15,200 research outputs found
A strongly convergent numerical scheme from Ensemble Kalman inversion
The Ensemble Kalman methodology in an inverse problems setting can be viewed
as an iterative scheme, which is a weakly tamed discretization scheme for a
certain stochastic differential equation (SDE). Assuming a suitable
approximation result, dynamical properties of the SDE can be rigorously pulled
back via the discrete scheme to the original Ensemble Kalman inversion.
The results of this paper make a step towards closing the gap of the missing
approximation result by proving a strong convergence result in a simplified
model of a scalar stochastic differential equation. We focus here on a toy
model with similar properties than the one arising in the context of Ensemble
Kalman filter. The proposed model can be interpreted as a single particle
filter for a linear map and thus forms the basis for further analysis. The
difficulty in the analysis arises from the formally derived limiting SDE with
non-globally Lipschitz continuous nonlinearities both in the drift and in the
diffusion. Here the standard Euler-Maruyama scheme might fail to provide a
strongly convergent numerical scheme and taming is necessary. In contrast to
the strong taming usually used, the method presented here provides a weaker
form of taming.
We present a strong convergence analysis by first proving convergence on a
domain of high probability by using a cut-off or localisation, which then
leads, combined with bounds on moments for both the SDE and the numerical
scheme, by a bootstrapping argument to strong convergence
Stochastic Resonance Can Drive Adaptive Physiological Processes
Stochastic resonance (SR) is a concept from the physics and engineering communities that has applicability to both systems physiology and other living systems. In this paper, it will be argued that stochastic resonance plays a role in driving behavior in neuromechanical systems. The theory of stochastic resonance will be discussed, followed by a series of expected outcomes, and two tests of stochastic resonance in an experimental setting. These tests are exploratory in nature, and provide a means to parameterize systems that couple biological and mechanical components. Finally, the potential role of stochastic resonance in adaptive physiological systems will be discussed
A multi-stage recurrent neural network better describes decision-related activity in dorsal premotor cortex
We studied how a network of recurrently connected
artificial units solve a visual perceptual decision-making
task. The goal of this task is to discriminate the dominant
color of a central static checkerboard and report the
decision with an arm movement. This task has been used
to study neural activity in the dorsal premotor (PMd)
cortex. When a single recurrent neural network (RNN)
was trained to perform the task, the activity of artificial
units in the RNN differed from neural recordings in PMd,
suggesting that inputs to PMd differed from inputs to the
RNN. We expanded our architecture and examined how
a multi-stage RNN performed the task. In the multi-stage
RNN, the last stage exhibited similarities with PMd by
representing direction information but not color
information. We then investigated how the
representation of color and direction information evolve
across RNN stages. Together, our results are a
demonstration of the importance of incorporating
architectural constraints into RNN models. These
constraints can improve the ability of RNNs to model
neural activity in association areas.https://doi.org/10.32470/CCN.2019.1123-0Accepted manuscrip
The structure of borders in a small world
Geographic borders are not only essential for the effective functioning of
government, the distribution of administrative responsibilities and the
allocation of public resources, they also influence the interregional flow of
information, cross-border trade operations, the diffusion of innovation and
technology, and the spatial spread of infectious diseases. However, as growing
interactions and mobility across long distances, cultural, and political
borders continue to amplify the small world effect and effectively decrease the
relative importance of local interactions, it is difficult to assess the
location and structure of effective borders that may play the most significant
role in mobility-driven processes. The paradigm of spatially coherent
communities may no longer be a plausible one, and it is unclear what structures
emerge from the interplay of interactions and activities across spatial scales.
Here we analyse a multi-scale proxy network for human mobility that
incorporates travel across a few to a few thousand kilometres. We determine an
effective system of geographically continuous borders implicitly encoded in
multi-scale mobility patterns. We find that effective large scale boundaries
define spatially coherent subdivisions and only partially coincide with
administrative borders. We find that spatial coherence is partially lost if
only long range traffic is taken into account and show that prevalent models
for multi-scale mobility networks cannot account for the observed patterns.
These results will allow for new types of quantitative, comparative analyses of
multi-scale interaction networks in general and may provide insight into a
multitude of spatiotemporal phenomena generated by human activity.Comment: 9 page
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