Smoothing Dynamic Systems with State-Dependent Covariance Matrices

Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that error covariance matrices are known and given. In this paper, we study a general class of inference problems where covariance matrices can depend functionally on unknown parameters. In the Kalman framework, this allows modeling situations where covariance matrices may depend functionally on the state sequence being estimated. We present an extended formulation and generalized Gauss-Newton (GGN) algorithm for inference in this context. When applied to dynamic systems inference, we show the algorithm can be implemented to preserve the computational efficiency of the classic Kalman smoother. The new approach is illustrated with a synthetic numerical example.Comment: 8 pages, 1 figur

Absorption and Screening in Phycomyces

In vivo absorption measurements were made through the photosensitive zones of Phycomyces sporangiophores and absorption spectra are presented for various growth media and for wavelengths between 400 and 580 mµ. As in mycelia, ß-carotene was the major pigment ordinarily found. The addition of diphenylamine to the growth media caused a decrease in ß-carotene and an increase in certain other carotenoids. Growth in the dark substantially reduced the amount of ß-carotene in the photosensitive zone; however, growth on a lactate medium failed to suppress ß-carotene in the growing zone although the mycelia appeared almost colorless. Also when diphenylamine was added to the medium the absorption in the growing zone at 460 mµ was not diminished although the colored carotenoids in the bulk of the sporangiophore were drastically reduced. Absorption which is characteristic of the action spectra was not found. Sporangiophores immersed in fluids with a critical refractive index show neither positive nor negative tropism. Measurements were made of the critical refractive indices for light at 495 and 510 mµ. The critical indices differed only slightly. Assuming primary photoreceptors at the cell wall, the change in screening due to absorption appears too large to be counterbalanced solely by a simple effect of the focusing change. The possibility is therefore advanced that the receptors are internal to most of the cytoplasm; i.e., near the vacuole

Rules for Minimal Atomic Multipole Expansion of Molecular Fields

A non-empirical minimal atomic multipole expansion (MAME) defines atomic charges or higher multipoles that reproduce electrostatic potential outside molecules. MAME eliminates problems associated with redundancy and with statistical sampling, and produces atomic multipoles in line with chemical intuition.Comment: 3.5 pages, 3 color PS figures embedde

Linear system identification using stable spline kernels and PLQ penalties

The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and variance. Recently, a different approach to linear system identification has been introduced, where model order determination is avoided by using a regularized least squares framework. In particular, the penalty term on the impulse response is defined by so called stable spline kernels. They embed information on regularity and BIBO stability, and depend on a small number of parameters which can be estimated from data. In this paper, we provide new nonsmooth formulations of the stable spline estimator. In particular, we consider linear system identification problems in a very broad context, where regularization functionals and data misfits can come from a rich set of piecewise linear quadratic functions. Moreover, our anal- ysis includes polyhedral inequality constraints on the unknown impulse response. For any formulation in this class, we show that interior point methods can be used to solve the system identification problem, with complexity O(n3)+O(mn2) in each iteration, where n and m are the number of impulse response coefficients and measurements, respectively. The usefulness of the framework is illustrated via a numerical experiment where output measurements are contaminated by outliers.Comment: 8 pages, 2 figure