A Remark on the Spontaneous Symmetry Breaking Mechanism in the Standard Model

In this paper we consider the Spontaneous Symmetry Breaking Mechanism (SSBM) in the Standard Model of particles in the unitary gauge. We show that the computation usually presented of this mechanism can be conveniently performed in a slightly different manner. As an outcome, the computation we present can change the interpretation of the SSBM in the Standard Model, in that it decouples the SU(2)-gauge symmetry in the final Lagrangian instead of breaking it.Comment: 16 page

The persistent cosmic web and its filamentary structure II: Illustrations

The recently introduced discrete persistent structure extractor (DisPerSE, Soubie 2010, paper I) is implemented on realistic 3D cosmological simulations and observed redshift catalogues (SDSS); it is found that DisPerSE traces equally well the observed filaments, walls, and voids in both cases. In either setting, filaments are shown to connect onto halos, outskirt walls, which circumvent voids. Indeed this algorithm operates directly on the particles without assuming anything about the distribution, and yields a natural (topologically motivated) self-consistent criterion for selecting the significance level of the identified structures. It is shown that this extraction is possible even for very sparsely sampled point processes, as a function of the persistence ratio. Hence astrophysicists should be in a position to trace and measure precisely the filaments, walls and voids from such samples and assess the confidence of the post-processed sets as a function of this threshold, which can be expressed relative to the expected amplitude of shot noise. In a cosmic framework, this criterion is comparable to friend of friend for the identifications of peaks, while it also identifies the connected filaments and walls, and quantitatively recovers the full set of topological invariants (Betti numbers) {\sl directly from the particles} as a function of the persistence threshold. This criterion is found to be sufficient even if one particle out of two is noise, when the persistence ratio is set to 3-sigma or more. The algorithm is also implemented on the SDSS catalogue and used to locat interesting configurations of the filamentary structure. In this context we carried the identification of an ``optically faint'' cluster at the intersection of filaments through the recent observation of its X-ray counterpart by SUZAKU. The corresponding filament catalogue will be made available online.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material (movie and data). Submitted to MNRA

A tractable method for describing complex couplings between neurons and population rate

Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the summed activity of all neurons in the population. However, an explicit, tractable model for these interactions is still lacking. Here we build a probabilistic model of population activity that reproduces the firing rate of each cell, the distribution of the population rate, and the linear coupling between them. This model is tractable, meaning that its parameters can be learned in a few seconds on a standard computer even for large population recordings. We inferred our model for a population of 160 neurons in the salamander retina. In this population, single-cell firing rates depended in unexpected ways on the population rate. In particular, some cells had a preferred population rate at which they were most likely to fire. These complex dependencies could not be explained by a linear coupling between the cell and the population rate. We designed a more general, still tractable model that could fully account for these non-linear dependencies. We thus provide a simple and computationally tractable way to learn models that reproduce the dependence of each neuron on the population rate

Blindfold learning of an accurate neural metric

The brain has no direct access to physical stimuli, but only to the spiking activity evoked in sensory organs. It is unclear how the brain can structure its representation of the world based on differences between those noisy, correlated responses alone. Here we show how to build a distance map of responses from the structure of the population activity of retinal ganglion cells, allowing for the accurate discrimination of distinct visual stimuli from the retinal response. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity, and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli

On the relative impact of subgrid-scale modelling and conjugate heat transfer in LES of hot jets in cross-flow over cold plates

This work describes numerical simulations of a hot jet in cross-flow with applications to anti-ice systems of aircraft engine nacelles. Numerical results are compared with experimental measurements obtained at ONERA to evaluate the performances of LES in this industrial context. The combination of complex geometries requiring unstructured meshes and high Reynolds number does not allow the resolution of boundary layers so that wall models must be employed. In this framework, the relative influence of subgrid-scale modelling and conjugate heat transfer in LESs of aerothermal flows is evaluated. After a general overview of the transverse jet simulation results, a LES coupled with a heat transfer solver in the walls is used to show that thermal boundary conditions at the wall have more influence on the results than subgrid scale models. Coupling fluid flow and heat transfer in solids simulations is the only method to specify their respective thermal boundary conditions

Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus

Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra ${\cal{M}}$. We show that the differential calculus, generated by the maximal subalgebra of the derivation algebra of ${\cal{M}}$ that can be related to infinitesimal symplectomorphisms, gives rise to a natural construction of Yang-Mills-Higgs models on ${\cal{M}}$ and a natural interpretation of the covariant coordinates as Higgs fields. We also compare in detail the main mathematical properties characterizing the present situation to those specific of two other noncommutative geometries, namely the finite dimensional matrix algebra $M_n({\mathbb{C}})$ and the algebra of matrix valued functions $C^\infty(M)\otimes M_n({\mathbb{C}})$. The UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also discussed.Comment: 23 pages, 2 figures. Improved and enlarged version. Some references have been added and updated. Two subsections and a discussion on the appearence of Higgs fiels in noncommutative gauge theories have been adde

A new model of fluid flow to determine pressure balance characteristics

Some projects such as the EUROMET project 463 have underlined the lack of agreement between experimental measurements and calculations by the finite element method (FEM), used to determine the piston fall rate of a high-pressure balance used in primary standards. This is significant because the piston fall rate is an essential parameter to characterize experimentally the mean gap between the piston and the cylinder and to determine the effective area (A p) at each pressure (p) point. By improving the method used to estimate the piston fall rate it is possible to improve the determination of the gap, the effective area and consequently the pressure distortion coefficient. One possible cause of the lack of agreement between the calculated and measured piston fall rates could be inappropriate modelling of the fluid flow. In fact, the former quasi-1D Stokes model assimilates the gap between the piston and the cylinder as formed by two parallel walls, which is an approximation. In addition, the velocity of the piston wall was neglected. In order to evaluate the influence of this model, the equations of the fluid flow are modified and are presented in this paper. Equations that were defined in a parallel-plane model are defined in an annular gap model. In addition to this, corrections due to the velocity of the piston wall are inserted. This research work is applied on a Desgranges et Huot DH 7594 piston-cylinder unit of PTB with a pressure up to 1 GPa, in the continuity of the EUROMET project 463 in order to quantify the influence of each correction that has been inserted in the new equations. This is carried out using the FEM. This analysis will allow us to evaluate the improvement of our knowledge of the behaviour of piston gauges and consequently to better evaluate the uncertainties due to the models.Laboratoire National d'Essais-LN

Numerical investigation of the real and ideal gap profiles in the calculation of the pressure distortion coefficient and piston fall rate of an LNE 200 MPa pressure balance

This paper aims to investigate, by means of numerical simulation, the effect of gap profiles on the calculation of the pressure distortion coefficient (λ) and the piston fall rate (vf) of two piston-cylinder units used in a Laboratoire National de Métrologie et d'Essais (LNE) 200 MPa pressure balance. The ideal mean gap width between the piston and the cylinder was obtained after measuring the piston fall rate at a low pressure, while the piston radius was obtained from the cross-float experiments at a low pressure. The real gap width was obtained from dimensional measurements by measuring the diameter and straightness of the piston and the cylinder. The piston and cylinder radial distortions were calculated using the finite element method. The pressure distribution in the gap was calculated on the basis of the Navier-Stokes equation for Newtonian viscous flow. The results such as pressure distributions, radial distortions, the pressure distortion coefficient and the piston fall rate were presented for the free-deformation operating mode of the assemblies. The calculation resulted in ideal and real gap profiles indicating that the average pressure distortion coefficient was in good agreement within 0.017 × 10-6 MPa-1 and the calculations of piston fall rate depended on the gap profile especially at the inlet and outlet zones of the engagement length.Laboratoire National de Métrologie et d'Essai

Closed-loop estimation of retinal network sensitivity reveals signature of efficient coding

According to the theory of efficient coding, sensory systems are adapted to represent natural scenes with high fidelity and at minimal metabolic cost. Testing this hypothesis for sensory structures performing non-linear computations on high dimensional stimuli is still an open challenge. Here we develop a method to characterize the sensitivity of the retinal network to perturbations of a stimulus. Using closed-loop experiments, we explore selectively the space of possible perturbations around a given stimulus. We then show that the response of the retinal population to these small perturbations can be described by a local linear model. Using this model, we computed the sensitivity of the neural response to arbitrary temporal perturbations of the stimulus, and found a peak in the sensitivity as a function of the frequency of the perturbations. Based on a minimal theory of sensory processing, we argue that this peak is set to maximize information transmission. Our approach is relevant to testing the efficient coding hypothesis locally in any context where no reliable encoding model is known