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

High signal to noise ratio THz spectroscopy with ASOPS and signal processing schemes for mapping and controlling molecular and bulk relaxation processes

Asynchronous Optical Sampling has the potential to improve signal to noise ratio in THz transient sperctrometry. The design of an inexpensive control scheme for synchronising two femtosecond pulse frequency comb generators at an offset frequency of 20 kHz is discussed. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing recorded THz transients in the time and frequency domain are outlined. Finally, possibilities for femtosecond pulse shaping using genetic algorithms are mentioned

Assessment of apoptosis in human breast tissue using an antibody against the active form of caspase 3: relation to tumour histopathological characteristics

Apoptosis is of important significance in the pathogenesis of cancer. Many methods are available for the measurement of apoptosis but the ‘gold standard’ is to identify apoptotic cells by their morphological features using microscopy. Caspase 3 is a cytosolic enzyme that is activated only in cells committed to undergo apoptosis. The activation of caspase 3 precedes the development of the classical morphological features of apoptosis. Using immunohistochemistry with an antibody against the active form of caspase 3, the apoptotic index (AI) was measured in 116 samples of human breast tissue (22 normal/benign and 94 invasive carcinomas). The AI obtained by measuring caspase activation has a strong correlation with the AI derived by morphological assessment (r = 0.736, P < 0.01). The AI is higher in the invasive group than in the benign group (P = 0.008), and in invasive cancer high AI is associated with high tumour grade (P = 0.013), positive node status (P < 0.001) and negative steroid receptor status (P = 0.001 for ER; P = 0.004 for PR). No significant association is observed between AI and tumour size. Measurement of apoptosis by immunohistochemistry using an antibody against the active form of caspase 3 is therefore reliable and correlates strongly with morphological assessment. © 2001 Cancer Research Campaign  http://www.bjcancer.co

Apoptosis in human tumours

British Journal of Cancer (2002) 86, 1661–1661 DOI: 10.1038/sj/bjc/6600312 www.bjcancer.co

Channel equalization for indoor lighting communications networks

We consider indoors communications networks using modulated LEDs to transmit the information packets. A generic indoor channel equalization formulation is proposed assuming the existence of both line of sight and diffuse emitters. The proposed approach is of relevance to emergent indoors distributed sensing modalities for which various lighting based network communications protocols are considered

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

Bond-graph Input-State-Output Port-Hamiltonian formulation of memristive networks for emulation of Josephson junction circuits

A bond graph Input-State-Output Port-Hamiltonian formulation of memristive networks for Josephson junction circuits in state space is presented. The methodology has applications to the modeling of SQUIDs and other non-linear transducers and enables the formulation of input-output models of complex components embedded in non-linear networks

Will early detection of non-axillary sentinel nodes affect treatment decisions?

Axillary lymph node involvement is the best prognostic factor for breast cancer survival. Staging breast cancers by axillary dissection remains standard management and is part of the UK national guidelines for breast cancer treatment. In the presence of involved axillary lymph nodes best treatment has been shown to be axillary clearance (Fentiman and Mansell, 1991), but clearly for women whose nodes are uninvolved avoidance of morbidity is optimal and this will be achieved by minimal dissection of the axilla. Thus, for node-negative women the introduction of the sentinel node biopsy technique may revolutionise the approach to the axilla. These will be women with mammographic screen detected small well and moderately differentiated tumours (Hadjiloucas and Bundred, 2000). The impact of sentinel node biopsy in women who have symptomatic large tumours is unproven, and around half of these women will require a second procedure to clear their axilla or radiotherapy as treatment. Even for those women found to have involved sentinel lymph nodes the ability to use early systemic chemotherapy followed by axillary clearance or radiotherapy may provide long-term survival gains. Sentinel node biopsy should not, however, become routine practice until randomised controlled trials have proven its benefit and safety in reducing morbidity. Several randomised controlled trials (including ALMANAC) are currently underway