Topological Information Data Analysis

Artificial Intelligence Applied to Forced Spirometry in Primary Care

Introduction

This study aims to create an artificial intelligence (AI) based machine learning (ML) model capable of predicting a spirometric obstructive pattern using variables with the highest predictive power derived from an active case-finding program for COPD in primary care.

Material and methods

A total of 1190 smokers, aged 30-80 years old with no prior history of respiratory disease, underwent spirometry with bronchodilation. The sample was analyzed using AI tools. Based on an exploratory data analysis (EDA), independent variables (according to mutual information analysis) were trained using a gradient boosting algorithm (GBT) and validated through cross-validation.

Results

With an area under the curve close to unity, the model predicted a spirometric obstructive pattern using variables with the highest predictive power: FEV1_theoretical_pre values. Sensitivity: 93%. Positive predictive value: 94%. Specificity: 97%. Negative predictive value: 96%. Accuracy: 95%. Precision: 94%.

Conclusion

An ML model can predict the presence of an obstructive pattern in spirometry in a primary care smoking population with no prior diagnosis of respiratory disease using the FEV1_theoretical_pre values with an accuracy and precision exceeding 90%. Further studies including clinical data and strategies for integrating AI into clinical workflow are needed.

A unified method for assessing the observability of dynamic complex systems

PROBLEM

Systems theory applied to biology and medicine assumes that the complexity of a system can be described by quasi-generic models to predict the behavior of many other similar systems. To this end, the aim of various research works in systems theory is to develop inductive modeling (based on data-intensive analysis) or deductive modeling (based on the deduction of mechanistic principles) to discover patterns and identify plausible correlations between past and present events, or to connect different causal relationships of interacting elements at different scales and compute mathematical predictions. Mathematical principles assume that there are constant and observable universal causal principles that apply to all biological systems. Nowadays, there are no suitable tools to assess the soundness of these universal causal principles, especially considering that organisms not only respond to environmental stimuli (and inherent processes) across multiple scales but also integrate information about and within these scales. This implies an uncontrollable degree of uncertainty.

METHODOLOGY

A method has been developed to detect the stability of causal processes by evaluating the information contained in the trajectories identified in a phase space. Time series patterns are analyzed using concepts from geometric information theory and persistent homology. In essence, recognizing these patterns in different time periods and evaluating their geometrically integrated information leads to the assessment of causal relationships. With this method, and together with the evaluation of persistent entropy in trajectories in relation to different individual systems, we have developed a method called Φ-S diagram as a complexity measure to recognize when organisms follow causal pathways leading to mechanistic responses.

RESULTS

We calculated the Φ-S diagram of a deterministic dataset available in the ICU repository to test the method's interpretability. We also calculated the Φ-S diagram of time series from health data available in the same repository. This includes patients' physiological response to sport measured with wearables outside laboratory conditions. We confirmed the mechanistic nature of both datasets in both calculations. In addition, there is evidence that some individuals show a high degree of autonomous response and variability. Therefore, persistent individual variability may limit the ability to observe the cardiac response. In this study, we present the first demonstration of the concept of developing a more robust framework for representing complex biological systems.

May the 4C's be with you: an overview of complexity-inspired frameworks for analysing resting-state neuroimaging data

Competing and complementary models of resting-state brain dynamics contribute to our phenomenological and mechanistic understanding of whole-brain coordination and communication, and provide potential evidence for differential brain functioning associated with normal and pathological behaviour. These neuroscientific theories stem from the perspectives of physics, engineering, mathematics and psychology and create a complicated landscape of domain-specific terminology and meaning, which, when used outside of that domain, may lead to incorrect assumptions and conclusions within the neuroscience community. Here, we review and clarify the key concepts of connectivity, computation, criticality and coherence-the 4C's-and outline a potential role for metastability as a common denominator across these propositions. We analyse and synthesize whole-brain neuroimaging research, examined through functional magnetic imaging, to demonstrate that complexity science offers a principled and integrated approach to describe, and potentially understand, macroscale spontaneous brain functioning.

A hands-on tutorial on network and topological neuroscience

The brain is an extraordinarily complex system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pairwise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

Alleviating the independence assumptions of averaged one-dependence estimators by model weighting

Of numerous proposals to refine naive Bayes by weakening its attribute independence assumption, averaged one-dependence estimators (AODE) has been shown to be able to achieve significantly higher classification accuracy at a moderate cost in classification efficiency. However, all one-dependence estimators (ODEs) in AODE have the same weights and are treated equally. To address this issue, model weighting, which assigns discriminate weights to ODEs and then linearly combine their probability estimates, has been proved to be an efficient and effective approach. Most information-theoretic weighting metrics, including mutual information, Kullback-Leibler measure and the information gain, place more emphasis on the correlation between root attribute (value) and class variable. We argue that the topology of each ODE can be divided into a set of local directed acyclic graphs (DAGs) based on the independence assumption, and multivariate mutual information is introduced to measure the extent to which the DAGs fit data. Based on this premise, in this study we propose a novel weighted AODE algorithm, called AWODE, that adaptively selects weights to alleviate the independence assumption and make the learned probability distribution fit the instance. The proposed approach is validated on 40 benchmark datasets from UCI machine learning repository. The experimental results reveal that, AWODE achieves bias-variance trade-off and is a competitive alternative to single-model Bayesian learners (such as TAN and KDB) and other weighted AODEs (such as WAODE).

A relational approach to consciousness: categories of level and contents of consciousness

Characterizing consciousness in and of itself is notoriously difficult. Here, we propose an alternative approach to characterize, and eventually define, consciousness through exhaustive descriptions of consciousness' relationships to all other consciousness. This approach is founded in category theory. Indeed, category theory can prove that two objects A and B in a category can be equivalent if and only if all the relationships that A holds with others in the category are the same as those of B; this proof is called the Yoneda lemma. To introduce the Yoneda lemma, we gradually introduce key concepts of category theory to consciousness researchers. Along the way, we propose several possible definitions of categories of consciousness, both in terms of level and contents, through the usage of simple examples. We propose to use the categorical structure of consciousness as a gold standard to formalize empirical research (e.g. color qualia structure at fovea and periphery) and, especially, the empirical testing of theories of consciousness.

A machine learning-based clustering approach to diagnose multi-component degradation of aircraft fuel systems

Accurate fault diagnosis and prognosis can significantly reduce maintenance costs, increase the safety and availability of engineering systems that have become increasingly complex. It has been observed that very limited researches have been reported on fault diagnosis where multi-component degradation are presented. This is essentially a challenging Complex Systems problem where features multiple components interacting simultaneously and nonlinearly with each other and its environment on multiple levels. Even the degradation of a single component can lead to a misidentification of the fault severity level. This paper introduces a new test rig to simulate the multi-component degradation of the aircraft fuel system. A machine learning-based data analytical approach based on the classification of clustering features from both time and frequency domains is proposed. The scope of this framework is the identification of the location and severity of not only the system fault but also the multi-component degradation. The results illustrate that (a) the fault can be detected with accuracy > 99%; (b) the severity of fault can be identified with an accuracy of almost 100%; (c) the degradation level can be successfully identified with the R-square value > 0.9.

What do people mean when they talk about mindfulness?

Psychological theories cast mindfulness as a form of awareness in which accepting the presence of stressful thoughts and feelings facilitates engaged exploration and identification of adaptive responses. Critics of mindfulness' popularization suggest that lay people misconstrue acceptance as a passive endorsement of experience, undermining engaged problem-solving. To evaluate this criticism, we traced the contemporary semantic meaning of mindfulness in three of the most extensive linguistic corpora of English language and found that general public's depictions of mindfulness highlight engagement-related processes. We further analyzed the nomological network of mindfulness. While mindfulness theories suggest a general convergence of facets representing awareness and acceptance, in a meta-analysis (k = 145; N = 41,966) of the Five Facet Mindfulness Questionnaire only expert- and clinical samples reported convergence, whereas lay people showed absent or even antagonistic associations. Further, contrary to the synergistic model of awareness and acceptance contributing to greater engagement, empirical probes of two lay samples (N_total = 406) show that acceptance is either unrelated or inversely related to markers of engagement. To overcome resulting conceptual and methodological challenges, we highlight the need for a contextualized mindfulness framework whereby acceptance enables the process of engaging with life's challenges rather than avoiding them.

Entropy 2021 Best Paper Award

On behalf of the Editor-in-Chief, Prof [...].

EEG Synchronization-Parameters in Patients With Subcortical Arteriosclerotic Encephalopathy and Gait Disorder

PURPOSE

Subcortical arteriosclerotic encephalopathy (SAE) is characterized by extensive white matter lesions in the MRI. Clinical symptoms are cognitive impairment, ranging from mild deficits to vascular dementia, impaired executive functioning, and gait disorders. In the EEG of SAE patients with vascular dementia, the lower frequencies are increased. However, it is unclear whether EEG changes also exist in SAE patients with gait disorders but without vascular dementia.

METHODS

The authors analyzed the EEGs of 50 nondemented patients with SAE and gait disorders and 50 healthy controls applying pointwise transinformation as a measure of synchronization.

RESULTS

Hundred seconds of waking EEG that appeared unaltered in visual analysis were sufficient to prove changes in synchronization. The authors found a decrease in the mean level of synchronization, combined with an elongation of synchronization time in all examined brain areas. These effects correlated slightly with the extent of subcortical lesions.

CONCLUSIONS

Changes in EEG synchronization in patients with SAE and gait disorders seem to occur independently of cognitive function. The causal relationship of the changes in EEG synchronization and gait disorders remains to be clarified. The results of this study might point to a decrease in coupling efficiency in these patients, with the increase in synchronization duration as a possible compensatory mechanism. Because a time-efficient signal transmission particularly during gait execution is crucial, reduced efficiency might contribute to an impairment of postural stabilization. The study results might indicate a neuronal network for planning and execution of motor activity and particularly gait, extending from the frontal over the central to the parietal cortex.

Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience

The large number of ion channels found in all nervous systems poses fundamental questions concerning how the characteristic intrinsic properties of single neurons are determined by the specific subsets of channels they express. All neurons display many different ion channels with overlapping voltage- and time-dependent properties. We speculate that these overlapping properties promote resilience in neuronal function. Individual neurons of the same cell type show variability in ion channel conductance densities even though they can generate reliable and similar behavior. This complicates a simple assignment of function to any conductance and is associated with variable responses of neurons of the same cell type to perturbations, deletions, and pharmacological manipulation. Ion channel genes often show strong positively correlated expression, which may result from the molecular and developmental rules that determine which ion channels are expressed in a given cell type.

A Complex Systems Perspective on Neuroimaging Studies of Behavior and Its Disorders

The study of complex systems deals with emergent behavior that arises as a result of nonlinear spatiotemporal interactions between a large number of components both within the system, as well as between the system and its environment. There is a strong case to be made that neural systems as well as their emergent behavior and disorders can be studied within the framework of complexity science. In particular, the field of neuroimaging has begun to apply both theoretical and experimental procedures originating in complexity science—usually in parallel with traditional methodologies. Here, we illustrate the basic properties that characterize complex systems and evaluate how they relate to what we have learned about brain structure and function from neuroimaging experiments. We then argue in favor of adopting a complex systems-based methodology in the study of neuroimaging, alongside appropriate experimental paradigms, and with minimal influences from noncomplex system approaches. Our exposition includes a review of the fundamental mathematical concepts, combined with practical examples and a compilation of results from the literature.

Beyond networks: Aligning qualitative and computational science studies

This article examines the thorny issue of the relationship (or lack thereof) between qualitative and quantitative approaches in Science and Technology Studies (STS). Although quantitative methods, broadly understood, played an important role in the beginnings of STS, these two approaches subsequently strongly diverged, leaving an increasing gap that only a few scholars have tried to bridge. After providing a short overview of the origins and development of quantitative analyses of textual corpora, we critically examine the state of the art in this domain. Focusing on the availability of advanced network structure analysis tools and Natural Language Processing workflows, we interrogate the fault lines between the increasing offer of computational tools in search of possible uses and the conceptual specifications of STS scholars wishing to explore the epistemic and ontological dimensions of techno-scientific activities. Finally, we point to possible ways to overcome the tension between ethnographic descriptions and quantitative methods while continuing to avoid the dichotomies (social/cognitive, organizing/experimenting) that STS has managed to discard.

A Path-Based Partial Information Decomposition

Based on the conceptual basis of information theory, we propose a novel mutual information measure-'path-based mutual information'. This information measure results from the representation of a set of random variables as a probabilistic graphical model. The edges in this graph are modeled as discrete memoryless communication channels, that is, the underlying data is ergodic, stationary, and the Markov condition is assumed to be applicable. The associated multilinear stochastic maps, tensors, transform source probability mass functions into destination probability mass functions. This allows for an exact expression of the resulting tensor of a cascade of discrete memoryless communication channels in terms of the tensors of the constituting communication channels in the paths. The resulting path-based information measure gives rise to intuitive, non-negative, and additive path-based information components-redundant, unique, and synergistic information-as proposed by Williams and Beer. The path-based redundancy satisfies the axioms postulated by Williams and Beer, the identity axiom postulated by Harder, and the left monotonicity axiom postulated Bertschinger. The ordering relations between redundancies of different joint collections of sources, as captured in the redundancy lattices of Williams and Beer, follow from the data processing inequality. Although negative information components can arise, we speculate that these either result from unobserved variables, or from adding additional sources that are statistically independent from all other sources to a system containing only non-negative information components. This path-based approach illustrates that information theory provides the concepts and measures for a partial information decomposition.

The Design of Global Correlation Quantifiers and Continuous Notions of Statistical Sufficiency

Using first principles from inference, we design a set of functionals for the purposes of ranking joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired behavior through the Principle of Constant Correlations (PCC), which constrains the correlation functional to behave in a consistent way under statistically independent inferential transformations. The PCC guides us in choosing the appropriate design criteria for constructing the desired functionals. Since the derivations depend on a choice of partitioning the variable space into n disjoint subspaces, the general functional we design is the n-partite information (NPI), of which the total correlation and mutual information are special cases. Thus, these functionals are found to be uniquely capable of determining whether a certain class of inferential transformations, ρ → ∗ ρ ' , preserve, destroy or create correlations. This provides conceptual clarity by ruling out other possible global correlation quantifiers. Finally, the derivation and results allow us to quantify non-binary notions of statistical sufficiency. Our results express what percentage of the correlations are preserved under a given inferential transformation or variable mapping.

Elements of qualitative cognition: An information topology perspective

Elementary quantitative and qualitative aspects of consciousness are investigated conjointly from the biology, neuroscience, physic and mathematic point of view, by the mean of a theory written with Bennequin that derives and extends information theory within algebraic topology. Information structures, that accounts for statistical dependencies within n-body interacting systems are interpreted a la Leibniz as a monadic-panpsychic framework where consciousness is information and physical, and arise from collective interactions. The electrodynamic intrinsic nature of consciousness, sustained by an analogical code, is illustrated by standard neuroscience and psychophysic results. It accounts for the diversity of the learning mechanisms, including adaptive and homeostatic processes on multiple scales, and details their expression within information theory. The axiomatization and logic of cognition are rooted in measure theory expressed within a topos intrinsic probabilistic constructive logic. Information topology provides a synthesis of the main models of consciousness (Neural Assemblies, Integrated Information, Global Neuronal Workspace, Free Energy Principle) within a formal Gestalt theory, an expression of information structures and patterns in correspondence with Galois cohomology and discrete symmetries. The methods provide new formalization of deep neural network with homologicaly imposed architecture applied to challenges in AI-machine learning.

Characterizing stochastic time series with ordinal networks

Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to their simplicity and computational efficiency. However, applications of ordinal networks have been mainly focused on time series arising from nonlinear dynamical systems, while basic properties of ordinal networks related to simple stochastic processes remain poorly understood. Here, we investigate several properties of ordinal networks emerging from random time series, noisy periodic signals, fractional Brownian motion, and earthquake magnitude series. For ordinal networks of random series, we present an approach for building the exact form of the adjacency matrix, which in turn is useful for detecting nonrandom behavior in time series and the existence of missing transitions among ordinal patterns. We find that the average value of a local entropy, estimated from transition probabilities among neighboring nodes of ordinal networks, is more robust against noise addition than the standard permutation entropy. We show that ordinal networks can be used for estimating the Hurst exponent of time series with accuracy comparable with state-of-the-art methods. Finally, we argue that ordinal networks can detect sudden changes in Earth's seismic activity caused by large earthquakes.

The Poincaré-Shannon Machine: Statistical Physics and Machine Learning Aspects of Information Cohomology

Previous works established that entropy is characterized uniquely as the first cohomology class in a topos and described some of its applications to the unsupervised classification of gene expression modules or cell types. These studies raised important questions regarding the statistical meaning of the resulting cohomology of information and its interpretation or consequences with respect to usual data analysis and statistical physics. This paper aims to present the computational methods of information cohomology and to propose its interpretations in terms of statistical physics and machine learning. In order to further underline the cohomological nature of information functions and chain rules, the computation of the cohomology in low degrees is detailed to show more directly that the k multivariate mutual information (Ik) are (k−1)-coboundaries. The (k−1)-cocycles condition corresponds to Ik=0, which generalizes statistical independence to arbitrary degree k. Hence, the cohomology can be interpreted as quantifying the statistical dependences and the obstruction to factorization. I develop the computationally tractable subcase of simplicial information cohomology represented by entropy Hk and information Ik landscapes and their respective paths, allowing investigation of Shannon’s information in the multivariate case without the assumptions of independence or of identically distributed variables. I give an interpretation of this cohomology in terms of phase transitions in a model of k-body interactions, holding both for statistical physics without mean field approximations and for data points. The I1 components define a self-internal energy functional Uk and (−1)kIk,k≥2 components define the contribution to a free energy functional Gk (the total correlation) of the k-body interactions. A basic mean field model is developed and computed on genetic data reproducing usual free energy landscapes with phase transition, sustaining the analogy of clustering with condensation. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, providing a trivial topological expression of the second law of thermodynamics. The local minima of free energy, related to conditional information negativity and conditional independence, characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. I give an interpretation of this complex in terms of unsupervised deep learning where the neural network architecture is given by the chain complex and conclude by discussing future supervised applications.