Neither ātman Nor anattā: Tapering Our Conception of Selfhood

I provide critical discussion of conception of and talk of psychic integration which I take to be both excessive and deficient; these viciously extreme positions are championed by the Apostle Paul and St. Augustine (and both their religious and their secular cultural descendants in the West), and by Jacques Lacan and María Lugones (and their contemporaries), respectively. I suggest that we must negotiate a Buddhist-inspired understanding located between these extremes in endorsing any acceptable conception of the self, generally speaking—a conception which, contra the strong antirealist about selves, allows for the continued use of selfhood in everyday discourse, but which, contra the strong realist about selves, does not fall into an unhealthy idealization of anything approximating perfect psychic wholeness

Transients from Initial Conditions: A Perturbative Analysis

The standard procedure to generate initial conditions (IC) in numerical simulations is to use the Zel'dovich approximation (ZA). Although the ZA correctly reproduces the linear growing modes of density and velocity perturbations, non-linear growth is inaccurately represented because of the ZA failure to conserve momentum. This implies that it takes time for the actual dynamics to establish the correct statistical properties of density and velocity fields. We extend perturbation theory (PT) to include transients as non-linear excitations of decaying modes caused by the IC. We focus on higher-order statistics of the density contrast and velocity divergence, characterized by the S_p and T_p parameters. We find that the time-scale of transients is determined, at a given order p, by the spectral index n. The skewness factor S_3 (T_3) attains 10% accuracy only after a=6 (a=15) for n=0, whereas higher (lower) n demands more (less) expansion away from the IC. These requirements become much more stringent as p increases. An Omega=0.3 model requires a factor of two larger expansion than an Omega=1 model to reduce transients by the same amount. The predicted transients in S_p are in good agreement with numerical simulations. More accurate IC can be achieved by using 2nd order Lagrangian PT (2LPT), which reproduces growing modes up to 2nd order and thus eliminates transients in the skewness. We show that for p>3 this reduces the required expansion by more than an order of magnitude compared to the ZA. Setting up 2LPT IC only requires minimal, inexpensive changes to ZA codes. We suggest simple steps for its implementation.Comment: 37 pages, 10 figure

Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces

Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this paper, we give another construction of these bases and, mainly, we show that the bases even form complete orthogonal Appell systems. Moreover, we study the corresponding Taylor series expansions. As an application, we construct quite explicitly orthogonal bases for homogeneous solutions of an arbitrary generalized Moisil-Theodoresco system.Comment: submitte

Random sets of isomorphism of linear operators on Hilbert space

This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets of the basis so that $T$ restricted to their span is a nice isomorphism. Our main result is a dimension-free optimal estimate of the size of $\Sigma(T)$. It improves and extends in several ways the principle of restricted invertibility due to Bourgain and Tzafriri. With an appropriate notion of randomness, we obtain a randomized principle of restricted invertibility.Comment: Published at http://dx.doi.org/10.1214/074921706000000815 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Isoperimetry of waists and local versus global asymptotic convex geometries

Existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of random rotations of K and L is nicely bounded. For L = subspace, this main result immediately yields the unexpected phenomenon: "If K has one nicely bounded section, then most sections of K are nicely bounded". This 'existence implies randomness' consequence was proved independently in [Giannopoulos, Milman and Tsolomitis]. The main result represents a new connection between the local asymptotic convex geometry (study of sections of convex bodies) and the global asymptotic convex geometry (study of convex bodies as a whole). The method relies on the new 'isoperimetry of waists' on the sphere due to Gromov

Image database system for glaucoma diagnosis support

Tato práce popisuje přehled standardních a pokročilých metod používaných k diagnose glaukomu v ranném stádiu. Na základě teoretických poznatků je implementován internetově orientovaný informační systém pro oční lékaře, který má tři hlavní cíle. Prvním cílem je možnost sdílení osobních dat konkrétního pacienta bez nutnosti posílat tato data internetem. Druhým cílem je vytvořit účet pacienta založený na kompletním očním vyšetření. Posledním cílem je aplikovat algoritmus pro registraci intenzitního a barevného fundus obrazu a na jeho základě vytvořit internetově orientovanou tři-dimenzionální vizualizaci optického disku. Tato práce je součásti DAAD spolupráce mezi Ústavem Biomedicínského Inženýrství, Vysokého Učení Technického v Brně, Oční klinikou v Erlangenu a Ústavem Informačních Technologií, Friedrich-Alexander University, Erlangen-Nurnberg.This master thesis describes a conception of standard and advanced eye examination methods used for glaucoma diagnosis in its early stage. According to the theoretical knowledge, a web based information system for ophthalmologists with three main aims is implemented. The first aim is the possibility to share medical data of a concrete patient without sending his personal data through the Internet. The second aim is to create a patient account based on a complete eye examination procedure. The last aim is to improve the HRT diagnostic method with an image registration algorithm for the fundus and intensity images and create an optic nerve head web based 3D visualization. This master thesis is a part of project based on DAAD co-operation between Department of Biomedical Engineering, Brno University of Technology, Eye Clinic in Erlangen and Department of Computer Science, Friedrich-Alexander University, Erlangen-Nurnberg.