Purdue University

About: Purdue University is a education organization based out in West Lafayette, Indiana, United States. It is known for research contribution in the topics: Population & Context (language use). The organization has 73219 authors who have published 163563 publications receiving 5775236 citations. The organization is also known as: Purdue & Purdue-West Lafayette.

Rings, Modules, and Algebras in Stable Homotopy Theory

Abstract: Introduction Prologue: the category of ${\mathbb L}$-spectra Structured ring and module spectra The homotopy theory of $R$-modules The algebraic theory of $R$-modules $R$-ring spectra and the specialization to $MU$ Algebraic $K$-theory of $S$-algebras $R$-algebras and topological model categories Bousfield localizations of $R$-modules and algebras Topological Hochschild homology and cohomology Some basic constructions on spectra Spaces of linear isometries and technical theorems The monadic bar construction Epilogue: The category of ${\mathbb L}$-spectra under $S$ Appendix A. Twisted half-smash products and function spectra Bibliography Index.

Migration and distribution of two populations of hippocampal granule cell precursors during the perinatal and postnatal periods.

Abstract: Methacrylate-embedded sections and short-survival thymidine radiograms of the hippocampal dentate gyrus were examined in perinatal and postnatal rats in order to trace the site of origin and migration of the precursors of granule cells and study the morphogenesis of the granular layer. The densely packed, spindle-shaped cells of the secondary dentate matrix (a derivative of the primary dentate neuroepithelium) stream in a subpial position towards the granular layer of the internal dentate limb during the perinatal and early postnatal periods. By an accretionary process, the crest of the granular layer forms on day E21 and on the subsequent days the granular layer of the internal dentate limb expands progressively in a lateral direction. Granule cells differentiation, as judged by the transformation of polymorph, darkly staining small cells into rounder, lightly staining larger granule cells, follows the same gradient from the external dentate limb to the internal dentate limb. The secondary dentate matrix is in a process of dissolution by day P5. This matrix is the source of what will later become the outer shell of the granular layer composed of early generated granule cells. The thicker inner shell of the granular layer, formed during the infantile and juvenile periods, derives from an intrinsic, tertiary germinal matrix. On day E22, the dentate migration of the secondary dentate matrix becomes partitioned into two components: (a) the subpial component of extradentate origin, referred to in this context as the first dentate migration, and (b) the second dentate migration. The latter is distributed in the basal polymorph layer throughout the entire dentate gyrus and is henceforth recognized as the tertiary dentate matrix. The tertiary dentate matrix is prominent between days P3 and P10. It is postulated that the great increase in granule cell population during the infantile period is principally due to cells derived from this intrinsic matrix of the dentate gyrus. Between days P20 and P30 the tertiary dentate matrix disappears in the basal polymorph layer and henceforth proliferative cells become largely confined to the subgranular zone at the base of the granular layer. The subgranular zone is the source of granule cells produced during the juvenile and adult periods.

Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage

Abstract: This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following problem. Given an image F defined on a square I, minimize over all g in the Besov space B11(L1(I)) the functional |F-g|L2(I)2+λ|g|(B11(L1(I))). We use the theory of nonlinear wavelet image compression in L2(I) to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i.i.d., mean zero, Gaussian noise. A new signal-to-noise ratio (SNR), which we claim more accurately reflects the visual perception of noise in images, arises in this derivation. We present extensive computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one knows (or can estimate) only two parameters about an image F: the largest α for which F∈Bqα(Lq(I)),1/q=α/2+1/2, and the norm |F|Bqα(Lq(I)). Both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than Donoho and Johnstone's VisuShrink procedure; an example suggests, however, that Donoho and Johnstone's (1994, 1995, 1996) SureShrink method, which uses a different shrinkage parameter for each dyadic level, achieves a lower error than our procedure.