Metamorphosis of images in reproducing kernel Hilbert spaces

Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the practical application of metamorphosis is a numerical method based on shooting from the initial momentum, as this would enable the use of statistical methods based on this momentum, as well as the estimation of templates from hyper-templates using morphing. In this paper we introduce a shooting method, in the particular case of morphing images that lie in a reproducing kernel Hilbert space (RKHS). We derive the relevant shooting equations from a Lagrangian frame of reference, present the details of the numerical approach, and illustrate the method through morphing of some simple images.     

Testing for Unit Roots in a Nearly Nonstationary Spatial Autoregressive Process

The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model _st= _s-1,t+_s,t-1- _s-1,t-1+_st. Moreover, for the sequence _n = e ^c/n , _n = e ^d/n of local Pitman-type alternatives, the limiting distribution of the normalized periodogram ordinate is shown to be a linear combination of two independent chi-square random variables whose coefficients depend on c and d. This result is used to tabulate the asymptotic power of a test for various values of c and d. A comparison is made between the periodogram test and a spatial domain test.     

Concentration of area in half-planes

For the standard class of normalized univalent functions analytic in the unit disk , we consider a problem on the minimal area of the image concentrated in any given half-plane. This question is related to a well-known problem posed by A. W. Goodman in 1949 that regards minimizing area covered by analytic univalent functions under certain geometric constraints. An interesting aspect of this problem is the unexpected behavior of the candidates for extremal functions constructed via geometric considerations.

     

Integrating modes of policy analysis and strategic management practice: requisite elements and dilemmas

There is a need to bring methods to bear on public problems that are inclusive, analytic, and quick. This paper describes the efforts of three pairs of academics working from three different though complementary theoretical foundations and intervention backgrounds (ie ways of working) who set out together to meet this challenge. Each of the three pairs had conducted dozens of interventions that had been regarded as successful or very successful by the client groups in dealing with complex policy and strategic problems. One approach focused on leadership issues and stakeholders, another on negotiating competitive strategic intent with attention to stakeholder responses, and the third on analysis of feedback ramifications in developing policies. This paper describes the 10-year longitudinal research project designed to address the above challenge. The important outcomes are reported: the requisite elements of a general integrated approach and the enduring puzzles and tensions that arose from seeking to design a wide-ranging multi-method approach.     

Convexity and the Average Curvature of Plane Curves

The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve D which bounds the convex set.     

Genetics in primary care: a USA faculty development initiative

The Genetics in Primary Care (GPC) project is a USA national faculty development initiative with the goal of enhancing the training of medical students and primary care residents by developing primary care faculty expertise in genetics. Educational strategies were developed for the project by an executive committee with input from an advisory committee, comprising individuals with primary care, medical education and genetics expertise. These committees identified the key issues in genetics education for primary care as (1) considering inherited disease in the differential diagnosis of common disorders; (2) using appropriate counseling strategies for genetic testing and diagnosis, and (3) understanding the implications of a genetic diagnosis for family members. The group emphasized the importance of a primary care perspective, which suggests that the clinical utility of genetic information is greatest when it has the potential to improve health outcomes. The group also noted that clinical practice already incorporates the use of family history information, providing a basis for discussing the application of genetic concepts in primary care. Genetics and primary care experts agreed that educational efforts will be most successful if they are integrated into existing primary care teaching programs, and use a case-based teaching format that incorporates both clinical and social dimensions of genetic disorders. Three core clinical skills were identified: (1) interpreting family history; (2) recognizing the variable clinical utility of genetic information, and (3) acquiring cultural competency. Three areas of potential controversy were identified as well: (1) the role of nondirective counseling versus shared decision-making in discussions of genetic testing; (2) the intrinsic value of genetic information when it does not influence health outcomes, and (3) indications for a genetics referral. The project provides an opportunity for ongoing discussion about these important issues.     

A Districtwide Study of Automaticity When Included in Concept‐Based Elementary School Mathematics Instruction

While conceptual understanding of properties, operations, and the base‐ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three elementary schools in a school district implements mandatory automaticity drills for 10 minutes each day while the remaining two elementary schools, with the same curriculum and very similar demographics, do not. This study looks at (a) the impact that schoolwide implementation of automaticity drills has on schoolwide computational math skills as measured by the ITBS and (b) the relationship between automaticity and conceptual understanding as measured by statewide standardized testing. The results suggest that while there may be an association between automaticity and higher performance on standardized tests, caution should be taken before assuming there are benefits to promoting automaticity drills. These results are consistent with those that support a process‐driven approach to automaticity based on familiarity with properties and strategies associated with the base‐ten number system; they are not consistent with those that support an answer‐driven approach to automaticity based on memorization of answers.     

Pompeiu sets in compact Heisenberg manifolds

A necessary and sufficient condition is presented for a set to be a Pompeiu subset of any compact homogeneous space with a finite invariant measure. The condition, which is expressed in terms of the intertwining operators of each primary summand of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds. Examples are presented demonstrating that the condition to be Pompeiu in these manifolds is quite different from the corresponding condition for a torus of the same dimension. This provides a contrast with the existing comparison between the Heisenberg group itself and Euclidean space in terms of Pompeiu sets. In addition, the closed linear span of all translates of any square integrable function on any compact homogeneous space is determined.