Measuring the degree of unitarity for any quantum process

Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary one. The DU, as an intrinsic property of a given quantum process, is able to quantify the distance between the process and the group of unitary ones, and is closely related to the noise of this quantum process. We derive analytical results of DU for qubit unital channels, and obtain the lower and upper bounds in general. The lower bound is tight for most of quantum processes, and is particularly tight when the corresponding DU is sufficiently large. The upper bound is found to be an indicator for the tightness of the lower bound. Moreover, we study the distribution of DU in random quantum processes with different environments. In particular, The relationship between the DU of any quantum process and the non-markovian behavior of it is also addressed.Comment: 7 pages, 2 figure

W-jet Tagging: Optimizing the Identification of Boosted Hadronically-Decaying W Bosons

A method is proposed for distinguishing highly boosted hadronically decaying W's (W-jets) from QCD-jets using jet substructure. Previous methods, such as the filtering/mass-drop method, can give a factor of ~2 improvement in S/sqrt(B) for jet pT > 200 GeV. In contrast, a multivariate approach including new discriminants such as R-cores, which characterize the shape of the W-jet, subjet planar flow, and grooming-sensitivities is shown to provide a much larger factor of ~5 improvement in S/sqrt(B). For longitudinally polarized W's, such as those coming from many new physics models, the discrimination is even better. Comparing different Monte Carlo simulations, we observe a sensitivity of some variables to the underlying event; however, even with a conservative estimates, the multivariate approach is very powerful. Applications to semileptonic WW resonance searches and all-hadronic W+jet searches at the LHC are also discussed. Code implementing our W-jet tagging algorithm is publicly available at http://jets.physics.harvard.edu/wtagComment: Version to appear in PR

Semivariogram methods for modeling Whittle-Mat\'ern priors in Bayesian inverse problems

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Mat\'ern covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs). We present a detailed mathematical description of this connection. We will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, $\mathbb{R}^2$ -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs. We show how this connection can be re-established using extended domains. We then introduce the semivariogram method for estimating the Mat\'ern covariance parameters, which specify the Gaussian prior needed for stabilizing the inverse problem. Results are extended from the isotropic case to the anisotropic case where the correlation length in one direction is larger than another. Finally, we consider the situation where the correlation length is spatially dependent rather than constant. We implement each method in two-dimensional image inpainting test cases to show that it works on practical examples

On model selection criteria for climate change impact studies

Climate change impact studies inform policymakers on the estimated damages of future climate change on economic, health and other outcomes. In most studies, an annual outcome variable is observed, e.g. annual mortality rate, along with higher-frequency regressors, e.g. daily temperature and precipitation. Practitioners use summaries of the higher-frequency regressors in fixed effects panel models. The choice over summary statistics amounts to model selection. Some practitioners use Monte Carlo cross-validation (MCCV) to justify a particular specification. However, conventional implementation of MCCV with fixed testing-to-full sample ratios tends to select over-fit models. This paper presents conditions under which MCCV, and also information criteria, can deliver consistent model selection. Previous work has established that the Bayesian information criterion (BIC) can be inconsistent for non-nested selection. We illustrate that the BIC can also be inconsistent in our framework, when all candidate models are misspecified. Our results have practical implications for empirical conventions in climate change impact studies. Specifically, they highlight the importance of a priori information provided by the scientific literature to guide the models considered for selection. We emphasize caution in interpreting model selection results in settings where the scientific literature does not specify the relationship between the outcome and the weather variables.Comment: Additional simulation results available from authors by reques

SOCR Analyses: Implementation and Demonstration of a New Graphical Statistics Educational Toolkit

The web-based, Java-written SOCR (Statistical Online Computational Resource) tools have been utilized in many undergraduate and graduate level statistics courses for seven years now (Dinov 2006; Dinov et al. 2008b). It has been proven that these resources can successfully improve students' learning (Dinov et al. 2008b). Being first published online in 2005, SOCR Analyses is a somewhat new component and it concentrate on data modeling for both parametric and non-parametric data analyses with graphical model diagnostics. One of the main purposes of SOCR Analyses is to facilitate statistical learning for high school and undergraduate students. As we have already implemented SOCR Distributions and Experiments, SOCR Analyses and Charts fulfill the rest of a standard statistics curricula. Currently, there are four core components of SOCR Analyses. Linear models included in SOCR Analyses are simple linear regression, multiple linear regression, one-way and two-way ANOVA. Tests for sample comparisons include t-test in the parametric category. Some examples of SOCR Analyses' in the non-parametric category are Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, Kolmogorov-Smirnoff test and Fligner-Killeen test. Hypothesis testing models include contingency table, Friedman's test and Fisher's exact test. The last component of Analyses is a utility for computing sample sizes for normal distribution. In this article, we present the design framework, computational implementation and the utilization of SOCR Analyses.

Cosmic Archaeology with Gravitational Waves from Cosmic Strings

Cosmic strings are generic cosmological predictions of many extensions of the Standard Model of particle physics, such as a $U(1)^\prime$ symmetry breaking phase transition in the early universe or remnants of superstring theory. Unlike other topological defects, cosmic strings can reach a scaling regime that maintains a small fixed fraction of the total energy density of the universe from a very early epoch until today. If present, they will oscillate and generate gravitational waves with a frequency spectrum that imprints the dominant sources of total cosmic energy density throughout the history of the universe. We demonstrate that current and future gravitational wave detectors, such as LIGO and LISA, could be capable of measuring the frequency spectrum of gravitational waves from cosmic strings and discerning the energy composition of the universe at times well before primordial nucleosynthesis and the cosmic microwave background where standard cosmology has yet to be tested. This work establishes a benchmark case that gravitational waves may provide an unprecedented, powerful tool for probing the evolutionary history of the very early universe.Comment: 6 pages, 3 figure