Nonparametric estimation of a convex bathtub-shaped hazard function

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ202 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Estimation of a discrete monotone distribution

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood estimator strictly dominates both the rearrangement and empirical estimators in cases when the distribution has intervals of constancy. For example, when the distribution is uniform on $\{0, ..., y \}$, the asymptotic risk of the method of rearrangements estimator (in squared $\ell_2$ norm) is $y/(y+1)$, while the asymptotic risk of the MLE is of order $(\log y)/(y+1)$. For strictly decreasing distributions, the estimators are asymptotically equivalent.Comment: 39 pages. See also http://www.stat.washington.edu/www/research/reports/2009/ http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.htm

Non-equilibrium dynamics and phase transitions

We study the poles of the retarded Green's functions of strongly coupled field theories exhibiting a variety of phase structures from a crossover up to a first order phase transition. These theories are modeled by a dual gravitational description. The poles of the holographic Green's functions appear at the frequencies of the quasinormal modes of the dual black hole background. We establish that near the transition, in all cases considered, the applicability of a hydrodynamic description breaks down already at lower momenta than in the conformal case. We establish the appearance of the spinodal region in the case of the first order phase transition at temperatures for which the speed of sound squared is negative. An estimate of the preferential scale attained by the unstable modes is also given. We additionally observe a novel diffusive regime for sound modes for a range of wavelengths.Comment: 5 pages, 4 figures. Some points are clarified. Typos corrtecte

Heavy Quark Production at the TESLA Collider and its Sensitivity to the Gluon Content in Photon

Heavy quark production is studied at the high energy linear e^+e^- collider (LC) TESLA both in its nominal and Photon Collider (PC) mode. Leading order cross-sections are calculated for the production of heavy quarks, e^+e^- -> e^+e^- Q\bar{Q}X, at high transverse momenta. The sensitivity of this process to the gluon content in the photon is studied.Comment: 16 pages, Latex, 10 ps figures, uses epsfig.sty. IFT 2001/3

Conformal defects in supergravity - backreacted Dirac delta sources

We construct numerically gravitational duals of theories deformed by localized Dirac delta sources for scalar operators both at zero and at finite temperature. We find that requiring that the backreacted geometry preserves the original scale invariance of the source uniquely determines the potential for the scalar field to be the one found in a certain Kaluza-Klein compactification of $11D$ supergravity. This result is obtained using an efficient perturbative expansion of the backreacted background at zero temperature and is confirmed by a direct numerical computation. Numerical solutions at finite temperatures are obtained and a detailed discussion of the numerical approach to the treatment of the Dirac delta sources is presented. The physics of defect configurations is illustrated with a calculation of entanglement entropy.Comment: 23 pages, 12 figure

Quasinormal modes and the phase structure of strongly coupled matter

We investigate the poles of the retarded Green's functions of strongly coupled field theories exhibiting a variety of phase structures from a crossover up to different first order phase transitions. These theories are modeled by a dual gravitational description. The poles of the holographic Green's functions appear at the frequencies of the quasinormal modes of the dual black hole background. We focus on quantifying linearized level dynamical response of the system in the critical region of phase diagram. Generically non-hydrodynamic degrees of freedom are important for the low energy physics in the vicinity of a phase transition. For a model with linear confinement in the meson spectrum we find degeneracy of hydrodynamic and non-hydrodynamic modes close to the minimal black hole temperature, and we establish a region of temperatures with unstable non-hydrodynamic modes in a branch of black hole solutions.Comment: 33 pages, 14 figure

Extended range harmonic filter

Two types of filters, leaky-wall and open-guide, are combined into single component. Combination gives 10 db or greater additional attenuation to fourth and higher harmonics, at expense of increasing loss of fundamental frequency by perhaps 0.05 to 0.08 db. Filter is applicable to all high power microwave transmitters, but is especially desirable for satellite transmitters

Cascaded half-harmonic generation of femtosecond frequency combs in mid-IR

For the growing demand of frequency combs in mid-infrared (mid-IR), known as the "molecular fingerprint" region of the spectrum [1], down conversion of near-IR frequency combs through half- harmonic generation offers numerous benefits including high conversion efficiency and intrinsic phase and frequency locking to the near-IR pump [2]. Hence cascaded half-harmonic generation promises a simple path towards extending the wavelength coverage of stable frequency combs. Here, we report a two-octave down-conversion of a frequency comb around 1 {\mu}m through cascaded half-harmonic generation with ~64% efficiency in the first stage, and ~18% in the second stage. We obtain broadband intrinsically-frequency-locked frequency combs with ~50-fs pulses at ~2 {\mu}m and ~110-fs pulses at ~4 {\mu}m. These results indicate the effectiveness of half-harmonic generation as a universal tool for efficient phase- and frequency-locked down-conversion, which can be beneficial for numerous applications requiring long-wavelength coherent sources