Minimization via duality

We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object

Measure Recognition Problem

This is an article in mathematics, specifically in set theory. On the example of the Measure Recognition Problem (MRP) the article highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra \algB and a property $\Phi$ of measures one can recognize by purely combinatorial means if \algB supports a strictly positive measure with property $\Phi$. The most famous instance of this problem is MRP(countable additivity), and in the first part of the article we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v zamonja and Plebanek (2006) gives an easy solution to the former of these problems, and gives some partial information about the latter. The long term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem which gives such a structure theorem for measure algebras

Control strategies for integration of electric motor assist and functional electrical stimulation in paraplegic cycling: Utility for exercise testing and mobile cycling

AIM: The aim of this study was to investigate feedback control strategies for integration of electric motor assist and functional electrical stimulation (FES) for paraplegic cycling, with particular focus on development of a testbed for exercise testing in FES cycling, in which both cycling cadence and workrate are simultaneously well controlled and contemporary physiological measures of exercise performance derived. A second aim was to investigate the possible benefits of the approach for mobile, recreational cycling. METHODS: A recumbent tricycle with an auxiliary electric motor is used, which is adapted for paraplegic users, and instrumented for stimulation control. We propose a novel integrated control strategy which simultaneously provides feedback control of leg power output (via automatic adjustment of stimulation intensity) and cycling cadence (via electric motor control). Both loops are designed using system identification and analytical (model-based) feedback design methods. Ventilatory and pulmonary gas exchange response profiles are derived using a portable system for real-time breath-by-breath acquisition. RESULTS:We provide indicative results from one paraplegic subject in which a series of feedback-control tests illustrate accurate control of cycling cadence, leg power control, and external disturbance rejection. We also provide physiological response profiles from a submaximal exercise step test and a maximal incremental exercise test, as facilitated by the control strategy. CONCLUSION: The integrated control strategy is effective in facilitating exercise testing under conditions of well-controlled cadence and power output. Our control approach significantly extends the achievable workrate range and enhances exercise-test sensitivity for FES cycling, thus allowing a more stringent characterization of physiological response profiles and estimation of key parameters of aerobic function.We further conclude that the control approach can significantly improve the overall performance of mobile recreational cycling

Noise and Measurement Efficiency of a Partially Coherent Mesoscopic Detector

We study the noise properties and efficiency of a mesoscopic resonant-level conductor which is used as a quantum detector, in the regime where transport through the level is only partially phase coherent. We contrast models in which detector incoherence arises from escape to a voltage probe, versus those in which it arises from a random time-dependent potential. Particular attention is paid to the back-action charge noise of the system. While the average detector current is similar in all models, we find that its noise properties and measurement efficiency are sensitive both to the degree of coherence and to the nature of the dephasing source. Detector incoherence prevents quantum limited detection, except in the non-generic case where the source of dephasing is not associated with extra unobserved information. This latter case can be realized in a version of the voltage probe model.Comment: 15 pages, 5 figures; revised dicussion of voltage probe model

Comparison of stimulation patterns for FES-cycling using measures of oxygen cost and stimulation cost

<b>Aim</b><p></p> The energy efficiency of FES-cycling in spinal cord injured subjects is very much lower than that of normal cycling, and efficiency is dependent upon the parameters of muscle stimulation. We investigated measures which can be used to evaluate the effect on cycling performance of changes in stimulation parameters, and which might therefore be used to optimise them. We aimed to determine whether oxygen cost and stimulation cost measurements are sensitive enough to allow discrimination between the efficacy of different activation ranges for stimulation of each muscle group during constant-power cycling. <p></p> <b>Methods</b><p></p> We employed a custom FES-cycling ergometer system, with accurate control of cadence and stimulated exercise workrate. Two sets of muscle activation angles (“stimulation patterns”), denoted “P1” and “P2”, were applied repeatedly (eight times each) during constant-power cycling, in a repeated measures design with a single paraplegic subject. Pulmonary oxygen uptake was measured in real time and used to determine the oxygen cost of the exercise. A new measure of stimulation cost of the exercise is proposed, which represents the total rate of stimulation charge applied to the stimulated muscle groups during cycling. A number of energy-efficiency measures were also estimated. <p></p> <b>Results</b><p></p> Average oxygen cost and stimulation cost of P1 were found to be significantly lower than those for P2 (paired <i>t</i>-test, <i>p</i> < 0.05): oxygen costs were 0.56 ± 0.03 l min<sup>−1</sup> and 0.61 ± 0.04 l min<sup>−1</sup>(mean ± S.D.), respectively; stimulation costs were 74.91 ± 12.15 mC min<sup>−1</sup> and 100.30 ± 14.78 mC min<sup>−1</sup> (mean ± S.D.), respectively. Correspondingly, all efficiency estimates for P1 were greater than those for P2. <p></p> <b>Conclusion</b><p></p> Oxygen cost and stimulation cost measures both allow discrimination between the efficacy of different muscle activation patterns during constant-power FES-cycling. However, stimulation cost is more easily determined in real time, and responds more rapidly and with greatly improved signal-to-noise properties than the ventilatory oxygen uptake measurements required for estimation of oxygen cost. These measures may find utility in the adjustment of stimulation patterns for achievement of optimal cycling performance. <p></p&gt

Quantum-Limited Measurement and Information in Mesoscopic Detectors

We formulate general conditions necessary for a linear-response detector to reach the quantum limit of measurement efficiency, where the measurement-induced dephasing rate takes on its minimum possible value. These conditions are applicable to both non-interacting and interacting systems. We assess the status of these requirements in an arbitrary non-interacting scattering based detector, identifying the symmetries of the scattering matrix needed to reach the quantum limit. We show that these conditions are necessary to prevent the existence of information in the detector which is not extracted in the measurement process.Comment: 13 pages, 1 figur

Impacts of Climate Change on indirect human exposure to pathogens and chemicals from agriculture

Objective: Climate change is likely to affect the nature of pathogens and chemicals in the environment and their fate and transport. Future risks of pathogens and chemicals could therefore be very different from those of today. In this review, we assess the implications of climate change for changes in human exposures to pathogens and chemicals in agricultural systems in the United Kingdom and discuss the subsequent effects on health impacts. Data sources: In this review, we used expert input and considered literature on climate change ; health effects resulting from exposure to pathogens and chemicals arising from agriculture ; inputs of chemicals and pathogens to agricultural systems ; and human exposure pathways for pathogens and chemicals in agricultural systems. Data synthesis: We established the current evidence base for health effects of chemicals and pathogens in the agricultural environment ; determined the potential implications of climate change on chemical and pathogen inputs in agricultural systems ; and explored the effects of climate change on environmental transport and fate of different contaminant types. We combined these data to assess the implications of climate change in terms of indirect human exposure to pathogens and chemicals in agricultural systems. We then developed recommendations on future research and policy changes to manage any adverse increases in risks. Conclusions: Overall, climate change is likely to increase human exposures to agricultural contaminants. The magnitude of the increases will be highly dependent on the contaminant type. Risks from many pathogens and particulate and particle-associated contaminants could increase significantly. These increases in exposure can, however, be managed for the most part through targeted research and policy changes

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.

Magnetotunneling spectroscopy of mesoscopic correlations in two-dimensional electron systems

An approach to experimentally exploring electronic correlation functions in mesoscopic regimes is proposed. The idea is to monitor the mesoscopic fluctuations of a tunneling current flowing between the two layers of a semiconductor double-quantum-well structure. From the dependence of these fluctuations on external parameters, such as in-plane or perpendicular magnetic fields, external bias voltages, etc., the temporal and spatial dependence of various prominent correlation functions of mesoscopic physics can be determined. Due to the absence of spatially localized external probes, the method provides a way to explore the interplay of interaction and localization effects in two-dimensional systems within a relatively unperturbed environment. We describe the theoretical background of the approach and quantitatively discuss the behavior of the current fluctuations in diffusive and ergodic regimes. The influence of both various interaction mechanisms and localization effects on the current is discussed. Finally a proposal is made on how, at least in principle, the method may be used to experimentally determine the relevant critical exponents of localization-delocalization transitions.Comment: 15 pages, 3 figures include

Heliospheric Transport of Neutron-Decay Protons

We report on new simulations of the transport of energetic protons originating from the decay of energetic neutrons produced in solar flares. Because the neutrons are fast-moving but insensitive to the solar wind magnetic field, the decay protons are produced over a wide region of space, and they should be detectable by current instruments over a broad range of longitudes for many hours after a sufficiently large gamma-ray flare. Spacecraft closer to the Sun are expected to see orders-of magnitude higher intensities than those at the Earth-Sun distance. The current solar cycle should present an excellent opportunity to observe neutron-decay protons with multiple spacecraft over different heliographic longitudes and distances from the Sun.Comment: 12 pages, 4 figures, to be published in special issue of Solar Physic