Schumpeterian economic dynamics as a quantifiable minimum model of evolution

We propose a simple quantitative model of Schumpeterian economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already existing goods, in other words new products can have destructive effects on existing goods. As a result of this competition mechanism existing goods may be driven out from the market - often causing cascades of secondary defects (Schumpeterian gales of destruction). The model leads to a generic dynamics characterized by phases of relative economic stability followed by phases of massive restructuring of markets - which could be interpreted as Schumpeterian business `cycles'. Model timeseries of product diversity and productivity reproduce several stylized facts of economics timeseries on long timescales such as GDP or business failures, including non-Gaussian fat tailed distributions, volatility clustering etc. The model is phrased in an open, non-equilibrium setup which can be understood as a self organized critical system. Its diversity dynamics can be understood by the time-varying topology of the active production networks.Comment: 21 pages, 11 figure

The Asymptotic Number of Attractors in the Random Map Model

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We derive here explicit formulas for the statistical distribution of the number of attractors in the system. As in related results, the number of operations involved by our formulas increases exponentially with n; therefore, they are not directly applicable to study the behavior of systems where n is large. However, our formulas lend themselves to derive useful asymptotic expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of Physics A: Mathematical and Genera

Spin and magnetization effects in plasmas

We give a short review of a number of different models for treating magnetization effects in plasmas. In particular, the transition between kinetic models and fluid models is discussed. We also give examples of applications of such theories. Some future aspects are discussed.Comment: 18 pages, 1 figure. To appear in Plasma Physics and Controlled Fusion, Special Issue for the 37th ICPP, Santiago, Chil

Transferring orbital and spin angular momenta of light to atoms

Light beams carrying orbital angular momentum, such as Laguerre-Gaussian beams, give rise to the violation of the standard dipolar selection rules during the interaction with matter yielding, in general, an exchange of angular momentum larger than hbar per absorbed photon. By means of ab initio 3D numerical simulations, we investigate in detail the interaction of a hydrogen atom with intense Gaussian and Laguerre-Gaussian light pulses. We analyze the dependence of the angular momentum exchange with the polarization, the orbital angular momentum, and the carrier-envelope phase of light, as well as with the relative position between the atom and the light vortex. In addition, a quantum-trajectory approach based on the de Broglie-Bohm formulation of quantum mechanics is used to gain physical insight into the absorption of angular momentum by the hydrogen atom

Computational core and fixed-point organisation in Boolean networks

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby the computational core of the network. Second we apply the cavity method to analyse number and organisation of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter one being characterised by the existence of an exponential number of macroscopically separated fixed-point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied to analysis and in silico experiments on the gene-regulatory networks of baker's yeast (saccaromices cerevisiae) and the segment-polarity genes of the fruit-fly drosophila melanogaster.Comment: 29 pages, 18 figures, version accepted for publication in JSTA

Prediction of lethal and synthetically lethal knock-outs in regulatory networks

The complex interactions involved in regulation of a cell's function are captured by its interaction graph. More often than not, detailed knowledge about enhancing or suppressive regulatory influences and cooperative effects is lacking and merely the presence or absence of directed interactions is known. Here we investigate to which extent such reduced information allows to forecast the effect of a knock-out or a combination of knock-outs. Specifically we ask in how far the lethality of eliminating nodes may be predicted by their network centrality, such as degree and betweenness, without knowing the function of the system. The function is taken as the ability to reproduce a fixed point under a discrete Boolean dynamics. We investigate two types of stochastically generated networks: fully random networks and structures grown with a mechanism of node duplication and subsequent divergence of interactions. On all networks we find that the out-degree is a good predictor of the lethality of a single node knock-out. For knock-outs of node pairs, the fraction of successors shared between the two knocked-out nodes (out-overlap) is a good predictor of synthetic lethality. Out-degree and out-overlap are locally defined and computationally simple centrality measures that provide a predictive power close to the optimal predictor.Comment: published version, 10 pages, 6 figures, 2 tables; supplement at http://www.bioinf.uni-leipzig.de/publications/supplements/11-01

A PALEOMAGNETIC AND ROCK MAGNETIC STUDY IN THE SALDAÑA FORMATION AND OVERLYING CRETACEOUS UNITS IN THE NORTHERN UPPER MAGDALENA VALLEY, COLOMBIA

  Lavas, mudstones and volcaniclastics rocks from the Saldaña (Upper Triassic - Lower Jurassic), Yaví and Alpujarra (Aptian) formations in the northern Upper Magdalena Valley were demagnetized using thermal and alternating field methods in order to isolate magnetic components and to establish a relative age of magnetization using several field tests. Magnetic mineralogy analyses permit the identification of the minerals that record uncovered magnetic components. Isolated components represent different events of magnetization. Directions parallel to the present Earth magnetic field were isolated in all the studied units. Characteristic components isolated from the Yaví Formation in Alpujarra area and from the Saldaña Formation in Olaya Herrera area, may correspond to primary or near-to-deposition events of magnetization. In Olaya Herrera, the characteristic component of the Saldaña Formation (D=179.9 I=7.1 N=8 k=17.19 α95=13.7) is carried by magnetite. Characteristic components uncovered in two different structural domains document 43±29ºcounterclockwise rotations previous to deposition of the Aptian Yaví Formation. Characteristic directions of the Yaví Formation are carried by hematite and magnetite, and the mean-site direction (D=5.2 I=6.2 N=7 k=40.15 α95=9.6) suggests a pre-folding event of magnetization.   Keywords: Paleomagnetism, Saldaña Formation, Yaví Formation, Triassic-Jurassic, Upper Magdalena ValleyRocas pertenecientes a las formaciones Saldaña (Triásico Superior-Jurásico Inferior), Yaví y Alpujarra (Aptiano) en el sector Norte del Valle Superior del Magdalena se desmagnetizaron por los métodos térmico y de campo alterno con el fin de aislar componentes de magnetización y establecer su edad relativa a partir de pruebas de campo (horizontalización de capas, prueba del contacto y discordancia). Análisis de mineralogía magnética permitieron definir los minerales magnéticos que registran dichos componentes. En estas unidades se logró aislar tanto el componente que registra la dirección del dipolo actual, así como componentes estables (característicos y primarios) de magnetización correspondientes a la edad de formación de cada unidad. El componente característico de la Fm. Saldaña, portado principalmente por magnetita, se aisló confiablemente en Olaya Herrera (D=179.9 I=7.1 N=8 k=17.19 α95=13.7), en donde se documentan rotaciones de bloques sentido anti-horario de 43±29º previo a la acumulación de la Fm. Yaví. El componente característico de la Fm. Yaví se aisló en tobas y lodolitas en el área de Alpujarra y su dirección (D=5.2 I=6.2 N=7 k=40.15 α95=9.6) sugiere un tiempo de magnetización pre-deformación de la Fm. Yaví. Hematita y magnetita son los minerales magnéticos que llevan este componente en la Fm. Yaví.   Palabras claves: Paleomagnetismo, Formación Saldaña, Formación Yaví, Triásico-Jurásico, Valle Superior del Magdalena         &nbsp

A PALEOMAGNETIC AND ROCK MAGNETIC STUDY IN THE SALDAÑA FORMATION AND OVERLYING CRETACEOUS UNITS IN THE NORTHERN UPPER MAGDALENA VALLEY, COLOMBIA

  Lavas, mudstones and volcaniclastics rocks from the Saldaña (Upper Triassic - Lower Jurassic), Yaví and Alpujarra (Aptian) formations in the northern Upper Magdalena Valley were demagnetized using thermal and alternating field methods in order to isolate magnetic components and to establish a relative age of magnetization using several field tests. Magnetic mineralogy analyses permit the identification of the minerals that record uncovered magnetic components. Isolated components represent different events of magnetization. Directions parallel to the present Earth magnetic field were isolated in all the studied units. Characteristic components isolated from the Yaví Formation in Alpujarra area and from the Saldaña Formation in Olaya Herrera area, may correspond to primary or near-to-deposition events of magnetization. In Olaya Herrera, the characteristic component of the Saldaña Formation (D=179.9 I=7.1 N=8 k=17.19 α95=13.7) is carried by magnetite. Characteristic components uncovered in two different structural domains document 43±29ºcounterclockwise rotations previous to deposition of the Aptian Yaví Formation. Characteristic directions of the Yaví Formation are carried by hematite and magnetite, and the mean-site direction (D=5.2 I=6.2 N=7 k=40.15 α95=9.6) suggests a pre-folding event of magnetization.   Keywords: Paleomagnetism, Saldaña Formation, Yaví Formation, Triassic-Jurassic, Upper Magdalena ValleyRocas pertenecientes a las formaciones Saldaña (Triásico Superior-Jurásico Inferior), Yaví y Alpujarra (Aptiano) en el sector Norte del Valle Superior del Magdalena se desmagnetizaron por los métodos térmico y de campo alterno con el fin de aislar componentes de magnetización y establecer su edad relativa a partir de pruebas de campo (horizontalización de capas, prueba del contacto y discordancia). Análisis de mineralogía magnética permitieron definir los minerales magnéticos que registran dichos componentes. En estas unidades se logró aislar tanto el componente que registra la dirección del dipolo actual, así como componentes estables (característicos y primarios) de magnetización correspondientes a la edad de formación de cada unidad. El componente característico de la Fm. Saldaña, portado principalmente por magnetita, se aisló confiablemente en Olaya Herrera (D=179.9 I=7.1 N=8 k=17.19 α95=13.7), en donde se documentan rotaciones de bloques sentido anti-horario de 43±29º previo a la acumulación de la Fm. Yaví. El componente característico de la Fm. Yaví se aisló en tobas y lodolitas en el área de Alpujarra y su dirección (D=5.2 I=6.2 N=7 k=40.15 α95=9.6) sugiere un tiempo de magnetización pre-deformación de la Fm. Yaví. Hematita y magnetita son los minerales magnéticos que llevan este componente en la Fm. Yaví.   Palabras claves: Paleomagnetismo, Formación Saldaña, Formación Yaví, Triásico-Jurásico, Valle Superior del Magdalena         &nbsp