundaries.Comment: V. 1: 10 pages, no fig's. V 2: 23 pages, no figures. Misprints corrected. Section 3 added, (new results). Intro expanded, refs added.V 3: 26 pages. Abstract changed. Section 2 split into 2. Section (4) added material. V 4, 28 pages, Intro rewritten. Changes in Sec.5 (presentation only). Refs added.V 5,intro changed V.6 address reviewer's comment

Case Report A Girl with Autoimmune Cytopenias, Nonmalignant Lymphadenopathy, and Recurrent Infections

We describe a girl, now 9 years of age, with chronic idiopathic thrombocytopenic purpura, persistent nonmalignant lymphadenopathy, splenomegaly, recurrent infections, and autoimmune hemolytic anemia. Her symptoms partly fit the definitions of both autoimmune lymphoproliferative syndrome (ALPS) and common variable immunodeficiency disorders (CVIDs). Genetic analysis showed no abnormalities in the ALPS-genes FAS, FASLG, and CASP10. The CVID-associated TACI gene showed a homozygous polymorphism (Pro251Leu), which is found also in healthy controls

Making machine intelligence less scary for criminal analysts: reflections on designing a visual comparative case analysis tool

A fundamental task in Criminal Intelligence Analysis is to analyze the similarity of crime cases, called CCA, to identify common crime patterns and to reason about unsolved crimes. Typically, the data is complex and high dimensional and the use of complex analytical processes would be appropriate. State-of-the-art CCA tools lack flexibility in interactive data exploration and fall short of computational transparency in terms of revealing alternative methods and results. In this paper, we report on the design of the Concept Explorer, a flexible, transparent and interactive CCA system. During this design process, we observed that most criminal analysts are not able to understand the underlying complex technical processes, which decrease the users' trust in the results and hence a reluctance to use the tool}. Our CCA solution implements a computational pipeline together with a visual platform that allows the analysts to interact with each stage of the analysis process and to validate the result. The proposed Visual Analytics workflow iteratively supports the interpretation of the results of clustering with the respective feature relations, the development of alternative models, as well as cluster verification. The visualizations offer an understandable and usable way for the analyst to provide feedback to the system and to observe the impact of their interactions. Expert feedback confirmed that our user-centred design decisions made this computational complexity less scary to criminal analysts