Bifurcations in Globally Coupled Map Lattices

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their stability. The complete bifurcation behaviour of coupled tent maps near the chaotic band merging point is presented. Furthermore the time independent states of coupled logistic equations are analyzed. The bifurcation diagram of the uncoupled map carries over to the map lattice. The analytical results are supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip

Segmented Strings in AdS3AdS_3

We study segmented strings in flat space and in $AdS_3$. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In $AdS_3$, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an $AdS_2$ subspace of $AdS_3$. The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We study several examples of closed segmented strings in $AdS_3$ and find an unexpected quasi-periodic behavior. We also work out a WKB analysis of quantum states of yo-yo strings in $AdS_3$ and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.Comment: 38 pages, 5 figure

New modelling technique for aperiodic-sampling linear systems

A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some restrictive conditions on the sampling sequence are imposed in order to guarantee the validity of the model. The particularization to the periodic case represents an alternative to the classic methods of discretization of continuous systems without using the Z-transform. This kind of representation can be used largely for identification and control purposes.Comment: 19 pages, 0 figure

Non-Linear Heart Rate Variability and Risk Stratification in Cardiovascular Disease

Traditional time and frequency domain heart rate variability (HRV) have cardiac patients at risk of mortality post-myocardial infarction. More recently, non linear HRV has been applied to risk stratification of cardiac patients. In this review we describe studies of non linear HRV and outcome in cardiac patients. We have included studies that used the three most common non-linear indices: power law slope, the short term fractal scaling exponent and measures based on Poincaré plots. We suggest that a combination of traditional and non-linear HRV may be optimal for risk stratification. Considerations in using non linear HRV in a clinical setting are described

Quantum Big Bang without fine-tuning in a toy-model

The question of possible physics before Big Bang (or after Big Crunch) is addressed via a schematic non-covariant simulation of the loss of observability of the Universe. Our model is drastically simplified by the reduction of its degrees of freedom to the mere finite number. The Hilbert space of states is then allowed time-dependent and singular at the critical time $t=t_c$. This option circumvents several traditional theoretical difficulties in a way illustrated via solvable examples. In particular, the unitary evolution of our toy-model quantum Universe is shown interruptible, without any fine-tuning, at the instant of its bang or collapse $t= t_c$.Comment: 20 pp., 1 fig., invited talk for the conference "10th Workshop on Quantization, Dualities and Integrable Systems" (April 22 - 24, 2011), http://qdis.emu.edu.tr/index.htm