Topology highlights mesoscopic functional equivalence between imagery and perception: The case of hypnotizability.

The functional equivalence (FE) between imagery and perception or motion has been proposed on the basis of neuroimaging evidence of large spatially overlapping activations between real and imagined sensori-motor conditions. However, similar local activation patterns do not imply the same mesoscopic integration of brain regions, which can be described by tools from Topological Data Analysis (TDA). On the basis of behavioral findings, stronger FE has been hypothesized in the individuals with high scores of hypnotizability scores (highs) with respect to low hypnotizable participants (lows) who differ between each other in the proneness to modify memory, perception and behavior according to specific imaginative suggestions. Here we present the first EEG evidence of stronger FE in highs. In fact, persistent homology shows that the highs EEG topological asset during real and imagined sensory conditions is significantly more similar than the lows. As a corollary finding, persistent homology shows lower restructuring of the EEG asset in highs than in lows during both sensory and imagery tasks with respect to basal conditions. Present findings support the view that greater embodiment of mental images may be responsible for the highs greater proneness to respond to sensori-motor suggestions and to report involuntariness in action. In addition, findings indicate hypnotizability-related sensory and cognitive information processing and suggest that the psycho-physiological trait of hypnotizability may modulate more than one aspect of the everyday life.

Spectral and topological analyses of the cortical representation of the head position: Does hypnotizability matter?

INTRODUCTION: The aim of this exploratory study was to assess the EEG correlates of head positions (which have never been studied in humans) in participants with different psychophysiological characteristics, as encoded by their hypnotizability scores. This choice is motivated by earlier studies suggesting different processing of vestibular/neck proprioceptive information in subjects with high (highs) and low (lows) hypnotizability scores maintaining their head rotated toward one side (RH). METHODS: We analyzed EEG signals recorded in 20 highs and 19 lows in basal conditions (head forward) and during RH using spectral analysis, which captures changes localized to specific recording sites, and topological data analysis (TDA), which instead describes large-scale differences in processing and representing sensorimotor information. RESULTS: Spectral analysis revealed significant differences related to head position for alpha 1, beta 2, beta 3, and gamma bands, but not to hypnotizability. TDA instead revealed global hypnotizability-related differences in the strengths of the correlations among recording sites during RH. Significant changes were observed in lows on the left parieto-occipital side and in highs in right frontoparietal region. Significant differences between the two groups were found in the occipital region, where changes were larger in lows than in highs. CONCLUSIONS: This study reports finding of the EEG correlates of changes in the head posture for the first time, indicating that hypnotizability is related to the head posture representation/processing on large-scale networks and that spectral and topological data analyses provide complementary results.

Analysis of Big Data in Gait Biomechanics: Current Trends and Future Directions.

The increasing amount of data in biomechanics research has greatly increased the importance of developing advanced multivariate analysis and machine learning techniques, which are better able to handle "big data". Consequently, advances in data science methods will expand the knowledge for testing new hypotheses about biomechanical risk factors associated with walking and running gait-related musculoskeletal injury. This paper begins with a brief introduction to an automated three-dimensional (3D) biomechanical gait data collection system: 3D GAIT, followed by how the studies in the field of gait biomechanics fit the quantities in the 5 V's definition of big data: volume, velocity, variety, veracity, and value. Next, we provide a review of recent research and development in multivariate and machine learning methods-based gait analysis that can be applied to big data analytics. These modern biomechanical gait analysis methods include several main modules such as initial input features, dimensionality reduction (feature selection and extraction), and learning algorithms (classification and clustering). Finally, a promising big data exploration tool called "topological data analysis" and directions for future research are outlined and discussed.

Navigating features: a topologically informed chart of electromyographic features space.

The success of biological signal pattern recognition depends crucially on the selection of relevant features. Across signal and imaging modalities, a large number of features have been proposed, leading to feature redundancy and the need for optimal feature set identification. A further complication is that, due to the inherent biological variability, even the same classification problem on different datasets can display variations in the respective optimal sets, casting doubts on the generalizability of relevant features. Here, we approach this problem by leveraging topological tools to create charts of features spaces. These charts highlight feature sub-groups that encode similar information (and their respective similarities) allowing for a principled and interpretable choice of features for classification and analysis. Using multiple electromyographic (EMG) datasets as a case study, we use this feature chart to identify functional groups among 58 state-of-the-art EMG features, and to show that they generalize across three different forearm EMG datasets obtained from able-bodied subjects during hand and finger contractions. We find that these groups describe meaningful non-redundant information, succinctly recapitulating information about different regions of feature space. We then recommend representative features from each group based on maximum class separability, robustness and minimum complexity.

Evolutionary escape on complex genotype-phenotype networks.

We study the problem of evolutionary escape that is the process whereby a population under sudden changes in the selective pressures acting upon it try to evade extinction by evolving from previously well-adapted phenotypes to those that are favoured by the new selective pressure. We perform a comparative analysis between results obtained by modelling genotype space as a regular hypercube (H-graphs), which is the scenario considered in previous work on the subject, to those corresponding to a complex genotype-phenotype network (B-graphs). In order to analyse the properties of the escape process on both these graphs, we apply a general theory based on multi-type branching processes to compute the evolutionary dynamics and probability of escape. We show that the distribution of distances between phenotypes in B-graphs exhibits a much larger degree of heterogeneity than in H-graphs. This property, one of the main structural differences between both types of graphs, causes heterogeneous behaviour in all results associated to the escape problem. We further show that, due to the heterogeneity characterising escape on B-graphs, escape probability can be underestimated by assuming a regular hypercube genotype network, even if we compare phenotypes at the same distance in H-graphs. Similarly, it appears that the complex structure of B-graphs slows down the rate of escape.

Surviving evolutionary escape on complex genotype-phenotype networks.

We study the problem of evolutionary escape and survival of cell populations with a genotype-phenotype structure. We refer to evolutionary escape as the process where a cell of a given ill-adapted population to reach a well-adapted phenotype. Similarly, survival refers to the dynamics of the population once the escape phenotype has been reached. The aim of this paper is to analyse the influence of topological properties associated to robustness and evolvability on the probability of escape and on the probability of survival. In order to explore these issues, we formulate a population dynamics model, consisting of a multi-type time-continuous branching process, where types are associated to genotypes and their birth and death probabilities depend on the associated phenotype (non-escape or escape). We exploit the separation of time scales introduced by the the difference in reproductive ratios between the ill-adapted phenotypes and the escape phenotype. Two dynamical regimes emerge: a fast-decaying regime associated to the escape process itself, and a slow regime which corresponds to the survival dynamics of the population once the escape phenotype has been reached. We exploit this separation of time scales to analyse the topological factors which determine escape and survival probabilities. We show that, while the escape probability depends on the degree of escape phenotype, the probability of survival is essentially determined by its robustness, measured in terms of a weighted clustering coefficient.

EM for phylogenetic topology reconstruction on nonhomogeneous data.

BACKGROUND: The reconstruction of the phylogenetic tree topology of four taxa is, still nowadays, one of the main challenges in phylogenetics. Its difficulties lie in considering not too restrictive evolutionary models, and correctly dealing with the long-branch attraction problem. The correct reconstruction of 4-taxon trees is crucial for making quartet-based methods work and being able to recover large phylogenies. METHODS: We adapt the well known expectation-maximization algorithm to evolutionary Markov models on phylogenetic 4-taxon trees. We then use this algorithm to estimate the substitution parameters, compute the corresponding likelihood, and to infer the most likely quartet. RESULTS: In this paper we consider an expectation-maximization method for maximizing the likelihood of (time nonhomogeneous) evolutionary Markov models on trees. We study its success on reconstructing 4-taxon topologies and its performance as input method in quartet-based phylogenetic reconstruction methods such as QFIT and QuartetSuite. Our results show that the method proposed here outperforms neighbor-joining and the usual (time-homogeneous continuous-time) maximum likelihood methods on 4-leaved trees with among-lineage instantaneous rate heterogeneity, and perform similarly to usual continuous-time maximum-likelihood when data satisfies the assumptions of both methods. CONCLUSIONS: The method presented in this paper is well suited for reconstructing the topology of any number of taxa via quartet-based methods and is highly accurate, specially regarding largely divergent trees and time nonhomogeneous data.

The topology of robustness and evolvability in evolutionary systems with genotype-phenotype map.

In this paper we formulate a topological definition of the concepts of robustness and evolvability. We start our investigation by formulating a multiscale model of the evolutionary dynamics of a population of cells. Our cells are characterised by a genotype-phenotype map: their chances of survival under selective pressure are determined by their phenotypes, whereas the latter are determined their genotypes. According to our multiscale dynamics, the population dynamics generates the evolution of a genotype-phenotype network. Our representation of the genotype-phenotype network is similar to previously described ones, but has a novel element, namely, our network contains two types of nodes: genotype and phenotype nodes. This network representation allows us to characterise robustness and evolvability in terms of its topological properties: phenotypic robustness by means of the clustering coefficient of the phenotype nodes, and evolvability as the emergence of giant connected component which allows navigation between phenotypes. This topological definition of evolvability allows us to characterise the so-called robustness of evolvability, which is defined in terms of the robustness against attack (i.e. edge removal) of the giant connected component. An investigation of the factors that affect the robustness of evolvability shows that phenotypic robustness and the cryptic genetic variation are key to the integrity of the ability to innovate. These results fit within the framework of a number of models which point out that robustness favours rather than hindering evolvability. We further show that the corresponding phenotype network, defined as the one-component projection of the whole genotype-phenotype network, exhibits the small-world phenomenon, which implies that in this type of evolutionary system the rate of adaptability is enhanced.