19,317 research outputs found
Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese
Mandarin Chinese is characterized by being a tonal language; the pitch (or
) of its utterances carries considerable linguistic information. However,
speech samples from different individuals are subject to changes in amplitude
and phase which must be accounted for in any analysis which attempts to provide
a linguistically meaningful description of the language. A joint model for
amplitude, phase and duration is presented which combines elements from
Functional Data Analysis, Compositional Data Analysis and Linear Mixed Effects
Models. By decomposing functions via a functional principal component analysis,
and connecting registration functions to compositional data analysis, a joint
multivariate mixed effect model can be formulated which gives insights into the
relationship between the different modes of variation as well as their
dependence on linguistic and non-linguistic covariates. The model is applied to
the COSPRO-1 data set, a comprehensive database of spoken Taiwanese Mandarin,
containing approximately 50 thousand phonetically diverse sample contours
(syllables), and reveals that phonetic information is jointly carried by both
amplitude and phase variation.Comment: 49 pages, 13 figures, small changes to discussio
Systemic Risk in a Unifying Framework for Cascading Processes on Networks
We introduce a general framework for models of cascade and contagion
processes on networks, to identify their commonalities and differences. In
particular, models of social and financial cascades, as well as the fiber
bundle model, the voter model, and models of epidemic spreading are recovered
as special cases. To unify their description, we define the net fragility of a
node, which is the difference between its fragility and the threshold that
determines its failure. Nodes fail if their net fragility grows above zero and
their failure increases the fragility of neighbouring nodes, thus possibly
triggering a cascade. In this framework, we identify three classes depending on
the way the fragility of a node is increased by the failure of a neighbour. At
the microscopic level, we illustrate with specific examples how the failure
spreading pattern varies with the node triggering the cascade, depending on its
position in the network and its degree. At the macroscopic level, systemic risk
is measured as the final fraction of failed nodes, , and for each of
the three classes we derive a recursive equation to compute its value. The
phase diagram of as a function of the initial conditions, thus allows
for a prediction of the systemic risk as well as a comparison of the three
different model classes. We could identify which model class lead to a
first-order phase transition in systemic risk, i.e. situations where small
changes in the initial conditions may lead to a global failure. Eventually, we
generalize our framework to encompass stochastic contagion models. This
indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
A Quadratically Regularized Functional Canonical Correlation Analysis for Identifying the Global Structure of Pleiotropy with NGS Data
Investigating the pleiotropic effects of genetic variants can increase
statistical power, provide important information to achieve deep understanding
of the complex genetic structures of disease, and offer powerful tools for
designing effective treatments with fewer side effects. However, the current
multiple phenotype association analysis paradigm lacks breadth (number of
phenotypes and genetic variants jointly analyzed at the same time) and depth
(hierarchical structure of phenotype and genotypes). A key issue for high
dimensional pleiotropic analysis is to effectively extract informative internal
representation and features from high dimensional genotype and phenotype data.
To explore multiple levels of representations of genetic variants, learn their
internal patterns involved in the disease development, and overcome critical
barriers in advancing the development of novel statistical methods and
computational algorithms for genetic pleiotropic analysis, we proposed a new
framework referred to as a quadratically regularized functional CCA (QRFCCA)
for association analysis which combines three approaches: (1) quadratically
regularized matrix factorization, (2) functional data analysis and (3)
canonical correlation analysis (CCA). Large-scale simulations show that the
QRFCCA has a much higher power than that of the nine competing statistics while
retaining the appropriate type 1 errors. To further evaluate performance, the
QRFCCA and nine other statistics are applied to the whole genome sequencing
dataset from the TwinsUK study. We identify a total of 79 genes with rare
variants and 67 genes with common variants significantly associated with the 46
traits using QRFCCA. The results show that the QRFCCA substantially outperforms
the nine other statistics.Comment: 64 pages including 12 figure
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
Pizzetti formulae for Stiefel manifolds and applications
Pizzetti's formula explicitly shows the equivalence of the rotation invariant
integration over a sphere and the action of rotation invariant differential
operators. We generalize this idea to the integrals over real, complex, and
quaternion Stiefel manifolds in a unifying way. In particular we propose a new
way to calculate group integrals and try to uncover some algebraic structures
which manifest themselves for some well-known cases like the Harish-Chandra
integral. We apply a particular case of our formula to an Itzykson-Zuber
integral for the coset SO(4)/[SO(2)xSO(2)]. This integral naturally appears in
the calculation of the two-point correlation function in the transition of the
statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in
random matrix theory
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