Lattice Point Generating Functions and Symmetric Cones

We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out the specific cases of a symmetry group of type A (previously known) and types B and D (new). We obtain several applications of the special cases in type B, including identities involving permutation statistics and lecture hall partitions.Comment: 19 page

Experimental investigation into vibro-acoustic emission signal processing techniques to quantify leak flow rate in plastic water distribution pipes

Leakage from water distribution pipes is a problem worldwide, and are commonly detected using the Vibro-Acoustic Emission (VAE) produced by the leak. The ability to quantify leak flow rate using VAE would have economic and operational benefits. However the complex interaction between variables and the leak’s VAE signal make classification of leak flow rate difficult and therefore there has been a lack of research in this area. The aim of this study is to use VAE monitoring to investigate signal processing techniques that quantify leak flow rate. A number of alternative signal processing techniques are deployed and evaluated, including VAE counts, signal Root Mean Square (RMS), peak in magnitude of the power spectral density and octave banding. A strong correlation between the leak flow rate and signal RMS was found which allowed for the development of a flow prediction model. The flow prediction model was also applied to two other media types representing buried water pipes and it was found that the surrounding media had a strong influence on the VAE signal which reduced the accuracy of flow classification. A further model was developed for buried pipes, and was found to yield good leak flow quantification using VAE. This paper therefore presents a useful method for water companies to prioritise maintenance and repair of leaks on water distribution pipes

Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part

The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this paper, we show that if the length of the cycle is 127, then the Ehrhart polynomial has a root whose real part is greater than the dimension. As a result, we have a smooth Fano polytope that is a counterexample to the two conjectures on the roots of Ehrhart polynomials.Comment: 4 pages, We changed the order of the auhors and omitted a lot of parts of the paper. (If you are interested in omitted parts, then please read v1

Rezidivierende Urolithiasis mit progredienter Niereninsuffizienz

Zusammenfassung: Bei einem 30-jährigen Patienten bestand bei rezidivierender Urolithiasis und progredienter Niereninsuffizienz die initiale Diagnose einer sekundären Hyperoxalurie. Die vertiefte Anamnese sowie neue klinische Aspekte ließen dann eine primäre Hyperoxalurie (PH) vermuten, die molekulargenetisch als PH1 bestätigt werden konnte. Pathogenese, klinischer Verlauf und therapeutische Optionen der PH werden diskutier

Cardiac surgery for the cyanotic infant

No Abstrac

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

Experimental investigation into techniques to predict leak shapes in water distribution systems using vibration measurements

Water loss from leaking pipes represents a substantial loss of revenue as well as environmental and public health concerns. Leak location is normally identified by placing sensors either side of the leak and recording and analysing the leak noise. The leak noise contains information about the leak’s characteristics, including its shape. Whilst a tool which non-invasively provides information about a leak’s shape from the leak noise would be useful for water industry practitioners, no tool currently exists. This study evaluates the effect of various leak shapes on the vibration signal and presents a unique methodology for predicting the leak shape from the vibration signal. An innovative signal processing technique which utilises the machine learning method Random Forest classifiers is used in combination with a number of signal features in order to develop a leak shape prediction algorithm. The results demonstrate a robust methodology for predicting leak shape at several leak flow rates and backfill types, providing a useful tool for water companies to assess leak repair based on leak shape

The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.Comment: 13 pages, LaTe

The inverse moment problem for convex polytopes

The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi

Large Transverse Momenta in Statistical Models of High Energy Interactions

The creation of particles with large transverse momenta in high energy hadronic collisions is a long standing problem. The transition from small- (soft) to hard- parton scattering `high-pt' events is rather smooth. In this paper we apply the non-extensive statistical framework to calculate transverse momentum distributions of long lived hadrons created at energies from low (sqrt(s)~10 GeV) to the highest energies available in collider experiments (sqrt(s)~2000 GeV). Satisfactory agreement with the experimental data is achieved. The systematic increase of the non-extensivity parameter with energy found can be understood as phenomenological evidence for the increased role of long range correlations in the hadronization process. Predictions concerning the rise of average transverse momenta up to the highest cosmic ray energies are also given and discussed.Comment: 20 pages, 10 figure