scholarly journals Structured decomposition improves systems serology prediction and interpretation

2021 ◽  
Author(s):  
Madeleine Murphy ◽  
Scott D. Taylor ◽  
Aaron S. Meyer
Keyword(s):  
Data Reduction ◽  
Humoral Response ◽  
Antigen Binding ◽  
General Strategy ◽  
List Type ◽  
Tensor Factorization ◽  
Missing Measurements ◽  
Functional Responses ◽  
Decomposition Structure

AbstractSystems serology measurements provide a comprehensive view of humoral immunity by profiling both the antigen-binding and Fc properties of antibodies. Identifying patterns in these measurements will help to guide vaccine and therapeutic antibody development, and improve our understanding of disorders. Furthermore, consistent patterns across diseases may reflect conserved regulatory mechanisms; recognizing these may help to combine modalities such as vaccines, antibody-based interventions, and other immunotherapies to maximize protection. A common feature of systems serology studies is structured biophysical profiling across disease-relevant antigen targets, properties of antibodies’ interaction with the immune system, and serological samples. These are typically produced alongside additional measurements that are not antigen-specific. Here, we report a new form of tensor factorization, total tensor-matrix factorization (TMTF), which can greatly reduce these data into consistently observed patterns by recognizing the structure of these data. We use a previous study of HIV-infected subjects as an example. TMTF outperforms standard methods like principal components analysis in the extent of reduction possible. Data reduction, in turn, improves the prediction of immune functional responses, classification of subjects based on their HIV control status, and interpretation of these resulting models. Interpretability is improved specifically through further data reduction, separation of the constant region from antigen-binding effects, and recognizing consistent patterns across individual measurements. Therefore, we propose that TMTF will be an effective general strategy for exploring and using systems serology.Summary pointsStructured decomposition provides substantial data reduction without loss of information.Predictions based on decomposed factors are accurate and robust to missing measurements.Decomposition structure improves the interpretability of modeling results.Decomposed factors represent meaningful patterns in the HIV humoral response.

scholarly journals The local structure of the free boundary in the fractional obstacle problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Matteo Focardi ◽  
Emanuele Spadaro
Keyword(s):  
Hausdorff Dimension ◽  
Free Boundary ◽  
Hausdorff Measure ◽  
Local Structure ◽  
Obstacle Problem ◽  
List Type ◽  
Minkowski Content ◽  
Local Finiteness ◽  
Lower Dimensional

AbstractBuilding upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in {\mathbb{R}^{n+1}} with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null {{\mathcal{H}}^{n-1}} measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] and therefore we retrieve the same results:(i)local finiteness of the {(n-1)}-dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure),(ii){{\mathcal{H}}^{n-1}}-rectifiability of the free boundary,(iii)classification of the frequencies and of the blowups up to a set of Hausdorff dimension at most {(n-2)} in the free boundary.Instead, if {\varphi\in C^{k+1}(\mathbb{R}^{n})}, {k\geq 2}, similar results hold only for distinguished subsets of points in the free boundary where the order of contact of the solution with the obstacle function φ is less than {k+1}.

scholarly journals Because space matters: conceptual framework to help distinguish slum from non-slum urban areas

2019 ◽  
Vol 4 (2) ◽  
pp. e001267 ◽  
Author(s):  
Richard Lilford ◽  
Catherine Kyobutungi ◽  
Robert Ndugwa ◽  
Jo Sartori ◽  
Samuel I Watson ◽  
...  
Keyword(s):  
Conceptual Framework ◽  
Urban Areas ◽  
Urban Landscape ◽  
Well Being ◽  
Urban Slum ◽  
List Type ◽  
Slum Area ◽  
Fine Grained ◽  
Basic Approaches

Despite an estimated one billion people around the world living in slums, most surveys of health and well-being do not distinguish between slum and non-slum urban residents. Identifying people who live in slums is important for research purposes and also to enable policymakers, programme managers, donors and non-governmental organisations to better target investments and services to areas of greatest deprivation. However, there is no consensus on what a slum is let alone how slums can be distinguished from non-slum urban precincts. Nor has attention been given to a more fine-grained classification of urban spaces that might go beyond a simple slum/non-slum dichotomy. The purpose of this paper is to provide a conceptual framework to help tackle the related issues of slum definition and classification of the urban landscape. We discuss:The concept of space as an epidemiological variable that results in ‘neighbourhood effects’.The problems of slum area definition when there is no ‘gold standard’.A long-list of variables from which a selection must be made in defining or classifying urban slum spaces.Methods to combine any set of identified variables in an operational slum area definition.Two basic approaches to spatial slum area definitions—top-down (starting with a predefined area which is then classified according to features present in that area) and bottom-up (defining the areal unit based on its features).Different requirements of a slum area definition according to its intended use.Implications for research and future development.

scholarly journals Limits to measurement in experiments governed by algorithms

2010 ◽  
Vol 20 (6) ◽  
pp. 1019-1050 ◽  
Author(s):  
EDWIN J. BEGGS ◽  
JOSÉ FÉLIX COSTA ◽  
JOHN V. TUCKER
Keyword(s):  
Physical Experiment ◽  
Complexity Classes ◽  
List Type ◽  
Turing Machines ◽  
Experimental Procedure ◽  
Physical Systems ◽  
Physical Measurements ◽  
Physical Experiments ◽  
Physical Quantities

We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment?In a programme to study the nature of computation possible by physical systems, and by algorithms coupled with physical systems, we have begun to analyse: (i)the algorithmic nature of experimental procedures; and(ii)the idea of using a physical experiment as an oracle to Turing Machines. To answer the question, we will extend our theory of experimental oracles so that we can use Turing machines to model the experimental procedures that govern the conduct of physical experiments. First, we specify an experiment that measures mass via collisions in Newtonian dynamics and examine its properties in preparation for its use as an oracle. We begin the classification of the computational power of polynomial time Turing machines with this experimental oracle using non-uniform complexity classes. Second, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on what can be measured using equipment. Indeed, the theorems suggest a new form of uncertainty principle for our knowledge of physical quantities measured in simple physical experiments. We argue that the results established here are representative of a huge class of experiments.

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