Multiway analysis of epilepsy tensors

MOTIVATION: The success or failure of an epilepsy surgery depends greatly on the localization of epileptic focus (origin of a seizure). We address the problem of identification of a seizure origin through an analysis of ictal electroencephalogram (EEG), which is proven to be an effective standard in epileptic focus localization. SUMMARY: With a goal of developing an automated and robust way of visual analysis of large amounts of EEG data, we propose a novel approach based on multiway models to study epilepsy seizure structure. Our contributions are 3-fold. First, we construct an Epilepsy Tensor with three modes, i.e. time samples, scales and electrodes, through wavelet analysis of multi-channel ictal EEG. Second, we demonstrate that multiway analysis techniques, in particular parallel factor analysis (PARAFAC), provide promising results in modeling the complex structure of an epilepsy seizure, localizing a seizure origin and extracting artifacts. Third, we introduce an approach for removing artifacts using multilinear subspace analysis and discuss its merits and drawbacks. RESULTS: Ictal EEG analysis of 10 seizures from 7 patients are included in this study. Our results for 8 seizures match with clinical observations in terms of seizure origin and extracted artifacts. On the other hand, for 2 of the seizures, seizure localization is not achieved using an initial trial of PARAFAC modeling. In these cases, first, we apply an artifact removal method and subsequently apply the PARAFAC model on the epilepsy tensor from which potential artifacts have been removed. This method successfully identifies the seizure origin in both cases.     

Distributed parallel processing in the vertical vestibulo-ocular reflex: Learning networks compared to tensor theory

The vestibulo-ocular reflex (VOR) is capable of producing compensatory eye movements in three dimensions. It utilizes the head rotational velocity signals from the semicircular canals to control the contractions of the extraocular muscles. Since canal and muscle coordinate frames are not orthogonal and differ from one another, a sensorimotor transformation must be produced by the VOR neural network. Tensor theory has been used to construct a linear transformation that can model the three-dimensional behavior of the VOR. But tensor theory does not take the distributed, redundant nature of the VOR neural network into account. It suggests that the neurons subserving the VOR, such as vestibular nucleus neurons, should have specific sensitivity-vectors. Actual data, however, are not in accord. Data from the cat show that the sensitivity-vectors of vestibular nucleus neurons, rather than aligning with any specific vectors, are dispersed widely. As an alternative to tensor theory, we modeled the vertical VOR as a three-layered neural network programmed using the back-propagation learning algorithm. Units in mature networks had divergent sensitivity-vectors which resembled those of actual vestibular nucleus neurons in the cat. This similarity suggests that the VOR sensorimotor transformation may be represented redundantly rather than uniquely. The results demonstrate how vestibular nucleus neurons can encode the VOR sensorimotor transformation in a distributed manner.     

Information flow in interaction networks II: channels, path lengths, and potentials

In our previous publication, a framework for information flow in interaction networks based on random walks with damping was formulated with two fundamental modes: emitting and absorbing. While many other network analysis methods based on random walks or equivalent notions have been developed before and after our earlier work, one can show that they can all be mapped to one of the two modes. In addition to these two fundamental modes, a major strength of our earlier formalism was its accommodation of context-specific directed information flow that yielded plausible and meaningful biological interpretation of protein functions and pathways. However, the directed flow from origins to destinations was induced via a potential function that was heuristic. Here, with a theoretically sound approach called the channel mode, we extend our earlier work for directed information flow. This is achieved by constructing a potential function facilitating a purely probabilistic interpretation of the channel mode. For each network node, the channel mode combines the solutions of emitting and absorbing modes in the same context, producing what we call a channel tensor. The entries of the channel tensor at each node can be interpreted as the amount of flow passing through that node from an origin to a destination. Similarly to our earlier model, the channel mode encompasses damping as a free parameter that controls the locality of information flow. Through examples involving the yeast pheromone response pathway, we illustrate the versatility and stability of our new framework.     

Semantics of case

This paper presents a framework which connects case assignment with the semantics of argument realization. Broad notions of agency and affectedness are decomposed into more fine-grained semantic properties, loosely based on Dowty??s Proto-Role theory, but conceived in terms of privative opposition and organized into a lattice. This lattice provides a semantic space of participant properties and supports defining hierarchical relations among participant types, interpreted as semantic prominence, as well as topological relations such as ??closeness??, interpreted as semantic similarity between participant types. Cases are defined as connected regions of this space, relating a given case to a structured set of semantic properties. A case system is represented as a semantic system, which embodies oppositions and contrasts, and operates against the backdrop of the general semantics of argument realization, where one can define notions such as maximal agents and maximal patients and represent generalizations from the research on transitivity. Core case markers (e.g. ergative, accusative) are represented as subspaces of the lattice spreading outwards from the maximal agent and maximal patient nodes of the lattice. Case alternations arise when the subspace of the lattice delimited by a predicate??s entailments for an argument is partitioned by different cases, exemplified with the genitive/accusative alternation in Russian occurring with direct objects of certain intensional predicates. This method also provides a treatment of case polysemy, viz. a single case subsuming multiple uses, by relating the diverse uses at the more abstract semantic level of the case??s region on the lattice, demonstrated with non-canonical uses of the dative.     

Bayesian regression analysis of skewed tensor responses

Tensor regression analysis is finding vast emerging applications in a variety of clinical settings, including neuroimaging, genomics, and dental medicine. The motivation for this paper is a study of periodontal disease (PD) with an order-3 tensor response: multiple biomarkers measured at prespecified tooth–sites within each tooth, for each participant. A careful investigation would reveal considerable skewness in the responses, in addition to response missingness. To mitigate the shortcomings of existing analysis tools, we propose a new Bayesian tensor response regression method that facilitates interpretation of covariate effects on both marginal and joint distributions of highly skewed tensor responses, and accommodates missing-at-random responses under a closure property of our tensor model. Furthermore, we present a prudent evaluation of the overall covariate effects while identifying their possible variations on only a sparse subset of the tensor components. Our method promises Markov chain Monte Carlo (MCMC) tools that are readily implementable. We illustrate substantial advantages of our proposal over existing methods via simulation studies and application to a real data set derived from a clinical study of PD. The R package BSTN available in GitHub implements our model.     

The neural systems of tool and action semantics: a perspective from functional imaging.

This review discusses the contributions of functional imaging (fMRI/PET) to our understanding of how action and tool concepts are represented and processed in the human brain. Category-selective deficits in neuropsychological patients have suggested a fine-grained functional specialization within the neural systems of semantics. However, the underlying principles of semantic organization remain controversial. The feature-based account of semantic memory (or 'sensory-motor theory') predicates category-selective effects (e.g. tool vs. animals) on anatomical segregation for different semantic features (e.g. action vs. visual). Within this framework, we will review functional imaging evidence that semantic processing of tools and actions may rely on activations within the visuo-motor system.     

A general framework for analyzing data from two short time-series microarray experiments

We propose a general theoretical framework for analyzing differentially expressed genes and behavior patterns from two homogenous short time-course data. The framework generalizes the recently proposed Hilbert-Schmidt Independence Criterion (HSIC)-based framework adapting it to the time-series scenario by utilizing tensor analysis for data transformation. The proposed framework is effective in yielding criteria that can identify both the differentially expressed genes and time-course patterns of interest between two time-series experiments without requiring to explicitly cluster the data. The results, obtained by applying the proposed framework with a linear kernel formulation, on various data sets are found to be both biologically meaningful and consistent with published studies.     

Elementary Flux Modes Analysis of Functional Domain Networks Allows a Better Metabolic Pathway Interpretation

Metabolic network analysis is an important step for the functional understanding of biological systems. In these networks, enzymes are made of one or more functional domains often involved in different catalytic activities. Elementary flux mode (EFM) analysis is a method of choice for the topological studies of these enzymatic networks. In this article, we propose to use an EFM approach on networks that encompass available knowledge on structure-function. We introduce a new method that allows to represent the metabolic networks as functional domain networks and provides an application of the algorithm for computing elementary flux modes to analyse them. Any EFM that can be represented using the classical representation can be represented using our functional domain network representation but the fine-grained feature of functional domain networks allows to highlight new connections in EFMs. This methodology is applied to the tricarboxylic acid cycle (TCA cycle) of Bacillus subtilis, and compared to the classical analyses. This new method of analysis of the functional domain network reveals that a specific inhibition on the second domain of the lipoamide dehydrogenase (pdhD) component of pyruvate dehydrogenase complex leads to the loss of all fluxes. Such conclusion was not predictable in the classical approach.     

An ecoclimatic framework for evaluating the resilience of vegetation to water deficit

The surge in global efforts to understand the causes and consequences of drought on forest ecosystems has tended to focus on specific impacts such as mortality. We propose an ecoclimatic framework that takes a broader view of the ecological relevance of water deficits, linking elements of exposure and resilience to cumulative impacts on a range of ecosystem processes. This ecoclimatic framework is underpinned by two hypotheses: (i) exposure to water deficit can be represented probabilistically and used to estimate exposure thresholds across different vegetation types or ecosystems; and (ii) the cumulative impact of a series of water deficit events is defined by attributes governing the resistance and recovery of the affected processes. We present case studies comprising Pinus edulis and Eucalyptus globulus, tree species with contrasting ecological strategies, which demonstrate how links between exposure and resilience can be examined within our proposed framework. These examples reveal how climatic thresholds can be defined along a continuum of vegetation functional responses to water deficit regimes. The strength of this framework lies in identifying climatic thresholds on vegetation function in the absence of more complete mechanistic understanding, thereby guiding the formulation, application and benchmarking of more detailed modelling.     

Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic

We investigated protein motions using normal modes within a database framework, determining on a large sample the degree to which normal modes anticipate the direction of the observed motion and were useful for motions classification. As a starting point for our analysis, we identified a large number of examples of protein flexibility from a comprehensive set of structural alignments of the proteins in the PDB. Each example consisted of a pair of proteins that were considerably different in structure given their sequence similarity. On each pair, we performed geometric comparisons and adiabatic-mapping interpolations in a high-throughput pipeline, arriving at a final list of 3,814 putative motions and standardized statistics for each. We then computed the normal modes of each motion in this list, determining the linear combination of modes that best approximated the direction of the observed motion. We integrated our new motions and normal mode calculations in the Macromolecular Motions Database, through a new ranking interface at http://molmovdb.org. Based on the normal mode calculations and the interpolations, we identified a new statistic, mode concentration, related to the mathematical concept of information content, which describes the degree to which the direction of the observed motion can be summarized by a few modes. Using this statistic, we were able to determine the fraction of the 3,814 motions where one could anticipate the direction of the actual motion from only a few modes. We also investigated mode concentration in comparison to related statistics on combinations of normal modes and correlated it with quantities characterizing protein flexibility (e.g., maximum backbone displacement or number of mobile atoms). Finally, we evaluated the ability of mode concentration to automatically classify motions into a variety of simple categories (e.g., whether or not they are "fragment-like"), in comparison to motion statistics. This involved the application of decision trees and feature selection (particular machine-learning techniques) to training and testing sets derived from merging the "list" of motions with manually classified ones.     

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage savings over direct approaches.     

Time scale hierarchies in the functional organization of complex behaviors

Traditional approaches to cognitive modelling generally portray cognitive events in terms of 'discrete' states (point attractor dynamics) rather than in terms of processes, thereby neglecting the time structure of cognition. In contrast, more recent approaches explicitly address this temporal dimension, but typically provide no entry points into cognitive categorization of events and experiences. With the aim to incorporate both these aspects, we propose a framework for functional architectures. Our approach is grounded in the notion that arbitrary complex (human) behaviour is decomposable into functional modes (elementary units), which we conceptualize as low-dimensional dynamical objects (structured flows on manifolds). The ensemble of modes at an agent's disposal constitutes his/her functional repertoire. The modes may be subjected to additional dynamics (termed operational signals), in particular, instantaneous inputs, and a mechanism that sequentially selects a mode so that it temporarily dominates the functional dynamics. The inputs and selection mechanisms act on faster and slower time scales then that inherent to the modes, respectively. The dynamics across the three time scales are coupled via feedback, rendering the entire architecture autonomous. We illustrate the functional architecture in the context of serial behaviour, namely cursive handwriting. Subsequently, we investigate the possibility of recovering the contributions of functional modes and operational signals from the output, which appears to be possible only when examining the output phase flow (i.e., not from trajectories in phase space or time).     

Standardized descriptions of primate locomotor and postural modes

As quantitative studies on primate positional behavior accumulate the lack of a standard positional mode terminology is becoming an increasingly serious deficiency. Inconsistent use of traditional terms and inappropriate conflation of mode categories hamper interspecific and interobserver comparisons. Some workers use common terms without definition, allowing at least the possibility of misunderstanding. Other researchers coin neologisms tailored to their study species and not clearly enough defined to allow application to other species. Such neologisms may overlap, may completely encompass, or may conflate previously defined labels. The result is, at best, the proliferation of synonyms and, at worst, the creation of confusion where clarity had existed. Historical precedents have sometimes resulted in “catch-all” terms that conflate any number of kinematically different behaviors (e.g. “brachiation,” “climbing,” and “quadrumanous climbing”). We recognize three areas where distinction of positional modes has some current importance: (1) Modes that require humeral abduction should be distinguished from adducted behaviors; (2) locomotor modes that involve ascent or descent should be distinguished from horizontal locomotor modes; and (3) suspensory modes should be distinguished from supported modes. We recommend a nomenclature that is not dedicated to or derived from any one taxonomic subset of the primates. Here we define 32 primate positional modes, divided more finely into 52 postural sub-modes and 74 locomotor sub-modes.     

A general modeling framework for describing spatially structured population dynamics

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network‐based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life‐history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network‐based population is modeled with discrete time steps. Using both theoretical and real‐world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network‐based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.     

Orthogonal Invariant Sets of the Diffusion Tensor and the Development of a Curvilinear Set Suitable for Low-Anisotropy Tissues

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional anisotropy and the diffusion mode. The alternative invariant set possesses a different structure to the other known invariant sets; the second and third members of the curvilinear set measure the degree of orthotropy and oblateness/prolateness, respectively. The proposed advantage of these invariants is that they may work well in situations of low diffusion anisotropy and isotropy, as is often observed in tissues such as cartilage. We also explore the other orthogonal invariant sets in terms of their geometry in relation to eigenvalue space; a cylindrical set, a spherical set (including fractional anisotropy and the mode), and a log-Euclidean set. These three sets have a common structure. The first invariant measures the magnitude of the diffusion, the second and third invariants capture aspects of the anisotropy; the magnitude of the anisotropy and the shape of the diffusion ellipsoid (the manner in which the anisotropy is realised). We also show a simple method to prove the orthogonality of the invariants within a set.     

Collective motions in proteins investigated by X-ray diffuse scattering

We have developed theoretical models for analysis of X-ray diffuse scattering from protein crystals. A series of models are proposed to be used for experimental data with different degrees of precision. First, we propose the normal mode model, where conformational dynamics of a protein is assumed to occur mostly in a limited conformational subspace spanned by a small number of low-frequency normal modes in the protein. When high precision data are available, variances and covariances of the normal mode variables can be determined from experimental data using this model. For experimental data with lower degrees of precision, we introduce a series of simpler models. These models express the covariance matrix using relatively simple empirical correlation functions by assuming the correlation between a pair of atoms to be isotropic. As an application of these simpler models, we calculate diffuse-scattering patterns from a human lysozyme crystal to examine how each adjustable parameter in the models affects general features of the resulting patterns. The results of the calculation are summarized as follows. (1) The higher order scattering makes a significant contribution at high resolutions. (2) The resulting simulated patterns are sensitive to changes in correlation lengths of about 1 Å, as well as to changes of the functional form of the correlation function. (3) But only the “average” value of the intra- and intermolecular correlation lengths seems to determine the gross features of the pattern. (4) The effect of the atom-dependent amplitude of fluctuations is difficult to observe. © 1994 John Wiley & Sons, Inc.     

Characterizing conformation changes in proteins through the torsional elastic response

The relationship between functional conformation changes and thermal dynamics of proteins is investigated with the help of the torsional network model (TNM), an elastic network model in torsion angle space that we recently introduced. We propose and test a null-model of “random” conformation changes that assumes that the contributions of normal modes to conformation changes are proportional to their contributions to thermal fluctuations. Deviations from this null model are generally small. When they are large and significant, they consist in conformation changes that are represented by very few low frequency normal modes and overcome small energy barriers. We interpret these features as the result of natural selection favoring the intrinsic protein dynamics consistent with functional conformation changes. These “selected” conformation changes are more frequently associated to ligand binding, and in particular phosphorylation, than to pairs of conformations with the same ligands. This deep relationship between the thermal dynamics of a protein, represented by its normal modes, and its functional dynamics can reconcile in a unique framework the two models of conformation changes, conformational selection and induced fit. The program TNM that computes torsional normal modes and analyzes conformation changes is available upon request. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.     

Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance–covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.     

Reproducibility of Structural,Resting-State BOLD and DTI Data between Identical Scanners

Increasingly, clinical trials based on brain imaging are adopting multiple sites/centers to increase their subject pool and to expedite the studies, and more longitudinal studies are using multiple imaging methods to assess structural and functional changes. Careful investigation of the test-retest reliability and image quality of inter- or intra- scanner neuroimaging measurements are critical in the design, statistical analysis and interpretation of results. We propose a framework and specific metrics to quantify the reproducibility and image quality for neuroimaging studies (structural, BOLD and Diffusion Tensor Imaging) collected across identical scanners and following a major hardware repair (gradient coil replacement). We achieved consistent measures for the proposed metrics: structural (mean volume in specific regions and stretch factor), functional (temporal Signal-to-Noise ratio), diffusion (mean Fractional Anisotropy and Mean Diffusivity in multiple regions). The proposed frame work of imaging metrics should be used to perform daily quality assurance testing and incorporated into multi-center studies.     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.