Reconstructing the Adjusted Census for Florida: A Case Study in Data Examination

Abstract

This article is a case study in the value of close examination of available data when one is attempting to make inferences. The article is also an example of what can be done to reconstruct government files when data have been concealed, whether for administrative or political reasons, as here, or to preserve confidentiality. The various methods currently used are under review by a panel under the aegis of the Committee on National Statistics of the National Research Council. The upshot of our work is that even suppressing half of the microlevel data in a file need not daunt a determined and reasonably adroit reconstructor equipped with modern computers. The particular problem discussed here arose due to a bizarre set of political and legal circumstances, explained in Section 1, whereby the U.S. Department of Commerce released a tape consisting of the adjusted population (cross-classified by age, race, and gender) of half the Census Blocks in the nation, together with certain summary adjusted information. This article concerns techniques used to fill in the other half of the adjusted block data for possible use in reapportionment.     

Regularity properties of the Zakharov system on the half line

In this paper, we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results, and the behavior of higher order Sobolev norms of the solutions. Smoothing means that the nonlinear part of the solution on the half line is smoother than the initial data. The gain in regularity coincides with the gain that was observed for the periodic Zakharov and the Zakharov on the real line. Uniqueness is proved in the class of smooth solutions. When the boundary value of the Schrödinger part of the solution is zero, uniqueness can be extended to the full range of local solutions. Under the same assumptions on the initial data, we also prove global-in-time existence and uniqueness of energy solutions. For more regular data, we prove that all higher Sobolev norms grow at most polynomially-in-time.     

An examination of the size of orders from customers,their characterisation and the implications for inventory control of slow moving items

This paper examines half a million observations of the size of orders from customers at an electrical wholesaler. It notes: the distribution of the size of customer orders for a single item (stock keeping unit or SKU) is very skewed and resembles a geometric distribution; while the average size of an order is different for different items, for one SKU the mean order size is effectively the same at different branches even when the branches have very different demand rates; across a range of SKUs there is a strong relationship linking the mean and the variance of order size. The general results above are shown to apply to even the slowest movers. This extension is important because for items with intermittent demand the size of customer orders is required to produce an unbiased estimate of demand. Also a knowledge of the distribution of demand is important for setting maximum and minimum stock levels and the scheme employed is described.     

上半平面上Bergman空间的再生核

探讨了上半平面上Ｂｅｒｇｍａｎ空间的完备性,给出了上半平面上Ｂｅｒｇｍａｎ空间的再生核,探讨了再生核的再生范围。     

Nonrepetitive colorings of graphs

A coloring of the vertices of a graph G is nonrepetitive if there is no even path in G whose first half looks the same as the second half. This notion arose as an analogue of the famous nonrepetitive sequences of Thue. We consider here the list analogue and the game analogue of nonrepetitive colorings.     

Banks’ criterion and symmetric stable laws with index of stability between one-half and one

In this paper we compare the sample mean and the sample median of independent and identically distributed data that come from a symmetric stable distribution using Banks’ (1997) criterion, which is an alternative to Pitman’s (1937) criterion for comparing estimators of a parameter of interest. For data from a symmetric stable distribution with index of stability between one half and one and odd sample size, we show that Banks’ criterion choses the sample median as an estimator of the location parameter of the distribution. For data from a normal distribution with even sample size, we show that Banks’ criterion favours the sample mean (thus “complementing” a similar result about odd sample sizes in Karunaratne and Hadjicostas (2009)). In the process, we prove some trigonometric inequalities, which are interesting in their own right.     

Half Sampling on Bipartite Graphs

On a bipartite graph G we consider the half sampling problem of uniquely recovering a function from its values on the even vertices, under the appropriate half bandlimited assumption with respect to a Laplacian on the graph. We discuss both finite and infinite graphs, give the appropriate definition of “half bandlimited” that involves splitting the mid frequency, and give an explicit solution to the problem. We discuss in detail the example of a regular tree. We also consider a related sampling problem on graphs that are generated by edge substitution.     

Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon

This paper reports on data from investigations on learners’ understanding of inclusion relations of quadrilaterals, building on the ideas from our earlier study (Fujita & Jones, 2007). By synthesising past and current theories in the teaching of geometry (van Hiele's model, figural concepts, prototype phenomenon, etc.), we propose a theoretical model and method to describe learners’ cognitive development of their understanding of inclusion relations of quadrilaterals, and in order to investigate the topic, data are collected from trainee teachers and lower secondary school students. The findings suggest that in general more than half of above average learners are likely to recognise quadrilaterals primarily by prototypical examples, even though they know the correct definition, and this causes them difficulty in understanding the inclusion relations of quadrilaterals.     

Convexity of the upper complex plane part of the numerical range of a quaternionic matrix

The quaternionic numerical range of a matrix with quaternion entries has a convex intersection with the upper half complex plane. The quaternionic analog of the elliptical range theorem is proved.     

A Boundary Value Problem for Conjugate Conductivity Equations

We give explicit integral formulas for the solutions of planar conjugate conductivity equations in a circular domain of the right half‐plane with conductivity , . The representations are obtained via the so‐called unified transform method or Fokas method, involving a Riemann–Hilbert problem on the complex plane when p is even and on a two‐sheeted Riemann surface when p is odd. They are given in terms of the Dirichlet and Neumann data on the boundary of the domain. For even exponent p, we also show how to make the conversion from one type of conditions to the other by using the global relation that follows from the closedness of some differential form. The method used to derive our integral representations could be applied in any bounded simply connected domain of the right half‐plane with a smooth boundary.     

On the convergence rate of Fourier series

The rate of convergence of a Fourier‐series representation of a given function depends on the nature of the function and of its derivatives. This is shown by using the graphical outputs of a desk computer for different cases. For full‐range series, the effects of continuity and discontinuity of the function and its first derivatives are shown first. The advantage of half‐range formulae due to the free choice of function in the second half‐range are demonstrated next, along with the importance of choice of sine and cosine series according to the function being represented. Finally, a method is given of modifying the given function in a simple manner whereby a dramatic increase in the rate of convergence of the Fourier series is obtained. Examples of the Gibbs overshoot and its elimination are included.     

学生面试问题的分配策略

就学生面试问题中的教师分配策略进行了系统的分析.首先我们分别给出并证明了在面试老师数一定,满足没有两个老师相同以及三个老师相同情形下的,可承担面试学生数的四个上界.然后提出了2种分配算法:排队算法和集合压缩算法,计算结果表明,所提算法可以很好的逼近理论上界.针对文理各半的情形,我们也同样提出并证明了类似的上界,两种分配策略同样适合文理各半的情形.在不分文理和文理各半的两种情况下,我们提出的分配策略都能很好的逼进甚至达到上界,同时也说明了我们理论界是一个很紧的上界.     

Rational decomposition of modular forms

We prove explicit formulas decomposing cusp forms of even weight for the modular group, in terms of generators having rational periods, and in terms of generators having rational Fourier coefficients. Using the Shimura correspondence, we also give a decomposition of Hecke cusp forms of half integral weight k+1/2 with k even in terms of forms with rational Fourier coefficients, given by Rankin–Cohen brackets of theta series with Eisenstein series.     

Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in Rⁿ. Pointwise growth estimates for these integrals are given and the estimates are proved sharp in a strong sense. For decaying data, a new type of modified Poisson integral is introduced and used to develop asymptotic expansions for solutions of these half space problems.     

Least Squares Computations by Givens Transformations Without Square Roots

The use of Givens transformations and the QR decomposition tosolve linear least squares problems has several advantages,particularly when the design matrix is sparse or large. A modificationthat eliminates the square roots and reduces the number of multiplicationsby one half, as well as facilitating weighted least squaresat no extra cost, makes the method even more attractive.     

THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS

51.IntroductionandMainResultsInthispaper,weconsiderthestabilityoftheperiodicsolutionsofthefollowingsecondorderHamiltoniansystemswherenisapositiveillteger.V:Rxac-RisafUnctionandforT>0itisT-periodicforthevariablet.VJdenotesitsgradientwithrespecttox.Wenowstatethemainresultsofthispaper.Forthesuperquadraticcase)wehavethefollowingtwotheoremsTheorem1.1.SmposeVsatiSfiesthefollowingconditions:(VI)VEC'(RxR",R)andV(t T,x)=V(t,x),V(t,x)ERxR".(V2)ThereexistconstantSp>2andco>0suchthat0相似文献   

Grabbing the gold

Imagine a tree with some integer amount of gold at each vertex. Two players can play a game by taking turns removing leaves one by one and taking the gold from those leaves. We prove a recent conjecture of Micek and Walczak that says that if a tree has an even number of vertices, the first player can always secure at least half of the gold.     

Hyperbolic Fibrations and q-Clans

We show there is a bijection between regular hyperbolic fibrations with constant back half and normalized q-clans. Thus there is also a bijection with flocks of a quadratic cone, once a conic of the flock has been specified. This yields a plethora of two-dimensional translation planes of even and odd order which arise from spreads admitting a regular elliptic cover.     

Ultraspherical moments on a set of disjoint intervals

Moment evaluations are important for the study of non-classical orthogonal polynomial systems for which explicit representations are not known. In this paper we compute, in terms of the hypergeometric function, the moments associated with a generalized ultraspherical weight on a collection of intervals with two symmetric gaps. These moments, parametrized by the endpoints of the gaps, are identified as a one parameter deformation between the full range ultraspherical moments and the half range ultraspherical moments.     

Two-link billiard trajectories: extremal properties and stability

Two-link periodic trajectories of a plane convex billiard, when a point mass moves along a segment which is orthogonal to the boundary of the billiard at its end points, are considered. It is established that, if the caustic of the boundary lies within the billiard, then, in a typical situation, there is an even number of two-link trajectories and half of them are hyperbolic (and, consequently, unstable) and the other half are of elliptic type. An example is given of a billiard for which the caustic intersects the boundary and all of the two-link trajectories are hyperbolic. The analysis of the stability is based on an analysis of the extremum of a function of the length of a segment of a convex billiard which is orthogonal to the boundary at one of its ends.