Multiple time scale models are an attractive alternative to longrange dependence models via heavy tails. They are Markovian models, hence analyzable, and capture some of the key phenomena manifest in long-range dependence. We analyze extensions of the AMS model of ATM traffic. The models includes both open types (where connection arrive and leave), and closed, fixed-population types. Connection...

In visualizing multivariate time series, it is difficult to simultaneously present both the dynamics and the structure of the data in an informative way. This paper presents an approach for the interactive visualization, exploration, and interpretation of multivariate time series. Our approach builds an abstract representation of the data based on a hierarchical, multiscale structure, where eac...

The existence of multiple time scales in molecular dynamics poses interesting and challenging questions from an analytical as well as from a numerical point of view In this paper we consider simpli ed models with two essential time scales and describe how these two time scales inter act The discussion focuses on classical molecular dynamics CMD with fast bond stretching and bending modes and th...

This paper presents preliminary results of complex action learning based on a multiple time-scales recurrent neural network (MTRNN) model embodied in the iCub humanoid robot. The model was implemented as part of Aquila cognitive robotics toolkit and accelerated through the compute unified device architecture (CUDA) making use of massively parallel GPU (graphics processing unit) devices that sig...

In this paper we construct extrapolated multirate discretization methods that allows one to efficiently solve problems that have components with different dynamics. This approach is suited for the time integration of multiscale ordinary and partial differential equations and provides highly accurate discretizations. We analyze the linear stability properties of the multirate explicit and linear...

Neural systems display rich short-term dynamics at various levels, e.g., spike-frequency adaptation (SFA) at the single-neuron level, and short-term facilitation (STF) and depression (STD) at the synapse level. These dynamical features typically cover a broad range of time scales and exhibit large diversity in different brain regions. It remains unclear what is the computational benefit for the...

To build a theory of social complexity, we need to understand how aggregate social properties arise from individual interaction rules. Here, I review a body of work on the developmental dynamics of pigtailed macaque social organization and conflict management that provides insight into the mechanistic causes of multi-scale social systems. In this model system coarse-grained, statistical represe...

This paper is concerned with the existence of multiple positive solutions for a functional dynamic equations with multi-point boundary conditions on time scales by using fixed point theorems in a cone. As an application, we also give an example to demonstrate our results.

Neurons in primary auditory cortex (A1) of cats show strong stimulus-specific adaptation (SSA). In probabilistic settings, in which one stimulus is common and another is rare, responses to common sounds adapt more strongly than responses to rare sounds. This SSA could be a correlate of auditory sensory memory at the level of single A1 neurons. Here we studied adaptation in A1 neurons, using thr...

The most common stochastic volatility models such as the Ornstein–Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull–White models define volatility as a Markovian process. In this work we check the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic....