Discreteness-induced oscillatory instabilities of dark solitons

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyze how it may occur for dark solitons of the discrete nonlinear Schrödinger and generalized Ablowitz-Ladik equations. [S0031-9007(98)08088-0

Modeling Epidemic Spread in Synthetic Populations - Virtual Plagues in Massively Multiplayer Online Games

A virtual plague is a process in which a behavior-affecting property spreads among characters in a Massively Multiplayer Online Game (MMOG). The MMOG individuals constitute a synthetic population, and the game can be seen as a form of interactive executable model for studying disease spread, albeit of a very special kind. To a game developer maintaining an MMOG, recognizing, monitoring, and ultimately controlling a virtual plague is important, regardless of how it was initiated. The prospect of using tools, methods and theory from the field of epidemiology to do this seems natural and appealing. We will address the feasibility of such a prospect, first by considering some basic measures used in epidemiology, then by pointing out the differences between real world epidemics and virtual plagues. We also suggest directions for MMOG developer control through epidemiological modeling. Our aim is understanding the properties of virtual plagues, rather than trying to eliminate them or mitigate their effects, as would be in the case of real infectious disease.Comment: Accepted for presentation at Digital Games Research Association (DiGRA) conference in Tokyo in September 2007. All comments to the authors (mail addresses are in the paper) are welcom

Gap and out-gap breathers in a binary modulated discrete nonlinear Schr\"odinger model

We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of 'exchange of stability' between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.Comment: 17 pages, 12 figures, submitted to Eur. Phys. J.

The Discrete Nonlinear Schr\"odinger equation - 20 Years on

We review work on the Discrete Nonlinear Schr\"odinger (DNLS) equation over the last two decades.Comment: 24 pages, 1 figure, Proceedings of the conference on "Localization and Energy Transfer in Nonlinear Systems", June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain; to be published by World Scientifi

Gazelles as Job Creators – A Survey and Interpretation of the Evidence

It is often claimed that small and young firms account for a disproportionately large share of net employment growth. We conduct a meta analysis of the empirical evidence regarding whether net employment growth rather is generated by a few rapidly growing firms – so-called Gazelles – that are not necessarily small and young. Gazelles are found to be outstanding job creators. They create all or a large share of new net jobs. On average, Gazelles are younger and smaller than other firms, but it is young age more than small size that is associated with rapid growth. Gazelles seem to be overrepresented in services.Firm growth; Flyers; Gazelles; High-growth firms; Rapidly growing firms

Institutional Effects on the Evolution of the Size Distribution of Firms

In this paper it is argued that the size distribution of firms may largely be determined by institutional factors. This hypothesis is tested in an exploratory fashion by studying the evolution of the size distribution of firms over time in Sweden for a period spanning from the late 1960s to the early 1990s. The data used is divided into finer size classes compared to most previous studies. This gives more scope for investigating the impact of institutions. Moreover, we use a unique data set, starting in 1984, to take account of corporate groups and government ownership. The analysis shows a poor development for intermediate-sized (10-199 employees) firms. This is likely to reflect the existence of a threshold that many firms are either unwilling or unable to cross. The analysis of the institutions and rules of the game determining the entrepreneurial and business conditions in Sweden indicate that the conditions have been unfavorable for small firms, and hence that too few small firms have managed to grow out of the smallest size classes. The conclusion is supported by an international comparison of the number of firms in different size classes. Data indicate that Sweden has fewer small (10-99) employees), and more large (500+) firms per capita than other European countries.Business taxation; Industrial policy; Industrial structure; Size distribution

Competencies and Institutions Fostering High-growth Firms

High-growth firms (HGFs) are critical for net job creation and economic growth. We analyze HGFs using the theory of competence blocs, linking firm growth to property rights and the interaction of complementary expertise. Specifically, we discuss how the institutional framework affects the prevalence and performance of HGFs. Firm growth is viewed as resulting from the perpetual discovery and use of productive knowledge. A key element in this process is the competence bloc, a nexus of economic actors with complementary competencies that are vital in order to generate and commercialize novel ideas. The institutional framework determines the incentives for these individuals to acquire and utilize knowledge. We identify a number of institutions that foster the emergence of competence blocs and the creation of HGFs. In particular, our analysis points to the pivotal roles played by tax structures, labor market regulation, and the contestability of currently closed service markets. Finally, we characterize institutions beneficial for sclerotic or dynamic capitalism, respectively, depending on whether they provide a favorable environment for the emergence of competence blocs and the creation of HGFs.Competence bloc; Dynamic capitalism; Entrepreneurship; Flyers; Gazelles; High-growth firms; Industrial policy; Innovation; Institutions; Labor security; Product market regulations; Property rights; Sclerotic capitalism; Self-employment; Tax policy.

Statistical mechanics of general discrete nonlinear Schr{\"o}dinger models: Localization transition and its relevance for Klein-Gordon lattices

We extend earlier work [Phys.Rev.Lett. 84, 3740 (2000)] on the statistical mechanics of the cubic one-dimensional discrete nonlinear Schrodinger (DNLS) equation to a more general class of models, including higher dimensionalities and nonlinearities of arbitrary degree. These extensions are physically motivated by the desire to describe situations with an excitation threshold for creation of localized excitations, as well as by recent work suggesting non-cubic DNLS models to describe Bose-Einstein condensates in deep optical lattices, taking into account the effective condensate dimensionality. Considering ensembles of initial conditions with given values of the two conserved quantities, norm and Hamiltonian, we calculate analytically the boundary of the 'normal' Gibbsian regime corresponding to infinite temperature, and perform numerical simulations to illuminate the nature of the localization dynamics outside this regime for various cases. Furthermore, we show quantitatively how this DNLS localization transition manifests itself for small-amplitude oscillations in generic Klein-Gordon lattices of weakly coupled anharmonic oscillators (in which energy is the only conserved quantity), and determine conditions for existence of persistent energy localization over large time scales.Comment: to be published in Physical Review