Sean Warnick

Necessary and Sufficient Conditions for Dynamical Structure Reconstruction of LTI Networks

This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input-output data, not even Boolean reconstruction is possible, in general, without more information about the system. We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality.

Brief paper: Robust dynamical network structure reconstruction

This paper addresses the problem of network reconstruction from data. Previous work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect measurements (no noise) and perfect system identification. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular network structures. We conclude with biologically inspired network reconstruction examples which include noise and nonlinearities.

Quality selection for Dynamic Adaptive Streaming over HTTP with Scalable Video Coding

Video streaming on the Internet is increasingly using Dynamic Adaptive Streaming over HTTP (DASH), which allows a client to dynamically adjust its video quality by choosing the appropriate quality level for each segment based on the current download rate. In this paper we examine the impact of Scalable Video Coding (SVC) on the clients quality selection policy. Given a variable download rate, when should the client try to maximize the current segments video quality, and when should it instead play it safe and ensure a minimum level of quality for future segments? We use a combination of analysis, dynamic programming, and simulation to show that a client should use a diagonal quality selection policy, which combines prefetching with backfilling to balance both of these concerns. We also illustrate the conditions that affect the slope of the diagonal policy.

Dynamical structure functions for the reverse engineering of LTI networks

This research explores the role and representation of network structure for LTI systems with partial state observations. We demonstrate that input-output representations, i.e. transfer functions, contain no internal structural information of the system. We further show that neither the additional knowledge of system order nor minimality of the true realization is generally sufficient to characterize network structure. We then introduce dynamical structure functions as an alternative, graphical-model based representation of LTI systems that contain both dynamical and structural information of the system. The main result uses dynamical structure to precisely characterize the additional information required to obtain network structure from the transfer function of the system.

Representing structure in linear interconnected dynamical systems

Interconnected dynamical systems are a pervasive component in our modern worlds infrastructure. One of the fundamental steps to understanding the complex behavior and dynamics of these systems is determining how to appropriately represent their structure. In this work, we discuss different ways of representing a systems structure. We define and present, in particular, four representations of system structure-complete computational, subsystem, signal, and zero pattern structure-and discuss some of their fundamental properties. We illustrate their application with a numerical example and show how radically different representations of structure can be consistent with a single LTI input-output system.

Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator

A graph-theoretic analysis of state inference for a class of network synchronization (or diffusive) processes is pursued. Precisely, estimation is studied for a nonrandom initial condition of a canonical synchronization dynamic defined on a graph, from noisy observations at a single network node. By characterizing the maximum-likelihood estimation of the initial condition and the associated Cramer–Rao bound, graph properties are identified (e.g., symmetries, interconnection strengths, spectral measures) that determine (1) whether or not estimation is possible and (2) the quality of the estimate.

Dynamical structure function identifiability conditions enabling signal structure reconstruction

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a systems signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars.

Minimal dynamical structure realisations with application to network reconstruction from data

Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterises minimal order state-space realisations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing algorithms to explicitly obtain a minimal reconstruction.

Mathematical relationships between representations of structure in linear interconnected dynamical systems

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical systems structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relation ships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example.

Robust dynamical network reconstruction

Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and nonlinearities. In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities.