A Tutorial on Estimating Time-Varying Vector Autoregressive Models

Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences from between-subjects data, and naturally address heterogeneity between subjects. A popular model for these data is the Vector Autoregressive (VAR) model, in which each variable is predicted as a linear function of all variables at previous time points. A key assumption of this model is that its parameters are constant (or stationary) across time. However, in many areas of psychological research time-varying parameters are plausible or even the subject of study. In this tutorial paper, we introduce methods to estimate time-varying VAR models based on splines and kernel-smoothing with/without regularization. We use simulations to evaluate the relative performance of all methods in scenarios typical in applied research, and discuss their strengths and weaknesses. Finally, we provide a step-by-step tutorial showing how to apply the discussed methods to an openly available time series of mood-related measurements

Cavity state preparation using adiabatic transfer

We show how to prepare a variety of cavity field states for multiple cavities. The state preparation technique used is related to the method of stimulated adiabatic Raman passage or STIRAP. The cavity modes are coupled by atoms, making it possible to transfer an arbitrary cavity field state from one cavity to another, and also to prepare non-trivial cavity field states. In particular, we show how to prepare entangled states of two or more cavities, such as an EPR state and a W state, as well as various entangled superpositions of coherent states in different cavities, including Schrodinger cat states. The theoretical considerations are supported by numerical simulations.Comment: 11 pages, 9 figures. Accepted in Phys. Rev.

Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio g=J/J' in square-lattice dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer couplings J and J'. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >= 1. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu = 0.71). We discuss special circumstances which allow nu<1 for the type of disorder considered here.Comment: 4+ pages, 3 figure

The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to $\exp( - c w_2^{3/2})$, where $w_2$ is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.Comment: 17 pages, 2 figure

Stereoscopic wide field of view imaging system

A stereoscopic imaging system incorporates a plurality of imaging devices or cameras to generate a high resolution, wide field of view image database from which images can be combined in real time to provide wide field of view or panoramic or omni-directional still or video images

Spectrum of Andreev Bound States in a Molecule Embedded Inside a Microwave-Excited Superconducting Junction

Non-dissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, so-called Andreev bound states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy.Comment: Published version; 4+ pages, 3 figure