Geometric Quantization on the Super-Disc

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a certain super-homogeneous space. First, we define an example of a super-homogeneous manifold: a super-disc. We show that it has a natural symplectic form, it can be used to introduce classical dynamics once a Hamiltonian is chosen. Existence of moment maps provide a Poisson realization of the underlying symmetry super-group. These are the natural operators to quantize via methods of geometric quantization, and we show that this can be done.Comment: 17 pages, Latex file. Subject: Mathematical physics, geometric quantizatio

A Simple Algebraic Derivation of the Covariant Anomaly and Schwinger Term

An expression for the curvature of the "covariant" determinant line bundle is given in even dimensional space-time. The usefulness is guaranteed by its prediction of the covariant anomaly and Schwinger term. It allows a parallel derivation of the consistent anomaly and Schwinger term, and their covariant counterparts, which clarifies the similarities and differences between them. In particular, it becomes clear that in contrary to the case for anomalies, the difference between the consistent and covariant Schwinger term can not be extended to a local form on the space of gauge potentials.Comment: 16 page

Effects of dental probing on occlusal surfaces - A scanning electron microscopy evaluation

The aim of this clinical-morphological study was to investigate the effects of dental probing on occlusal surfaces by scanning electron microscopy (SEM). Twenty sound occlusal surfaces of third molars and 20 teeth with initial carious lesions of 17- to 26-year-old patients (n = 18) were involved. Ten molars of each group were probed with a sharp dental probe (No. 23) before extraction; the other molars served as negative controls. After extraction of the teeth, the crowns were separated and prepared for the SEM study. Probing-related surface defects, enlargements and break-offs of occlusal pits and fissures were observed on all occlusal surfaces with initial carious lesions and on 2 sound surfaces, respectively. No traumatic defects whatsoever were visible on unprobed occlusal surfaces. This investigation confirms findings of light-microscopic studies that using a sharp dental probe for occlusal caries detection causes enamel defects. Therefore, dental probing should be considered as an inappropriate procedure and should be replaced by a meticulous visual inspection. Critical views of tactile caries detection methods with a sharp dental probe as a diagnostic tool seem to be inevitable in undergraduate and postgraduate dental education programmes. Copyright (c) 2007 S. Karger AG, Basel

Recommender Systems Notation

As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations appear in research papers, books, lecture notes, blog posts, and software documentation. The disciplinary diversity of the field has not contributed to consistency in notation; scholars whose home base is in information retrieval have different habits and expectations than those in machine learning or human-computer interaction. In the course of years of teaching and research on recommender systems, we have seen the value in adopting a consistent notation across our work. This has been particularly highlighted in our development of the Recommender Systems MOOC on Coursera (Konstan et al. 2015), as we need to explain a wide variety of algorithms and our learners are not well-served by changing notation between algorithms. In this paper, we describe the notation we have adopted in our work, along with its justification and some discussion of considered alternatives. We present this in hope that it will be useful to others writing and teaching about recommender systems. This notation has served us well for some time now, in research, online education, and traditional classroom instruction. We feel it is ready for broad use

NS Fivebrane and Tachyon Condensation

We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of as a gerbe.Comment: 20 pages, harvma

Tumor growth instability and the onset of invasion

Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell proliferation by itself cannot generate the invasive branching behaviour observed experimentally, (ii) heterotype chemotaxis provides an instability mechanism that leads to the onset of tumor invasion and (iii) homotype chemotaxis does not provide such an instability mechanism but enhances the mean speed of the tumor surface. The numerical results not only support the assumptions needed to perform the mathematical analysis but they also provide evidence of (i), (ii) and (iii). Finally, both the analytical study and the numerical work agree with the experimental phenomena.Comment: 12 pages, 8 figures, revtex

TWINLATIN: Twinning European and Latin-American river basins for research enabling sustainable water resources management. Combined Report D3.1 Hydrological modelling report and D3.2 Evaluation report

Water use has almost tripled over the past 50 years and in some regions the water demand already exceeds supply (Vorosmarty et al., 2000). The world is facing a “global water crisis”; in many countries, current levels of water use are unsustainable, with systems vulnerable to collapse from even small changes in water availability. The need for a scientifically-based assessment of the potential impacts on water resources of future changes, as a basis for society to adapt to such changes, is strong for most parts of the world. Although the focus of such assessments has tended to be climate change, socio-economic changes can have as significant an impact on water availability across the four main use sectors i.e. domestic, agricultural, industrial (including energy) and environmental. Withdrawal and consumption of water is expected to continue to grow substantially over the next 20-50 years (Cosgrove & Rijsberman, 2002), and consequent changes in availability may drastically affect society and economies. One of the most needed improvements in Latin American river basin management is a higher level of detail in hydrological modelling and erosion risk assessment, as a basis for identification and analysis of mitigation actions, as well as for analysis of global change scenarios. Flow measurements are too costly to be realised at more than a few locations, which means that modelled data are required for the rest of the basin. Hence, TWINLATIN Work Package 3 “Hydrological modelling and extremes” was formulated to provide methods and tools to be used by other WPs, in particular WP6 on “Pollution pressure and impact analysis” and WP8 on “Change effects and vulnerability assessment”. With an emphasis on high and low flows and their impacts, WP3 was originally called “Hydrological modelling, flooding, erosion, water scarcity and water abstraction”. However, at the TWINLATIN kick-off meeting it was agreed that some of these issues resided more appropriately in WP6 and WP8, and so WP3 was renamed to focus on hydrological modelling and hydrological extremes. The specific objectives of WP3 as set out in the Description of Work are

A four-season prospective study of muscle strain reoccurrences in a professional football club

The aim of this investigation was to characterise muscle strain reinjuries and examine their impact on playing resources in a professional football club. Muscle strains and reoccurrences were prospectively diagnosed over four seasons in first-team players (n = 46). Altogether, 188 muscle strains were diagnosed with 44 (23.4%) of these classed as reinjuries, leading to an incidence of 1.32 strain reoccurrences per 1,000 hours exposure (95% Confidence Interval [CI], 0.93–1.71). The incidence of recurrent strains was higher in match-play compared with training (4.51, 95% CI, 2.30–6.72 vs 0.94, 95% CI, 0.59–1.29). Altogether, 50.0% of players sustained at least 1 reoccurrence of a muscle strain, leading to approximately 3 days lost and 0.4 matches missed per player per season. The incidence of recurrent strains was highest in centre-forwards (2.15, 95% CI, 1.06–3.24), peaked in May (3.78, 95% CI, 0.47–7.09), and mostly affected the hamstrings (38.6% of all reoccurrences). Mean layoff for nonreoccurrences and recurrences was similar: ∼7.5 days. These results provide greater insight into the extent of the problem of recurrent muscle strains in professional football

A prospective analysis of the injury incidence of young male professional football players on artificial turf

Background: The effects of synthetic surfaces on the risk of injuries is still debated in literature and the majority of published data seems to be contradictory. For such reasons the understanding of injury incidence on such surfaces, especially in youth sport, is fundamental for injury prevention. Objectives: The aim of this study was to prospectively report the epidemiology of injuries in young football players, playing on artificial turfs, during a one sports season. Patients and Methods: 80 young male football players (age 16.1 ± 3.7 years; height 174 ± 6.6 cm; weight 64.2 ± 6.3 kg) were enrolled in a prospective cohort study. The participants were then divided in two groups; the first included players age ranging from 17 to 19 (OP) whereas the second included players age ranging from 13 to 16 (YP). Injury incidence was recorded prospectively, according to the consensus statement for soccer. Results: A total of 107 injuries (35 from the OP and 72 from the YP) were recorded during an exposure time of 83.760 hours (incidence 1.28/1000 per player hours); 22 during matches (incidence 2.84/1000 per player hours, 20.5%) and 85 during training (incidence 1.15/1000 per player hours, 79.5%). Thigh and groin were the most common injury locations (33.6% and 21.5%, respectively) while muscle injuries such as contractures and strains were the most common injury typologies (68.23%). No statistical differences between groups were displayed, except for the rate of severe injuries during matches, with the OP displaying slightly higher rates compared to the YP. Severe injuries accounted for 10.28% of the total injuries reported. The average time lost due to injuries was 14 days. Re-injuries accounted for 4.67% of all injuries sustained during the season. Conclusions: In professional youth soccer injury rates are reasonably low. Muscle injuries are the most common type of injuries while groin and thigh the most common locations. Artificial turf pitches don’t seem to contribute to injury incidence in young football players