Downloads & Free Reading Options - Results

We propose a practical standard-compliant multiple description (MD) image Coding technique. Multiple descriptions of an image are generated in the spatial domain by an adaptive prefiltering and uniform down sampling process. The resulting side descriptions are conventional square sample grids that are interleaved with one the other. As such each side description can be coded by any of the existing image compression standards. A side decoder reconstructs the input image by first decompressing the down-sampled image and then solving a least-squares inverse problem, guided by a two-dimensional windowed piecewise autoregressive model.The central decoder is algorithmically similar to the side decoder, but it improves the reconstruction quality by using received side descriptions as additional constraints when solving the underlyinginverse problem. Compared with its predecessors the proposed image MD technique offers the lowest encoder complexity, complete standard compliance, competitive rate-distortion performance, and superior subjective quality. ©2008 Microsoft Corporation. All rights reserved.

In today's episode, I talk with Aaron Irizarry about what to do when your design and dev team starts to fall apart.Today's episode is sponsored by Dolby. One of the most important things you can do for your application is ensure that the quality of your audio is strong. You already know Dolby and sound quality go hand-in-hand. Check out how Dolby can help you make your iOS applications better at [spec.fm/dolby](https://spec.fm/dolbyios).

In today's episode, I talk with Aaron Irizarry about what to do when your design and dev team starts to fall apart.Today's episode is sponsored by Dolby. One of the most important things you can do for your application is ensure that the quality of your audio is strong. You already know Dolby and sound quality go hand-in-hand. Check out how Dolby can help you make your iOS applications better at [spec.fm/dolby](https://spec.fm/dolbyios).

Least squares problems arise when one attempts to fit a model y = n(x,beta) to points (y1,x1),...,(yn,xn). Solutions to such problems are obtained by optimizing the sum of squared deviations over an admissible region. This paper discusses the basic theory of optimization for a general objective function and applies this material to both the linear and nonlinear least squares problems. In linear least squares normal equations for both the full rank and less than full rank cases are considered and the Kuhn-Tucker conditions are used to obtain the normal equations under linear inequality constraints. In nonlinear least squares, different iterative procedures, which may be used to obtain a solution, are discussed. The methods considered are steepest descent, Newton-Raphson, Gauss-Newton, Hartley's modified Gauss-Newton, and that of Marquardt. Results are obtained which relate Marquardt's method to equality constrained least squares. (Author)

Parallel nonnegative least squares (NNLS) solvers are developed specifically for NNLS problems that arise when the Energy Conserving Sampling and Weighting hyper-reduction procedure is used when constructing a reduced-order model (ROM) from high-fidelity, finite element calculations. With this approach, nonzero entries in the NNLS solution define a subset of the finite element mesh where the nonlinear terms need to be evaluated when integrating the ROM, and their values are weighting factors for each element; hence, a sparse solution is sought to reduce the computational work of integrating the ROM. The NNLS solution does not have to be optimal but it must satisfy some criteria associated with the accuracy of the ROM. The goal, therefore, is to produce approximate NNLS solutions that are sparse but meet some tolerance. Two algorithms are considered and scalable codes are developed: one uses the Lawson and Hanson active set method and the other the projected quasi-Newton iterative method. The latter does not inherently produce sparse solutions but can be modified to promote this. Both codes are parallelized using ScaLAPACK and performance results are presented

Parallel nonnegative least squares (NNLS) solvers are developed specifically for NNLS problems that arise when the Energy Conserving Sampling and Weighting hyper-reduction procedure is used when constructing a reduced-order model (ROM) from high-fidelity, finite element calculations. With this approach, nonzero entries in the NNLS solution define a subset of the finite element mesh where the nonlinear terms need to be evaluated when integrating the ROM, and their values are weighting factors for each element; hence, a sparse solution is sought to reduce the computational work of integrating the ROM. The NNLS solution does not have to be optimal but it must satisfy some criteria associated with the accuracy of the ROM. The goal, therefore, is to produce approximate NNLS solutions that are sparse but meet some tolerance. Two algorithms are considered and scalable codes are developed: one uses the Lawson and Hanson active set method and the other the projected quasi-Newton iterative method. The latter does not inherently produce sparse solutions but can be modified to promote this. Both codes are parallelized using ScaLAPACK and performance results are presented

Arms and del carmen squares

Red Squares Door Game by Joel Dunlap. Version 1.0. Compatible with most BBS systems. DESQview aware. Uploaded by the author.

This paper suggests a generalized Gauss-Seidel approach to sparse linear and nonlinear least squares problems. The algorithm, closely related to one given by Elfving, uses the work of Curtis, Powell, and Reid as extended by Coleman and More) to divide the variables into nondisjoint groups of structurally orthogonal columns and then projects the updated residual into each column subspace of the Jacobian in turn. In the linear case, this procedure can be viewed as an alternate ordering of the variables in the Gauss-Seidel method. Preliminary tests indicate that this leads quickly to cheap solutions of limited accuracy for linear problems, and that this approach is promising for an inexact Gauss Newton analog of the inexact Newton approach of Dembo, Eisenstat, and Steihaug.

This document introduces a user interface that provides fast and efficient general least-square analysis of experimental data. It is suitable for use in the Sunwindows environment on Sun UNIX workstation. The package is capable of providing solutions of both linear and non-linear least-squares models of experimental data, and incorporates full graphics and error analysis. Known uncertainties in the data are easily incorporated as weights for each experimental point if required. An overview of the operational details of the package is given in Section 2. Examples of how to use the package are given in Section 3. The linear least-squares analysis allows unweighted, y-weighted and x - and y-weighted optimisation, and in the former cases either the slope or intercept may be fixed if required. Since the theory of unweighted and y- weighted linear least-squares is well known 1, 2, it will not be described in this document. The theory for the case where both the dependent and independent variables exhibit uncertainties is not well known however, and as such is outlined in Appendix A. Appendix B details the theory of non-linear least- squares optimisation using the Levenberg-Marquardt algorithm, which is the routine implemented in this package.

This document introduces a user interface that provides fast and efficient general least-square analysis of experimental data. It is suitable for use in the Sunwindows environment on Sun UNIX workstation. The package is capable of providing solutions of both linear and non-linear least-squares models of experimental data, and incorporates full graphics and error analysis. Known uncertainties in the data are easily incorporated as weights for each experimental point if required. An overview of the operational details of the package is given in Section 2. Examples of how to use the package are given in Section 3. The linear least-squares analysis allows unweighted, y-weighted and x - and y-weighted optimisation, and in the former cases either the slope or intercept may be fixed if required. Since the theory of unweighted and y- weighted linear least-squares is well known 1, 2, it will not be described in this document. The theory for the case where both the dependent and independent variables exhibit uncertainties is not well known however, and as such is outlined in Appendix A. Appendix B details the theory of non-linear least- squares optimisation using the Levenberg-Marquardt algorithm, which is the routine implemented in this package.

This is the entire video from the Bluebonnet Squares' weekly club dance on August 22, 2005. It is almost 3 times as long as the shorter clip which is also available on this site. You will see great execution of the caller Pat Barbour's calls as these dancers didn't miss a beat! Great job on calls which included "Plus" moves "Load the Boat" and "Relay the Deucey". Enjoy!

Customized version of http://www.thingiverse.com/thing:40703 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=40703

We report preliminary results obtained from the large eddy simulation of a backward facing step at a Reynolds number of 5100. The numerical platform is based on a high order Legendre spectral element spatial discretization and a least squares time integration scheme. A non-reflective outflow boundary condition is in place to minimize the effect of downstream influence. Smagorinsky model with Van Driest near wall damping is used for sub-grid scale modeling. Comparisons of mean velocity profiles and wall pressure show good agreement with benchmark data. More studies are needed to evaluate the sensitivity of this method on numerical parameters before it is applied to complex engineering problems.

The object of Cribbage Squares Solitaire is to build the best possible cribbage hands in both the rows and columns. Cards are dealt from the deck one at a time. You select the position to place this card by moving the mouse to that position in the grid and clicking the left mouse button. Alternatively, you can also drag the card to desired position in the grid. When 16 cards have been dealt from the deck the computer will turn over the Starter card and will then score the hands based on the traditional rules of cribbage. Each row's total will appear to the right of the row, and each column's total will appear beneath the column. Clicking on a row or column score will show a breakdown of how the score was tallied. Your goal is to make the highest possible total score. You may consider that you 'win the game' if you reach 60.

It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on the part of the student except for addition and multiplication, reflection and rotation; but, using questions and exercises throughout, finishes by posing a problem tough enough to test postgraduate mathematics students, to which no-one has yet managed to find a solution. In this article, the author invites students and their teachers to engage with the mathematics of magic squares. (Contains 13 figures.)

The wide array of uses for least-squares estimation testifies to its effectiveness. The key to structuring a problem for at least-squares solution is finding a Markov representation of the problem. This representation defines a recursive approach to estimation. When multiple estimates are available at each time step, the processing time can be decreased by using data fusion networks to reduce the information to a single estimate. Hierarchical networks, using both parallel and serial combination of data, can be devised. The cases presented herein can be used to preprocess the for any recursive least-squares method.

The wide array of uses for least-squares estimation testifies to its effectiveness. The key to structuring a problem for at least-squares solution is finding a Markov representation of the problem. This representation defines a recursive approach to estimation. When multiple estimates are available at each time step, the processing time can be decreased by using data fusion networks to reduce the information to a single estimate. Hierarchical networks, using both parallel and serial combination of data, can be devised. The cases presented herein can be used to preprocess the for any recursive least-squares method.

This report describes the determination of burst-point coordinates from azimuth and elevation measurements by the method of least squares. The observations are made from a number of observation towers and observed are angles of azimuth and elevation. Both angles are treated as regressand variables, and the burst-point coordinates are determined by minimizing the sum of the correction squares of all observations. Two numerical solution methods are presented, both producing identical results. Methods for the detection of outliers in burst-point observations are shortly discussed. The presented coordinate determination is based on the concept of least-squares regression and differs from another algorithm that has been recently proposed in the Ballistic Research Laboratory Report BRL-MR-3894.

This report describes the determination of burst-point coordinates from azimuth and elevation measurements by the method of least squares. The observations are made from a number of observation towers and observed are angles of azimuth and elevation. Both angles are treated as regressand variables, and the burst-point coordinates are determined by minimizing the sum of the correction squares of all observations. Two numerical solution methods are presented, both producing identical results. Methods for the detection of outliers in burst-point observations are shortly discussed. The presented coordinate determination is based on the concept of least-squares regression and differs from another algorithm that has been recently proposed in the Ballistic Research Laboratory Report BRL-MR-3894.

This report describes the determination of burst-point coordinates from azimuth and elevation measurements by the method of least squares. The observations are made from a number of observation towers and observed are angles of azimuth and elevation. Both angles are treated as regressand variables, and the burst-point coordinates are determined by minimizing the sum of the correction squares of all observations. Two numerical solution methods are presented, both producing identical results. Methods for the detection of outliers in burst-point observations are shortly discussed. The presented coordinate determination is based on the concept of least-squares regression and differs from another algorithm that has been recently proposed in the Ballistic Research Laboratory Report BRL-MR-3894.

If the observations for fitting a polytomous logistic regression model satisfy certain normality assumptions, the maximum likelihood estimates of the regression coefficients are the discriminant function estimates. This paper shows that these estimates, their unbiased counterparts, and associated test statistics for variable selection can be calculated using ordinary least squares regression techniques, thereby providing a convenient procedure or performing discriminant analysis and fitting logistic regression models in the normal case. If the normality assumptions are violated, the discriminant function estimates and test statistics afford readily calculated alternatives to other procedures for fitting logistic regression models, such as the conditional maximum likelihood estimates, that present theoretical and computational difficulties. Empirical evidence is provided to show that the results of fitting logistic regression models using the discriminant function approach often agree closely with those obtained by conditional maximum likelihood. (Author)

Dual-parameter gamma ray spectrometer systems with large volume Nal (Tl) crystals and low backgrounds were used for nondestructive determination of K, Th, U and cosmic ray produced radionuclides in 60 lunar samples. The total weight of samples measured with this system is 28 kg, and the individual sample weights varied from 2 to 2300 g. Samples from Apollo 11, 12, 14, 15 and 16 were measured. Operation of the spectrometers in the coincidence mode and analyzing single coincidence spectra permits the simultaneous determination of 8-10 radionuclides in each lunar sample.

This paper introduces an iterative scheme for acoustic model inversion where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. Observed data are matched to predicted waveforms via piecewise-polynomial warpings, obtained by solving a nonconvex optimization problem in a multiscale fashion from low to high frequencies. This multiscale process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Custom adjoint sources are then defined from the warped waveforms. The proposed velocity updates are obtained as the migration of these adjoint sources, and cannot be interpreted as the negative gradient of any given objective function. The new method, referred to as RGLS, is successfully applied to a few scenarios of model velocity estimation in the transmission setting. We show that the new method can converge to the correct model in situations where conventional least-squares inversion suffers from cycle-skipping and converges to a spurious model.

Knitting and Mixed Craft podcast hosted by your friend Kim. Stop by every week for chatter, knit-a-longs, project sharing, questions, knitting, crochet, spinning and cross stitch and papercrafts and all mixed crafts i enjoy, i also have a ravelry group please come in and join in the fun. http://www.ravelry.com/groups/knitspinfibre, also the knitspinfibre podcast on Itunes and on youtube http://www.ravelry.com/projects/kimmies-knits

We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For the ridge estimator and the ordinary least squares estimator, and their variants, we provide new risk bounds of order $d/n$ without logarithmic factor unlike some standard results, where $n$ is the size of the training data. We also provide a new estimator with better deviations in the presence of heavy-tailed noise. It is based on truncating differences of losses in a min--max framework and satisfies a $d/n$ risk bound both in expectation and in deviations. The key common surprising factor of these results is the absence of exponential moment condition on the output distribution while achieving exponential deviations. All risk bounds are obtained through a PAC-Bayesian analysis on truncated differences of losses. Experimental results strongly back up our truncated min--max estimator.

We developed a least squares fitter used for extracting expected physics parameters from the correlated experimental data in high energy physics. This fitter considers the correlations among the observables and handles the nonlinearity using linearization during the $\chi^2$ minimization. This method can naturally be extended to the analysis with external inputs. By incorporating with Lagrange multipliers, the fitter includes constraints among the measured observables and the parameters of interest. We applied this fitter to the study of the $D^{0}-\bar{D}^{0}$ mixing parameters as the test-bed based on MC simulation. The test results show that the fitter gives unbiased estimators with correct uncertainties and the approach is credible.

The main result of this article is that the component of the Alexeev-Koll\'{a}r-Shepherd-Barron moduli space of stable surfaces parameterizing stable degenerations of symmetric squares of curves is isomorphic to the moduli space of stable curves. The moduli space of stable curves is used to ensure that any degeneration can be replaced by a degeneration to the symmetric square of a stable curve. These degenerations are not stable, however, but are partially resolved by the relative Hilbert scheme of length two subschemes in the fibers of a family of stable curves. The article gives a geometric description of the relative minimal models of these Hilbert schemes.

We investigate the structure of Kubo - Martin - Schwinger (KMS) states on some extension of the universal enveloping algebra of SL(2,C}. We find that there exists a one-to-one correspondence between the set of all covariant KMS states on this algebra and the set of all probability measures d\mu on the real half-line, which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.

Active regions (ARs) are the main sources of variety in solar dynamic events. Automated detection and identification tools need to be developed for solar features for a deeper understanding of the solar cycle. Of particular interest here are the dynamical properties of the ARs, regardless of their internal structure and sunspot distribution. We studied the oscillatory dynamics of two ARs: NOAA 11327 and NOAA 11726 using two different methods of pattern recognition. We developed a novel method of automated AR border detection and compared it to an existing method for the proof-of-concept. The first method uses least-squares fitting on the smallest ellipse enclosing the AR, while the second method applies regression on the convex hull.} After processing the data, we found that the axes and the inclination angle of the ellipse and the convex hull oscillate in time. These oscillations are interpreted as the second harmonic of the standing long-period kink oscillations (with the node at the apex) of the magnetic flux tube connecting the two main sunspots of the ARs. In both ARs we have estimated the distribution of the phase speed magnitude along the magnetic tubes (along the two main spots) by interpreting the obtained oscillation of the inclination angle as the standing second harmonic kink mode. After comparing the obtained results for fast and slow kink modes, we conclude that both of these modes are good candidates to explain the observed oscillations of the AR inclination angles, as in the high plasma $\beta$ regime the phase speeds of these modes are comparable and on the order of the Alfv\'{e}n speed. Based on the properties of the observed oscillations, we detected the appropriate depth of the sunspot patterns, which coincides with estimations made by helioseismic methods. The latter analysis can be used as a basis for developing a magneto-seismological tool for ARs.

Positive definite forms $f$ which are sums of squares are constructed to have the additional property that the members of any collection of forms whose squares sum to $f$ must share a nontrivial complex root.

Let $\mathbf H_2$ denote the set of even integers $n \not\equiv 1 \pmod 3$. We prove that when $H \ge X^{0.33}$, almost all integers $n \in \mathbf H_2$, $X < n \le X + H$ can be represented as the sum of a prime and the square of a prime. We also prove a similar result for sums of three squares of primes.

The 2D Least Median of Squares (LMS) is a popular tool in robust regression because of its high breakdown point: up to half of the input data can be contaminated with outliers without affecting the accuracy of the LMS estimator. The complexity of 2D LMS estimation has been shown to be $\Omega(n^2)$ where $n$ is the total number of points. This high theoretical complexity along with the availability of graphics processing units (GPU) motivates the development of a fast, parallel, GPU-based algorithm for LMS computation. We present a CUDA based algorithm for LMS computation and show it to be much faster than the optimal state of the art single threaded CPU algorithm. We begin by describing the proposed method and analyzing its performance. We then demonstrate how it can be used to modify the well-known Hough Transform (HT) in order to efficiently detect image lines in noisy images. Our method is compared with standard HT-based line detection methods and shown to overcome their shortcomings in terms of both efficiency and accuracy.

A simple formula is proved to be a tight estimate for the condition number of the full rank linear least squares residual with respect to the matrix of least squares coefficients and scaled 2-norms. The tight estimate reveals that the condition number depends on three quantities, two of which can cause ill-conditioning. The numerical linear algebra literature presents several estimates of various instances of these condition numbers. All the prior values exceed the formula introduced here, sometimes by large factors.

The least squares estimate of the autoregressive parameter of a conditionally heteroscedastic autoregression is consistent and asymptotically normal. Failure to recognize conditional heteroscedasticity results in the underestimation of the variance of the least squares estimate, and in extreme cases, this effect can be substantial. The least squares estimate is not asymptotically distribution free, rather, the asymptotic distribution depends on the form of the conditional heteroscedasticity. (Author)

"I am sure at one time or another you have all played a variation of this game with a piece of paper and a pencil. It has been around for a long time. I used to play it a lot to keep myself awake during many a boring chemistry class. Perhaps you did too. Originally, I made this program to amuse my five year old sister. It worked great! She would stay plugged in for hours, making designs and watching the letters of her name appear on the computer screen. Soon, however, I caught my father and brother playing this game and decided to modify it for public use. Well, here it is, made entirely for your amusement! I was only sixteen years old when I made Squares. It was written in Turbo Pascal version 5.5. This is the first program that I have ever written as shareware. I hope that you enjoy it."

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where the uncertainties in the major stochastic steps are quantified. Such stochastic steps involve approximating the NLS objective function using Monte-Carlo methods, and this is equivalent to the estimation of the trace of corresponding symmetric positive semi-definite (SPSD) matrices. For the latter, we prove tight necessary and sufficient conditions on the sample size (which translates to cost) to satisfy the prescribed probabilistic accuracy. We show that these conditions are practically computable and yield small sample sizes. They are then incorporated in our stochastic algorithm to quantify the uncertainty in each randomized step. The bounds we use are applications of more general results regarding extremal tail probabilities of linear combinations of gamma distributed random variables. We derive and prove new results concerning the maximal and minimal tail probabilities of such linear combinations, which can be considered independently of the rest of this paper.

We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a (global) best approximation. The analysis is complemented by remarks on programming and by a number of numerical examples including applications from medicine (MBC, MIC).

Two vectors in $\BZ^3$ are called \emph{twins} if they are orthogonal and have the same length. The paper describes twin pairs using cubic lattices, and counts the number of twin pairs with a given length. Integers $M$ with the property that each integral vector with length $\sqrt{M}$ has a twin are called twin-complete. They are completely characterized modulo a famous conjecture in number theory. The main tool is the decomposition theory of Hurwitz integral quaternions. Throughout the paper we made a concerted effort to keep the exposition as elementary as possible.

2 p. l., 102 p. 18 x 11 cm

Algorithms and original data matrix approaches compared for linear least squares problem

Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations.

Tracklist: 1. Lenny 2. The Wind Cries Mary

An almost square of type 2 is an integer $n$ that can be factored in two different ways as $n = a_1 b_1 = a_2 b_2$ with $a_1$, $a_2$, $b_1$, $b_2 \approx \sqrt{n}$. In this paper, we shall improve upon previous result on short intervals containing an almost square of type 2. This leads to an inquiry of finding a short interval around $x$ that contains an integer divisible by some integer in $[x^c, 2 x^c]$ with $0 < c < 1$.

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with $n \gg d$. Then, existing exact methods find a solution vector in $O(nd^2)$ time. We present two randomized algorithms that provide very accurate relative-error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. Both of our algorithms preprocess the data with the Randomized Hadamard Transform. One then uniformly randomly samples constraints and solves the smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on those projected coordinates. In both cases, solving the smaller problem provides relative-error approximations, and, if $n$ is sufficiently larger than $d$, the approximate solution can be computed in $O(nd \log d)$ time.

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performance. We propose a generalization of the singular value decomposition (SVD) and principal components analysis (PCA) that is appropriate for massive data sets with structured variables or known two-way dependencies. By finding the best low rank approximation of the data with respect to a transposable quadratic norm, our decomposition, entitled the Generalized least squares Matrix Decomposition (GMD), directly accounts for structural relationships. As many variables in high-dimensional settings are often irrelevant or noisy, we also regularize our matrix decomposition by adding two-way penalties to encourage sparsity or smoothness. We develop fast computational algorithms using our methods to perform generalized PCA (GPCA), sparse GPCA, and functional GPCA on massive data sets. Through simulations and a whole brain functional MRI example we demonstrate the utility of our methodology for dimension reduction, signal recovery, and feature selection with high-dimensional structured data.

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program. Often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy. The two algorithms - RDC-SOS and RDC-NOE-SOS, have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. We introduce a statistical tool, the Cramer-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any methodology. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements, achieving more accurate and faster reconstructions compared to the current state of the art.

Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set K. The idea consists of approximating from above the indicator function of K with a sequence of polynomials of increasing degree d, so that the integrals of these polynomials generate a convergence sequence of upper bounds on the volume of K. We show that the asymptotic rate of this convergence is at least O(1/ log log d).

It has often been claimed in recent papers that one can find a degree d Sum-of-Squares proof if one exists via the Ellipsoid algorithm. In [O17], Ryan O'Donnell notes this widely quoted claim is not necessarily true. He presents an example of a polynomial system with bounded coeffcients that admits low-degree proofs of non-negativity, but these proofs necessarily involve numbers with an exponential number of bits, causing the Ellipsoid algorithm to take exponential time. In this paper we obtain both positive and negative results on the bit complexity of SoS proofs. First, we propose a suffcient condition on a polynomial system that implies a bound on the coefficients in an SoS proof. We demonstrate that this sufficient condition is applicable for common use-cases of the SoS algorithm, such as Max-CSP, Balanced Separator, Max- Clique, Max-Bisection, and Unit-Vector constraints. On the negative side, O'Donnell asked whether every polynomial system containing Boolean constraints admits proofs of polynomial bit complexity. We answer this question in the negative, giving a counterexample system and non-negative polynomial which has degree two SoS proofs, but no SoS proof with small coefficients until degree Omega(sqrt(n))

1Tale of Timothy Turtle

By Arthur Scott Bailey

One of Bailey's "Sleepy-Time Tales," this is the story of Timothy Turtle, a grumpy old turtle trying to live his life alongside Black Creek. Timothy's adventures lead him to encounters with other Black Creek creatures, Fatty Coon, Mr. Crow, Brownie Beaver, Peter Mink, Ferdinand Frog, and even the local boy, Johnnie Green. (Summary by Robin Cotter)

2Tale of Peter Mink

By Arthur Scott Bailey

Arthur Scott Bailey (1877 – 1949) was author of more than forty children's books. Bailey's writing has been described thusly by the Newark Evening News: "Mr. Bailey centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. He made it a habit to never 'write down' to children and frequently used words beyond the average juvenile vocabulary, believing that youngsters respond to the stimulus of the unfamiliar." (Summary from Wikipedia)

3Tale of Daddy Long Legs

By Arthur Scott Bailey

Arthur Scott Bailey (1877 – 1949) was author of more than forty children's books. He was born on November 15, 1877, in St. Albans, Vermont, United States, the second child of Winfield Scott Bailey and Harriet Sarah Goodhue. THERE was great excitement in the neighborhood of Farmer Green's house. Rusty Wren had found some strange tracks. And nobody knew whose they were. Now, when they were puzzled like that the field- and forest-folk usually went straight to Mr. Crow for advice. But this time it happened that the old gentleman had gone on an excursion to the further side of Blue Mountain, where Brownie Beaver lived. And there seemed to be no one else at hand who was likely to be able to explain the mystery. http://www.gutenberg.org/etext/21426

4Tale of Master Meadow Mouse

By Arthur Scott Bailey

This volume in the series, Sleepy-Time Tales, follows the adventures of Master Meadow Mouse as he moves his home to various (safer) places, and tells how he cleverly avoids creatures such as Fatty Coon, Mr. Crow, and Mr. Great Blue Heron, just to name a few. (Summary by Laura Caldwell)

Bailey's writing has been described thusly by the Newark Evening News: "Mr. Bailey centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. He made it a habit to never 'write down' to children and frequently used words beyond the average juvenile vocabulary, believing that youngsters respond to the stimulus of the unfamiliar. (Wikipedia)

This is a story of the English Civil War where a witching woman conquerors hearts and marks.

7Tale of Grandfather Mole

By Arthur Scott Bailey

Arthur Scott Bailey (1877 – 1949) was the author of more than forty children's books. Bailey's writing has been described thusly by the Newark Evening News: "Mr. Bailey centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. He made it a habit to never 'write down' to children and frequently used words beyond the average juvenile vocabulary, believing that youngsters respond to the stimulus of the unfamiliar."

8Tale of Major Monkey

By Arthur Scott Bailey

Arthur Scott Bailey was the author of more than forty children's books. Mr. Bailey centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. (Summary Wikipedia)

9Tale of Benny Badger

By Arthur Scott Bailey

"Mr. Bailey centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. He made it a habit to never 'write down' to children and frequently used words beyond the average juvenile vocabulary, believing that youngsters respond to the stimulus of the unfamiliar." (Summary – Wikipedia)

10Tale of Betsy Butterfly

By Arthur Scott Bailey

Arthur Scott Bailey (1877 – 1949) was the author of more than forty children's books. "Mr. Bailey centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. He made it a habit to never 'write down' to children and frequently used words beyond the average juvenile vocabulary, believing that youngsters respond to the stimulus of the unfamiliar." (Wikipedia)

11Tale of Brownie Beaver

By Arthur Scott Bailey

Arthur Scott Bailey was the author of more than forty children's books, centered all his plots in the animal, bird and insect worlds, weaving natural history into the stories in a way that won educator's approval without arousing the suspicions of his young readers. The Tale of Brownie Beaver is another adventure of the friends and neighbours of Pleasant Valley. You will hear how Brownie keeps a house safe from a Freshet and how he receives his weekly newspaper and not to forget the making of a new suit. (summary by Lucy Burgoyne)

12A-Birding on a Bronco

By Florence A. Merriam Bailey

Florence Augusta Merriam Bailey was an American ornithologist and nature writer. She started observing bird behavior at a time when most bird study was based on collections and skins. By 1885, she began to write articles focusing on protecting birds. Her introduction of a birdwatching field guide, aimed at living birds, is considered the first in the tradition of modern bird guides. She wrote the first of these at the age of 26, initially as a series of notes in the Audubon Magazine and later as books. In "A-Birding on a Bronco," she writes an engaging memoir about her several trips to study birds on a ranch in California in the late 1800's.

13Highwayman

By H. C. Bailey

A romance and adventure novel, set in England during the reign of Queen Anne. The book is much unlike the author's later detective short stories. The actual book is difficult to locate and appears to have been forgotten. It is not even listed by Wikipedia as part of the author's work, never mind have any information on the book itself. (Summary by JCarson)

14Tale of Buster Bumblebee

By Arthur Scott Bailey

Buster Bumblebee and his family move into a new home. Excitement and buzzing abound. Buster meet a strange fellow called a carpenter bee, way too many chirpy crickets, and even finds his own long lost sister. Later in his adventurous life, Buster learns of another kind of Bee, a Raising Bee and how much food is available for everyone there. All in all, this tale will bring smiles and grins to listeners young and old as it tells of Buster Bumblebee, a young bee with a lot to learn but a heart of gold. (Summary by phil chenevert)

15Tale of Mrs. LadyBug

By Arthur Scott Bailey

Have you ever seen a LadyBug and wondered what the cute little bug with the dots on her back was thinking? And why she seemed in such a rush? Well here is your chance to peek into her thoughts and enjoy some of her daily triumphs and disasters. "Little Mrs. Ladybug was a worker. Nobody could deny that. To be sure, she had to stop now and then to talk to her neighbors, because Mrs. Ladybug dearly loved a bit of gossip. At the same time there wasn't anyone in Pleasant Valley that helped Farmer Green more than she did. She tried her hardest to keep the trees in the orchard free from insects. Some of her less worthy neighbors were known sometimes to say with a sniff, "If Mrs. Ladybug didn't enjoy her work she wouldn't care about helping Farmer Green. If she hadn't such a big appetite she'd stop to chat even more than she does now." (Summary by the book and phil chenevert)

16Tale of Pony Twinkleheels

By Arthur Scott Bailey

"When Johnnie Green sent him along the road at a trot, Twinkleheels' tiny feet moved so fast that you could scarcely have told one from another. Being a pony, and only half as big as a horse, he had to move his legs twice as quickly as a horse did in order to travel at a horse's speed. Twinkleheels' friends knew that he didn't care to be beaten by any horse, no matter how long-legged. "It's spirit, not size, that counts," Farmer Green often remarked as he watched Twinkleheels tripping out of the yard, sometimes with Johnnie on his back, sometimes drawing Johnnie in a little, red-wheeled buggy. Old dog Spot agreed with Farmer Green. When Twinkleheels first came to live on the farm Spot had thought him something of a joke." (Summary by author)

17Tale of Cuffy Bear

By Arthur Scott Bailey

A whimsical tale about the life of Cuffy bear on Blue Mountain. Cuffy is a very mischievous, disobedient bear who gets into all kinds of scrapes because he refuses to listen to his parents. He most always ends up in trouble or pain as a result of his mishaps. (Summary by Kerry Darden)

18Tale of Miss Kitty Cat

By Arthur Scott Bailey

The rats and the mice thought that Miss Kitty Cat was a terrible person. She was altogether too fond of hunting them. They agreed, however, that in one way it was pleasant to have her about the farmhouse. When she washed her face, while sitting on the doorsteps, they knew—so they said!—that it was going to rain. And then Mrs. Rat never would let her husband leave home without taking his umbrella. As a rule Miss Kitty Cat didn't look at all frightful. Almost always she appeared quite unruffled, going about her business in a quiet way and making no fuss over anything. Of course when old dog Spot chased—and cornered—her, she was quite a different sort of creature. Then she arched her back, puffed her tail out to twice its usual size, and spat fiercely at Spot. He learned not to get within reach of her sharp claws, when she behaved in that fashion. For old Spot had a tender nose. And no one knew it better than Miss Kitty Cat. (Summary by Arthur Scott Bailey)

19Tale of Henrietta Hen

By Arthur Scott Bailey

The Tale of Henrietta Hen is a cute children's book filled with the adventures of a hen named Henrietta. (Summary by SarahParshall)

20Tale of Freddie Firefly

By Arthur Scott Bailey

He was able to draw a deep breath again as they reached the field of red clover, where Peppery Polly Bumblebee settled quickly upon a clover-top and began sucking up the sweet nectar with her long tongue. For some time she worked busily without saying a word. And indeed, how could she have spoken with her tongue buried deep in the heart of a clover blossom? (From <i>The Tale of Freddy Firefly</i>)

21Tale of Dickie Deer Mouse

By Arthur Scott Bailey

"All the four-footed folk in the neighborhood agreed that Dickie Deer Mouse was well worth knowing. Throughout Pleasant Valley there was no one else so gentle as he . . . He was always tastefully dressed in fawn color and white. And except sometimes in the spring, when he needed a new coat, he was a real joy to see. For he both looked and acted like a well-bred little person."<br><br>In one of Bailey's "Sleepy-Time Tales", we follow a polite little mouse called Dickie as he hunts for a summer home, finds food, and avoids various predators. But winter is coming, and Dickie must look for a cozy place to sleep. He then makes a slight mistake, with results that could be disastrous -- or not. In this recording the voice of Dickie is read by five-year-old SuperCoconut, while her older sister narrates and reads the other characters. (Summary by Rachel)

22Vignettes of San Francisco

By Almira Bailey

A collection of observations and stories about San Franciscan life - the people, the buildings, the parks, the food, the street-cars, the bay, Alcatraz, the sounds and the smells and the characteristics and idiosyncrasies of this fascinating city. Excerpt...IN the same way that the poets have loved Rome and made their pilgrimages there - as good Moslems travel toward Mecca, so there are some of us who have come to San Francisco. Then when we arrive and find it all that we have dreamed, our love for it becomes its highest tribute. - Summary by Unknown

23Tale of Ferdinand Frog

By Arthur Scott Bailey

The wild folk in Pleasant Valley agreed that Ferdinand Frog was an agreeable person to have around. No matter what happened, he was always cheerful. Nobody ever heard of his losing his temper, though to be sure he was sometimes the means of other peoples losing theirs. These stories are about Ferdinand Frog's adventures with his animal neighbours. - Summary by Jude Somers

24Tale of Buster Bumblebee (version 2)

By Arthur Scott Bailey

This charming collection of short stories features a bumblebee called Buster, his (extensive) family, and a great number of other animals who he meets after they move home to a new meadow. - Summary by Rosslyn Carlyle

25Tale of Jolly Robin

By Arthur Scott Bailey

Arthur Scott Bailey, a native of the state of Vermont, wrote over forty children's books using a variety of animals, birds and even insects to entertain. The Tale of Jolly Robin is one of 16 stories of his Tuck-Me-In Tales series. - Summary by Larry Wilson

26Tale of Old Mr. Crow

By Arthur Scott Bailey

Arthur Scott Bailey, a native of the state of Vermont, wrote over forty children's books using a variety of animals, birds and even insects to entertain. The Tale of Old Mr. Crow is one of 16 stories of his Tuck-Me-In Tales series. - Summary by Larry Wilson