10,958 research outputs found
Resolving structural variability in network models and the brain
Large-scale white matter pathways crisscrossing the cortex create a complex
pattern of connectivity that underlies human cognitive function. Generative
mechanisms for this architecture have been difficult to identify in part
because little is known about mechanistic drivers of structured networks. Here
we contrast network properties derived from diffusion spectrum imaging data of
the human brain with 13 synthetic network models chosen to probe the roles of
physical network embedding and temporal network growth. We characterize both
the empirical and synthetic networks using familiar diagnostics presented in
statistical form, as scatter plots and distributions, to reveal the full range
of variability of each measure across scales in the network. We focus on the
degree distribution, degree assortativity, hierarchy, topological Rentian
scaling, and topological fractal scaling---in addition to several summary
statistics, including the mean clustering coefficient, shortest path length,
and network diameter. The models are investigated in a progressive, branching
sequence, aimed at capturing different elements thought to be important in the
brain, and range from simple random and regular networks, to models that
incorporate specific growth rules and constraints. We find that synthetic
models that constrain the network nodes to be embedded in anatomical brain
regions tend to produce distributions that are similar to those extracted from
the brain. We also find that network models hardcoded to display one network
property do not in general also display a second, suggesting that multiple
neurobiological mechanisms might be at play in the development of human brain
network architecture. Together, the network models that we develop and employ
provide a potentially useful starting point for the statistical inference of
brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material
Exploiting network topology for large-scale inference of nonlinear reaction models
The development of chemical reaction models aids understanding and prediction
in areas ranging from biology to electrochemistry and combustion. A systematic
approach to building reaction network models uses observational data not only
to estimate unknown parameters, but also to learn model structure. Bayesian
inference provides a natural approach to this data-driven construction of
models. Yet traditional Bayesian model inference methodologies that numerically
evaluate the evidence for each model are often infeasible for nonlinear
reaction network inference, as the number of plausible models can be
combinatorially large. Alternative approaches based on model-space sampling can
enable large-scale network inference, but their realization presents many
challenges. In this paper, we present new computational methods that make
large-scale nonlinear network inference tractable. First, we exploit the
topology of networks describing potential interactions among chemical species
to design improved "between-model" proposals for reversible-jump Markov chain
Monte Carlo. Second, we introduce a sensitivity-based determination of move
types which, when combined with network-aware proposals, yields significant
additional gains in sampling performance. These algorithms are demonstrated on
inference problems drawn from systems biology, with nonlinear differential
equation models of species interactions
Using Topological Data Analysis for diagnosis pulmonary embolism
Pulmonary Embolism (PE) is a common and potentially lethal condition. Most
patients die within the first few hours from the event. Despite diagnostic
advances, delays and underdiagnosis in PE are common.To increase the diagnostic
performance in PE, current diagnostic work-up of patients with suspected acute
pulmonary embolism usually starts with the assessment of clinical pretest
probability using plasma d-Dimer measurement and clinical prediction rules. The
most validated and widely used clinical decision rules are the Wells and Geneva
Revised scores. We aimed to develop a new clinical prediction rule (CPR) for PE
based on topological data analysis and artificial neural network. Filter or
wrapper methods for features reduction cannot be applied to our dataset: the
application of these algorithms can only be performed on datasets without
missing data. Instead, we applied Topological data analysis (TDA) to overcome
the hurdle of processing datasets with null values missing data. A topological
network was developed using the Iris software (Ayasdi, Inc., Palo Alto). The PE
patient topology identified two ares in the pathological group and hence two
distinct clusters of PE patient populations. Additionally, the topological
netowrk detected several sub-groups among healthy patients that likely are
affected with non-PE diseases. TDA was further utilized to identify key
features which are best associated as diagnostic factors for PE and used this
information to define the input space for a back-propagation artificial neural
network (BP-ANN). It is shown that the area under curve (AUC) of BP-ANN is
greater than the AUCs of the scores (Wells and revised Geneva) used among
physicians. The results demonstrate topological data analysis and the BP-ANN,
when used in combination, can produce better predictive models than Wells or
revised Geneva scores system for the analyzed cohortComment: 18 pages, 5 figures, 6 tables. arXiv admin note: text overlap with
arXiv:cs/0308031 by other authors without attributio
Sequential Monte Carlo with transformations
This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an extremely flexible and general algorithm for Bayesian model comparison that is suitable for use in applications where the acceptance rate in reversible jump Markov chain Monte Carlo is low. We use this approach on model comparison for mixture models, and for inferring coalescent trees sequentially, as data arrives
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