48,510 research outputs found
Uncertainty propagation in neuronal dynamical systems
One of the most notorious characteristics of neuronal electrical activity is its
variability, whose origin is not just instrumentation noise, but mainly the intrinsically
stochastic nature of neural computations. Neuronal models based
on deterministic differential equations cannot account for such variability,
but they can be extended to do so by incorporating random components.
However, the computational cost of this strategy and the storage requirements
grow exponentially with the number of stochastic parameters, quickly
exceeding the capacities of current supercomputers. This issue is critical in
Neurodynamics, where mechanistic interpretation of large, complex, nonlinear
systems is essential. In this paper we present accurate and computationally
efficient methods to introduce and analyse variability in neurodynamic
models depending on multiple uncertain parameters. Their use is illustrated
with relevant example
Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processes
The Fokker-Planck equations describe time evolution of probability densities
of stochastic dynamical systems and are thus widely used to quantify random
phenomena such as uncertainty propagation. For dynamical systems driven by
non-Gaussian L\'evy processes, however, it is difficult to obtain explicit
forms of Fokker-Planck equations because the adjoint operators of the
associated infinitesimal generators usually do not have exact formulation. In
the present paper, Fokker- Planck equations are derived in terms of infinite
series for nonlinear stochastic differential equations with non-Gaussian L\'evy
processes. A few examples are presented to illustrate the method.Comment: 14 page
Modeling and inference of spatio-temporal protein dynamics across brain networks
Models of misfolded proteins (MP) aim at discovering the bio-mechanical
propagation properties of neurological diseases (ND) by identifying plausible
associated dynamical systems. Solving these systems along the full disease
trajectory is usually challenging, due to the lack of a well defined time axis
for the pathology. This issue is addressed by disease progression models (DPM)
where long-term progression trajectories are estimated via time
reparametrization of individual observations. However, due to their loose
assumptions on the dynamics, DPM do not provide insights on the bio-mechanical
properties of MP propagation. Here we propose a unified model of
spatio-temporal protein dynamics based on the joint estimation of long-term MP
dynamics and time reparameterization of individuals observations. The model is
expressed within a Gaussian Process (GP) regression setting, where constraints
on the MP dynamics are imposed through non--linear dynamical systems. We use
stochastic variational inference on both GP and dynamical system parameters for
scalable inference and uncertainty quantification of the trajectories.
Experiments on simulated data show that our model accurately recovers
prescribed rates along graph dynamics and precisely reconstructs the underlying
progression. When applied to brain imaging data our model allows the
bio-mechanical interpretation of amyloid deposition in Alzheimer's disease,
leading to plausible simulations of MP propagation, and achieving accurate
predictions of individual MP deposition in unseen data
A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints
Accurate estimation of parameters is paramount in developing high-fidelity
models for complex dynamical systems. Model-based optimal experiment design
(OED) approaches enable systematic design of dynamic experiments to generate
input-output data sets with high information content for parameter estimation.
Standard OED approaches however face two challenges: (i) experiment design
under incomplete system information due to unknown true parameters, which
usually requires many iterations of OED; (ii) incapability of systematically
accounting for the inherent uncertainties of complex systems, which can lead to
diminished effectiveness of the designed optimal excitation signal as well as
violation of system constraints. This paper presents a robust OED approach for
nonlinear systems with arbitrarily-shaped time-invariant probabilistic
uncertainties. Polynomial chaos is used for efficient uncertainty propagation.
The distinct feature of the robust OED approach is the inclusion of chance
constraints to ensure constraint satisfaction in a stochastic setting. The
presented approach is demonstrated by optimal experimental design for the
JAK-STAT5 signaling pathway that regulates various cellular processes in a
biological cell.Comment: Submitted to ADCHEM 201
A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming
This work presents the concept of kernel mean embedding and kernel
probabilistic programming in the context of stochastic systems. We propose
formulations to represent, compare, and propagate uncertainties for fairly
general stochastic dynamics in a distribution-free manner. The new tools enjoy
sound theory rooted in functional analysis and wide applicability as
demonstrated in distinct numerical examples. The implication of this new
concept is a new mode of thinking about the statistical nature of uncertainty
in dynamical systems
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