Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userModeling Heterogeneity in Networks using Uncertainty Quantification Tools
207
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty Quantification. The crucial assumption underlying this mathematical and computational technology transfer is that the evolving states of the nodes in a network quickly become correlated with the corresponding node identities: features of the nodes imparted by the network structure (e.g. the node degree, the node clustering coefficient). The node dynamics thus depend on heterogeneous (rather than uncertain) parameters, whose distribution over the network results from the network structure. Knowing these distributions allows us to obtain an efficient coarse-grained representation of the network state in terms of the expansion coefficients in suitable orthogonal polynomials. This representation is closely related to mathematical/computational tools for uncertainty quantification (the Polynomial Chaos approach and its associated numerical techniques). The Polynomial Chaos coefficients provide a set of good collective variables for the observation of dynamics on a network, and subsequently, for the implementation of reduced dynamic models of it. We demonstrate this idea by performing coarse-grained computations of the nonlinear dynamics of information propagation on our illustrative network model using the Equation-Free approach
rate research
Read More
Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable time and resources. The need for UQ is especially acute for neural models, which are becoming increasingly standard yet are challenging to interpret. While several approaches to UQ have been proposed in the literature, there is no clear consensus on the comparative performance of these models. In this paper, we study this question in the context of regression tasks. We systematically evaluate several methods on five benchmark datasets using multiple complementary performance metrics. Our experiments show that none of the methods we tested is unequivocally superior to all others, and none produces a particularly reliable ranking of errors across multiple datasets. While we believe these results show that existing UQ methods are not sufficient for all common use-cases and demonstrate the benefits of further research, we conclude with a practical recommendation as to which existing techniques seem to perform well relative to others.
We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which the critical state is reached when the largest eigenvalue of the weighted non-backtracking (WNB) matrix is exactly one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintain the largest size of the giant connected component.
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows throughout the grid. Whether such a steady state exists for a given network is of eminent practical importance. The loss of a steady state typically leads to power outages up to a complete blackout. But also the existence of multiple steady states is undesirable, as it can lead to sudden transitions, circulating flows and eventually also to power outages. Steady states are typically calculated numerically, but this approach gives only limited insight into the existence and (non-)uniqueness of steady states. Analytic results are available only for special network configuration, in particular for grids with negligible Ohmic losses or radial networks without any loops. In this article, we introduce a method to systematically construct the solutions of the real power load-flow equations in the presence of Ohmic losses. We calculate the steady states explicitly for elementary networks demonstrating different mechanisms leading to multistability. Our results also apply to models of coupled oscillators which are widely used in theoretical physics and mathematical biology.
Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.
How do local topological changes affect the global operation and stability of complex supply networks? Studying supply networks on various levels of abstraction, we demonstrate that and how adding new links may not only promote but also degrade stable operation of a network. Intriguingly, the resulting overloads may emerge remotely from where such a link is added, thus resulting in nonlocal failure. We link this counter-intuitive phenomenon to Braess paradox originally discovered in traffic networks. We use elementary network topologies to explain its underlying mechanism for different types of supply networks and find that it generically occurs across these systems. As an important consequence, upgrading supply networks such as communication networks, biological supply networks or power grids requires particular care because even adding only single connections may destabilize normal network operation and induce disturbances remotely from the location of structural change and even global cascades of failures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
