Advances in Feature Selection with Mutual Information

The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically justified stopping criterion in the feature selection greedy procedure, and the estimation itself suffers from the curse of dimensionality. This chapter shows how to deal with these problems. The two first ones are addressed by using resampling techniques that provide a statistical basis to select the estimator parameters and to stop the search procedure. The third one is addressed by modifying the mutual information criterion into a measure of how features are complementary (and not only informative) for the problem at hand

Tensor Meson Production in Proton-Proton Collisions from the Color Glass Condensate

We compute the inclusive cross-section of $f_{2}$ tensor mesons production in proton-proton collisions at high-energy. We use an effective theory inspired from the tensor meson dominance hypothesis that couples gluons to $f_{2}$ mesons. We compute the differential cross-section in the $k_{\perp}$-factorization and in the Color Glass Condensate formalism in the low density regime. We show that the two formalisms are equivalent for this specific observable. Finally, we study the phenomenology of $f_{2}$ mesons by comparing theoretical predictions of different parameterizations of the unintegrated gluon distribution function. We find that $f_{2}$-meson production is another observable that can be used to put constraints on these distributions.Comment: 26 pages, 3 figures, to be submitted in Phys. Rev.

Two-sample Bayesian Nonparametric Hypothesis Testing

In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 )}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$, with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to evaluate the evidence for the null hypothesis $H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. Our method is based upon a nonparametric P\'{o}lya tree prior centered either subjectively or using an empirical procedure. We show that the P\'{o}lya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null $\mathrm{Pr}(H_0|\{\mathbf {y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.Comment: Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Thermal annealing study of swift heavy-ion irradiated zirconia

Sintered samples of monoclinic zirconia (alpha-ZrO2) have been irradiated at room temperature with 6.0-GeV Pb ions in the electronic slowing down regime. X-ray diffraction (XRD) and micro-Raman spectroscopy measurements showed unambiguously that a transition to the 'metastable' tetragonal phase (beta-ZrO2) occurred at a fluence of 6.5x10^12 cm-2 for a large electronic stopping power value (approx 32.5 MeV $\mu$m-1). At a lower fluence of 1.0x10^12 cm-2, no such phase transformation was detected. The back-transformation from beta- to alpha-ZrO2 induced by isothermal or isochronal thermal annealing was followed by XRD analysis. The back-transformation started at an onset temperature around 500 K and was completed by 973 K. Plots of the residual tetragonal phase fraction deduced from XRD measurements versus annealing temperature or time are analyzed with first- or second-order kinetic models. An activation energy close to 1 eV for the back-transformation process is derived either from isothermal annealing curves, using the so-called "cross-cut" method, or from the isochronal annealing curve, using a second-order kinetic law. Correlation with the thermal recovery of ion-induced paramagnetic centers monitored by EPR spectroscopy is discussed. Effects of crystallite size evolution and oxygen migration upon annealing are also addressed

Preheating after Small-Field Inflation

Whereas preheating after chaotic and hybrid inflation models has been abundantly studied in the literature, preheating in small field inflation models, where the curvature of the inflaton potential is negative during inflation, remains less explored. In these models, a tachyonic instability at the end of inflation leads to a succession of exponentially large increases and \emph{decreases} of the inflaton fluctuations as the inflaton condensate oscillates around the minimum of its potential. The net effect is a competition between low-momentum modes which grow and decrease significantly, and modes with higher momenta which grow less but also decrease less. We develop an analytical description of this process, which is analogous to the quantum mechanical problem of tunneling through a volcano-shaped potential. Depending on the parameters, preheating may be so efficient that it completes in less than one oscillation of the inflaton condensate. Preheating after small field inflation may also be followed by a long matter-dominated stage before the universe thermalizes, depending on the energy scale of inflation and the details of the inflaton interactions. Finally, another feature of these models is that the spectrum of the inflaton fluctuations at the end of preheating may be peaked around the Hubble scale. In fact, because preheating starts when the second slow-roll parameter $|\eta|$ becomes of order unity while the first slow-roll parameter $\epsilon$ is still much smaller than one, the universe is still inflating during preheating and the modes amplified by the initial tachyonic instability leave the Hubble radius. This may lead to an abundant production of primordial black holes and gravitational waves with frequencies today which are naturally small enough to fall into the range accessible by high-sensitivity interferometric experiments.Comment: 34 pages, 16 figures. v2: 1 ref. added, accepted for publication in Phys.Rev.

NP-hardness of decoding quantum error-correction codes

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio

Dynamical Evolution of Globular Cluster Systems formed in Galaxy Mergers: Deep HST/ACS Imaging of Old and Intermediate-Age Globular Clusters in NGC 3610

(ABRIDGED) The ACS camera on board the Hubble Space Telescope has been used to obtain deep images of the giant elliptical galaxy NGC 3610, a well-established dissipative galaxy merger remnant. These observations supersede previous WFPC2 images which revealed the presence of a population of metal-rich globular clusters (GCs) of intermediate age (~1.5-4 Gyr). We detect a total of 580 GC candidates, 46% more than from the previous WFPC2 images. The new photometry strengthens the significance of the previously found bimodality of the color distribution of GCs. Peak colors in V-I are 0.93 +/-0.01 and 1.09 +/- 0.01 for the blue and red subpopulations, respectively. The luminosity function (LF) of the inner 50% of the metal-rich (`red') population of GCs differs markedly from that of the outer 50%. In particular, the LF of the inner 50% of the red GCs shows a flattening consistent with a turnover that is about 1.0 mag fainter than the turnover of the blue GC LF. This is consistent with predictions of recent models of GC disruption for the age range mentioned above and for metallicities that are consistent with the peak color of the red GCs as predicted by population synthesis models. We determine the specific frequency of GCs in NGC 3610 and find a present-day value of S_N = 1.4 +/- 0.6. We estimate that this value will increase to S_N = 3.8 +/- 1.7 at an age of 10 Gyr, which is consistent with typical S_N values for `normal' ellipticals. Our findings constitute further evidence in support of the notion that metal-rich GC populations formed during major mergers involving gas-rich galaxies can evolve dynamically (through disruption processes) into the red, metal-rich GC populations that are ubiquitous in `normal' giant ellipticals.Comment: 15 pages, 14 figures, 4 tables. Accepted for publication in The Astronomical Journal. Figure 6 somewhat degraded to adhere to astro-ph rule

Spin-polarized stable phases of the 2-D electron fluid at finite temperatures

The Helmholtz free energy F of the interacting 2-D electron fluid is calculated nonperturbatively using a mapping of the quantum fluid to a classical Coulomb fluid [Phys. Rev. Letters, vol. 87, 206404 (2001)]. For density parameters rs such that rs<~25, the fluid is unpolarized at all temperatures t=T/EF where EF is the Fermi energy. For lower densities, the system becomes fully spin polarized for t<~0.35, and partially polarized for 0.35<t< 2, depending on the density. At rs ~25-30, and t ~0.35, an ''ambispin'' phase where F is almost independent of the spin polarization is found. These results support recent claims, based on quantum Monte Carlo results, for a stable, fully spin-polarized fluid phase at T = 0 for rs larger than about 25-26.Comment: Latex manuscript (4-5 pages) and two postscript figures; see also http://nrcphy1.phy.nrc.ca/ims/qp/chandre/chnc