Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with an appropriate momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The trajectories lie on ellipses. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and extends to o(4,2). (c) 2010 Elsevier B.V. All rights reserved.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Broadening public input into science policy decision making: can the democratic model for science communication influence scientific, innovation and technological trajectories?

This PhD thesis investigates the potential use of science communication models to engage a broader swathe of actors in decision making in relation to scientific and technological innovation in order to address possible democratic deficits in science and technology policy-making. A four-pronged research approach has been employed to examine different representations of the public(s) and different modes of engagement. The first case study investigates whether patient-groups could represent an alternative needs-driven approach to biomedical and health sciences R & D. This is followed by enquiry into the potential for Science Shops to represent a bottom-up approach to promote research and development of local relevance. The barriers and opportunities for the involvement of scientific researchers in science communication are next investigated via a national survey which is comparable to a similar survey conducted in the UK. The final case study investigates to what extent opposition or support regarding nanotechnology (as an emerging technology) is reflected amongst the YouTube user community and the findings are considered in the context of how support or opposition to new or emerging technologies can be addressed using conflict resolution based approaches to manage potential conflict trajectories. The research indicates that the majority of communication exercises of relevance to science policy and planning take the form of a one-way flow of information with little or no facility for public feedback. This thesis proposes that a more bottom-up approach to research and technology would help broaden acceptability and accountability for decisions made relating to new or existing technological trajectories. This approach could be better integrated with and complementary to government, institutional, e.g. university, and research funding agencies activities and help ensure that public needs and issues are better addressed directly by the research community. Such approaches could also facilitate empowerment of societal stakeholders regarding scientific literacy and agenda-setting. One-way information relays could be adapted to facilitate feedback from representative groups e.g. Non-governmental organisations or Civil Society Organisations (such as patient groups) in order to enhance the functioning and socio-economic relevance of knowledge-based societies to the betterment of human livelihoods.

Supercontinuum Generation by Stimulated Raman Scattering and Parametric Four-Wave Mixing in Photonic Crystal Fibers

Supercontinuum generation is investigated experimentally and numerically in a highly nonlinear indexguiding photonic crystal optical fiber in a regime in which self-phase modulation of the pump wave makes a negligible contribution to spectral broadening. An ultrabroadband octave-spanning white-light continuum is generated with 60-ps pump pulses of subkilowatt peak power. The primary mechanism of spectral broadening is identified as the combined action of stimulated Raman scattering and parametric four-wave mixing. The observation of a strong anti-Stokes Raman component reveals the importance of the coupling between stimulated Raman scattering and parametric four-wave mixing in highly nonlinear photonic crystal fibers and also indicates that non-phase-matched processes contribute to the continuum. Additionally, the pump input polarization affects the generated continuum through the influence of polarization modulational instability. The experimental results are in good agreement with detailed numerical simulations. These findings demonstrate the importance of index-guiding photonic crystal fibers for the design of picosecond and nanosecond supercontinuum light sources. © 2002 Optical Society of America.

Anomalous helicon wave absorption and parametric excitation of electrostatic fluctuations in a helicon-produced plasma

The nonlinear nature of the rf absorption in a helicon-produced plasma was recently evidenced by the observation that the helicon wave damping as well as the level of short-scale electrostatic fluctuations excited in the helicon plasma increases with rf power. Correlation methods using electrostatic probes as well as microwave back-scattering at the upper-hybrid resonance allow identifying the fluctuations as ion-sound and Trivelpiece– Gould waves satisfying the frequency and wavenumber matching conditions for the parametric decay instability of the helicon pump wave. Furthermore, the growth rates and thresholds deduced from their temporal growth are in good agreement with theoretical predictions for the parametric decay instability that takes into account realistic damping rates for the decay waves as well as a non-vanishing parallel wavenumber of the helicon pump. The close relationship between the rf absorption and the excitation of the fluctuations was investigated in more detail by performing time- and space-resolved measurements of the helicon wave field and the electrostatic fluctuations.

Quasi-classical model of non-destructive wavepacket manipulation by intense ultrashort nonresonant laser pulses

A quasi-classical model (QCM) of nuclear wavepacket generation, modification and imaging by three intense ultrafast near-infrared laser pulses has been developed. Intensities in excess of 10(13) W cm(-2) are studied, the laser radiation is non-resonant and pulse durations are in the few-cycle regime, hence significantly removed from the conditions typical of coherent control and femtochemistry. The 1s sigma ground state of the D-2 precursor is projected onto the available electronic states in D-2(+) (1s sigma(g) ground and 2p sigma(u) dissociative) and D+ + D+ (Coulomb explosion) by tunnel ionization by an ultrashort 'pump' pulse, and relative populations are found numerically. A generalized non-adiabatic treatment allows the dependence of the initial vibrational population distribution on laser intensity to be calculated. The wavepacket is approximated as a classical ensemble of particles moving on the 1s sigma(g) potential energy surface (PES), and hence follow trajectories of different amplitudes and frequencies depending on the initial vibrational state. The 'control' pulse introduces a time-dependent polarization of the molecular orbital, causing the PES to be modified according to the dynamic Stark effect and the transition dipole. The trajectories adjust in amplitude, frequency and phase-offset as work is done on or by the resulting force; comparing the perturbed and unperturbed trajectories allows the final vibrational state populations and phases to be determined. The action of the 'probe' pulse is represented by a discrete internuclear boundary, such that elements of the ensemble at a larger internuclear separation are assumed to be photodissociated. The vibrational populations predicted by the QCM are compared to recent quantum simulations (Niederhausen and Thumm 2008 Phys. Rev. A 77 013404), and a remarkable agreement has been found. The applicability of this model to femtosecond and attosecond time-scale experiments is discussed and the relation to established femtochemistry and coherent control techniques are explored.

Cooperative bank efficiency in Japan: a parametric distance function analysis

This study examines the relative performance of Japanese cooperative banks between 1998 and 2009, explicitly modeling non-performing loans as an undesirable output. Three key findings emerge. First, the sector is characterized by increasing returns to scale which supports the ongoing amalgamation process within the sector. Second, although restricted in product offerings, markets and their membership base, Japanese cooperatives secured both technical progress (a positive shift in the frontier) and a decrease in technical inefficiency (distance from the frontier). Third, the analysis highlighted that regulatory pressure to reduce non-performing loans will have an adverse impact on both output and performance. 

On the existence and stability of electrostatic structures in non-Maxwellian electron-positron-ion plasmas

Electrostatic solitary waves in plasmas are the focus of many current studies of localized electrostatic disturbances in both laboratory and astrophysical plasmas. Here, an investigation of the nonlinear dynamics of plasma evolving in two dimensions, in the presence of excess superthermal background electrons and positrons, is undertaken. We investigate the effect of a magnetic field on weakly nonlinear ion acoustic waves. Deviation from the Maxwellian distribution is effectively modelled by the kappa model. A linear dispersion relation is derived, and a decrease in frequency and phase speed in both parallel and perpendicular modes can be seen, when the proportion of positrons to electrons increases. We show that ion acoustic solitary waves can be generated during the nonlinear evolution of a plasma fluid, and their nonlinear propagation is governed by a Zakharov-Kuznetsov (ZK) type equation. A multiple scales perturbation technique is used to derive the ZK equation. The solitary wave structures are dependent on the relation between the system parameters, specifically the superthermality of the system, the proportion of positron content, magnetic field strength, and the difference between electron and positron temperature. The parametric effect of these on electrostatic shock structures is investigated. In particular, we find that stronger superthermality leads to narrower excitations with smaller potential amplitudes. Increased positron concentration also suppresses both the amplitude and the width of solitary wave structures. However, the structures are only weakly affected by temperature differentials between electrons and positrons in our model. © 2013 AIP Publishing LLC.

The Millennium child with autism: Early childhood trajectories for health, education and economic wellbeing

Objective: Most of what we know about children with autism spectrum disorder (ASD) is based on post-diagnostic, retrospective, self-select studies. Oftentimes, there is no direct comparison between trajectories of children with ASD and children without ASD.

Methods: To circumvent both of these problems, the present secondary data analysis utilised a large-scale longitudinal general population survey of children born in the year 2000 (i.e. the Millennium Cohort Study; MCS; n=18522). Bi-annual MCS data were available from five data sweeps (children aged 9 months to 11 years of age).

Results: Pre-diagnostic data showed early health problems differentiated children later diagnosed with autism from non-diagnosed peers. Prevalence was much higher than previously estimated (3.5% for 11-year olds). Post-diagnosis, trajectories deteriorated significantly for the children with ASD and their families in relation to education, health and economic wellbeing.

Conclusion: These findings raise many issues for service delivery and the rights of persons with disabilities and their families.

Comprehensive numerical modelling of the performance of a second harmonic generation stage coupled with a low-gain optical parametric amplifier

We present a comprehensive model for predicting the full performance of a second harmonic generation-optical parametric amplification system that aims at enhancing the temporal contrast of laser pulses. The model simultaneously takes into account all the main parameters at play in the system such as the group velocity mismatch, the beam divergence, the spectral content, the pump depletion, and the length of the nonlinear crystals. We monitor the influence of the initial parameters of the input pulse and the interdependence of the two related non-linear processes on the performance of the system and show its optimum configuration. The influence of the initial beam divergence on the spectral and the temporal characteristics of the generated pulse is discussed. In addition, we show that using a crystal slightly longer than the optimum length and introducing small delay between the seed and the pump ensures maximum efficiency and compensates for the spectral shift in the optical parametric amplification stage in case of chirped input pulse. As an example, calculations for bandwidth transform limited and chirped pulses of sub-picosecond duration in beta barium borate crystal are presented.

Back-trajectories Show Export of Airborne Fungal Spores (Ganoderma sp.) From Forests to Agricultural and Urban Areas in England

We propose here the hypothesis that all of United Kingdom (UK) is likely to be affected by Ganoderma sp. spores, an important plant pathogen. We suggest that the main sources of this pathogen, which acts as a bioaerosol, are the widely scattered woodlands in the country, although remote sources must not be neglected. The hypothesis is based on related studies on bioaerosols and supported by new observations from a non-forest site and model calculations to support our hypothesis. Hourly concentrations of Ganoderma sp. spores were measured from 2006 to 2010 using a 7-day volumetric spore trap at the city of Worcester. The concentrations peak during the night and early in the morning. This suggests that the main spore sources are located a few hours away with respect to air masses transport and reach urban areas thanks to air masses transport. The back-trajectory analysis was applied to determine the location of Ganoderma sp. spore sources. The analysis of back-trajectories demonstrated that 78% of the air masses reached Worcester from a 180° arc direction from the East to West. Three episodes were selected for detailed investigation and they revealed that during the episodes air masses always passed main UK woodlands before the arrival in Worcester, independently of their origin, but the long distance transport under certain conditions might be possible. Our studies suggest that the sources of UK Ganoderma sp. spores are mainly to be found in UK. Hence our studies suggest that research and mitigation strategies in UK should give their main attention to national sources, without neglecting the contribution from long distance transport.

Non-assisted versus neuro-navigated and XperCT-guided external ventricular catheter placement: a comparative cadaver study.

BACKGROUND AND PURPOSE: Accurate placement of an external ventricular drain (EVD) for the treatment of hydrocephalus is of paramount importance for its functionality and in order to minimize morbidity and complications. The aim of this study was to compare two different drain insertion assistance tools with the traditional free-hand anatomical landmark method, and to measure efficacy, safety and precision. METHODS: Ten cadaver heads were prepared by opening large bone windows centered on Kocher's points on both sides. Nineteen physicians, divided in two groups (trainees and board certified neurosurgeons) performed EVD insertions. The target for the ventricular drain tip was the ipsilateral foramen of Monro. Each participant inserted the external ventricular catheter in three different ways: 1) free-hand by anatomical landmarks, 2) neuronavigation-assisted (NN), and 3) XperCT-guided (XCT). The number of ventricular hits and dangerous trajectories; time to proceed; radiation exposure of patients and physicians; distance of the catheter tip to target and size of deviations projected in the orthogonal plans were measured and compared. RESULTS: Insertion using XCT increased the probability of ventricular puncture from 69.2 to 90.2 % (p = 0.02). Non-assisted placements were significantly less precise (catheter tip to target distance 14.3 ± 7.4 mm versus 9.6 ± 7.2 mm, p = 0.0003). The insertion time to proceed increased from 3.04 ± 2.06 min. to 7.3 ± 3.6 min. (p < 0.001). The X-ray exposure for XCT was 32.23 mSv, but could be reduced to 13.9 mSv if patients were initially imaged in the hybrid-operating suite. No supplementary radiation exposure is needed for NN if patients are imaged according to a navigation protocol initially. CONCLUSION: This ex vivo study demonstrates a significantly improved accuracy and safety using either NN or XCT-assisted methods. Therefore, efforts should be undertaken to implement these new technologies into daily clinical practice. However, the accuracy versus urgency of an EVD placement has to be balanced, as the image-guided insertion technique will implicate a longer preparation time due to a specific image acquisition and trajectory planning.

Mitochondrial uncoupling as a regulator of life-history trajectories in birds: an experimental study in the zebra finch.

Mitochondria have a fundamental role in the transduction of energy from food into ATP. The coupling between food oxidation and ATP production is never perfect, but may nevertheless be of evolutionary significance. The 'uncoupling to survive' hypothesis suggests that 'mild' mitochondrial uncoupling evolved as a protective mechanism against the excessive production of damaging reactive oxygen species (ROS). Because resource allocation and ROS production are thought to shape animal life histories, alternative life-history trajectories might be driven by individual variation in the degree of mitochondrial uncoupling. We tested this hypothesis in a small bird species, the zebra finch (Taeniopygia guttata), by treating adults with the artificial mitochondrial uncoupler 2,4-dinitrophenol (DNP) over a 32-month period. In agreement with our expectations, the uncoupling treatment increased metabolic rate. However, we found no evidence that treated birds enjoyed lower oxidative stress levels or greater survival rates, in contrast to previous results in other taxa. In vitro experiments revealed lower sensitivity of ROS production to DNP in mitochondria isolated from skeletal muscles of zebra finch than mouse. In addition, we found significant reductions in the number of eggs laid and in the inflammatory immune response in treated birds. Altogether, our data suggest that the 'uncoupling to survive' hypothesis may not be applicable for zebra finches, presumably because of lower effects of mitochondrial uncoupling on mitochondrial ROS production in birds than in mammals. Nevertheless, mitochondrial uncoupling appeared to be a potential life-history regulator of traits such as fecundity and immunity at adulthood, even with food supplied ad libitum.

Semi-Parametric Weak Instrument Regressions with an Application to the Risk-Return Trade-off

Recent work shows that a low correlation between the instruments and the included variables leads to serious inference problems. We extend the local-to-zero analysis of models with weak instruments to models with estimated instruments and regressors and with higher-order dependence between instruments and disturbances. This makes this framework applicable to linear models with expectation variables that are estimated non-parametrically. Two examples of such models are the risk-return trade-off in finance and the impact of inflation uncertainty on real economic activity. Results show that inference based on Lagrange Multiplier (LM) tests is more robust to weak instruments than Wald-based inference. Using LM confidence intervals leads us to conclude that no statistically significant risk premium is present in returns on the S&P 500 index, excess holding yields between 6-month and 3-month Treasury bills, or in yen-dollar spot returns.