Remarks on Time-Space Noncommutative Field Theories

We propose a physical interpretation of the perturbative breakdown of unitarity in time-like noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closed-string modes. In this way, we give a unified view of the string-theoretical and the field-theoretical no-go arguments against time-like noncommutative theories. We also perform a quantitative study of various locality and causality properties of noncommutative field theories at the quantum level.Comment: 19 pages, LaTe

Blackhole/String Transition for the Small Schwarzschild Blackhole of AdS5×S5AdS_5 \times S^5 and Critical Unitary Matrix Models

In this paper we discuss the blackhole-string transition of the small Schwarzschild blackhole of $AdS_5 \times S^5$ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak {\it and} strong coupling, can be expressed entirely in terms of constant Polyakov lines which are $SU (N)$ matrices. In showing this we have taken into account that there are no Nambu-Goldstone modes associated with the fact that the 10 dimensional blackhole solution sits at a point in $S^5$. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order $N = \infty$ phase transition with the blackhole-string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of $N^{-2/3}$. The $N = \infty$ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the Lorenztian section of the small Schwarzschild blackhole.Comment: 44 pages, Minor changes,the submitted version in the journa

Over-parameterisation, a major obstacle to the use of artificial neural networks in hydrology?

International audienceRecently Feed-Forward Artificial Neural Networks (FNN) have been gaining popularity for stream flow forecasting. However, despite the promising results presented in recent papers, their use is questionable. In theory, their "universal approximator? property guarantees that, if a sufficient number of neurons is selected, good performance of the models for interpolation purposes can be achieved. But the choice of a more complex model does not ensure a better prediction. Models with many parameters have a high capacity to fit the noise and the particularities of the calibration dataset, at the cost of diminishing their generalisation capacity. In support of the principle of model parsimony, a model selection method based on the validation performance of the models, "traditionally" used in the context of conceptual rainfall-runoff modelling, was adapted to the choice of a FFN structure. This method was applied to two different case studies: river flow prediction based on knowledge of upstream flows, and rainfall-runoff modelling. The predictive powers of the neural networks selected are compared to the results obtained with a linear model and a conceptual model (GR4j). In both case studies, the method leads to the selection of neural network structures with a limited number of neurons in the hidden layer (two or three). Moreover, the validation results of the selected FNN and of the linear model are very close. The conceptual model, specifically dedicated to rainfall-runoff modelling, appears to outperform the other two approaches. These conclusions, drawn on specific case studies using a particular evaluation method, add to the debate on the usefulness of Artificial Neural Networks in hydrology. Keywords: forecasting; stream-flow; rainfall-runoff; Artificial Neural Network

Powering AGNs with super-critical black holes

We propose a novel mechanism for powering the central engines of Active Galactic Nuclei through super-critical (type II) black hole collapse. In this picture, ~$10^3 M_\odot$ of material collapsing at relativistic speeds can trigger a gravitational shock, which can eject a large percentage of the collapsing matter at relativistic speeds, leaving behind a "light" black hole. In the presence of a poloidal magnetic field, the plasma collimates along two jets, and the associated electron synchrotron radiation can easily account for the observed radio luminosities, sizes and durations of AGN jets. For Lorentz factors of order 100 and magnetic fields of a few hundred $\mu G$, synchrotron electrons can shine for $10^6$ yrs, producing jets of sizes of order 100 kpc. This mechanism may also be relevant for Gamma Ray Bursts and, in the absence of magnetic field, supernova explosions.Comment: 4 pages, 1 figur

Large N Expansion and Softly Broken Supersymmetry

We examine the supersymmetric non-linear O(N) sigma model with a soft breaking term. In two dimensions, we found that the mass difference between supersymmetric partner fields vanishes accidentally. In three dimensions, the mass difference is observed but O(N) symmetry is always broken also in the strong coupling region.Comment: Plain Latex(8pages), No Figur

Feynman Path Integral on the Noncommutative Plane

We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.Comment: 7pages, latex 2e, no figures. Accepted for publication on J.Phys.

Exact Chiral Symmetry on the Lattice

Developments during the last eight years have refuted the folklore that chiral symmetries cannot be preserved on the lattice. The mechanism that permits chiral symmetry to coexist with the lattice is quite general and may work in Nature as well. The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD.Comment: 30 pages, LaTeX, reference adde

Correlated and zonal errors of global astrometric missions: a spherical harmonic solution

We propose a computer-efficient and accurate method of estimation of spatially correlated errors in astrometric positions, parallaxes and proper motions obtained by space and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors, rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects of space astrometry, such as SIM or JASMINE.Comment: Accepted by AJ, to be published in 201

Isotropic representation of noncommutative 2D harmonic oscillator

We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field effect. The equivalence of the spectra of the isotropic and anisotropic representation is traced back to the existence of SU(2) invariance of the noncommutative model.Comment: 15 pages, RevTex4, no figures; article format, improved version of the previous paper; new references and aknowledgements adde

Differential geometry construction of anomalies and topological invariants in various dimensions

In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.Comment: 27 pages, references added, matches published versio