2,376 research outputs found
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
Learning Continuous Network Emerging Dynamics from Scarce Observations via Data-Adaptive Stochastic Processes
Learning network dynamics from the empirical structure and spatio-temporal
observation data is crucial to revealing the interaction mechanisms of complex
networks in a wide range of domains. However, most existing methods only aim at
learning network dynamic behaviors generated by a specific ordinary
differential equation instance, resulting in ineffectiveness for new ones, and
generally require dense observations. The observed data, especially from
network emerging dynamics, are usually difficult to obtain, which brings
trouble to model learning. Therefore, how to learn accurate network dynamics
with sparse, irregularly-sampled, partial, and noisy observations remains a
fundamental challenge. We introduce Neural ODE Processes for Network Dynamics
(NDP4ND), a new class of stochastic processes governed by stochastic
data-adaptive network dynamics, to overcome the challenge and learn continuous
network dynamics from scarce observations. Intensive experiments conducted on
various network dynamics in ecological population evolution, phototaxis
movement, brain activity, epidemic spreading, and real-world empirical systems,
demonstrate that the proposed method has excellent data adaptability and
computational efficiency, and can adapt to unseen network emerging dynamics,
producing accurate interpolation and extrapolation with reducing the ratio of
required observation data to only about 6\% and improving the learning speed
for new dynamics by three orders of magnitude.Comment: preprin
Monotonic Gaussian Process for Spatio-Temporal Disease Progression Modeling in Brain Imaging Data
International audienceWe introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is constrained by anatomically plausible statistical priors. To model realistic trajectories, the temporal sources are defined as monotonic and time-reparametrized Gaussian Processes. To account for the non-stationarity of brain images, we model the spatial sources as sparse codes convolved at multiple scales. The method was tested on synthetic data favourably comparing with standard blind source separation approaches. The application on large-scale imaging data from a clinical study allows to disentangle differential temporal progression patterns mapping brain regions key to neurodegeneration, while revealing a disease-specific time scale associated to the clinical diagnosis
Monotonic Gaussian Process for Spatio-Temporal Disease Progression Modeling in Brain Imaging Data
We introduce a probabilistic generative model for disentangling
spatio-temporal disease trajectories from series of high-dimensional brain
images. The model is based on spatio-temporal matrix factorization, where
inference on the sources is constrained by anatomically plausible statistical
priors. To model realistic trajectories, the temporal sources are defined as
monotonic and time-reparametrized Gaussian Processes. To account for the
non-stationarity of brain images, we model the spatial sources as sparse codes
convolved at multiple scales. The method was tested on synthetic data
favourably comparing with standard blind source separation approaches. The
application on large-scale imaging data from a clinical study allows to
disentangle differential temporal progression patterns mapping brain regions
key to neurodegeneration, while revealing a disease-specific time scale
associated to the clinical diagnosis
Revealing networks from dynamics: an introduction
What can we learn from the collective dynamics of a complex network about its
interaction topology? Taking the perspective from nonlinear dynamics, we
briefly review recent progress on how to infer structural connectivity (direct
interactions) from accessing the dynamics of the units. Potential applications
range from interaction networks in physics, to chemical and metabolic
reactions, protein and gene regulatory networks as well as neural circuits in
biology and electric power grids or wireless sensor networks in engineering.
Moreover, we briefly mention some standard ways of inferring effective or
functional connectivity.Comment: Topical review, 48 pages, 7 figure
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
- …