Seasonality with Trend and Cycle Interactions in Unobserved components Models

Summary. Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, which is often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. We formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle-dependent seasonal fluctuations. © 2009 Royal Statistical Society

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen

The ways that fibroblasts remodel their environment are central to wound healing, development of musculoskeletal tissues, and progression of pathologies such as fibrosis. However, the changes that fibroblasts make to the material around them and the mechanical consequences of these changes have proven difficult to quantify, especially in realistic, viscoelastic three-dimensional culture environments, leaving a critical need for quantitative data. Here, we observed the mechanisms and quantified the mechanical effects of fibroblast remodeling in engineered tissue constructs (ETCs) comprised of reconstituted rat tail (type I) collagen and human fibroblast cells. To study the effects of remodeling on tissue mechanics, stress-relaxation tests were performed on ETCs cultured for 24, 48, and 72 h. ETCs were treated with deoxycholate and tested again to assess the ECM response. Viscoelastic relaxation spectra were obtained using the generalized Maxwell model. Cells exhibited viscoelastic damping at two finite time constants over which the ECM showed little damping, approximately 0.2 s and 10-30 s. Different finite time constants in the range of 1-7000 s were attributed to ECM relaxation. Cells remodeled the ECM to produce a relaxation time constant on the order of 7000 s, and to merge relaxation finite time constants in the 0.5-2 s range into a single time content in the 1 s range. Results shed light on hierarchical deformation mechanisms in tissues, and on pathologies related to collagen relaxation such as diastolic dysfunction. Statement of Significance As fibroblasts proliferate within and remodel a tissue, they change the tissue mechanically. Quantifying these changes is critical for understanding wound healing and the development of pathologies such as cardiac fibrosis. Here, we characterize for the first time the spectrum of viscoelastic (rate-dependent) changes arising from the remodeling of reconstituted collagen by fibroblasts. The method also provides estimates of the viscoelastic spectra of fibroblasts within a three-dimensional culture environment. Results are of particular interest because of the ways that fibroblasts alter the mechanical response of collagen at loading frequencies associated with cardiac contraction in humans. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Invariant imbedding, method of characteristics, and parameter estimation

AbstractParameter estimation in a physical system from observed data is carried out by a method which combines invariant imbedding formalism and the method of characteristics. This avoids the necessity of making use of an initial guess for the parameter necessary if one adopts quasilinearization techniques. Numerical results for a simple one parameter system is presented

Application of invariant imbedding to the estimation of process duration

AbstractThis work deals with the application of invariant imbedding to solve a particularly important design problem, namely, the duration of the process. A numerical example is used to illustrate the approach. The advantage of this approach is its straightforward nature and uses only the usual design data. It avoids any iterations and thus no convergence problems need to be considered

The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur

Laser collimation of an atomic gallium beam

The linear-perpendicular-linear polarization gradient technique was used for investigating laser collimation of a gallium atomic beam in one dimension. The full angular divergence of the atomic beam was reduced to 0.3 mrad by operating on a particular electron transition at 294.45 nm. The transverse velocity of the atoms was reduced to 11 cm/s, which was about half of the Doppler cooling limit. The one-dimensional kinetic energy of atoms was reduced to 6 neV. The transition state exhibited optical pumping of the atoms by the cooling laser