Computation of symbolic dynamics for one-dimensional maps

In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation.     

Graph Duality in Surface Dynamics

Journal of Nonlinear Science - We compare one-dimensional representations for the isotopy stable dynamics of homeomorphisms in two dimensions. We consider the skeleton graph representative, which...     

Complex structured singular value analysis using fixed-structure dynamic D-scales

Models of systems are always inexact. Hence, to better predict the performance of a system it is necessary to take into account uncertainty in a nominal model of a system. The structured singular value was developed to nonconservatively analyze robust stability and performance for systems with multiple-block uncertainty. In practice, optimization techniques are used to compute an upper bound on the structured singular value. For dynamic uncertainty with bounded magnitude and arbitrary phase (i.e., "complex uncertainty"), the standard approach to computing an upper bound involves finding diagonal scaling matrices D(jω) that minimize σ_max (D(jω)G(jω)D^-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding stable, minimum phase, rational function D(s) (if it exists) is hence arbitrary, which can lead to very high order controllers when D(s) is used for controller synthesis. This paper develops a fixed-structure approach to computing an upper bound for the complex structured singular value. In particular, by relying on results from mixed-norm H₂/H_∞ analysisD(s) is a priori constrained to be a rational matrix function of a chosen order and a new approach to computing an upper bound on the structured singular value is developed. The results are illustrated using two examples which clearly demonstrate the suboptimality of standard curve fitting. The proposed approach can be extended to mixed uncertainty and structured singular value controller synthesis without D — K type iteration.     

Almost One Bit Violation for the Additivity of the Minimum Output Entropy

In a previous paper, we proved that, in the appropriate asymptotic regime, the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_k,t. We also showed that the set K_k,t is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of \({\ell^p}\) norms on the set K_k,t and prove that the maximum is attained on a vector of shape (a, b, . . . , b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show that for any \({\varepsilon > 0}\), it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183, and that for appropriate choice of parameters, the violation can be as large as \({\log 2 -\varepsilon}\). Conversely, our result implies that, with probability one in the limit, one does not obtain a violation of additivity using conjugate random quantum channels and the Bell state, in dimension 182 and less.     

A radiofrequency coil configuration for imaging the human vertebral column at 7 T

We describe the design and testing of a quadrature transmit, eight-channel receive array RF coil configuration for the acquisition of images of the entire human spinal column at 7 T. Imaging parameters were selected to enable data acquisition in a clinically relevant scan time. Large field-of-view (FOV) scanning enabled sagittal imaging of the spine in two or three-stations, depending upon the height of the volunteer, with a total scan time of between 10 and 15 min. A total of 10 volunteers have been scanned, with results presented for the three subjects spanning the range of heights and weights, namely one female (1.6 m, 50 kg), one average male (1.8 m, 70 kg), and one large male (1.9 m, 100 kg).     

Vibrationally assisted transitions and phonon spectra in crystalline solids

The vibrationally assisted electronic (vibronic) transitions of localized centers in crystalline solids provide relevant information regarding the phonon spectra of the host materials. We present the vibronic spectra of some compounds with particular attention to the case of the transition metal ions V²⁺ and Cr³⁺ embedded in simple ionic crystals such as MgO or more complex systems such as YAG. The vibronic spectra are interpreted in light of the radiative selection rules and are compared with phonon data obtained with other techniques such as neutron scattering, infrared and Raman spectroscopies. Conclusions regarding the effectiveness of vibronic spectra in uncovering the phonon spectral distributions are presented.     

Synthetic gene network for entraining and amplifying cellular oscillations

We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.