Convexity is a classical idea. Archimedes used a version of convexity in his considerations of arc length. Yet the idea was not formalized until 1934 in the monograph of Bonneson and Fenchel [BOF]. The classical definition of convexity is this: An open domain Ω ⊆ R is convex if, whenever P,Q ∈ Ω, then the segment PQ connecting P to Q lies in Ω. We call this the synthetic definition of convexity...

This paper provides an overview of methods of masking microdata so that the data can be placed in public-use files. It divides the methods according to whether they have been demonstrated to provide analytic properties or not. For those methods that have been shown to provide one or two sets of analytic properties in the masked data, we indicate where the data may have limitations for most anal...

Landmark-based registration using radial basis functions (RBF) is an efficient and mathematically transparent method for the registration of medical images. To ensure invertibility and diffeomorphism of the RBF-based vector field, various regularization schemes have been suggested. Here, we report a novel analytic method of RBF regularization and demonstrate its power for Gaussian RBF. Our anal...

Brentano clearly asserts, in his Vienna lectures of 1887–1888, that descriptive psychology is an a priori or “exact” science. Since he rejects Kant's idea synthetic priori, this means the psychologist's laws are analytic. My aim paper to clarify and discuss view. I examine Brentano's epistemology Psychology from Empirical Standpoint then its later developments. conclude with difficulty inherent...

Block-design construction tasks reliably assess cognitive deficits due to brain injury. We examined the important aspects of this task with four experiments using normal subjects. Two problem-solving strategies are identified: an analytic strategy in which subjects mentally segment each block in the design to be constructed and a synthetic strategy, which involves wholistic pattern matching. Th...

Analytic functions represent the state-of-the-art way of performing complex data analysis within a single SQL statement. In particular, an important class of analytic functions that has been frequently used in commercial systems to support OLAP and decision support applications is the class of window functions. A window function returns for each input tuple a value derived from applying a funct...

We present an analytic model for the fully nonlinear power spectrum P and bispectrum Q of the cosmological mass density field. The model is based on physical properties of dark matter halos, with the three main model inputs being analytic halo density profiles, halo mass functions, and halo-halo spatial correlations, each of which has been well studied in the literature. We demonstrate that thi...

MicroRNAs are small (approximately 22 nt) RNAs that regulate gene expression and play important roles in both normal and disease physiology. The use of microarrays for global characterization of microRNA expression is becoming increasingly popular and has the potential to be a widely used and valuable research tool. However, microarray profiling of microRNA expression raises a number of data an...

We investigate the notion of an execution architecture in the setting of the program algebra PGA, and distinguish two sorts of these: analytic architectures, designed for the purpose of explanation and provided with a process-algebraic, compositional semantics, and synthetic architectures, focusing on how a program may be a physical part of an execution architecture. Then we discuss in detail t...