Low-complexity RLS algorithms using dichotomous coordinate descent iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of O(N-2) operations per sample; N being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3N multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2N multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented

Characterizations of Student's t-distribution via regressions of order statistics

Utilizing regression properties of order statistics, we characterize a family of distributions introduced by Akhundov, Balakrishnan, and Nevzorov (2004), that includes the t-distribution with two degrees of freedom as one of its members. Then we extend this characterization result to t-distribution with more than two degrees of freedom.Comment: To appear in "Statistics

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples

Christward movement among urban dwellers in north India : a study on Delhi

https://place.asburyseminary.edu/ecommonsatsdissertations/2139/thumbnail.jp

The Nonexistence of Instrumental Variables

The method of instrumental variables (IV) and the generalized method of moments (GMM) has become a central technique in health economics as a method to help to disentangle the complex question of causality. However the application of these techniques require data on a sufficient number of instrumental variables which are both independent and relevant. We argue that in general such instruments cannot exist. This is a reason for the widespread finding of weak instruments.

Egg-laying substrate selection for optimal camouflage by quail

Camouflage is conferred by background matching and disruption, which are both affected by microhabitat [1]. However, microhabitat selection that enhances camouflage has only been demonstrated in species with discrete phenotypic morphs [2 and 3]. For most animals, phenotypic variation is continuous [4 and 5]; here we explore whether such individuals can select microhabitats to best exploit camouflage. We use substrate selection in a ground-nesting bird (Japanese quail, Coturnix japonica). For such species, threat from visual predators is high [6] and egg appearance shows strong between-female variation [7]. In quail, variation in appearance is particularly obvious in the amount of dark maculation on the light-colored shell [8]. When given a choice, birds consistently selected laying substrates that made visual detection of their egg outline most challenging. However, the strategy for maximizing camouflage varied with the degree of egg maculation. Females laying heavily maculated eggs selected the substrate that more closely matched egg maculation color properties, leading to camouflage through disruptive coloration. For lightly maculated eggs, females chose a substrate that best matched their egg background coloration, suggesting background matching. Our results show that quail “know” their individual egg patterning and seek out a nest position that provides most effective camouflage for their individual phenotyp