Reducible von Neumann models and uniqueness

This paper can be regarded as a result of basic research on the technological characteristics of the von Neumann models and their consequences. It introduces a new taxonomy of reducible technologies, explores their key distinguishing features, and specifies which ones ensure the uniqueness of von Neumann equilibrium. A comprehensive comparison is also given between the familiar (in)decomposability ideas and the reducibility concepts suggested here. All these are carried out with a modern approach. Simultaneously, the reader may also acquire a complete picture of and guidance on the fundamental von Neumann models here.

Vállalatok egy Neumann-típusú gazdaságban (Firms in a Neumann’s model economy)

A dolgozat a klasszikusnak tekinthető Neumann-féle növekedési modell egy új alapra helyezését tartalmazza. Az eredeti Neumann-modellben expliciten vállalatok nem szerepelnek, csak technológiák vagy eljárások. A dolgozat egy olyan Neumann-típusú modellt vizsgál, amelyben az egyes technológiáknak vállalatokat feleltet meg, és azt vizsgálja, hogy ilyen feltételezés mellett egy ilyen gazdaságban léteznek-e olyan megoldások, amelyek mellett a vállalatok maximalizálják a nyereségüket. Ennek vizsgálata közben arra az eredményre juthatunk, hogy erre az esetre a klasszikus Neumann-modell által feltételezett nempozitív nyereséget felül kell vizsgálni, ami a klasszikus matematikai közgazdaságtan dualitáson alapuló alapfeltételezése. ______ The paper investigates a generalization of the classical growth model of John von Neumann. There are only technologies in model of von Neumann. The aim of the paper is to rename technologies as firms and it is analyzed whether there exist equilibrium prices and quantities for firms to maximize the total profit. The paper reexamines the classical assumption about the duality of prices, i.e. it is allowed a nonnegative profit of firms.

Bródy András és a dualitás matematikai elmélete. A gazdasági növekedés Neumann-modellje

A dolgozat megírására két váratlan esemény egyidejű bekövetkezése ösztönzött. Az első nagy örömömre szolgált, a második azonban nagy szomorúsággal tölt el. Az örömteli és megtisztelő esemény Zalai Ernő felkérése volt arra, hogy véleményezzem a Közgazdasági Szemlében megjelent kiváló, a Neumann-modellel foglalkozó dolgozatát. Mivel a Zalai Ernő által vezetett kutatások kapcsán a témával én is foglalkoztam korábban, a felkérésnek, amint tudtam, eleget tettem. A dolgozat olvasása közben kaptam a hírt: Bródy András immáron nincsen közöttünk. A váratlan és tragikus hír azért is megrázó volt, mert Zalai Ernő dolgozata éppen azokat a kérdéseket feszegette, amelyeket először Bródy András vetett fel, és amelyek kiváló és máig páratlanul szellemes vizsgálatával közel harminc évvel ezelőtt Bródy András engem is a téma tanulmányozására inspirált.

Neumann versus Leontief. Két modell – két gazdaságkép (Neumann vs Leontief. Two models, two approaches to the economy)

A szerző a tisztán elméleti célokra kifejlesztett Neumann-modellt és a gyakorlati alkalmazások céljára kifejlesztett Leontief-modellt veti össze. A Neumann-modell és a Leontief-modell éves termelési periódust feltételező, zárt, stacionárius változatának hasonló matematikai struktúrája azt a feltételezést sugallja, hogy az utóbbi a Neumann-modell sajátos eseteként értelmezhető. Az egyes modellek közgazdasági tartalmát és feltevéseit részletesen kibontva és egymással összevetve a szerző megmutatja, hogy a fenti következtetés félrevezető, két merőben különböző modellről van szó, nem lehet az egyikből a másikat levezetni. Az ikertermelés és technológiai választék lehetősége a Neumann-modell elengedhetetlen feltevése, az éves termelési periódus feltevése pedig kizárja folyam jellegű kibocsátások explicit figyelembevételét. Mindezek feltevések ugyanakkor idegenek a Leontief-modelltől. A két modell valójában egy általánosabb állomány–folyam jellegű zárt, stacionárius modell sajátos esete, méghozzá azok folyamváltozókra redukált alakja. _____ The paper compares the basic assumptions and methodology of the Von Neumann model, developed for purely abstract theoretical purposes, and those of the Leontief model, designed originally for practical applications. Study of the similar mathematical structures of the Von Neumann model and the closed, stationary Leontief model, with a unit length of production period, often leads to the false conclusion that the latter is just a simplified version of the former. It is argued that the economic assumptions of the two models are quite different, which makes such an assertion unfounded. Technical choice and joint production are indispensable features of the Von Neumann model, and the assumption of unitary length of production period excludes the possibility of taking service flows explicitly into account. All these features are completely alien to the Leontief model, however. It is shown that the two models are in fact special cases of a more general stock-flow stationary model, reduced to forms containing only flow variables.

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Automatically Evolving Rotation-invariant Texture Image Descriptors by Genetic Programming

In computer vision, training a model that performs classification effectively is highly dependent on the extracted features, and the number of training instances. Conventionally, feature detection and extraction are performed by a domain-expert who, in many cases, is expensive to employ and hard to find. Therefore, image descriptors have emerged to automate these tasks. However, designing an image descriptor still requires domain-expert intervention. Moreover, the majority of machine learning algorithms require a large number of training examples to perform well. However, labelled data is not always available or easy to acquire, and dealing with a large dataset can dramatically slow down the training process. In this paper, we propose a novel Genetic Programming based method that automatically synthesises a descriptor using only two training instances per class. The proposed method combines arithmetic operators to evolve a model that takes an image and generates a feature vector. The performance of the proposed method is assessed using six datasets for texture classification with different degrees of rotation, and is compared with seven domain-expert designed descriptors. The results show that the proposed method is robust to rotation, and has significantly outperformed, or achieved a comparable performance to, the baseline methods.

Ines Maria Breinbauer / Gabriele Weiß (Hrsg.): Orte des Empirischen in der Bildungstheorie, Einsätze theoretischer Erziehungswissenschaft II. Würzburg: Königshausen & Neumann, 2011 [Rezension]

Rezension von: Ines Maria Breinbauer / Gabriele Weiß (Hrsg.): Einsätze theoretischer Erziehungswissenschaft II. Würzburg: Königshausen & Neumann, 2011 (183 S., ISBN 978-3-8260-4800-5; 19,80 EUR)