Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models

A common finding in the empirical literature is that financial volatility exhibits high persistence, or slow mean reversion of the order of months. We present evidence that financial volatility data contains more than a single time scale. After showing that the expectation of the sum of the estimates of the autoregressive coefficients of a GARCH(1,1) model is one when there are unknown parameter changes, we explore the phenomenon in simulations. For parameter changes within realistic ranges for stock-price volatility we obtain global estimates close to integration while the average data- generating mean reversion is of the order of a few days. Spectral analysis of the Dow Jones Industrial Average and the S&P500 index between 1985 and 2001 reveals a short time scale of the magnitude of 5- 10 days present in the data. Thus, two different time scales exist in the data, one of the order of months corresponding to different volatility regimes, and one of the order of days corresponding to the average mean reversion within regimes.GARCH, volatility persistence, regime switching, long memory, short memory, structural change

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part I

Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009. The main aims of this contribution are: (i) To suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be possible to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we attempt, through a multidisciplinary analysis, to provide elements of a definition. (ii) To link the detected MHz and kHz EM anomalies with equivalent last stages of the L'Aquila earthquake preparation process. (iii) To put forward physically meaningful arguments to support a way of quantifying the time to global failure and the identification of distinguishing features beyond which the evolution towards global failure becomes irreversible. The whole effort is unfolded in two consecutive parts. We clarify we try to specify not only whether or not a single EM anomaly is pre-seismic in itself, but mainly whether a combination of kHz, MHz, and ULF EM anomalies can be characterized as pre-seismic one

How Can We Define The Concept of Long Memory? An Econometric Survey

In this paper we discuss different aspects of long mzmory behavior and specify what kinds of parametric models follow them. We discuss the confusion which can arise when empirical autocorrelation function of a short memory process decreases in an hyperbolic way.Long-memory, Switching, Estimation theory, Spectral