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Professor Dresden called to our attention the following theorem :
If S1, S2, … , Sm are m line segments parallel to the y-axis, all of equal lengths, whose projections on the x-axis are equally spaced, and if we assume that a straight line can be made to intersect every set of three among these segments, then there exists a straight line intersecting all the segments.
One of the authors having just presented Cauchy's theorem on convex polyhedra to a class on “Convexity” at the University of Wisconsin, a discussion on Cauchy's lemma on convex polygons led to an exchange of letters which are here reproduced. The three letters are independently readable. Two new proofs of Cauchy's lemma are given, of which the second (§3) is very short.
We shall say that a plane set D has the Kakeya property if a unit segment can be turned continuously in D through 360° back to its original position. The famous solution of this problem by A. S. Besicovitch (1; 2; 4; 5; 6), to the effect that there are sets of arbitrarily small area having the Kayeka property, leaves open the problem obtained by adding the new condition that the set D be also simply connected. Since we do not know whether there is an attainable minimum, we define the Kakeya constant K to be the greatest lower bound of areas of simply connected sets having the Kakeya property. We shall refer to such sets as Kakeya sets.
The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.
The following report, which has been drawn up partly on the basis of the reports of the members of the Commission, touches briefly and without any attempt at completeness a few points of the recent developments in certain important fields falling within the domain of the Commission.
Electronic communications, as well as other categories of interactions within social networks, exhibit bursts of activity localised in time. We adopt a self-exciting Hawkes process model for this behaviour. First we investigate parameter estimation of such processes and find that, in the parameter regime we encounter, the choice of triggering function is not as important as getting the correct parameters once a choice is made. Then we present a relaxed maximum likelihood method for filling in missing data in records of communications in social networks. Our optimisation algorithm adapts a recent curvilinear search method to handle inequality constraints and a non-vanishing derivative. Finally we demonstrate the method using a data set composed of email records from a social network based at the United States Military Academy. The method performs differently on this data and data from simulations, but the performance degrades only slightly as more information is removed. The ability to fill in large blocks of missing social network data has implications for security, surveillance, and privacy.
Hyperemesis gravidarum (HG), severe nausea and vomiting of pregnancy, is characterized by prolonged maternal stress, undernutrition and dehydration. Maternal stress and malnutrition of pregnancy are linked to poor neonatal outcome and associated with poor adult health, and we recently showed that in utero exposure to HG may lead to increased risks of psychological and behavioral disorders in the offspring. In addition, we have shown familial aggregation of HG, which is strong evidence for a genetic component to the disease. In this study, we compare the rates of psychological and behavioral disorders in 172 adults with and 101 adults without a sibling with HG. The rate of emotional/behavioral disorders is identical (15%) in both groups. The results suggest that the etiology of HG is not likely to include genetic factors associated with emotional and behavioral disorders. In addition, this study provides evidence that the increased incidence of psychological/behavioral disorders among offspring of women with HG is attributable to the HG pregnancy itself, rather than to confounding genetic factors linked to HG.
Using ab-initio calculations and kinetic Monte Carlo simulations, we demonstrate that the deposition geometries of palladium are strongly dependent on the polarization direction of the LiNbO3 substrate. Different stoichiometries and atomic structures of the positively and the negatively polarized substrates cause substantially different bonding configurations of palladium and energy barriers for the movement of Pd clusters. Our simulations predict that palladium atoms form bulky clusters on the positive surface, while they are deposited in a dispersed or planar manner on the negative surface at moderate temperature. We suggest that Inoue and coworkers’ observation [J. Phys. Chem.88, 1148 (1984)] that the catalytic activity of palladium depends on polarization direction of LiNbO3 substrate is, at least in part, due to differences in the geometric structures of palladium and the LiNbO3 surface.
This note pursues two aims: the first is historical and the second is factual.
1. We present James Stirling's discovery (1730) that Newton's general interpolation series with divided differences simplifies if the points of interpolation form a geometric progression. For its most important case of extrapolation at the origin. Karl Schellbach (1864) develops his algorithm of q-differences that also leads naturally to theta-functions. Carl Runge (1891) solves the same extrapolation at the origin, without referring to the Stirling-Schellbach algorithm. Instead, Runge uses “Richardson's deferred approach to the limit” 20 years before Richardson.
2. Recently, the author found a close connection to Romberg's quadrature formula in terms of “binary” trapezoidal sums. It is shown that the problems of Stirling, Schellbach, and Runge, are elegantly solved by Romberg's algorithm. Numerical examples are given briefly. Fuller numerical details can be found in the author's MRC T.S. Report #2173, December 1980, Madison, Wisconsin. Thanks are due to the referee for suggesting the present stream-lined version.
Hyperemesis gravidarum (HG), severe nausea and vomiting of pregnancy, is characterized by long-term maternal stress, undernutrition and dehydration. While maternal stress and malnutrition of pregnancy are linked to poor neonatal outcome and associated with poor adult health, long-term outcome of fetal exposure to HG has never been explored. The purpose of this study is to determine whether long-term emotional and behavioral diagnoses may be associated with fetal exposure to HG. Emotional and behavioral diagnoses of adults born of a pregnancy complicated by HG were compared to diagnoses from non-exposed controls. Offspring exposed to HG in utero were significantly more likely to have a psychological and behavioral disorder (OR = 3.6, P < 0.0001) with diagnoses primarily of depression, bipolar disorder and anxiety. In utero exposure to HG may lead to increased risks of psychological and behavioral disorders in the offspring.
In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.
We met in Ottawa—my brother Ronald and I from Los Angeles and my sister Nuria Nono from Venice—to inaugurate the Canadian presentation of a multimedia exhibition that we had produced about our father, in the hope that it would inspire others to learn about his life and works. Professor James Wright invited us to Ottawa to open the exhibition, which he had rescued from the east coast of the United States, and to attend a concert series and symposium devoted to our father's work, hosted by Carleton University. We were all impressed by the schedule of events and felt that through the comprehensive presentation of lectures, concerts, and the exhibition, others would have the opportunity to experience the breadth of our father's life and works. Professor Wright had not only transferred the multi-media exhibition to Canada but had organized an imposing series of events that would encourage the performance and study of Arnold Schoenberg's compositions. Canada has a history of being Schoenbergfriendly (one thinks of the film producer Larry Weinstein, and, of course, Glenn Gould, among others), and our family was delighted to accept this invitation to take part in the events, and to visit Ottawa for the first time.
The presentations by participants from Canada, the United States, Austria, and Australia were consistently engaging and excellent. As a non-musicologist, I acknowledge that I prefer listening to music about words rather than words about music. But the combination of lectures and performances resulted in an altogether satisfying and music-enhancing experience.
Our family contribution included the opportunity to add a personal touch to the proceedings by discussing our early memories of growing up in Los Angeles. Following the chamber music theme we were able to recall the many visiting performers and ensembles that had performed in our home. But we also revealed the music that we sang together—our ladies club and gentleman's anthems, of course composed by our father, and a special song that he had written for Nuria (the “Nullele-Pullele” lied). And we had the opportunity to discuss and display the many games that he made for us, the tennis scoring system which he developed for my brother in order to help them both analyze the match, and some of his “tinkering” inventions.
The origin and spread of money-based commodity markets is normally attributed to a natural evolution from barter and is usually seen as a solution to problems of exchange. I want to propose that markets to a considerable degree develop historically out of a different set of dynamics. These are concerned with the state-building tasks of territorial conquest and control, and are closely related to specific modes of war fighting. In this connection, markets develop not only to facilitate exchange per se but also to facilitate the mobilization of resources and their management across space and time. This need to manage resources geographically and temporally contributes not only to the spread of commodity markets but also to the development of markets in land and in labor.
Christian Dustmann, Professor of Economics University College, London; Director Centre for Research and Analysis on Migration (CReAM), UK,
Uta Schoenberg, Assistant Professor of Economics University of Rochester, UK
Competitiveness and performance of national economies is inherently linked to the productivity of their workforces. Some of this productivity is created by full-time primary, secondary, and postsecondary education. A significant part is built up later when workers participate in the workforce. With strong complementarities between technology and skills, training and education is now being considered as a key factor in global competitiveness. Industrialized countries seek to improve, and are willing to substantially invest in, their education and training institutions.
Only recently, the Organisation for Economic Co-operation and Development (OECD) Programme for International Student Assessment study has led to critical scrutiny of primary and secondary education systems in those countries that achieved relatively low scores, and triggered a wave of research and reform suggestions (see, e.g., Fertig & Schmidt, 2002; Fertig, 2003). At least equally important are postsecondary education schemes. Although primary and secondary education provides skills that are largely general and provide mostly academic knowledge, postsecondary schemes are tailored toward specialization, and often toward provision of skills that are specific to the needs and requirements of particular labor markets.
There are large differences between postsecondary education systems across industrialized countries. For instance, in the Anglo-Saxon countries, postsecondary education is usually state provided, through universities, colleges, and vocational schools. There is some concern about the emphasis on the academic bias of this system, with school-based vocational training schemes and specialized colleges not being able to provide workers with the “hands-on” skills the labor market requires.
This paper presents empirical evidence concerning the finite sample performance of conventional and generalized empirical likelihood–type estimators that utilize instruments in the context of linear structural models characterized by endogenous explanatory variables. There are suggestions in the literature that traditional and nontraditional asymptotically efficient estimators based on moment equations may, for the relatively small sample sizes usually encountered in econometric practice, have relatively large biases and/or variances and provide an inadequate basis for estimation and inference. Given this uncertainty we use a range of data sampling processes and Monte Carlo sampling procedures to accumulate finite sample empirical evidence concerning these questions for a family of generalized empirical likelihood–type estimators in comparison to conventional 2SLS and GMM estimators. Solutions to EL-type empirical moment-constrained optimization problems present formidable numerical challenges. We identify effective optimization algorithms for meeting these challenges.
It is known in the literature that a number of moment-based estimators for the linear structural model are asymptotically normally distributed and mutually asymptotically equivalent. There is also a growing body of evidence (see, for example, Newey and Smith 2004 and the references therein) that traditional asymptotically efficient moment-based estimators may exhibit large biases and/or variances when applied to the relatively small samples usually encountered in applied economic research.
Econometric models that specify a set of moment-orthogonality conditions relating to the underlying data sampling process, and involving parameters, data outcomes, and model noise, lead to a corresponding set of unbiased empirical estimating functions. These estimating functions often involve instrumental variables (IV), whose number exceeds the number of unknown parameters of interest and overdetermines the model parameters.
Repeated neuropsychological assessments are common with older adults,
and the determination of clinically significant change across time is
an important issue. Regression-based prediction formulas have been
utilized with other patient and healthy control samples to predict
follow-up test performance based on initial performance and demographic
variables. Comparisons between predicted and observed follow-up
performances can assist clinicians in determining the significance of
change in the individual patient. In the current study, multiple
regression-based prediction equations for the 5 Indexes and Total Score
of the RBANS were developed for a sample of 223 community dwelling
older adults. These algorithms were then validated on a separate
elderly sample (N = 222). Minimal differences were present
between observed and predicted follow-up scores in the validation
sample, suggesting that the prediction formulas are clinically useful
for practitioners who assess older adults. A case example is presented
that illustrates how the algorithms can be used clinically.
(JINS, 2004, 10, 828–834.)
We conducted the first seroepidemiological study to evaluate the exposure of zoo animals to Borrelia burgdorferi s.l. in German zoos and wildlife parks. A total of 1487 individuals representing 148 ungulate and carnivore species belonging to 19 families were examined using a non-species dependent ELISA. Specific antibodies were detected in 154 (10·4%) animals; 168 (11·3%) sera produced borderline results. The percentage of seropositive individuals was related to species and origin (zoo), and increased with age of the animals. Sex and season did not influence seroprevalence. Examination of 600 ticks (Ixodes ricinus; caught from vegetation in the zoos) by darkfield microscopy and indirect immunofluorescence technique revealed infection rates within the range typical for Central Europe. The results substantiate that there is an infection risk for zoo animals. A differential diagnosis of Lyme borreliosis should be taken into account in case of suspicious clinical symptoms and possible contact to ticks.
The poly(A)-limiting element (PLE) is a cis-acting
sequence that acts to limit poly(A) tail length on pre-mRNA
to <20 nt. Functional PLEs are present in a number of
genes, underscoring the generality of this control mechanism.
The current study sought to define further the position
requirements for poly(A) length regulation and the core
sequence that comprises a PLE. Increasing the spacing between
the PLE and the upstream 3′ splice site or between
the PLE and the downstream AAUAAA had no effect on poly(A)
length control. However, moving the PLE from the terminal
exon to either an upstream exon or intron eliminated poly(A)
length control. Poly(A) length control was further evaluated
using a battery of constructs in which the PLE was maintained
in the terminal exon, but where upstream introns were either
deleted, modified, or replaced with a polypyrimidine tract.
Poly(A) length control was retained in all cases, indicating
that the key feature is the presence of the PLE in the
terminal exon. A battery of mutations demonstrated the
importance of the 5′ pyrimidine-rich portion of the
element. Finally, UV crosslinking experiments identified
an ∼62-kDa protein in Hela nuclear extract that binds
to a wild-type 23-nt PLE RNA oligonucleotides but not to
a mutated nonfunctional form of the element.