On the total curvatures of a tame function

Given a definable function f, enough differentiable, we study the continuity of the total curvature function t --> K(t), total curvature of the level {f=t}, and the total absolute curvature function t-->|K| (t), total absolute curvature of the level {f=t}. We show they admits at most finitely many discontinuities

Development after international adoption

This thesis examined the development of adopted children to shed more light on the effects of deprivation on child development and the potential for catch-up and recovery after placement in the more advantageous environment of an adoptive family. In the first part of the thesis a meta-analysis is presented in which we compared adopted children’s attachment relationships with the normative attachment distribution of nonadopted children raised by their biological parents, and - as a comparison - we also compared the attachment distribution of foster children with the normative distribution. The second and third parts of the thesis focus on the development of former foster and post-institutionalized children, 11 to 16 months old at arrival, two and six months after their adoption from China. Several salient developmental domains were studied: attachment, cognitive and motor development, physical growth, stress regulation, and social-emotional behavior.LEI Universiteit LeidenNetherlands Organization for Scientific Research (NWO 400-03-208). Additional support was received from Wereldkinderen, and for the meta-analysis described in Chapter 2 from VSBfonds, Fonds Psychische Gezondheid, and Stichting Kinderpostzegels Nederland.FSW - Gezinsopvoeding - Ou

Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.Comment: 20 page

Monotone functions and maps

In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R^n. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equivalent conditions for a bounded continuous definable function or map to be monotone. We show that the class of graphs of monotone maps is closed under intersections with affine coordinate subspaces and projections to coordinate subspaces. We prove that the graph of a monotone map is a topologically regular cell. These results generalize and expand the corresponding results obtained in Basu et al. for semi-monotone sets.Comment: 30 pages. Version 2 appeared in RACSAM. In version 3 Corollaries 1 and 2 were corrected. In version 4 Theorem 3 is correcte

\Lambda-buildings and base change functors

We prove an analog of the base change functor of \Lambda-trees in the setting of generalized affine buildings. The proof is mainly based on local and global combinatorics of the associated spherical buildings. As an application we obtain that the class of generalized affine building is closed under ultracones and asymptotic cones. Other applications involve a complex of groups decompositions and fixed point theorems for certain classes of generalized affine buildings.Comment: revised version, 29 pages, to appear in Geom. Dedicat

Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla

Euler-Bessel and Euler-Fourier Transforms

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible \zed-valued functions to continuous $\real$-valued functions over a vector space. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the logarithmic blowup of the topological Fourier transform; and a novel Morse index formula for the transforms. We then apply the theory to problems of target reconstruction from enumerative sensor data, including localization and shape discrimination. This last application utilizes an extension of spatially variant apodization (SVA) to mitigate sidelobe phenomena