One-loop Corrections to the S Parameter in the Four-site Model

We compute the leading chiral-logarithmic corrections to the S parameter in the four-site Higgsless model. In addition to the usual electroweak gauge bosons of the Standard Model, this model contains two sets of heavy charged and neutral gauge bosons. In the continuum limit, the latter gauge bosons can be identified with the first excited Kaluza-Klein states of the W^\pm and Z bosons of a warped extra-dimensional model with an SU(2)_L \times SU(2)_R \times U(1)_X bulk gauge symmetry. We consider delocalized fermions and show that the delocalization parameter must be considerably tuned from its tree-level ideal value in order to reconcile experimental constraints with the one-loop results. Hence, the delocalization of fermions does not solve the problem of large contributions to the S parameter in this class of theories and significant contributions to S can potentially occur at one-loop.Comment: 28 pages, 7 figure

Adaptive tracking for complex systems using reduced-order models

Reduced-order models are considered in the context of parameter adaptive controllers for tracking workspace trajectories. A dual-arm manipulation task is used to illustrate the methodology and provide simulation results. A parameter adaptive controller is designed to track the desired position trajectory of a payload using a four-parameter model instead of a full-order, nine-parameter model. Several simulations with different payload-to-arm mass ratios are used to illustrate the capabilities of the reduced-order model in tracking the desired trajectory

On the exact solutions of the Bianchi IX cosmological model in the proper time

It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belinskii et al. to one more arbitrary constant. We perform the perturbative Painlev\'e test in the proper time variable, and confirm the possible existence of such an extension.Comment: 8 pages, no figure, standard Latex, to appear in Regular and chaotic dynamics (1998

Is there a true Model-D critical dynamics?

We show that non-locality in the conservation of both the order parameter and a noncritical density (model D dynamics) leads to new fixed points for critical dynamics. Depending upon the parameters characterizing the non-locality in the two fields, we find four regions: (i) model-A like where both the conservations are irrelevant (ii) model B-like with the conservation in the order parameter field relevant and the conservation in the coupling field irrelevant (iii) model C like where the conservation in the order parameter field is irrelevant but the conservation in the coupling field is relevant, and (iv) model D-like where both the conservations are relevant. While the first three behaviours are already known in dynamical critical phenomena, the last one is a novel phenomena due entirely to the non-locality in the two fields.Comment: 4 pages revtex4; to appear in Journal of Physics A Letter

A Comparison of Frequency Downshift Models of Wave Trains on Deep Water

Frequency downshift (FD) in wave trains on deep water occurs when a measure of the frequency, typically the spectral peak or the spectral mean, decreases as the waves travel down a tank or across the ocean. Many FD models rely on wind or wave breaking. We consider seven models that do not include these effects and compare their predictions with four sets of experiments that also do not include these effects. The models are the (i) nonlinear Schr\"odinger equation (NLS), (ii) dissipative NLS equation (dNLS), (iii) Dysthe equation, (iv) viscous Dysthe equation (vDysthe), (v) Gordon equation (Gordon) (which has a free parameter), (vi) Islas-Schober equation (IS) (which has a free parameter), and (vii) a new model, the dissipative Gramstad-Trulsen (dGT) equation. The dGT equation has no free parameters and addresses some of the difficulties associated with the Dysthe and vDysthe equations. We compare a measure of overall error and the evolution of the spectral amplitudes, mean, and peak. We find: (i) The NLS and Dysthe equations do not accurately predict the measured spectral amplitudes. (ii) The Gordon equation, which is a successful model of FD in optics, does not accurately model FD in water waves, regardless of the choice of free parameter. (iii) The dNLS, vDysthe, dGT, and IS (with optimized free parameter) models all do a reasonable job predicting the measured spectral amplitudes, but none captures all spectral evolutions. (iv) The vDysthe, dGT, and IS (with optimized free parameter) models do the best at predicting the observed evolution of the spectral peak and the spectral mean. (v) The IS model, optimized over its free parameter, has the smallest overall error for three of the four experiments. The vDysthe equation has the smallest overall error in the other experiment

Modelling Time-varying Dark Energy with Constraints from Latest Observations

We introduce a set of two-parameter models for the dark energy equation of state (EOS) $w(z)$ to investigate time-varying dark energy. The models are classified into two types according to their boundary behaviors at the redshift $z=(0,\infty)$ and their local extremum properties. A joint analysis based on four observations (SNe + BAO + CMB + $H_0$) is carried out to constrain all the models. It is shown that all models get almost the same $\chi^2_{min}\simeq 469$ and the cosmological parameters $(\Omega_M, h, \Omega_bh^2)$ with the best-fit results $(0.28, 0.70, 2.24)$, although the constraint results on two parameters $(w_0, w_1)$ and the allowed regions for the EOS $w(z)$ are sensitive to different models and a given extra model parameter. For three of Type I models which have similar functional behaviors with the so-called CPL model, the constrained two parameters $w_0$ and $w_1$ have negative correlation and are compatible with the ones in CPL model, and the allowed regions of $w(z)$ get a narrow node at $z\sim 0.2$. The best-fit results from the most stringent constraints in Model Ia give $(w_0,w_1) = (-0.96^{+0.26}_{-0.21}, -0.12^{+0.61}_{-0.89})$ which may compare with the best-fit results $(w_0,w_1) = (-0.97^{+0.22}_{-0.18}, -0.15^{+0.85}_{-1.33})$ in the CPL model. For four of Type II models which have logarithmic function forms and an extremum point, the allowed regions of $w(z)$ are found to be sensitive to different models and a given extra parameter. It is interesting to obtain two models in which two parameters $w_0$ and $w_1$ are strongly correlative and appropriately reduced to one parameter by a linear relation $w_1 \propto (1+w_0)$.Comment: 30 pages, 7 figure

Effect of filling methods on the forecasting of time series with missing values

Master's Project (M.S.) University of Alaska Fairbanks, 2014The Gulf of Alaska Mooring (GAK1) monitoring data set is an irregular time series of temperature and salinity at various depths in the Gulf of Alaska. One approach to analyzing data from an irregular time series is to regularize the series by imputing or filling in missing values. In this project we investigated and compared four methods (denoted as APPROX, SPLINE, LOCF and OMIT) of doing this. Simulation was used to evaluate the performance of each filling method on parameter estimation and forecasting precision for an Autoregressive Integrated Moving Average (ARIMA) model. Simulations showed differences among the four methods in terms of forecast precision and parameter estimate bias. These differences depended on the true values of model parameters as well as on the percentage of data missing. Among the four methods used in this project, the method OMIT performed the best and SPLINE performed the worst. We also illustrate the application of the four methods to forecasting the Gulf of Alaska Mooring (GAK1) monitoring time series, and discuss the results in this project