Channel noise effects on neural synchronization

Synchronization in neural networks is strongly tied to the implementation of cognitive processes, but abnormal neuronal synchronization has been linked to a number of brain disorders such as epilepsy and schizophrenia. Here we examine the effects of channel noise on the synchronization of small Hodgkin-Huxley neuronal networks. The principal feature of a Hodgkin-Huxley neuron is the existence of protein channels that transition between open and closed states with voltage dependent rate constants. The Hodgkin-Huxley model assumes infinitely many channels, so fluctuations in the number of open channels do not affect the voltage. However, real neurons have finitely many channels which lead to fluctuations in the membrane voltage and modify the timing of the spikes, which may in turn lead to large changes in the degree of synchronization. We demonstrate that under mild conditions, neurons in the network reach a steady state synchronization level that depends only on the number of neurons in the network. The channel noise only affects the time it takes to reach the steady state synchronization level.Comment: 7 Figure

Properties of the reaction front in a reaction-subdiffusion process

We study the reaction front for the process $A+B\to C$ in which the reagents move subdiffusively. We propose a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. Scaling solutions to these equations are presented and compared with those of a direct numerical integration of the equations. We find that for reactants whose mean square displacement varies sublinearly with time as $\sim t^\gamma$, the scaling behaviors of the reaction front can be recovered from those of the corresponding diffusive problem with the substitution $t\to t^\gamma$Comment: Errata corrected, one reference update

Breathers and Thermal Relaxation in Fermi-Pasta-Ulam Arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters

How Strong is the Case for Dollarization in Costa Rica? A Note on the Business Cycle Comovements with the United States

We evaluate the proposal for official dollarization in Costa Rica by applying a new approach to measure the business cycle comovements with the United States. While the literature often focuses on the correlation of shocks, we point out that the response of each country to the shocks is also an important aspect of stabilization policy. We analyze whether Costa Rica and the United States share a common synchronized response to shocks, i.e. a common business cycle, using the Engle and Kozicki (1993) and Cubadda (1999, 2007) serial correlation common features tests, in a quarterly GDP data set from 1991 to 2008. Although we find some tendency towards common AR(p) structures and common long run trends, we reject the hypothesis that the two countries share a common business cycle. Based on this evidence, we conclude that official dollarization in Costa Rica would impede the efforts of its stabilization policy, despite the relatively high contemporaneous correlation of shocks.Dollarization, Business Cycle Comovement, Serial Correlation Common Feature, Central America, Costa Rica

How Strong is the Case for Dollarization in Costa Rica? A Note on the Business Cycle Comovements with the United States

We evaluate the proposal for official dollarization in Costa Rica by applying a new approach to measure the business cycle comovements with the United States. While the literature often focuses on the correlation of shocks, we point out that the response of each country to the shocks is also an important aspect of stabilization policy. We analyze whether Costa Rica and the United States share a common synchronized response to shocks, i.e. a common business cycle, using the Engle and Kozicki (1993) and Cubadda (1999, 2007) serial correlation common features tests, in a quarterly GDP data set from 1991 to 2008. Although we find some tendency towards common AR(p) structures and common long run trends, we reject the hypothesis that the two countries share a common business cycle. Based on this evidence, we conclude that official dollarization in Costa Rica would impede the efforts of its stabilization policy, despite the relatively high contemporaneous correlation of shocks.dollarization, business cycle comovement, serial correlation common feature, Central America, Costa Rica

Common Trends and Common Cycles among Interest Rates of the G7-Countries

In this paper we re-investigate the comovements of interest rates in the G7-countries. We propose a structured modus operandi to analyze the time series characteristics of interest rates and to test for common features. We conduct cointegration, serial correlation common feature and codependence tests with nominal and real interest rates using quarterly data from 1975 to 2007. Overall we only find little evidence of comovements. Common trends are occasionally observed, but the majority of interest rates are not cointegrated. Although some evidence for codependence of higher order is found among European countries, common cycles appear to exist only in rare cases and cannot be generalized for all interest rates.interest rates, comovement, cointegration, serial correlation common feature, codependence

How Strong is the Case for Dollarization in Central America? An Empirical Analysis of Business Cycles, Credit Market Imperfections and the Exchange Rate

In this paper, we contrast two different views in the debate on official dollarization. The Mundell (1961) framework of optimal currency areas and a model on boom-bust cycles, by Schneider and Tornell (2004), who take account of credit market imperfections prevalent in middle income countries. We highlight that the role of the exchange rate is strikingly different in the two models. While in the Mundell framework the exchange rate is expected to smooth the business cycle, the other model predicts that the exchange rate plays an amplifying role. We empirically evaluate both models for eight highly dollarized Central American economies, and find that the main benefit of official dollarization derives from avoiding a mismatch between foreign currency liabilities and domestic revenues, as well as the boom-bust episodes that are likely to follow from it. Using a new method of Cubadda (1999, 2007), we furthermore test for cyclical comovement and reject the hypothesis that the countries form an optimal currency area with the United States according to the Mundell definition.dollarization, real exchange rate, business cycle comovement, serial correlation, common feature, boom-bust cycles, credit market imperfections, Central America