Compact surfaces as configuration spaces of mechanical linkages

There exists a homeomorphism between any compact orientable closed surface and the configuration space of an appropriate mechanical linkage defined by a weighted graph embedded in the Euclidean plan

Looking forward to making predictions

As described in the preceding pages, since the BGS was established in 1835, the British population has coped with many challenges. These have ranged from finding resources to fuel the Industrial Revolution, understanding and combating water-borne diseases such as typhoid, the threat of invasion and aerial bombardment, through to modern-day environmental problems and climate change. To help deal with these problems, decisionmakers from governments and other organisations have required our help and advice

Conceptualizing Care Continua: Lessons from Hiv, Hepatitis C virus, Tuberculosis and implications for the Development of Improved Care and Prevention Continua

Background: To examine the application of continuum models to tuberculosis, HIV, and other conditions; to theorize the concept of continua; and to learn lessons that could inform the development of improved care and prevention continua as public health metrics. Methods: An analytic review of literature drawn from several fields of health care. Results: The continuum construct is now part of public health evaluation systems for HIV, and is increasingly used in public health and the medical literature. Issues with the comparability and optimal design of care continuum models have been raised, and their methodologic and theoretic underpinnings and scope of focus have been underaddressed. Review of relevant publications suggests that a key limitation of current models is their lack of measures reflecting incidence and mortality. Issues relating to continua data being longitudinal or cross-sectional, definition of numerators and denominators for each step, data sources, measures of timeliness of step completion, theoretic models to facilitate inferences of causes of care continuum gaps, how measures of prevention efforts, reinfection/relapses, and interactions of continua for co-occurring comorbidities should be reflected, and how analyses of differences in retention over time, across geographic regions, and in response to interventions should be conducted are critical to the development of sound care and prevention continuum models. Conclusion: Lessons learned from the application of continuum models to HIV and other conditions suggest that the application of well-formulated constructs of care and prevention continua, that depict, in well defined, standardized steps, incidence and mortality, along with degrees of and time to screening, engagement in care and prevention, treatment and treatment outcomes, including relapse or reinfection, may be vital tools in evaluating intervention and program outcomes, and in improving population health and population health metrics for a wide range conditions

Machine learning for a combined electroencephalographic anesthesia index to detect awareness under anesthesia

Spontaneous electroencephalogram (EEG) and auditory evoked potentials (AEP) have been suggested to monitor the level of consciousness during anesthesia. As both signals reflect different neuronal pathways, a combination of parameters from both signals may provide broader information about the brain status during anesthesia. Appropriate parameter selection and combination to a single index is crucial to take advantage of this potential. The field of machine learning offers algorithms for both parameter selection and combination. In this study, several established machine learning approaches including a method for the selection of suitable signal parameters and classification algorithms are applied to construct an index which predicts responsiveness in anesthetized patients. The present analysis considers several classification algorithms, among those support vector machines, artificial neural networks and Bayesian learning algorithms. On the basis of data from the transition between consciousness and unconsciousness, a combination of EEG and AEP signal parameters developed with automated methods provides a maximum prediction probability of 0.935, which is higher than 0.916 (for EEG parameters) and 0.880 (for AEP parameters) using a cross-validation approach. This suggests that machine learning techniques can successfully be applied to develop an improved combined EEG and AEP parameter to separate consciousness from unconsciousness