On the minimal number of matrices which form a locally hypercyclic, non-hypercyclic tuple

In this paper we extend the notion of a locally hypercyclic operator to that of a locally hypercyclic tuple of operators. We then show that the class of hypercyclic tuples of operators forms a proper subclass to that of locally hypercyclic tuples of operators. What is rather remarkable is that in every finite dimensional vector space over $\mathbb{R}$ or $\mathbb{C}$, a pair of commuting matrices exists which forms a locally hypercyclic, non-hypercyclic tuple. This comes in direct contrast to the case of hypercyclic tuples where the minimal number of matrices required for hypercyclicity is related to the dimension of the vector space. In this direction we prove that the minimal number of diagonal matrices required to form a hypercyclic tuple on $\mathbb{R}^n$ is $n+1$, thus complementing a recent result due to Feldman.Comment: 15 pages, title changed, section for infinite dimensional spaces adde

Wavelet based detection of changes in the composition of RLC networks

The current work discusses the compositional analysis of spectra that may be related to amorphous materials that lack discernible Lorentzian, Debye or Drude responses. We propose to model such response using a 3-dimensional random RLC network using a descriptor formulation which is converted into an input-output transfer function representation. A wavelet identification study of these networks is performed to infer the composition of the networks. It was concluded that wavelet filter banks enable a parsimonious representation of the dynamics in excited randomly connected RLC networks. Furthermore, chemometric classification using the proposed technique enables the discrimination of dielectric samples with different composition. The methodology is promising for the classification of amorphous dielectrics

Materials for phantoms for terahertz pulsed imaging

Phantoms are commonly used in medical imaging for quality assurance, calibration, research and teaching. They may include test patterns or simulations of organs, but in either case a tissue substitute medium is an important component of the phantom. The aim of this work was to identify materials suitable for use as tissue substitutes for the relatively new medical imaging modality terahertz pulsed imaging. Samples of different concentrations of the candidate materials TX151 and napthol green dye were prepared, and measurements made of the frequency-dependent absorption coefficient (0.5 to 1.5 THz) and refractive index (0.5 to 1.0 THz). These results were compared qualitatively with measurements made in a similar way on samples of excised human tissue (skin, adipose tissue and striated muscle). Both materials would be suitable for phantoms where the dominant mechanism to be simulated is absorption (similar to ∼100 cm(-1) at 1 THz) and where simulation of the strength of reflections from boundaries is not important; for example, test patterns for spatial resolution measurements. Only TX151 had a frequency-dependent refractive index close to that of tissue, and could therefore be used to simulate the layered structure of skin, the complexity of microvasculature or to investigate frequency-dependent interference effects that have been noted in terahertz images

Conversion of descriptor representations to state-space form: an extension of the shuffle algorithm

This paper proposes a systematic procedure for the determination of state-space models from an available descriptor representation of a linear dynamic system. The goal is to determine a state equation, a set of algebraic equations and an output equation in terms of the state and input variables. It is shown that standard methods may fail to convert the descriptor representation to state-space form, even for simple electrical circuit models obtained from Kirchoff’s laws and constitutive element equations. A novel procedure to address this problem is then proposed as an extension of the classic shuffle algorithm combined with a singular value decomposition approach. In addition to an illustrative example involving a simple electrical circuit, the proposed method is employed in a case study involving the modeling of three-dimensional RLC networks with a large number of components

Classification of lactose and mandelic acid THz spectra using subspace and wavelet-packet algorithms

Copyright © 2007 SPIE - The International Society for Optical Engineering.This work compares classification results of lactose, mandelic acid and dl-mandelic acid, obtained on the basis of their respective THz transients. The performance of three different pre-processing algorithms applied to the time-domain signatures obtained using a THz-transient spectrometer are contrasted by evaluating the classifier performance. A range of amplitudes of zero-mean white Gaussian noise are used to artificially degrade the signal-to-noise ratio of the time-domain signatures to generate the data sets that are presented to the classifier for both learning and validation purposes. This gradual degradation of interferograms by increasing the noise level is equivalent to performing measurements assuming a reduced integration time. Three signal processing algorithms were adopted for the evaluation of the complex insertion loss function of the samples under study; a) standard evaluation by ratioing the sample with the background spectra, b) a subspace identification algorithm and c) a novel wavelet-packet identification procedure. Within class and between class dispersion metrics are adopted for the three data sets. A discrimination metric evaluates how well the three classes can be distinguished within the frequency range 0.1-1.0 THz using the above algorithms.Xiaoxia Yin ; Sillas Hadjiloucas ; Bernd M. Fischer ; Brian W.-H. Ng ; Henrique M. Paiva ; Roberto K. H. Galvão ; Gillian C. Walker ; John W. Bowen ; Derek Abbot

Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractionalorder internal model control and external adaptive control

A fractional-order internal model control technique is applied to a three-dimensional resistive-capacitive network to enforce desired closed loop dynamics of first order. In order to handle model mismatch issues resulting from the random allocation of the components within the network, the control law is augmented with a model-reference adaptive strategy in an external loop. By imposing a control law on the system to obey first order dynamics, a calibrated transient response is ensured. The methodology enables feedback control of complex systems with emergent responses and is robust in the presence of measurement noise or under conditions of poor model identification. Furthermore, it is also applicable to systems that exhibit higher order fractional dynamics. Examples of feedback-controlled transduction include cantilever positioning in atomic force microscopy or the control of complex de-excitation lifetimes encountered in many types of spectroscopies, e.g., nuclear magnetic, electron-spin, microwave, multiphoton fluorescence, Förster resonance, etc. The proposed solution should also find important applications in more complex electronic, microwave, and photonic lock-in problems. Finally, there are further applications across the broader measurement science and instrumentation community when designing complex feedback systems at the system level, e.g., ensuring the adaptive control of distributed physiological processes through the use of biomedical implants

Tensor based multichannel reconstruction for breast tumours identification from DCE-MRIs

A new methodology based on tensor algebra that uses a higher order singular value decomposition to perform three-dimensional voxel reconstruction from a series of temporal images obtained using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is proposed. Principal component analysis (PCA) is used to robustly extract the spatial and temporal image features and simultaneously de-noise the datasets. Tumour segmentation on enhanced scaled (ES) images performed using a fuzzy C-means (FCM) cluster algorithm is compared with that achieved using the proposed tensorial framework. The proposed algorithm explores the correlations between spatial and temporal features in the tumours. The multi-channel reconstruction enables improved breast tumour identification through enhanced de-noising and improved intensity consistency. The reconstructed tumours have clear and continuous boundaries; furthermore the reconstruction shows better voxel clustering in tumour regions of interest. A more homogenous intensity distribution is also observed, enabling improved image contrast between tumours and background, especially in places where fatty tissue is imaged. The fidelity of reconstruction is further evaluated on the basis of five new qualitative metrics. Results confirm the superiority of the tensorial approach. The proposed reconstruction metrics should also find future applications in the assessment of other reconstruction algorithms

Constrained pre-equalization accounting for multi-path fading emulated using large RC networks: applications to wireless and photonics communications

Multi-path propagation is modelled assuming a multi-layer RC network with randomly allocated resistors and capacitors to represent the transmission medium. Due to frequency-selective attenuation, the waveforms associated with each propagation path incur path-dependent distortion. A pre-equalization procedure that takes into account the capabilities of the transmission source as well as the transmission properties of the medium is developed. The problem is cast within a Mixed Integer Linear Programming optimization framework that uses the developed nominal RC network model, with the excitation waveform customized to optimize signal fidelity from the transmitter to the receiver. The objective is to match a Gaussian pulse input accounting for frequency regions where there would be pronounced fading. Simulations are carried out with different network realizations in order to evaluate the sensitivity of the solution with respect to changes in the transmission medium mimicking the multi-path propagation. The proposed approach is of relevance where equalization techniques are difficult to implement. Applications are discussed within the context of emergent communication modalities across the EM spectrum such as light percolation as well as emergent indoor communications assuming various modulation protocols or UWB schemes as well as within the context of space division multiplexing