Application of remote sensing to state and regional problems

The author has identified the following significant results. The Lowndes County data base is essentially complete with 18 primary variables and 16 proximity variables encoded into the geo-information system. The single purpose, decision tree classifier is now operational. Signatures for the thematic extraction of strip mines from LANDSAT Digital data were obtained by employing both supervised and nonsupervised procedures. Dry, blowing sand areas of beach were also identified from the LANDSAT data. The primary procedure was the analysis of analog data on the I2S signal slicer

Algorithm for normal random numbers

We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell like distribution that may be used as a source of normally distributed random deviates follows when N tends to infinity. The algorithm passes various performance tests, including Monte Carlo simulation of a finite 2D Ising model using Wolff's algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.Comment: 5 pages, 3 encapsulated Postscript Figures. Submitted to Phys.Rev.Letters. For related work, see http://pipe.unizar.es/~jf

Measured quantum probability distribution functions for Brownian motion

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres

How Stands Collapse II

I review ten problems associated with the dynamical wave function collapse program, which were described in the first of these two papers. Five of these, the \textit{interaction, preferred basis, trigger, symmetry} and \textit{superluminal} problems, were discussed as resolved there. In this volume in honor of Abner Shimony, I discuss the five remaining problems, \textit{tails, conservation law, experimental, relativity, legitimization}. Particular emphasis is given to the tails problem, first raised by Abner. The discussion of legitimization contains a new argument, that the energy density of the fluctuating field which causes collapse should exert a gravitational force. This force can be repulsive, since this energy density can be negative. Speculative illustrations of cosmological implications are offered.Comment: 37 page

Stochastic Physics, Complex Systems and Biology

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibrium, spontaneous random "mutations" and "adaptations". On an evlutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.Comment: 10 page

Almost commuting unitary matrices related to time reversal

The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the mathematical behavior of almost commuting Hermitian matrices to depend on two factors. One factor will be the approximate polynomial relations satisfied by the matrices. The other factor is what algebra the matrices are in, either the matrices over A for A the real numbers, A the complex numbers or A the algebra of quaternions. There are potential obstructions keeping k-tuples of almost commuting operators from being close to a commuting k-tuple. We consider two-dimensional geometries and so this obstruction lives in KO_{-2}(A). This obstruction corresponds to either the Chern number or spin Chern number in physics. We show that if this obstruction is the trivial element in K-theory then the approximation by commuting matrices is possible.Comment: 33 pages, 2 figures. In version 2 some formulas have been corrected and some proofs have been rewritten to improve the expositio

Human ecological perspectives within a residential treatment setting for children

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44272/1/10566_2005_Article_BF01554427.pd

Intermediate follow-up following intravascular stenting for treatment of coarctation of the aorta

Background : We report a multiinstitutional study on intermediate-term outcome of intravascular stenting for treatment of coarctation of the aorta using integrated arch imaging (IAI) techniques. Methods and Results : Medical records of 578 patients from 17 institutions were reviewed. A total of 588 procedures were performed between May 1989 and Aug 2005. About 27% (160/588) procedures were followed up by further IAI of their aorta (MRI/CT/repeat cardiac catheterization) after initial stent procedures. Abnormal imaging studies included: the presence of dissection or aneurysm formation, stent fracture, or the presence of reobstruction within the stent (instent restenosis or significant intimal build-up within the stent). Forty-one abnormal imaging studies were reported in the intermediate follow-up at median 12 months (0.5–92 months). Smaller postintervention of the aorta (CoA) diameter and an increased persistent systolic pressure gradient were associated with encountering abnormal follow-up imaging studies. Aortic wall abnormalities included dissections ( n = 5) and aneurysm ( n = 13). The risk of encountering aortic wall abnormalities increased with larger percent increase in CoA diameter poststent implant, increasing balloon/coarc ratio, and performing prestent angioplasty. Stent restenosis was observed in 5/6 parts encountering stent fracture and neointimal buildup ( n = 16). Small CoA diameter poststent implant and increased poststent residual pressure gradient increased the likelihood of encountering instent restenosis at intermediate follow-up. Conclusions : Abnormalities were observed at intermediate follow-up following IS placement for treatment of native and recurrent coarctation of the aorta. Not exceeding a balloon:coarctation ratio of 3.5 and avoidance of prestent angioplasty decreased the likelihood of encountering an abnormal follow-up imaging study in patients undergoing intravascular stent placement for the treatment of coarctation of the aorta. We recommend IAI for all patients undergoing IS placement for treatment of CoA. © 2007 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57392/1/21191_ftp.pd

An Empirical Comparison of Information-Theoretic Criteria in Estimating the Number of Independent Components of fMRI Data

BACKGROUND: Independent Component Analysis (ICA) has been widely applied to the analysis of fMRI data. Accurate estimation of the number of independent components of fMRI data is critical to reduce over/under fitting. Although various methods based on Information Theoretic Criteria (ITC) have been used to estimate the intrinsic dimension of fMRI data, the relative performance of different ITC in the context of the ICA model hasn't been fully investigated, especially considering the properties of fMRI data. The present study explores and evaluates the performance of various ITC for the fMRI data with varied white noise levels, colored noise levels, temporal data sizes and spatial smoothness degrees. METHODOLOGY: Both simulated data and real fMRI data with varied Gaussian white noise levels, first-order auto-regressive (AR(1)) noise levels, temporal data sizes and spatial smoothness degrees were carried out to deeply explore and evaluate the performance of different traditional ITC. PRINCIPAL FINDINGS: Results indicate that the performance of ITCs depends on the noise level, temporal data size and spatial smoothness of fMRI data. 1) High white noise levels may lead to underestimation of all criteria and MDL/BIC has the severest underestimation at the higher Gaussian white noise level. 2) Colored noise may result in overestimation that can be intensified by the increase of AR(1) coefficient rather than the SD of AR(1) noise and MDL/BIC shows the least overestimation. 3) Larger temporal data size will be better for estimation for the model of white noise but tends to cause severer overestimation for the model of AR(1) noise. 4) Spatial smoothing will result in overestimation in both noise models. CONCLUSIONS: 1) None of ITC is perfect for all fMRI data due to its complicated noise structure. 2) If there is only white noise in data, AIC is preferred when the noise level is high and otherwise, Laplace approximation is a better choice. 3) When colored noise exists in data, MDL/BIC outperforms the other criteria