39,205 research outputs found
Intermittency in Turbulence: Multiplicative random process in space and time
We present a simple stochastic algorithm for generating multiplicative
processes with multiscaling both in space and in time. With this algorithm we
are able to reproduce a synthetic signal with the same space and time
correlation as the one coming from shell models for turbulence and the one
coming from a turbulent velocity field in a quasi-Lagrangian reference frame.Comment: 23 pages, 12 figure
Inherent Weight Normalization in Stochastic Neural Networks
Multiplicative stochasticity such as Dropout improves the robustness and
generalizability of deep neural networks. Here, we further demonstrate that
always-on multiplicative stochasticity combined with simple threshold neurons
are sufficient operations for deep neural networks. We call such models Neural
Sampling Machines (NSM). We find that the probability of activation of the NSM
exhibits a self-normalizing property that mirrors Weight Normalization, a
previously studied mechanism that fulfills many of the features of Batch
Normalization in an online fashion. The normalization of activities during
training speeds up convergence by preventing internal covariate shift caused by
changes in the input distribution. The always-on stochasticity of the NSM
confers the following advantages: the network is identical in the inference and
learning phases, making the NSM suitable for online learning, it can exploit
stochasticity inherent to a physical substrate such as analog non-volatile
memories for in-memory computing, and it is suitable for Monte Carlo sampling,
while requiring almost exclusively addition and comparison operations. We
demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and
event-based classification benchmarks (N-MNIST and DVS Gestures). Our results
show that NSMs perform comparably or better than conventional artificial neural
networks with the same architecture
Additive-multiplicative stochastic models of financial mean-reverting processes
We investigate a generalized stochastic model with the property known as mean
reversion, that is, the tendency to relax towards a historical reference level.
Besides this property, the dynamics is driven by multiplicative and additive
Wiener processes. While the former is modulated by the internal behavior of the
system, the latter is purely exogenous. We focus on the stochastic dynamics of
volatilities, but our model may also be suitable for other financial random
variables exhibiting the mean reversion property. The generalized model
contains, as particular cases, many early approaches in the literature of
volatilities or, more generally, of mean-reverting financial processes. We
analyze the long-time probability density function associated to the model
defined through a It\^o-Langevin equation. We obtain a rich spectrum of shapes
for the probability function according to the model parameters. We show that
additive-multiplicative processes provide realistic models to describe
empirical distributions, for the whole range of data.Comment: 8 pages, 3 figure
Evidence for an additive inhibitory component of contrast adaptation
The latency of visual responses generally decreases as contrast increases.
Recording in the lateral geniculate nucleus (LGN), we find that response
latency increases with increasing contrast in ON cells for some visual stimuli.
We propose that this surprising latency trend can be explained if ON cells rest
further from threshold at higher contrasts. Indeed, while contrast changes
caused a combination of multiplicative gain change and additive shift in LGN
cells, the additive shift predominated in ON cells. Modeling results supported
this theory: the ON cell latency trend was found when the distance-to-threshold
shifted with contrast, but not when distance-to-threshold was fixed across
contrasts. In the model, latency also increases as surround-to-center ratios
increase, which has been shown to occur at higher contrasts. We propose that
higher-contrast full-field stimuli can evoke more surround inhibition, shifting
the potential further from spiking threshold and thereby increasing response
latency
Analyzing Multiple-Probe Microarray: Estimation and Application of Gene Expression Indexes
Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re-examined this problem using a new profile likelihood-based transformation estimation approach that is more statistically elegant and computationally efficient. We demonstrate the applicability of the proposed method using a benchmark Affymetrix U95A spiked-in experiment. Moreover, We introduced a new multivariate expression index and used the empirical study to shows its promise in terms of improving model fitting and power of detecting differential expression over the commonly used univariate expression index. As the other important content of the work, we discussed two generally encountered practical issues in application of gene expression index: normalization and summary statistic used for detecting differential expression. Our empirical study shows somewhat different findings from the MAQC project (MAQC, 2006)
Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise
A random multiplicative process with additive noise is described by a
Langevin equation. We show that the fluctuation-dissipation relation is
satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment
Using CMB lensing to constrain the multiplicative bias of cosmic shear
Weak gravitational lensing is one of the key probes of cosmology. Cosmic
shear surveys aimed at measuring the distribution of matter in the universe are
currently being carried out (Pan-STARRS) or planned for the coming decade (DES,
LSST, EUCLID, WFIRST). Crucial to the success of these surveys is the control
of systematics. In this work a new method to constrain one such family of
systematics, known as multiplicative bias, is proposed. This method exploits
the cross-correlation between weak lensing measurements from galaxy surveys and
the ones obtained from high resolution CMB experiments. This cross-correlation
is shown to have the power to break the degeneracy between the normalization of
the matter power spectrum and the multiplicative bias of cosmic shear and to be
able to constrain the latter to a few percent.Comment: 5 pages, 1 figur
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