Life, Death and Preferential Attachment

Scientific communities are characterized by strong stratification. The highly skewed frequency distribution of citations of published scientific papers suggests a relatively small number of active, cited papers embedded in a sea of inactive and uncited papers. We propose an analytically soluble model which allows for the death of nodes. This model provides an excellent description of the citation distributions for live and dead papers in the SPIRES database. Further, this model suggests a novel and general mechanism for the generation of power law distributions in networks whenever the fraction of active nodes is small.Comment: 5 pages, 2 figure

Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons

We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or `short-cuts' and the delay in the neuronal interactions. Persistent activity arises for a small fraction of `short-cuts', while a transition to failure occurs at a critical value of the `short-cut' density. The persistent activity consists of multi-stable periodic attractors, the number of which is at least on the order of the number of neurons in the network. For long enough delays, network activity at high `short-cut' densities is shown to exhibit exceedingly long chaotic transients whose failure-times averaged over many network configurations follow a stretched exponential. We show how this functional form arises in the ensemble-averaged activity if each network realization has a characteristic failure-time which is exponentially distributed.Comment: 14 pages 23 figure

A renormalization group model for the stick-slip behavior of faults

A fault which is treated as an array of asperities with a prescribed statistical distribution of strengths is described. For a linear array the stress is transferred to a single adjacent asperity and for a two dimensional array to three ajacent asperities. It is shown that the solutions bifurcate at a critical applied stress. At stresses less than the critical stress virtually no asperities fail on a large scale and the fault is locked. At the critical stress the solution bifurcates and asperity failure cascades away from the nucleus of failure. It is found that the stick slip behavior of most faults can be attributed to the distribution of asperities on the fault. The observation of stick slip behavior on faults rather than stable sliding, why the observed level of seismicity on a locked fault is very small, and why the stress on a fault is less than that predicted by a standard value of the coefficient of friction are outlined

Antifungal effect and reduction of Ulmus minor symptoms to Ophiostoma novo-ulmi by carvacrol and salicylic acid

There are still no effective means to control Dutch elm disease (DED), caused by the vascular fungi Ophiostoma ulmi and O. novo-ulmi. Plant phenolics may provide a new strategy for DED control, given their known antifungal activity against pathogens and their involvement in plant defence mechanisms. The in vitro antifungal activity of salicylic acid, carvacrol, thymol, phenol, o-cresol, m-cresol, p-cresol, and 2,5-xylenol against the DED pathogens was tested. Also, the protective effect of watering Ulmus minor seedlings with these compounds was tested against O. novo-ulmi. Salicylic acid, carvacrol, and thymol showed the strongest antifungal in vitro activity, while carvacrol and salicylic acid provided the strongest in vivo protection against O. novo-ulmi (63 and 46% reduction of leaf wilting symptoms with respect to controls, respectively). The effect of the treatments on tree phenology was low, and a significant negative relation was observed between the number of days to bud burst and the leaf wilting symptoms after inoculation, probably determined by genetic differences among the elm tree progenies used. The treatments with salicylic acid, carvacrol and thymol induced the highest shift in phenolic metabolite profile with respect to control trees. The protective effect of carvacrol and salicylic acid is discussed in terms of their combined activity as antifungal compounds and as inductors of tree defence responses

On-line learning in multilayer neural networks

We present an analytic solution to the problem of on-line gradient-descent learning for two-layer neural networks with an arbitrary number of hidden units in both teacher and student networks. The technique, demonstrated here for the case of adaptive input-to-hidden weights, becomes exact as the dimensionality of the input space increases

Macroscopic Dynamics of Neural Networks with Heterogeneous Spiking Thresholds

Mean-field theory links the physiological properties of individual neurons to the emergent dynamics of neural population activity. These models provide an essential tool for studying brain function at different scales; however, for their application to neural populations on large scale, they need to account for differences between distinct neuron types. The Izhikevich single neuron model can account for a broad range of different neuron types and spiking patterns, thus rendering it an optimal candidate for a mean-field theoretic treatment of brain dynamics in heterogeneous networks. Here, we derive the mean-field equations for networks of all-to-all coupled Izhikevich neurons with heterogeneous spiking thresholds. Using methods from bifurcation theory, we examine the conditions under which the mean-field theory accurately predicts the dynamics of the Izhikevich neuron network. To this end, we focus on three important features of the Izhikevich model that are subject here to simplifying assumptions: (i) spike-frequency adaptation, (ii) the spike reset conditions, and (iii) the distribution of single-cell spike thresholds across neurons. Our results indicate that, while the mean-field model is not an exact model of the Izhikevich network dynamics, it faithfully captures its different dynamic regimes and phase transitions. We thus present a mean-field model that can represent different neuron types and spiking dynamics. The model is comprised of biophysical state variables and parameters, incorporates realistic spike resetting conditions, and accounts for heterogeneity in neural spiking thresholds. These features allow for a broad applicability of the model as well as for a direct comparison to experimental data.Comment: 13 pages, 4 figure

Utilización de metil jasmonato para la inducción de resistencia ante Fusarium oxysporum, F. circinatum y Ophiostoma novo-ulmi

Damping off is probably the most common disease affecting seedlings in forest nurseries. In south-western Europe, the pitch canker and the Dutch elm disease cause relevant economic looses in forests, mostly in adult trees. The ability of the chemical plant elicitor methyl jasmonate (MeJA) to induce resistance in Pinus pinaster against Fusarium oxysporum and F. circinatum, and in Ulmus minor against Ophiostoma novo-ulmi was examined. In a first experiment, an aqueous solution of MeJA 5 mM was applied to P. pinaster seeds by immersion or spray, and different concentrations of MeJA (0, 0.1, 0.5, 1, 5 and 10 mM) were tested in seedlings before inoculations with F. oxysporum (105 and 107 spores mL–1). In a second experiment, 6-months-old P. pinaster seedlings were sprayed with 0 and 25 mM of MeJA, and later challenged with mycelium of F. circinatum. Finally, 4-year-old U. minor trees were sprayed with 0, 50 and 100 mM of MeJA and subsequently inoculated with O. novo-ulmi (106 spores mL–1). MeJA did not protect P. pinaster seeds and seedlings against F. oxysporum, probably because plants were too young for the physiological mechanisms responsible for resistance to be induced. Based on the morphological changes observed in the treated 6-months-old P. pinaster seedlings (reduction of growth and increased resin duct density), there is evidence that MeJA could have activated the mechanisms of resistance. However, 25 mM MeJA did not reduce plant mortality, probably because the spread of the virulent F. circinatum strain within the tree tissues was faster than the formation of effective defense responses. Based on the lack of phenological changes observed in the treated elms, there is no evidence that MeJA would cause induction of resistance. These results suggest that the use of MeJA to prevent F. oxysporum and F. circinatum in P. pinaster seedlings in nurseries and O. novo-ulmi in U. minor trees should be discarded.El “damping off” es una de las enfermedades más comunes en los viveros forestales. En árboles adultos del suroeste de Europa, el chancro resinoso y la grafiosis del olmo son enfermedades que están causando importantes pérdidas económicas en los bosques. Se ha estudiado la capacidad del metil jasmonato (MeJA), un elicitador químico de plantas, para inducir resistencia en Pinus pinaster ante Fusarium oxysporum y F. circinatum, y en Ulmus minor ante Ophiostoma novo-ulmi. En un primer experimento se aplicó una solución acuosa de MeJA 5 mM a semillas de P. pinaster mediante inmersión o pulverización de las mismas, y diferentes concentraciones de MeJA (0, 0.1, 0.5, 1, 5 and 10 mM) fueron pulverizadas en plántulas de P. pinaster antes de las inoculaciones con F. oxysporum (105 y 107 esporas mL–1). En un segundo experimento, plántulas de P. pinaster de 6 meses de edad fueron pulverizadas con MeJA 0 y 25 mM, y posteriormente inoculadas con micelio de F. circinatum. Por último, brinzales de U. minor de 4 años de edad fueron pulverizados con MeJA a 0, 50 y 100 mM e inmediatamente inoculados con O. novo-ulmi (106 esporas mL–1). El MeJA no protegió a las semillas ni a las plántulas de P. pinaster ante F. oxysporum, quizá debido a que las plántulas eran demasiado jóvenes para inducir los mecanismos fisiológicos responsables de la resistencia. Basándonos en los cambios morfológicos observados en las plántulas de 6 meses de P. pinaster (reducción del crecimiento e incremento de la densidad de los canales resiníferos), hay evidencia de que el MeJA pudo haber activado los mecanismos de resistencia. El MeJA a 25 mM no consiguió reducir la mortalidad probablemente porque la dispersión de F. circinatum en el interior de los tejidos fue más rápida que la formación de respuestas defensivas efectivas. Basándonos en la falta de cambios fenológicos de los olmos tratados, no hay evidencias de que el MeJA pueda haber causado una inducción de resistencia. Los resultados sugieren que el uso del MeJA para prevenir los patógenos F. oxysporum y F. circinatum en plántulas de P. pinaster en viveros y O. novo-ulmi en brinzales de U. minor debe ser descartado

The dynamics of motor learning through the formation of internal models

A medical student learning to perform a laparoscopic procedure or a recently paralyzed user of a powered wheelchair must learn to operate machinery via interfaces that translate their actions into commands for an external device. Since the user\u2019s actions are selected from a number of alternatives that would result in the same effect in the control space of the external device, learning to use such interfaces involves dealing with redundancy. Subjects need to learn an externally chosen many-to-one map that transforms their actions into device commands. Mathematically, we describe this type of learning as a deterministic dynamical process, whose state is the evolving forward and inverse internal models of the interface. The forward model predicts the outcomes of actions, while the inverse model generates actions designed to attain desired outcomes. Both the mathematical analysis of the proposed model of learning dynamics and the learning performance observed in a group of subjects demonstrate a first-order exponential convergence of the learning process toward a particular state that depends only on the initial state of the inverse and forward models and on the sequence of targets supplied to the users. Noise is not only present but necessary for the convergence of learning through the minimization of the difference between actual and predicted outcomes