40,257 research outputs found
Network estimation in State Space Model with L1-regularization constraint
Biological networks have arisen as an attractive paradigm of genomic science
ever since the introduction of large scale genomic technologies which carried
the promise of elucidating the relationship in functional genomics. Microarray
technologies coupled with appropriate mathematical or statistical models have
made it possible to identify dynamic regulatory networks or to measure time
course of the expression level of many genes simultaneously. However one of the
few limitations fall on the high-dimensional nature of such data coupled with
the fact that these gene expression data are known to include some hidden
process. In that regards, we are concerned with deriving a method for inferring
a sparse dynamic network in a high dimensional data setting. We assume that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some unknown or hidden process. We build an
input-dependent linear state space model from these hidden states and
demonstrate how an incorporated regularization constraint in an
Expectation-Maximization (EM) algorithm can be used to reverse engineer
transcriptional networks from gene expression profiling data. This corresponds
to estimating the model interaction parameters. The proposed method is
illustrated on time-course microarray data obtained from a well established
T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4,
CASP4, CD69, and C3X1 to have higher number of inwards directed connections and
FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed
connections. We recommend these genes to be object for further investigation.
Caspase 4 is also found to activate the expression of JunD which in turn
represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359
Signal detection in extracellular neural ensemble recordings using higher criticism
Information processing in the brain is conducted by a concerted action of
multiple neural populations. Gaining insights in the organization and dynamics
of such populations can best be studied with broadband intracranial recordings
of so-called extracellular field potential, reflecting neuronal spiking as well
as mesoscopic activities, such as waves, oscillations, intrinsic large
deflections, and multiunit spiking activity. Such signals are critical for our
understanding of how neuronal ensembles encode sensory information and how such
information is integrated in the large networks underlying cognition. The
aforementioned principles are now well accepted, yet the efficacy of extracting
information out of the complex neural data, and their employment for improving
our understanding of neural networks, critically depends on the mathematical
processing steps ranging from simple detection of action potentials in noisy
traces - to fitting advanced mathematical models to distinct patterns of the
neural signal potentially underlying intra-processing of information, e.g.
interneuronal interactions. Here, we present a robust strategy for detecting
signals in broadband and noisy time series such as spikes, sharp waves and
multi-unit activity data that is solely based on the intrinsic statistical
distribution of the recorded data. By using so-called higher criticism - a
second-level significance testing procedure comparing the fraction of observed
significances to an expected fraction under the global null - we are able to
detect small signals in correlated noisy time-series without prior filtering,
denoising or data regression. Results demonstrate the efficiency and
reliability of the method and versatility over a wide range of experimental
conditions and suggest the appropriateness of higher criticism to characterize
neuronal dynamics without prior manipulation of the data
Neural Connectivity with Hidden Gaussian Graphical State-Model
The noninvasive procedures for neural connectivity are under questioning.
Theoretical models sustain that the electromagnetic field registered at
external sensors is elicited by currents at neural space. Nevertheless, what we
observe at the sensor space is a superposition of projected fields, from the
whole gray-matter. This is the reason for a major pitfall of noninvasive
Electrophysiology methods: distorted reconstruction of neural activity and its
connectivity or leakage. It has been proven that current methods produce
incorrect connectomes. Somewhat related to the incorrect connectivity
modelling, they disregard either Systems Theory and Bayesian Information
Theory. We introduce a new formalism that attains for it, Hidden Gaussian
Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden
by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS
is equivalent to a frequency domain Linear State Space Model (LSSM) but with
sparse connectivity prior. The mathematical contribution here is the theory for
high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS
can attenuate the leakage effect in the most critical case: the distortion EEG
signal due to head volume conduction heterogeneities. Its application in EEG is
illustrated with retrieved connectivity patterns from human Steady State Visual
Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence
for noninvasive procedures of neural connectivity: concurrent EEG and
Electrocorticography (ECoG) recordings on monkey. Open source packages are
freely available online, to reproduce the results presented in this paper and
to analyze external MEEG databases
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