Privacy Preserving Probabilistic Record Linkage (P3RL): a novel method for linking existing health-related data and maintaining participant confidentiality.

BACKGROUND Record linkage of existing individual health care data is an efficient way to answer important epidemiological research questions. Reuse of individual health-related data faces several problems: Either a unique personal identifier, like social security number, is not available or non-unique person identifiable information, like names, are privacy protected and cannot be accessed. A solution to protect privacy in probabilistic record linkages is to encrypt these sensitive information. Unfortunately, encrypted hash codes of two names differ completely if the plain names differ only by a single character. Therefore, standard encryption methods cannot be applied. To overcome these challenges, we developed the Privacy Preserving Probabilistic Record Linkage (P3RL) method. METHODS In this Privacy Preserving Probabilistic Record Linkage method we apply a three-party protocol, with two sites collecting individual data and an independent trusted linkage center as the third partner. Our method consists of three main steps: pre-processing, encryption and probabilistic record linkage. Data pre-processing and encryption are done at the sites by local personnel. To guarantee similar quality and format of variables and identical encryption procedure at each site, the linkage center generates semi-automated pre-processing and encryption templates. To retrieve information (i.e. data structure) for the creation of templates without ever accessing plain person identifiable information, we introduced a novel method of data masking. Sensitive string variables are encrypted using Bloom filters, which enables calculation of similarity coefficients. For date variables, we developed special encryption procedures to handle the most common date errors. The linkage center performs probabilistic record linkage with encrypted person identifiable information and plain non-sensitive variables. RESULTS In this paper we describe step by step how to link existing health-related data using encryption methods to preserve privacy of persons in the study. CONCLUSION Privacy Preserving Probabilistic Record linkage expands record linkage facilities in settings where a unique identifier is unavailable and/or regulations restrict access to the non-unique person identifiable information needed to link existing health-related data sets. Automated pre-processing and encryption fully protect sensitive information ensuring participant confidentiality. This method is suitable not just for epidemiological research but also for any setting with similar challenges.

Preface : (Boundary Element Method) Computers and Structures 83 (2005)

The Boundary Element Method is a powerful numerical technique well rooted in everyday engineering practice. This is shown by boundary element methods included in the most important commercial computer packages and in the continuous publication of books composed to explain the features of the method to beginners or practicing engineers. Our first paper in Computers & Structures on Boundary Elements was published in 1979 (C & S 10, pp. 351–362), so this Special Issue is for us not only the accomplishment of our obligation to show other colleagues the possibilities of a numerical technique in which we believe, but also the celebration of our particular silver jubilee with this Journal.

Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Efficiency of the u,v method of estimation

Given a pool of motorists, how do we estimate the total intensity of those who had a prespecified number of traffic accidents in the past year? We previously have proposed the u,v method as a solution to estimation problems of this type. In this paper, we prove that the u,v method provides asymptotically efficient estimators in an important special case.

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

Sequence scanning: A method for rapid sequence acquisition from large-fragment DNA clones.

A strategy of "sequence scanning" is proposed for rapid acquisition of sequence from clones such as bacteriophage P1 clones, cosmids, or yeast artificial chromosomes. The approach makes use of a special vector, called LambdaScan, that reliably yields subclones with inserts in the size range 8-12 kb. A number of subclones, typically 96 or 192, are chosen at random, and the ends of the inserts are sequenced using vector-specific primers. Then long-range spectrum PCR is used to order and orient the clones. This combination of shotgun and directed sequencing results in a high-resolution physical map suitable for the identification of coding regions or for comparison of sequence organization among genomes. Computer simulations indicate that, for a target clone of 100 kb, the scanning of 192 subclones with sequencing reads as short as 350 bp results in an approximate ratio of 1:2:1 of regions of double-stranded sequence, single-stranded sequence, and gaps. Longer sequencing reads tip the ratio strongly toward increased double-stranded sequence.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

Jacobi Cujacij ... Opera omnia in decem tomos distributa quibus continentur tam priora, sive quae ipse superstes edi curavit : quam posteriora, sive quae post obitum ejus edita sunt; jam à Carolo Annibale Fabroto J. C. disposita. Accessere in hac novissima editione ab eruditissimo viro graecorum versio locorum hactenus ab omnibus desiderata ... praeterea dissertatio Emundi Merillii, & interpretatio ab eodem facta variantium ex Cujacio observatarum, quae per totum opus suo quae que loco variante notantur; postremo controversiae Joannis Roberti ejusdemque notae in responsiones à Cujacio nomine Antonii Mercatoris editas; quae majori eruditorum commodo in ipsis observationibus afferuntur, studio & diligentia Liborj Ranii ...

Binder's title: Civiacii opera, tom. XI.

D. Philippi Jacobi Speneri Operis heraldici, pars generalis & specialis.

Each volume has also an added t.p., engraved, dated 1690 and 1680, respectively.

A new and easy method of learning Hebrew without points. : To which is annex'd, by way of praxis, The book of Proverbs, divided according to the metre: with the masoretical reading in Roman letters, the interlinear version of Santes Pagninus, &c. A grammatical analysis, and short notes critical and explanatory ... /

Errata: p. [2]-[3] at end.

The chirurgical works of Percivall Pott, with his last corrections. : to which are added, a short account of the life of the author, a method of curing the hydrocele by injection, and occasional notes and observations /

Published in London in 1771 and 1808.

The gentleman's recreation : in four parts, viz. hunting, hawking, fowling, fishing ; wherein those ... exercises are largely treated of, and the terms of art for hunting and hawking more amply enlarged ... : also the method of breeding and managing a hunting-horse: unto which is now annex'd an appendix of choice receipts for the cure of several maladies : whereto is added, a perfect abstract of all the forest-laws, and of every particular act of Parliament since Magna charta ... to which is prefix'd a large sculpture, giving easy directions for blowing the horn : and other sculptures proper to each recreation, /

The "Forest laws" have special t.p.: An abridgment of Manwood's forest law and of all the acts of Parliament ... which related to hunting, hawking, fishing or fowling. London : Printed by H.P. for N.C., 1721.

The English malady, or, A treatise of nervous diseases of all kinds : as spleen, vapours, lowness of spirits, hypochondriacal, and hysterical distempers, &c., in three parts: Part I. Of the nature and cause of nervous distempers : Part II. Of the cure of nervous distempers : Part III. Variety of cases that illustrate and confirm the method of cure : with the author's own case at large /

Each part has special title page.

A compendium of the anatomy of the human body : intended principally for the use of students ... This edition is prefixed with A compendious history of anatomy, and The Ruyschian art and method of making preparations to exhibit the structure of the human body, illustrated with a representation of the quicksilver tray and its appendages, which is not in the London edition.

"A compendious history of anatomy" and "The Ruyschian art and method of making preparations to exhibit the structure of the human body" (32 p. at front of v. 1) are by Robert Hooper, and are reprinted, with slight changes in text, from his The anatomist's vade-mecum, 4th ed., London, 1802.