The evolution of trilingual code-switching from infancy to school age: the shaping of trilingual competence through dynamic language dominance

This article reports on a study of the code-switches produced by two children who acquired their three languages in early childhood. We compared formal and functional aspects of their switches recorded at two different stages of their development. Of particular interest was the consideration of sociolinguistic variables that have intervened in the children’s environment. We undertook a quantitative and qualitative analysis of the children’s code-switches to ascertain the frequency of switching, the use of each of the three languages employed for switching and the linguistic complexity of the switches. We assumed that the sociolinguistic conditions that changed the linguistic landscape in which these children operated would be reflected not only in the development of each of their languages, but also in the kind of switches that they produced. We tried to establish whether it is the case that certain forms and functions of code-switches constitute a "core" of trilingual language behaviour while others are prone to change. Ultimately, our aim was to gain an insight into the specific trilingual language production processes over a given period of time that can shed light on the development and nature of trilingual competence

Forecasting UK Industrial Production Over the Business Cycle

This paper examines the information available through leading indicators for modelling and forecasting the UK quarterly index of production (seasonally adjusted). The emphasis is on one-quarter ahead prediction, especially over the 1990s recession. Linear specifications considered are univariate autoregressive models together with dynamic single indicator and multiple indicator models. Both univariate and leading indicator versions of nonlinear Markov switching specifications are also examined. In the latter case, the transition probabilities are modelled as logistic functions of the leading indicators, allowing the lead times to differ for the expansion to expansion and recession to recession probabilities. Despite general evidence that the term structure of interest rates helps regime classification in the Markov switching models, these models perform relatively poorly in forecasting the 1990s production recession. It is suggested that this poor performance may be due to the nature of that recession, which differed from previous major UK postwar recessions in having no single quarter where industrial production declined substantially. However, a three indicator linear specification does well. The leading indicator variables in this latter model are a short-term interest rate, the stock market dividend yield and the optimism balance from the quarterly survey conducted by the Confederation of British Industry.

Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions

Using time dependent nonlinear (s-wave scattering length) coupling between the components of a weakly interacting two component Bose-Einstein condensate (BEC), we show the possibility of matter wave switching (fraction of atoms transfer) between the components via shape changing/intensity redistribution (matter redistribution) soliton interactions. We investigate the exact bright-bright N-soliton solution of an effective one-dimensional (1D) two component BEC by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. In particular, we show that the effective 1D coupled Gross-Pitaevskii (GP) equations with time dependent parameters can be transformed into the well known completely integrable Manakov model described by coupled nonlinear Schr\"odinger (CNLS) equations by effecting a change of variables of the coordinates and the wave functions under certain conditions related to the time dependent parameters. We obtain the one-soliton solution and demonstrate the shape changing/matter redistribution interactions of two and three soliton solutions for the time independent expulsive harmonic trap potential, periodically modulated harmonic trap potential and kink-like modulated harmonic trap potential. The standard elastic collision of solitons occur only for a specific choice of soliton parameters.Comment: 11 pages, 14 figures, 1 tabl

A computational method for solving time-delay optimal control problems with free terminal time

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system (which influences the variable time delays in the new system). We develop a gradient-based optimization approach for solving this approximate problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach

Risk management and extreme scenario development using multiple regime switching approaches : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Finance at Massey University

Over the last twenty-five years, there have been an increasingly large number of extreme events in the financial markets. This includes market crashes and natural disasters that have led to extremely large losses and claims. Extreme event risk affects all aspects of risk assessment modeling and management. Traditional risk measurement methods focus on probability of laws governing average of sums, and do not focus on the tails of distribution. The investigation concerns the characterization and development of extreme markets scenarios for use in risk measurement and capital adequacy determination frameworks. The first part of the investigation concerns the development of event timelines that can be used for characterizing whether a period of time should be considered normal or extreme market conditions or regimes. The time lines have allowed the identification of the different times when the markets were calm and when the markets were turbulent. They assist in building scenarios, and also to identify the scenarios for decomposition of data to model the different regions, either the tail or the center of the distribution using the mentioned regime switching models. The information from the event time line can be used to define scenarios in a stress testing context. In this investigation, extreme value analysis, which is an extension of the standard VaR techniques, useful in measuring extreme events has been used, which fits density functions by placing more weights in the tails than the normal Gaussian distribution and model the upper and lower tail of an underlying distribution. Extreme value distribution functions including "fat tailed" will be fitted to the tails of critical market factors to model the extreme market events that are not given appropriate probability of occurrence under normal conditions. The Hill estimator, which is recognized as the consistent estimator for empirical analysis is used for calculating the tail index parameter for EVT modeling, However, it has to be noted that the Hill estimator is efficient when the underlying distribution is fat-tailed as compared to the gaussian, where the tail index estimates tend to go to infinity. The performance of Extreme value theory estimation technique with multiple regimes on real and simulated financial time series for efficient results, compared to the standard VaR techniques has been studied. In this investigation, multiple regime switching approach has been used to identify regimes and measure risk accordingly. It is assumed that the center of the returns distribution is normally distributed with 90 percent of the data in the in the center region and each tail contains 5 percent of the data. Three regime switching models have been used in this analysis which includes, the Unconditional LT-C-RT (Left tail - Center - Right Tail) transfers, the 3 State Regime Markov Transition Model and the Geometric Time in Trail Model. The regime switching models are modeled using the following procedures: 1) The Unconditional LT-C-RT (Left Tail - Center - Right Tail) model is an IID model (Independent and Identically Distributed) model and has a simple Bernoulli approach where the market is in a normal state with probability P or an abnormal state with probability 1 - p . The transition between states is independent of the last state. 2) A Markov chain approach where the next state of the market is a function of the current state. That there are the following transitions possible: 2.1) Normal to normal 2.2) Normal to abnormal 2.3) Abnormal to abnormal 2.4) Abnormal to normal 3). The Geometric Time in Tail model is a hybrid Bernoulli approach where the markets stays in a given state based on a duration model and when the duration in a given states has expired, the sampling of the next state using a independent Bernoulli approach similar to approach one. This implies that the after the market has stayed in a given regime for the sample duration time, it can stay in the current regime with probability p or leave the regime with probability 1 - p. The sample duration can be based on the exponential distribution for continuous time and the geometric distribution for discrete time such as daily movements. Tail index estimation results using EVT indicate the presence of fat tails in equity data and the results of Value-at-Risk (VaR) and Expected Shortfall (ES) are considerably similar for the three regime switching models. The comparison of results from the multiple regime switching models to the one region distribution results, which serve as the base case prove the efficiency of using this approach for a better risk measure

A comparative study on global wavelet and polynomial models for nonlinear regime-switching systems

A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems

Guidelines for Weighting Factors Adjustment in Finite State Model Predictive Control of Power Converters and Drives

INTERNATIONAL CONFERENCE ON INDUSTRIAL TECHNOLOGY () (.2009.VICTORIA, AUSTRALIA)Model Predictive Control with a finite control set has emerged as a promising control tool for power converters and drives. One of the major advantages is the possibility to control several system variables with a single control law, by including them with appropriate weighting factors. However, at the present state of the art, these coefficients are determined empirically. There is no analytical or numerical method proposed yet to obtain an optimal solution. In addition, the empirical method is not always straightforward, and no procedures have been reported. This paper presents a first approach to a set of guidelines that reduce the uncertainty of this process. First a classification of different types of cost functions and weighting factors is presented. Then the different steps of the empirical process are explained. Finally, results for several power converters and drives applications are analyzed, which show the effectiveness of the proposed guidelines to reach appropriate weighting factors and control performance