23,356 research outputs found
Avalanche analysis from multi-electrode ensemble recordings in cat, monkey and human cerebral cortex during wakefulness and sleep
Self-organized critical states are found in many natural systems, from
earthquakes to forest fires, they have also been observed in neural systems,
particularly, in neuronal cultures. However, the presence of critical states in
the awake brain remains controversial. Here, we compared avalanche analyses
performed on different in vivo preparations during wakefulness, slow-wave sleep
and REM sleep, using high-density electrode arrays in cat motor cortex (96
electrodes), monkey motor cortex and premotor cortex and human temporal cortex
(96 electrodes) in epileptic patients. In neuronal avalanches defined from
units (up to 160 single units), the size of avalanches never clearly scaled as
power-law, but rather scaled exponentially or displayed intermediate scaling.
We also analyzed the dynamics of local field potentials (LFPs) and in
particular LFP negative peaks (nLFPs) among the different electrodes (up to 96
sites in temporal cortex or up to 128 sites in adjacent motor and pre-motor
cortices). In this case, the avalanches defined from nLFPs displayed power-law
scaling in double log representations, as reported previously in monkey.
However, avalanche defined as positive LFP (pLFP) peaks, which are less
directly related to neuronal firing, also displayed apparent power-law scaling.
Closer examination of this scaling using more reliable cumulative distribution
functions (CDF) and other rigorous statistical measures, did not confirm
power-law scaling. The same pattern was seen for cats, monkey and human, as
well as for different brain states of wakefulness and sleep. We also tested
other alternative distributions. Multiple exponential fitting yielded optimal
fits of the avalanche dynamics with bi-exponential distributions. Collectively,
these results show no clear evidence for power-law scaling or self-organized
critical states in the awake and sleeping brain of mammals, from cat to man.Comment: In press in: Frontiers in Physiology, 2012, special issue "Critical
Brain Dynamics" (Edited by He BY, Daffertshofer A, Boonstra TW); 33 pages, 13
figures. 3 table
Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques
Ordinal missing data are common in measurement equivalence/invariance (ME/I) testing studies. However, there is a lack of guidance on the appropriate method to deal with ordinal missing data in ME/I testing. Five methods may be used to deal with ordinal missing data in ME/I testing, including the continuous full information maximum likelihood estimation method (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squared estimation method combined with pairwise deletion (WLSMV_PD). The current study evaluates the relative performance of these methods in producing valid chi-square difference tests (Δχ2) and accurate parameter estimates. The result suggests that all methods except for WLSMV_PD can reasonably control the type I error rates of (Δχ2) tests and maintain sufficient power to detect noninvariance in most conditions. Only pFIML and lFIML yield accurate factor loading estimates and standard errors across all the conditions. Recommendations are provided to researchers based on the results
Data-Driven Robust Optimization
The last decade witnessed an explosion in the availability of data for
operations research applications. Motivated by this growing availability, we
propose a novel schema for utilizing data to design uncertainty sets for robust
optimization using statistical hypothesis tests. The approach is flexible and
widely applicable, and robust optimization problems built from our new sets are
computationally tractable, both theoretically and practically. Furthermore,
optimal solutions to these problems enjoy a strong, finite-sample probabilistic
guarantee. \edit{We describe concrete procedures for choosing an appropriate
set for a given application and applying our approach to multiple uncertain
constraints. Computational evidence in portfolio management and queuing confirm
that our data-driven sets significantly outperform traditional robust
optimization techniques whenever data is available.Comment: 38 pages, 15 page appendix, 7 figures. This version updated as of
Oct. 201
Can power-law scaling and neuronal avalanches arise from stochastic dynamics?
The presence of self-organized criticality in biology is often evidenced by a
power-law scaling of event size distributions, which can be measured by linear
regression on logarithmic axes. We show here that such a procedure does not
necessarily mean that the system exhibits self-organized criticality. We first
provide an analysis of multisite local field potential (LFP) recordings of
brain activity and show that event size distributions defined as negative LFP
peaks can be close to power-law distributions. However, this result is not
robust to change in detection threshold, or when tested using more rigorous
statistical analyses such as the Kolmogorov-Smirnov test. Similar power-law
scaling is observed for surrogate signals, suggesting that power-law scaling
may be a generic property of thresholded stochastic processes. We next
investigate this problem analytically, and show that, indeed, stochastic
processes can produce spurious power-law scaling without the presence of
underlying self-organized criticality. However, this power-law is only apparent
in logarithmic representations, and does not survive more rigorous analysis
such as the Kolmogorov-Smirnov test. The same analysis was also performed on an
artificial network known to display self-organized criticality. In this case,
both the graphical representations and the rigorous statistical analysis reveal
with no ambiguity that the avalanche size is distributed as a power-law. We
conclude that logarithmic representations can lead to spurious power-law
scaling induced by the stochastic nature of the phenomenon. This apparent
power-law scaling does not constitute a proof of self-organized criticality,
which should be demonstrated by more stringent statistical tests.Comment: 14 pages, 10 figures; PLoS One, in press (2010
Modelling catastrophe claims with left-truncated severity distributions (extended version)
In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non-homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies. This is an extended version of the article: Chernobai et al. (2006) Modelling catastrophe claims with left-truncated severity distributions, Computational Statistics 21(3-4): 537-555.Natural Catastrophe, Property Insurance, Loss Distribution, Truncated Data, Ruin Probability
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