Universal approximation of input-output maps and dynamical systems by neural network architectures

It is well known that feedforward neural networks can approximate any continuous function supported on a finite-dimensional compact set to arbitrary accuracy. However, many engineering applications require modeling infinite-dimensional functions, such as sequence-to-sequence transformations or input-output characteristics of systems of differential equations. For discrete-time input-output maps having limited long-term memory, we prove universal approximation guarantees for temporal convolutional nets constructed using only a finite number of computation units which hold on an infinite-time horizon. We also provide quantitative estimates for the width and depth of the network sufficient to achieve any fixed error tolerance. Furthemore, we show that discrete-time input-output maps given by state-space realizations satisfying certain stability criteria admit such convolutional net approximations which are accurate on an infinite-time scale. For continuous-time input-output maps induced by dynamical systems that are stable in a similar sense, we prove that continuous-time recurrent neural nets are capable of reproducing the original trajectories to within arbitrarily small error tolerance over an infinite-time horizon. For a subset of these stable systems, we provide quantitative estimates on the number of neurons sufficient to guarantee the desired error bound

Fitting an immersed submanifold to data via Sussmann's orbit theorem

This paper describes an approach for fitting an immersed submanifold of a finite-dimensional Euclidean space to random samples. The reconstruction mapping from the ambient space to the desired submanifold is implemented as a composition of an encoder that maps each point to a tuple of (positive or negative) times and a decoder given by a composition of flows along finitely many vector fields starting from a fixed initial point. The encoder supplies the times for the flows. The encoder-decoder map is obtained by empirical risk minimization, and a high-probability bound is given on the excess risk relative to the minimum expected reconstruction error over a given class of encoder-decoder maps. The proposed approach makes fundamental use of Sussmann's orbit theorem, which guarantees that the image of the reconstruction map is indeed contained in an immersed submanifold

The medication mismanagement system : causes, evidence of user innovation, and a view towards a product/service solution for the elderly

Thesis (S.M. in Management and Engineering)--Massachusetts Institute of Technology, Engineering Systems Division, System Design and Management Program, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 77-78).Introduction: What could be easier than taking a pill? The doctor prescribes it, the pharmacist provides it and the patient swallows it with a glass of water twice a day for a cure; a very straightforward system of cause and effect. Unfortunately, statistics show that 66% of all Americans fail to take any of their prescription medicines (American Heart Association, 2009) and as a result many of the medical innovations that have increased life expectancy by 47 years since 1900 (Wan He, 2005) remain left unclaimed. So why than do Seniors, facing the pain of arthritis or the impending certainty of death from congestive heart failure, refuse to take their pills? The first half of this thesis seeks an answer to this question while debunking the view that this is a simple problem of ignorance or laziness on the part of the patient. In place of this oversimplified view, the problem of "medication management" is defined and cast in an in-depth and nuanced way that includes issues involving the patient, their caregiver, the disease state, social circumstances and financial constraints. The second half of this thesis focuses on possible solutions. While rethinking the entire medication system can result in great gains, the innovations discussed (both lead user and off-the-shelf innovations) all work within the current medication system and are addressable by product/service designers. By adhering to these two constraints the resulting solutions remain quickly implementable, cost effective and relevant to industry. In the end we find that end users have created a series of innovations and product modifications that address the physical and cognitive barriers they face, while product manufactures are innovating products and services that address the motivational issues users face.by Joshua A. Hanson.S.M.in Management and Engineerin

Assessing Competitive Reaction Rates in the Nitration of 2-Methylbiphenyl, Biphenyl, and Toluene to Determine Steric Restriction in Resonance-Stabilized Planarization of the Carbocation Intermediates

Electrophilic aromatic substitution (EAS) reactions have long been a fundamental addition to sophomore-level organic chemistry classes, allowing students the opportunity to explore the electron donating and withdrawing effects of electrons contained in the substituents of the aromatic reactant. In this paper we present preliminary findings on the nitration of methylated biphenyls using kinetic and regioselective assessments to analyze steric influences on the planarization of 2-methylbiphenyl after EAS nitration. Our preliminary findings show that nitration favors the methylated phenyl ring of 2-methylbiphenyl, indicating that the steric influence of the methyl group restricts planarization of the carbocation intermediate. Furthermore, a competition nitration reaction between biphenyl and toluene provides proof of concept for kinetic assessment of nitration rates that will eventually be applied to 2-methylbiphenyl; this competitive nitration showed that biphenyl nitrates 1.87 ± 0.61 (95% C.I.) times faster than toluene

The epidemiology and outcomes of central nervous system infections in Far North Queensland, tropical Australia; 2000-2019

Background: The epidemiology of central nervous system (CNS) infections in tropical Australia is incompletely defined. Methods: A retrospective study of all individuals in Far North Queensland, tropical Australia, who were diagnosed with a CNS infection between January 1, 2000, and December 31, 2019. The microbiological aetiology of the infection was correlated with patients' demographic characteristics and their clinical course. Results: There were 725 cases of CNS infection during the study period, meningitis (77.4%) was the most common, followed by brain abscess (11.6%), encephalitis (9.9%) and spinal infection (1.1%). Infants (24.3%, p<0.0001) and Aboriginal and Torres Strait Islander Australians (175/666 local residents, 26.3%, p<0.0001) were over-represented in the cohort. A pathogen was identified in 513 cases (70.8%); this was viral in 299 (41.2%), bacterial in 175 (24.1%) and fungal in 35 (4.8%). Cryptococcal meningitis (24 cases) was diagnosed as frequently as pneumococcal meningitis (24 cases). There were only 2 CNS infections with a S. pneumoniae serotype in the 13-valent pneumococcal vaccine after its addition to the National Immunisation schedule in 2011. Tropical pathogens-including Cryptococcus species (9/84, 11%), Mycobacterium tuberculosis (7/84, 8%) and Burkholderia pseudomallei (5/ 84, 6%)-were among the most common causes of brain abscess. However, arboviral CNS infections were rare, with only one locally acquired case-a dengue infection in 2009-diagnosed in the entire study period. Intensive Care Unit admission was necessary in 14.3%; the overall case fatality rate was 4.4%. Conclusion: Tropical pathogens cause CNS infections as commonly as traditional bacterial pathogens in this region of tropical Australia. However, despite being highlighted in the national consensus guidelines, arboviruses were identified very rarely. Prompt access to sophisticated diagnostic and supportive care in Australia's well-resourced public health system is likely to have contributed to the cohort's low case-fatality rate