Supersymmetric quantum theory and (non-commutative) differential geometry

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in algebraic data consisting of an algebra of functions on a manifold and a family of supersymmetry generators represented on a Hilbert space. We show that known types of differential geometry can be classified in terms of the supersymmetries they exhibit. Replacing commutative algebras of functions by non-commutative *-algebras of operators, while retaining supersymmetry, we arrive at a formulation of non-commutative geometry encompassing and extending Connes' original approach. We explore different types of non-commutative geometry and introduce notions of non-commutative manifolds and non-commutative phase spaces. One of the main motivations underlying our work is to construct mathematical tools for novel formulations of quantum gravity, in particular for the investigation of superstring vacua.Comment: 125 pages, Plain TeX fil

Supersymmetric quantum theory and non-commutative geometry

Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail.Comment: 77 pages, PlainTeX, no figures; present paper is a significantly extended version of the second half of hep-th/9612205. Assumptions in Sect. 2.2.5 clarified; final version to appear in Commun.Math.Phy

The Gravitational Sector in the Connes-Lott Formulation of the Standard Model

We study the Riemannian aspect and the Hilbert-Einstein gravitational action of the non-commutative geometry underlying the Connes-Lott construction of the action functional of the standard model. This geometry involves a two-sheeted, Euclidian space-time. We show that if we require the space of forms to be locally isotropic and the Higgs scalar to be dynamical, then the Riemannian metrics on the two sheets of Euclidian space-time must be identical. We also show that the distance function between the two sheets is determined by a single, real scalar field whose VEV sets the weak scale.Comment: Latex file, 29 page

Utilisation d'un réseau de neurones pour appliquer le modèle de Muskingum aux réseaux d'assainissement

L'application du modèle de Muskingum pour simuler l'écoulement à surface libre dans les canaux d'irrigation a été largement utilisée et validée. Par extension, ce modèle est également employé pour simuler les écoulements en réseau d'assainissement. Or, nous avons pu montrer des erreurs allant jusqu'à 80% du débit de pointe entre le modèle de Muskingum à paramètres fixes et le modèle de référence de Barré de Saint-Venant. Nous proposons une nouvelle paramétrisation du modèle de Muskingum pour l'écoulement en collecteur circulaire en réseau d'assainissement et ceci pour un large domaine de longueurs, pentes et diamètres de collecteurs. Ce nouveau modèle non-linéaire a été calé par minimisation d'une fonction objectif traduisant la proximité du modèle proposé avec les résultats de la résolution des équations de Barré de Saint-Venant pour des hydrogrammes rectangulaires. Un réseau de neurones a été utilisé pour paramétrer le modèle. Cette nouvelle application des équations de Muskingum permet l'obtention d'erreurs relatives moyennes inférieures à 6% sur la valeur et l'instant du débit de pointe, ceci dans le cas de collecteurs ayant jusqu'à 6500 m de longueur, des pentes variant entre 0.5% et 1% et des diamètres entre 150 et 2500 mm et des hydrogrammes de débit de pointe proche de la capacité du collecteur. Le modèle a également été validé sur un hydrogramme de forme quelconque.Certain towns and cities frequently suffer from failures of their sewer networks, especially in rainy weather. Pollution of the host environment, as the direct consequence of occasionally untimely spills, is not appreciated by the natural environment or the human population. Improving the quality of the natural environment therefore involves an increasingly sophisticated control of the hydraulics and the pollutant load in drainage systems, and especially in sewer networks. Real-time management of sewer networks can provide a solution for the protection of the natural environment. In this case, control strategies are provided for the sluices and pumps of the sewer network during a rainy event to minimize the urban effluent. Moreover, a better understanding and modeling of the transport of pollution in the mains is required.To that end, not only must the hydraulic operation of the mains be correctly modeled (shape of the hydrograph, value and temporal position of the peak flow), but this numerical model must also be stable and converge towards the solution, irrespective of the initial conditions for modeling of the pollution, and the computer time must be compatible with the requirements of real-time management. The most representative model of unidimensional flows is that of Barré de Saint-Venant (1871). The non-linearity of the model, resulting in difficulties in solving these equations, together with the computer time required, are such that not all the criteria for a real-time application can be met. The conceptual equations model of Muskingum is another model that can be used.In the case of round sewerage mains with a slope ranging from practically nil to a few per-thousandths and a few kilometers long, the K and α coefficients traditionally used do not yield correct results with respect to the benchmark model of Barré de Saint-Venant. To keep the advantages of the simplification of the Muskingum equations, and to avoid having to solve the Barré de Saint Venant system, we propose new parameters for the Muskingum equations and we use optimization and correlation calculation techniques using neural networks.In modeling the mains of a sewer network, the discretization of their length, within the usual limits [50 m; 1000 m] is chosen empirically. This discretization plays an essential part in the propagation of the wave in a main. To take this effect into account, the round main of length L is discretized into N sections, and K is expressed on the basis of the maximum speed of the flow Vmax. The model setting parameters are now N and α, and will be calibrated for a wide range of slopes, lengths and flow rates for round mains with a constant roughness.The calculation procedure is as follows: - Setting of the optimal values of N and alpha giving results close to those calculated by Barré de Saint Venant; - Determination of correlations of the parameters N and alpha according to the slope, length and diameter; - Validation of the Muskingum model in relation to that of Barré de Saint-Venant. The parameters alpha and N are set by minimizing an objective function giving the agreement between the results of the hydraulic simulations by Barré de Saint-Venant and the simulations of the proposed model. The objective function is defined by the sum of the relative quadratic deviations of the values and times of maximum flow rates. The maximum errors are in fact reduced from 90% to 10% on peak flows and from 30% to 10% at a given point in time during the peak flow. The mean error is reduced forty-fold for peak flow, and five-fold in the temporal position, with a reduction of the same order for the standard deviations. Correlations of alpha and N are sought according to the slope, length and diameter of the mains modeled. As linear type relations failed to provide satisfactory results, the multi-layer Perceptron type (artificial) neural network model was used. The model includes 3 inputs and 2 outputs. The first, essential stage consists of finding the optimal number of neurons in the masked layer. It is important to mention that despite maximum errors of 40% and 20% on the prediction of time and peak flow rate, mean errors of only 3% and 4% are observed. Given this result, 4 neurons were chosen in the masked layer. This model therefore includes 3 inputs, 4 neurons in the masked layer, and 2 outputs. Following the learning phase with the results of the optimization phase, the so-called prediction phase was then performed. This consists of using the neural network with data with intermediary values with respect to those used in the learning phase. The neural network is used solely to predict values within the minimum and maximum limits of the learning phase. The prediction (or validation) phase revealed that the mean errors are in the order of 2.7% for the peak flow value and 5.5% for the instant of the same flow. The choice of 4 neurons in the masked layer during the prediction phase gives results with the same order of magnitude as in the learning phase, thus validating the structure of the neural network chosen. Subsequently, the proximity of the value and of the time position of the maximum flow rate for the propagation of rectangular hydrograms was studied. The performance of the model proposed is now verified by studying the propagation of a hydrogram of any given shape. Use of this model, validated on a hydrogram of any given shape and presenting several peaks of different intensities, yields a satisfactory reproduction of the output hydrogram and is a distinct improvement on the classic Muskingum model

American Military Culture and Civil-Military Relations Today

We demonstrate a standard-free method to retrieve compositional information in AlxIn1-xN thin films by measuring the bulk plasmon energy (E-p), employing electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM). Two series of samples were grown by magnetron sputter epitaxy (MSE) and metal organic vapor phase epitaxy (MOVPE), which together cover the full compositional range 0 <= x <= 1. Complementary compositional measurements were obtained using Rutherford backscattering spectroscopy (RBS) and the lattice parameters were obtained by X-ray diffraction (XRD). It is shown that E-p follows a linear relation with respect to composition and lattice parameter between the alloying elements from AlN to InN allowing for straightforward compositional analysis. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei

Magnetic and electronic properties of Eu\u3csub\u3e4\u3c/sub\u3eSr\u3csub\u3e4\u3c/sub\u3eGa\u3csub\u3e16\u3c/sub\u3eGe\u3csub\u3e30\u3c/sub\u3e

Magnetization, static and ac magnetic susceptibility, nuclear forward scattering, and electrical resistivity measurements have been performed on polycrystalline Eu4Sr4Ga16Ge30, a type I clathrate that has divalent strontium and europium ions encapsulated within a Ga-Ge framework. These data are compared with those of type I clathrates Eu8Ga16Ge30 and Eu6Sr2Ga16Ge30. The ferromagnetic ordering of these Eu-containing clathrates is substantially altered by the incorporation of strontium, as compared to Eu8Ga16Ge30. Ferromagnetism, accompanied by a relatively large negative magnetoresistance, is observed below 15 and 20 K in Eu4Sr4Ga16Ge30 and Eu6Sr2Ga16Ge30, respectively. An effective magnetic moment of 7.83 μB per Eu ion is observed above 30 K for Eu4Sr4Ga16Ge30, a moment which is close to the free-ion moment of 7.94 μB per europium(II) ion

Circulating Inflammatory and Oxidative Stress Responses to Steady-State Moderate-Intensity and High-Intensity Interval Exercise in Mid-Spectrum Chronic Kidney Disease

Inflammation and oxidative stress can be potent modulators of vascular function. These factors may transiently respond to moderate-intensity steady state exercise (SSE) in a manner that improves post-exercise vascular function in healthy adults. Whether exercise imparts similar effects in adults with Stage 3 or 4 chronic kidney disease (CKD) remains understudied. Moreover, a comparison of SSE and high-intensity interval exercise (HIIE) may add to clinically-relevant findings for improving vascular function in mid-spectrum CKD. PURPOSE: To determine the influence of SSE and a comparable amount of HIIE on post-exercise inflammation and oxidative stress in patients diagnosed with secondary Stage 3 or 4 CKD. METHODS: Twenty participants (n = 6 men; n = 14 women; age 62.0 + 9.9 yr; weight 80.9 + 16.2 kg; body fat 37.3 + 8.5% of weight; VO2max 19.4 + 4.7 ml/kg/min) completed 30 min of SSE at 65% VO2reserve or HIIE by treadmill walking (90% and 20% of VO2reserve in 3:2 min ratio) in a randomized crossover design. Both exercise conditions averaged ~ 65% VO2reserve. Blood samples were obtained by the same technician under standardized conditions just before, 1hr and 24hrs after exercise. Total antioxidant capacity (TAC), paraoxonase1 (PON1), asymmetric dimethylarginine (ADMA), 3nitrotyrosine (3NT) and interleukin-6 (IL6) responses were analyzed using 2 (condition) by 3 (sample point) repeated measures ANOVAs. RESULTS: Relative to pre-exercise measures: TAC increased by 4.3% 24hr after exercise (p = 0.012). PON1 was maintained 1hr and elevated by 6.1% 24hr after SSE, but not HIIE (p = 0.035). When corrected for plasma volume shifts, ADMA increased 30 ng/ml at 1hr but was 58 ng/ml lower 24hrs after exercise (p = 0.0006). 3NT and IL6 remained stable in the hours after exercise (p \u3e 0.05). CONCLUSION: Modest inflammatory and oxidative stress marker responses to either SSE and HIIE may contribute to improved vascular function in mid-spectrum CKD