7,744 research outputs found
Early Warning Analysis for Social Diffusion Events
There is considerable interest in developing predictive capabilities for
social diffusion processes, for instance to permit early identification of
emerging contentious situations, rapid detection of disease outbreaks, or
accurate forecasting of the ultimate reach of potentially viral ideas or
behaviors. This paper proposes a new approach to this predictive analytics
problem, in which analysis of meso-scale network dynamics is leveraged to
generate useful predictions for complex social phenomena. We begin by deriving
a stochastic hybrid dynamical systems (S-HDS) model for diffusion processes
taking place over social networks with realistic topologies; this modeling
approach is inspired by recent work in biology demonstrating that S-HDS offer a
useful mathematical formalism with which to represent complex, multi-scale
biological network dynamics. We then perform formal stochastic reachability
analysis with this S-HDS model and conclude that the outcomes of social
diffusion processes may depend crucially upon the way the early dynamics of the
process interacts with the underlying network's community structure and
core-periphery structure. This theoretical finding provides the foundations for
developing a machine learning algorithm that enables accurate early warning
analysis for social diffusion events. The utility of the warning algorithm, and
the power of network-based predictive metrics, are demonstrated through an
empirical investigation of the propagation of political memes over social media
networks. Additionally, we illustrate the potential of the approach for
security informatics applications through case studies involving early warning
analysis of large-scale protests events and politically-motivated cyber
attacks
Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices
Approximating the set of reachable states of a dynamical system is an
algorithmic yet mathematically rigorous way to reason about its safety.
Although progress has been made in the development of efficient algorithms for
affine dynamical systems, available algorithms still lack scalability to ensure
their wide adoption in the industrial setting. While modern linear algebra
packages are efficient for matrices with tens of thousands of dimensions,
set-based image computations are limited to a few hundred. We propose to
decompose reach set computations such that set operations are performed in low
dimensions, while matrix operations like exponentiation are carried out in the
full dimension. Our method is applicable both in dense- and discrete-time
settings. For a set of standard benchmarks, it shows a speed-up of up to two
orders of magnitude compared to the respective state-of-the art tools, with
only modest losses in accuracy. For the dense-time case, we show an experiment
with more than 10.000 variables, roughly two orders of magnitude higher than
possible with previous approaches
Predictive Analysis for Social Processes II: Predictability and Warning Analysis
This two-part paper presents a new approach to predictive analysis for social
processes. Part I identifies a class of social processes, called positive
externality processes, which are both important and difficult to predict, and
introduces a multi-scale, stochastic hybrid system modeling framework for these
systems. In Part II of the paper we develop a systems theory-based,
computationally tractable approach to predictive analysis for these systems.
Among other capabilities, this analytic methodology enables assessment of
process predictability, identification of measurables which have predictive
power, discovery of reliable early indicators for events of interest, and
robust, scalable prediction. The potential of the proposed approach is
illustrated through case studies involving online markets, social movements,
and protest behavior
Multi-scale modeling of follicular ovulation as a reachability problem
During each ovarian cycle, only a definite number of follicles ovulate, while
the others undergo a degeneration process called atresia. We have designed a
multi-scale mathematical model where ovulation and atresia result from a
hormonal controlled selection process. A 2D-conservation law describes the age
and maturity structuration of the follicular cell population. In this paper, we
focus on the operating mode of the control, through the study of the
characteristics of the conservation law. We describe in particular the set of
microscopic initial conditions leading to the macroscopic phenomenon of either
ovulation or atresia, in the framework of backwards reachable sets theory
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