Fixed Points of Hopfield Type Neural Networks

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according to the Hebb rule from the set of memorized patterns which are treated as distorted copies of the standard-vector. It is found that the dependence of the set of the fixed points on the value of the distortion parameter can be described analytically. The obtained results are interpreted in the terms of neural networks and the Ising model.Comment: RevTEX, 19 pages, 2 Postscript figures, the full version of the earler brief report (cond-mat/9901251

Spatial and temporal characterization of a Bessel beam produced using a conical mirror

We experimentally analyze a Bessel beam produced with a conical mirror, paying particular attention to its superluminal and diffraction-free properties. We spatially characterized the beam in the radial and on-axis dimensions, and verified that the central peak does not spread over a propagation distance of 73 cm. In addition, we measured the superluminal phase and group velocities of the beam in free space. Both spatial and temporal measurements show good agreement with the theoretical predictions.Comment: 5 pages, 6 figure

Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs

We give sufficient conditions for essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs. Two of the main theorems of the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as follows: the ordering of presentation has been modified in several places, more details have been provided in several places, some notations have been changed, two examples have been added, and several new references have been inserted. The final version of this preprint will appear in Integral Equations and Operator Theor

Vortex structure of thin mesoscopic disks in the presence of an inhomogeneous magnetic field

The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ''model'' magnetic field profiles with zero average field which may result from a ferromagnetic disk or circulating currents in a loop near the superconductor. We calculated the dependences of both the ground and metastable states on the magnitude and shape of the magnetic field profile for different values of the order parameter angular moment, i.e. the vorticity. The regions of existence of the multi-vortex state and the giant vortex state are found. We analysed the phase transitions between these states and studied the contribution from ring-shaped vortices. A new transition between different multi-vortex configurations as the ground state is found. Furthermore, we found a vortex state consisting of a central giant vortex surrounded by a collection of anti-vortices which are located in a ring around this giant vortex. The limit to a disk with an infinite radius, i.e. a film, will also be discussed. We also extended our results to ''real'' magnetic field profiles and to the case in which an external homogeneous magnetic field is present.Comment: 17 pages, 23 figures. Submitted to PR

A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory. The differential equation arises as a quantization of a certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and Tsuda.Comment: 15 pages, v2: typos corrected and references added, v3: discussion, appendix and references adde

Quantum hypercomputation based on the dynamical algebra su(1,1)

An adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is presented. The method that was used was to replace the Weyl-Heisenberg algebra by other dynamical algebra of low dimension that admits infinite-dimensional irreducible representations with naturally defined generalized coherent states. We have selected the Lie algebra $\mathfrak{su}(1,1)$, due to that this algebra posses the necessary characteristics for to realize the hypercomputation and also due to that such algebra has been identified as the dynamical algebra associated to many relatively simple quantum systems. In addition to an algebraic adaptation of KHQA over the algebra $\mathfrak{su}(1,1)$, we presented an adaptations of KHQA over some concrete physical referents: the infinite square well, the infinite cylindrical well, the perturbed infinite cylindrical well, the P{\"o}sch-Teller potentials, the Holstein-Primakoff system, and the Laguerre oscillator. We conclude that it is possible to have many physical systems within condensed matter and quantum optics on which it is possible to consider an implementation of KHQA.Comment: 25 pages, 1 figure, conclusions rewritten, typing and language errors corrected and latex format changed minor changes elsewhere and

Preparing to work: dramaturgy, cynicism and normative ‘remote’ control in the socialization of graduate recruits in management consulting

online) This paper examines the socialization of graduate recruits into a knowledge intensive labour process and organizational culture. Theoretically the paper draws upon the idea of ‘preparing for work’ to position this early socialization as a crucial moment in the production of subjectivities suited (and booted) for the labour process of management consulting. Empirically the paper reports on a two-day induction session for new graduate recruits joining a global management consultancy and their responses to this training. Particular attention is given to the use of role-play and a dramaturgical workshop used in part of the training process. The paper argues that the utilization of dramaturgy in training is consistent with the overall approach to control developed in the firm in response to the fact that the labour process of consulting is often conducted on client sites, away from any direct supervisory gaze. As such, the consultants were subjected to a form of cultural control that was designed to function independently of direct supervision. This control did not operate directly upon the new employees professed values, however, but at one step removed so that a ‘cynical distance’ from the content of the organization’s culture was accepted so long as a professional ‘ethic of behaviour’ was established. By focusing on an ‘ethic of behaviour’ these young professionals were encouraged to internalize a self-control akin to that of an actor, rather than internalizing the corporate values entirely

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Stability of multiquantum vortices in dilute Bose-Einstein condensates

Multiply quantized vortices in trapped Bose-Einstein condensates are studied using the Bogoliubov theory. Suitable combinations of a localized pinning potential and external rotation of the system are found to energetically stabilize, both locally and globally, vortices with multiple circulation quanta. We present a phase diagram for stable multiply quantized vortices in terms of the angular rotation frequency and the width of the pinning potential. We argue that multiquantum vortices could be experimentally created using these two expedients.Comment: 5 pages, 4 figure

Global value chains and human development: a class-relational framework

Global Value Chain proponents argue that regional and human development can be achieved through ‘strategic coupling’ with transnational corporations. This argument is misleading for two reasons. First, GVC abstracts firm-firm and firm-state relations from their class-relational basis, obscuring fundamental developmental processes. Second, much GVC analysis promotes linear conceptions of development. This article provides a class-relational framework for GVC analysis. The formation and functioning of GVCs and the developmental effects associated with them are products of histories of evolving and often conflictive, class relations. A study of export horticulture in North East Brazil provides empirical support for these arguments