On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix

Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-by-element basis, may not yield a positive semi-definite (PSD) estimate. Devlin et al. [1], claimed that element-wise PCC is not guaranteed to be PSD in dimensions p>3 for real signals. However, no justification or proof was available on this issue. In this letter, it is proved that for real signals with p<=3 and for complex signals with p<=2, a PSD estimate is guaranteed. Counterexamples are presented for higher dimensions which yield invalid covariance estimates.Comment: IEEE Signal Processing Letters, Volume 15, pp. 73-76, 200

Constrained expectation maximisation algorithm for estimating ARMA models in state space representation

This paper discusses the fitting of linear state space models to given multivariate time series in the presence of constraints imposed on the four main parameter matrices of these models. Constraints arise partly from the assumption that the models have a block-diagonal structure, with each block corresponding to an ARMA process, that allows the reconstruction of independent source components from linear mixtures, and partly from the need to keep models identifiable. The first stage of parameter fitting is performed by the expectation maximisation (EM) algorithm. Due to the identifiability constraint, a subset of the diagonal elements of the dynamical noise covariance matrix needs to be constrained to fixed values (usually unity). For this kind of constraints, so far, no closed-form update rules were available. We present new update rules for this situation, both for updating the dynamical noise covariance matrix directly and for updating a matrix square-root of this matrix. The practical applicability of the proposed algorithm is demonstrated by a low-dimensional simulation example. The behaviour of the EM algorithm, as observed in this example, illustrates the well-known fact that in practical applications, the EM algorithm should be combined with a different algorithm for numerical optimisation, such as a quasi-Newton algorithm

Experimentation of Entangled photon-pairs generation using an ultrafast source at gigahertz

In this dissertation we will present the experimental study of polarization entangled photon pairs generation, through spontaneous parametric down conversion (SPDC) using an ultrafast source at gigahertz. The laser source that we used is the TACCOR 8. The optical process of second harmonic generation (SHG) is generated by a periodically poled KTP (PPKTP) crystal. Finally, we measured the photon-pairs generation rate in the best case of conversion efficiency of SHG with PPKTP

Modern Climatology - Full Text

Climatology, the study of climate, is no longer regarded as a single discipline that treats climate as something that fluctuates only within the unchanging boundaries described by historical statistics. The field has recognized that climate is something that changes continually under the influence of physical and biological forces and so, cannot be understood in isolation but rather, is one that includes diverse scientific disciplines that play their role in understanding a highly complex coupled “whole system” that is the Earth’s climate. The modern era of climatology is echoed in this book. On the one hand it offers a broad synoptic perspective but also considers the regional standpoint as it is this that affects what people need from climatology, albeit water resource managers or engineers etc. Aspects on the topic of climate change – what is often considered a contradiction in terms – is also addressed. It is all too evident these days that what recent work in climatology has revealed carries profound implications for economic and social policy; it is with these in mind that the final chapters consider acumens as to the application of what has been learned to date. This book is divided into four sections that cover sub-disciplines in climatology. The first section contains four chapters that pertain to synoptic climatology, i.e., the study of weather disturbances including hurricanes, monsoon depressions, synoptic waves, and severe thunderstorms; these weather systems directly impact humanity. The second section on regional climatology has four chapters that describe the climate features within physiographically defined areas. The third section is on climate change which involves both past (paleoclimate) and future climate: The first two chapters cover certain facets of paleoclimate while the third is centered towards the signals (observed or otherwise) of climate change. The fourth and final section broaches the sub-discipline that is often referred to as applied climatology; this represents the important goal of all studies in climatology–one that affects modes of living. Here, three chapters are devoted towards the application of climatological research that might have useful application for operational purposes in industrial, manufacturing, agricultural, technological and environmental affairs. Please click here to explore the components of this work.https://digitalcommons.usu.edu/modern_climatology/1014/thumbnail.jp

One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined to a 1D trap. We review existing results for various dynamic correlation functions, in particular the density structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and discuss its impact on the transport properties of 1D systems at finite temperatures. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.Comment: 61 pages, 18 figures, published version, minor typos correcte

Deeply Virtual Compton Scattering at Hall A, Jefferson Lab

The Standard Model of particle physics defines quarks and leptons as the basic building blocks of all matter. The interaction between them are mediated by force carrying gauge bosons. Quantum ChromoDynamics (QCD), the theory that explains the strong interaction is still not complete enough to derive the physical observables of a Quark-Gluon system from the fundamental degrees of freedom of it’s constituents. Experimentally observable single particle densities provide important insights into our understanding of the quark-gluon system and hence help fill in the gaps of QCD. Generalized Parton Distributions (GPDs) provide simultaneous information of both spacial and longitudinal momentum distributions of constituents of a quark-gluon system. Deeply Virtual Compton Scattering (DVCS) is understood to be the simplest and cleanest process to access GPDs. Even though the exclusive DVCS is simple to understand, the experimental process however, is complex with the Bethe-Heitler and Associated DVCS being in the mix of the electron proton scattering. Over the years, 3 generations of DVCS experiments have been conducted in the Experimental Hall-A of Thomas Jefferson National Accelerator Facility (JLab). This thesis presents the extraction of DVCS cross section in 9 total kinematic points from the 3rd generation experiment (DVCS3) conducted after the 12 GeV upgrade of the Continuous Electron Beam Accelerator Facility (CEBAF) of JLab during Fall 2014 - Fall 2016

Measurement of Virtual Compton Scattering Below Pion Threshold at Invariant Four-Momentum Transfer Squared Q²=1.(GEV/C)²

Experimental Virtual Compton Scattering (VCS) off the proton is a new tool to access the Generalized Polarizabilities (GPs) of the proton that parameterize the response of the proton to an electromagnetic perturbation. The Q2 dependence of the GPs leads, by Fourier transform, to a description of the rearrangement of the charge and magnetization distributions. The VCS reaction γ* + p → p + γ was experimentally accessed through the reaction e + p → e + p + γ of electroproduction of photons off a cryogenic liquid Hydrogen target. Data were collected in Hall A at Jefferson Lab between March and April 1998 below pion threshold at Q2 = 1. and 1.9 (GeV/c)2 and also in the resonance region. Both the scattered electron and the recoil proton were analyzed with the Hall A High Resolution Spectrometer pair while the signature of the emitted real photon is obtained with a missing mass technique. A few experimental and analysis aspects will be treated. Cross-sections were extracted from the data set taken at Q2 = 1. (GeV/c)2 and preliminary results for the structure functions PLL − PTT/∈; and PLT, which involve the GPs, were obtained