Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes

PURPOSE. To investigate objectively and noninvasively the role of cognitive demand on autonomic control of systemic cardiovascular and ocular accommodative responses in emmetropes and myopes of late-onset. METHODS. Sixteen subjects (10 men, 6 women) aged between 18 and 34 years (mean ± SD: 22.6 ± 4.4 years), eight emmetropes (EMMs; mean spherical equivalent [MSE] refractive error ± SD: 0.05 ± 0.24 D) and eight with late-onset myopia (LOMs; MSE ± SD: -3.66 ± 2.31 D) participated in the study. Subjects viewed stationary numerical digits monocularly within a Badal optical system (at both 0.0 and -3.0 D) while performing a two-alternative, forced-choice paradigm that matched cognitive loading across subjects. Five individually matched cognitive levels of increasing difficulty were used in random order for each subject. Five 20-second, continuous-objective recordings of the accommodative response measured with an open-view infrared autorefractor were obtained for each cognitive level, whereas simultaneous measurement of heart rate was continuously recorded with a finger-mounted piezoelectric pulse transducer for 5 minutes. Fast Fourier transformation of cardiovascular function allowed the relative power of the autonomic components to be assessed in the frequency domain, whereas heart period gave an indication of the time-domain response. RESULTS. Increasing the cognitive demand led to a significant reduction in the accommodative response in all subjects (0.0 D: by -0.35 ± 0.33 D; -3.0 D: by -0.31 ± 0.40 D, P < 0.001). The greater lag of LOMs compared with EMMs was not significant (P = 0.07) at both distance (0.38 ± 0.35 D) and near (0.14 ± 0.42 D). Mean heart period reduced with increasing levels of workload (P < 0.0005). LOMs exhibited a relative elevation in sympathetic system activity compared to EMMs. Within refractive groups, however, accommodative shifts with increasing cognition correlated with parasympathetic activity (r = 0.99, P < 0.001), more than with sympathetic activity (r = 0.62, P > 0.05). CONCLUSIONS. In an equivalent workload paradigm, increasing cognitive demand caused a reduction in accommodative response that was attributable principally to a concurrent reduction in the relative power of the parasympathetic component of the autonomic nervous system (ANS). The disparity in accommodative response between EMMs and LOMs, however, appears to be augmented by changes in the sympathetic nervous component of the systemic ANS. Copyright © Association for Research in Vision and Ophthalmology.

On the robustness of random Boolean formulae

Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models. © 2010 IOP Publishing Ltd.

The corporatization of community pharmacy:implications for service provision, the public health function, and pharmacy's claims to professional status in the United Kingdom

Background Pharmacy has experienced both incomplete professionalization and deprofessionalization. Since the late 1970s, a concerted attempt has been made to re-professionalize pharmacy in the United Kingdom (UK) through role extension—a key feature of which has been a drive for greater pharmacy involvement in public health. However, the continual corporatization of the UK community pharmacy sector may reduce the professional autonomy of pharmacists and may threaten to constrain attempts at reprofessionalization. Objectives The objectives of the research: to examine the public health activities of community pharmacists in the UK; to explore the attitudes of community pharmacists toward recent relevant UK policy and barriers to the development of their public health function; and, to investigate associations between activity, attitudes, and the type of community pharmacy worked in (eg, supermarket, chain, independent). Methods A self-completion postal questionnaire was sent to a random sample of practicing community pharmacists, stratified for country and sex, within Great Britain (n = 1998), with a follow-up to nonresponders 4 weeks later. Data were analyzed using SPSS (SPSS Inc., Chicago, IL, USA) (v12.0). A final response rate of 51% (n = 1023/1998) was achieved. Results The level of provision of emergency hormonal contraception on a patient group direction, supervised administration of medicines, and needle-exchange schemes was lower in supermarket pharmacies than in the other types of pharmacy. Respondents believed that supermarkets and the major multiple pharmacy chains held an advantageous position in terms of attracting financing for service development despite suggesting that the premises of such pharmacies may not be the most suitable for the provision of such services. Conclusions A mixed market in community pharmacy may be required to maintain a comprehensive range of pharmacy-based public health services and provide maximum benefit to all patients. Longitudinal monitoring is recommended to ensure that service provision is adequate across the pharmacy network.

Contrast sensitivity for complex and random gratings

This thesis studied the effect of (i) the number of grating components and (ii) parameter randomisation on root-mean-square (r.m.s.) contrast sensitivity and spatial integration. The effectiveness of spatial integration without external spatial noise depended on the number of equally spaced orientation components in the sum of gratings. The critical area marking the saturation of spatial integration was found to decrease when the number of components increased from 1 to 5-6 but increased again at 8-16 components. The critical area behaved similarly as a function of the number of grating components when stimuli consisted of 3, 6 or 16 components with different orientations and/or phases embedded in spatial noise. Spatial integration seemed to depend on the global Fourier structure of the stimulus. Spatial integration was similar for sums of two vertical cosine or sine gratings with various Michelson contrasts in noise. The critical area for a grating sum was found to be a sum of logarithmic critical areas for the component gratings weighted by their relative Michelson contrasts. The human visual system was modelled as a simple image processor where the visual stimuli is first low-pass filtered by the optical modulation transfer function of the human eye and secondly high-pass filtered, up to the spatial cut-off frequency determined by the lowest neural sampling density, by the neural modulation transfer function of the visual pathways. The internal noise is then added before signal interpretation occurs in the brain. The detection is mediated by a local spatially windowed matched filter. The model was extended to include complex stimuli and its applicability to the data was found to be successful. The shape of spatial integration function was similar for non-randomised and randomised simple and complex gratings. However, orientation and/or phase randomised reduced r.m.s contrast sensitivity by a factor of 2. The effect of parameter randomisation on spatial integration was modelled under the assumption that human observers change the observer strategy from cross-correlation (i.e., a matched filter) to auto-correlation detection when uncertainty is introduced to the task. The model described the data accurately.

Design of a flat-top fiber Bragg filter via quasi-random modulation of the refractive index

The statistics of the reflection spectrum of a short-correlated disordered fiber Bragg grating are studied. The averaged spectrum appears to be flat inside the bandgap and has significantly suppressed sidelobes compared to the uniform grating of the same bandwidth. This is due to the Anderson localization of the modes of a disordered grating. This observation prompts a new algorithm for designing passband reflection gratings. Using the stochastic invariant imbedding approach it is possible to obtain the probability distribution function for the random reflection coefficient inside the bandgap and obtain both the variance of the averaged reflectivity as well as the distribution of the time delay of the grating.

Persistence in a random bond ising model of socio-econo dynamics

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a nite temperature on hypercubic lattices in dimensions up to ve. The model includes a \social" local eld which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We nd no evidence of \blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic elds. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in dierent scenarios.

Developing the public health function of locum pharmacists under the auspices of the new pharmacy contract

Focal Point - There are reduced opportunities for locum pharmacists to access training and education that meets their needs and enables them to play a full role under the new pharmacy contract - Eighty-six per cent of locums consider themselves to be more health professional than business person, compared to just 48% of pharmacy owners - Forty per cent of locums believe that a lack of access to training is a major barrier to the development of their public health function - While locum pharmacists are arguably more likely to embrace 'professionalising', patient-care-based roles, they are also the group least likely to be able to access the necessary training to fulfill such roles Introduction It has been suggested that locum pharmacists do not want the business-based responsibilities (e.g. staff management, meeting targets, etc) that come with pharmacy management.1 Research also suggests that locums derive great satisfaction from the health-professional aspects of the pharmacists’ role (e.g. patient contact, the provision of advice, etc).1 However, upon the introduction of the new pharmacy contract (April 2005), concerns were expressed that it was becoming increasingly difficult for locum pharmacists to access training and education that would meet their needs and enable them to play a full role under the new framework.2,3 Method After piloting, in August 2006 a self-completion postal questionnaire was sent to a random sample of practising community pharmacists, stratified for country and sex, within Great Britain (n = 1998), with a follow-up to non-responders 4 weeks later. Data were analysed using SPSS (v12.0). A final response rate of 51% (n = 1023/1998) was achieved. Respondents were asked ‘indicate how you view yourself as a pharmacist’ – in terms of their relative focus on the health-professional and business aspects of their role. Respondents were also asked ‘do you consider a lack of training opportunities to be a barrier to the development of the public health role of community pharmacists?’. Results Locums were significantly more likely than owners or employees to consider each factor a major barrier. Discussion Four in 10 locums consider a lack of training opportunities to constitute a major barrier to the development of their public health function. Pharmacy may not be able to provide the services required of it by the policy agenda if pharmacists are unable to be involved in extended role activities through a lack of training opportunities. Therefore, the paradox that needs to be addressed is that while locum pharmacists are arguably more likely to embrace ‘professionalising’, patient-care-based roles, they are also the group least likely to be able to access training to fulfil such roles. The training needs of this large subset of the pharmacist population need to be assessed and met if the whole community pharmacy workforce is going to maximise its contribution to public health under the new contractual framework. References 1 Shann P, Hassell K. An exploration of the diversity and complexity of the pharmacy locum workforce. London: Royal Pharmaceutical Society of Great Britain; 2004. 2 Almond M. Locums – key players in workforce – cast adrift as contract launched. Pharm J 2005;274:420. 3 Bishop DH. A lack of appreciation of what really happens. Pharm J 2005;274:451.

Are dyslexics' visual deficits limited to measures of dorsal stream function?

We tested the hypothesis that the differences in performance between developmental dyslexics and controls on visual tasks are specific for the detection of dynamic stimuli. We found that dyslexics were less sensitive than controls to coherent motion in dynamic random dot displays. However, their sensitivity to control measures of static visual form coherence was not significantly different from that of controls. This dissociation of dyslexics' performance on measures that are suggested to tap the sensitivity of different extrastriate visual areas provides evidence for an impairment specific to the detection of dynamic properties of global stimuli, perhaps resulting from selective deficits in dorsal stream functions. © 2001 Lippincott Williams & Wilkins.

A randomised controlled trial investigating the effect of nutritional supplementation on visual function in normal, and age-related macular disease affected eyes:design and methodology [ISRCTN78467674]

Background: Age-related macular disease is the leading cause of blind registration in the developed world. One aetiological hypothesis involves oxidation, and the intrinsic vulnerability of the retina to damage via this process. This has prompted interest in the role of antioxidants, particularly the carotenoids lutein and zeaxanthin, in the prevention and treatment of this eye disease. Methods: The aim of this randomised controlled trial is to determine the effect of a nutritional supplement containing lutein, vitamins A, C and E, zinc, and copper on measures of visual function in people with and without age-related macular disease. Outcome measures are distance and near visual acuity, contrast sensitivity, colour vision, macular visual field, glare recovery, and fundus photography. Randomisation is achieved via a random number generator, and masking achieved by third party coding of the active and placebo containers. Data collection will take place at nine and 18 months, and statistical analysis will employ Student's t test. Discussion: A paucity of treatment modalities for age-related macular disease has prompted research into the development of prevention strategies. A positive effect on normals may be indicative of a role of nutritional supplementation in preventing or delaying onset of the condition. An observed benefit in the age-related macular disease group may indicate a potential role of supplementation in prevention of progression, or even a degree reversal of the visual effects caused by this condition.

Breaks in the UK household sector money demand function

We use non-parametric procedures to identify breaks in the underlying series of UK household sector money demand functions. Money demand functions are estimated using cointegration techniques and by employing both the Simple Sum and Divisia measures of money. P-star models are also estimated for out-of-sample inflation forecasting. Our findings suggest that the presence of breaks affects both the estimation of cointegrated money demand functions and the inflation forecasts. P-star forecast models based on Divisia measures appear more accurate at longer horizons and the majority of models with fundamentals perform better than a random walk model.

On reliable computation by noisy random Boolean formulas

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from a single majority-like gate. We show that these gates can be used to compute any Boolean function reliably below the noise bound.

NLSE-based model of a random distributed feedback fiber laser

In this work we propose a NLSE-based model of power and spectral properties of the random distributed feedback (DFB) fiber laser. The model is based on coupled set of non-linear Schrödinger equations for pump and Stokes waves with the distributed feedback due to Rayleigh scattering. The model considers random backscattering via its average strength, i.e. we assume that the feedback is incoherent. In addition, this allows us to speed up simulations sufficiently (up to several orders of magnitude). We found that the model of the incoherent feedback predicts the smooth and narrow (comparing with the gain spectral profile) generation spectrum in the random DFB fiber laser. The model allows one to optimize the random laser generation spectrum width varying the dispersion and nonlinearity values: we found, that the high dispersion and low nonlinearity results in narrower spectrum that could be interpreted as four-wave mixing between different spectral components in the quasi-mode-less spectrum of the random laser under study could play an important role in the spectrum formation. Note that the physical mechanism of the random DFB fiber laser formation and broadening is not identified yet. We investigate temporal and statistical properties of the random DFB fiber laser dynamics. Interestingly, we found that the intensity statistics is not Gaussian. The intensity auto-correlation function also reveals that correlations do exist. The possibility to optimize the system parameters to enhance the observed intrinsic spectral correlations to further potentially achieved pulsed (mode-locked) operation of the mode-less random distributed feedback fiber laser is discussed.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05