A notion of entropy is defined for the non-singular action of finite co-ordinate changes on X - the infinite product of two- point spaces. This quantity - average co-ordinate or AC entropy - is calculated for product measures and G-measures on X, and an equivalence relation is established for which AC entropy is an invariant. The Inverse Vitali Lemma is discussed in a measure preserving context, and it is shown that for a certain class of measures on X known as odometer bounded, the result will still hold for odometer actions. The foundations for a non-singular version of Rudolph's restricted orbit equivalence are established, and a size for non-singular orbit equivalence is introduced. It is shown that provided the Inverse Vitali Lemma still holds, the non-singular orbit equivalence classes can be described using this new size.

Thesis (Ph.D.)--University of Texas at Arlington, 2009.

Compressed Sensing (CS) is a framework where we measure data through a non-adaptive linear mapping with far fewer measurements that the ambient dimension of the data. This is made possible by the exploitation of the inherent structure (simplicity) in the data being measured. The central issues in this framework is the design and analysis of the measurement operator (matrix) and recovery algorithms. Restricted isometry constants (RIC) of the measurement matrix are the most widely used tool for the analysis of CS recovery algorithms. The addition of the subscripts 1 and 2 below reflects the two RIC variants developed in the CS literature, they refer to the ℓ1-norm and ℓ2-norm respectively. The RIC2 of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the ℓ2-norm. This, and related quantities, provide a mechanism by which standard eigen-analysis can be applied to topics relying on sparsity. Specifically, the upper and lower RIC2 of a matrix A of size n × N is the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all (N/k)matrices formed by taking k columns from A. Calculation of the RIC2 is intractable for most matrices due to its combinatorial nature; however, many random matrices typically have bounded RIC2 in some range of problem sizes (k, n,N). We provide the best known bound on the RIC2 for Gaussian matrices, which is also the smallest known bound on the RIC2 for any large rectangular matrix. Our results are built on the prior bounds of Blanchard, Cartis, and Tanner in Compressed Sensing: How sharp is the Restricted Isometry Property?, with improvements achieved by grouping submatrices that share a substantial number of columns. RIC2 bounds have been presented for a variety of random matrices, matrix dimensions and sparsity ranges. We provide explicit formulae for RIC2 bounds, of n × N Gaussian matrices with sparsity k, in three settings: a) n/N fixed and k/n approaching zero, b) k/n fixed and n/N approaching zero, and c) n/N approaching zero with k/n decaying inverse logarithmically in N/n; in these three settings the RICs a) decay to zero, b) become unbounded (or approach inherent bounds), and c) approach a non-zero constant. Implications of these results for RIC2 based analysis of CS algorithms are presented. The RIC2 of sparse mean zero random matrices can be bounded by using concentration bounds of Gaussian matrices. However, this RIC2 approach does not capture the benefits of the sparse matrices, and in so doing gives pessimistic bounds. RIC1 is a variant of RIC2 where the nearness to an isometry is measured in the ℓ1-norm, which is both able to better capture the structure of sparse matrices and allows for the analysis of non-mean zero matrices. We consider a probabilistic construction of sparse random matrices where each column has a fixed number of non-zeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency matrices of fixed left degree expander graphs. We present formulae for the expected cardinality of the set of neighbours for these graphs, and present a tail bound on the probability that this cardinality will be less than the expected value. Deducible from this bound is a similar bound for the expansion of the graph which is of interest in many applications. These bounds are derived through a more detailed analysis of collisions in unions of sets using a dyadic splitting technique. This bound allows for quantitative sampling theorems on existence of expander graphs and the sparse random matrices we consider and also quantitative CS sampling theorems when using sparse non mean-zero measurement matrices.

This quantitative study utilized secondary data furnished by 652 institutions of higher education which participated in the 2008 Voluntary Support of Education (VSE) national study managed by the Council for Aid to Education. This study investigated the relationships among private and public status across baccalaureate, masters and doctoral degree typologies and total alumni giving, restricted giving and unrestricted giving per full time equivalent (FTE) for the 2007/08 academic year. The independent variable included the three degree-granting sub-categories of institution as categorized by either public or private status. The dependent variables included total computed alumni giving for 2008 per FTE, restricted alumni giving for 2008 per FTE and unrestricted giving by alumni for 2008 per FTE. ANOVA main effects were calculated and statistical significance determined using the &#945; < .05 level. Tukey Post-Hoc calculations were computed and Cohen's f 2 was used to determine effect sizes. Total alumni giving per student FTE differed at statistical significance across the six institution types, F (5, 651) = 37.181, p < .001, f 2 = .29. Total restricted giving per student FTE differed at statistical significance across the six types, F (5, 651) = 28.90, p < .001, f 2 = .22. Total unrestricted giving per student FTE differed at statistical significance across the six types, F (5, 651) = 35.371, p < .001, f 2 = .27. This study's restricted giving index documents alumni make differentiated choices concerning gifts based on institution type. Recommendations are issued for further research and professional practice.

The impact of raising a child with autism spectrum disorder (ASD) is frequently accompanied by elevated caregiver stress. Examining the variables that predict these elevated rates will help us understand how caregiver stress is impacted by and impacts child behaviors. This study explored how restricted and repetitive behaviors (RRBs) contributed concurrently and longitudinally to caregiver stress in a large sample of preschoolers with ASD using parallel process multilevel growth models. Results indicated that initial rates of and change in RRBs predicted fluctuations in caregiver stress over time. When caregivers reported increased child RRBs, this was mirrored by increases in caregiver stress. Our data support the importance of targeted treatments for RRBs as change in this domain may lead to improvements in caregiver wellbeing.

A well known result due to Ankeny and Rivlin [1] states that if p(z) = ∑v=0n avzv is a polynomial of degree n satisfying p(z) ≠ 0 for |z| < 1 then for R > 1 max |z|=R|p(Z)| ≤Rn+1/2 max|z|=1|p(z)|. It was proposed by late Professor R.P. Boas, Jr. to obtain an inequality analogous to this inequality for polynomials having no zeros in |z| < K. K > 0. In this paper, we obtain some results in this direction, by considering polynomials of the form p(z) = a0 + ∑v=tn a vzv1 ≤ t ≤ n which have no zeros in |z| < K, K ≥1.

No description available.

Public criticism of executive pay has increased significantly in recent years. Shareholders express concern that the level of pay to many executives does not match the level of increase in shareholder wealth. The government has even gotten involved in the issue by changing tax laws related to compensation and taking an interest in how compensation is recorded in financial statements. This study investigates the relationship between adoption of compensation components and improved firm performance. Specifically, performance and restricted stock plan adoptions are analyzed for nine industries. Variable change is analyzed pre and post adoption for adopters; these adopters are then compared to non-adopters and to non-adopting peers. Data were gathered from COMPUSTAT and analyzed using four statistical methods; ttests, analysis of variance, multivariate analysis of variance and analysis of means. The study covers 20 years of adoptions and involves 335 adopting firms. Results of the study indicate that, when solely analyzing adopters, adoptions of performance or restricted stock plans improve firm performance for some industries but not for others. The study further indicates for most industry groups, the improvement experienced by adopters is not as significant as the improvement realized by the non-adopting segment of the industry. Lastly, when adopters are compared to non-adopting peers the study finds peers perform as well as or better than adopters. These results imply adoption of restricted stock plans works as intended for some industries by improving firm performance but may not improve performance to the levels reached by the industry as a whole. / Ph. D.

A fundamental question on visual system in neuroscience is how the visual stimuli are functionally related to neural responses. This relationship is often explained by the notion of receptive fields, an approximated linear or quasi-linear filter that encodes the high dimensional visual stimuli into neural spikes. Traditional methods for estimating the filter do not efficiently exploit prior information about the structure of neural receptive fields. Here, we propose several approaches to design the prior distribution over the filter, considering the neurophysiological fact that receptive fields tend to be localized both in space-time and spatio-temporal frequency domain. To automatically regularize the estimation of neural receptive fields, we use the evidence optimization technique, a MAP (maximum a posteriori) estimation under a prior distribution whose parameters are set by maximizing the marginal likelihood. Simulation results show that the proposed methods can estimate the receptive field using datasets that are tens to hundreds of times smaller than those required by traditional methods. / text

<p>The recent state of art in the magnetic resonance area putsforward the electron paramagnetic resonance, EPR, and nuclearmagnetic resonance, NMR, experiments on prominent positions forinvestigations of molecular and electronic structure. A mostdifficult aspect of such experiments is usually the properinterpretation of data obtained from high-resolution spectra,that, however, at the same time opens a great challenge forpure theoretical methods to interpret the spectral features.This thesis constitutes an effort in this respect, as itpresents and discusses calculations of EPR and NMR parametersof paramagnetic molecules. The calculations are based on newmethodology for determination of properties of paramagneticmolecules in the framework of the density functional theory,which has been developed in our laboratory.</p><p>Paramagnetic molecules are, in some sense, very special. Thepresence of unpaired electrons essentially modifies theirspectra. The experimental determination of the magneticresonance parameters of such molecules is, especially in theNMR case, quite complicated and requires special techniques ofspectral detection. The significant efforts put into suchexperiments are completely justi fied though by the importantroles of paramagnetic species playing in many areas, such as,for example, molecular magnets, active centers in biologicalsystems, and defects in inorganic conductive materials.</p><p>The first two papers of this thesis deal with thetheoretical determination of NMR parameters, such as thenuclear shielding tensors and the chemical shifts, inparamagnetic nitroxides that form core units in molecularmagnets. The developed methodology aimed to realize highaccuracy in the calculations in order to achieve successfulapplications for the mentioned systems. Theeffects of hydrogenbonding are also described in that context. Our theory forevaluation of nuclear shielding tensors in paramagneticmolecules is consistent up to the second order in the finestructure constant and considers orbital, fully isotropicdipolar, and isotropic contact contributions to the shieldingtensor.</p><p>The next three projects concern electron paramagneticresonance. The wellknown EPR parameters, such as the g-tensorsand the hyperfine coupling constants are explored. Calculationsof electronic g-tensors were carried out in the framework of aspin-restricted open-shell Kohn-Sham method combined with thelinear response theory recently developed in our laboratory.The spincontamination problem is then automatically avoided.The solvent effects, described by the polarizable continuummodel, are also considered. For calculations of the hyperfinecoupling constants a so-called restricted-unrestricted approachhas been developed in the context of density functional theory.Comparison of experimentally and theoretically determinedparameters shows that qualitative mutual agreement of the twosets of data can be easily achieved by employing the proposedformalisms.</p>