Robust network reconstruction in polynomial time

This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work [1] on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method. © 2012 IEEE.

Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach

Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. © 2012 IEEE.

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 system's 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. © 2012 IEEE.

Implementation of shading effect for reconstruction of smooth layerbased 3D holographic images

A holographic rendering algorithm using a layer-based structure with angular tiling supports view-dependent shading and accommodation cues. This approach also has the advantages of rapid computation speed and visual reduction of layer gap artefacts compared to other approaches. Holograms rendered with this algorithm are displayed using an SLM to demonstrate view-dependent shading and occlusion. © 2013 SPIE-IS&T.

Free energy surface reconstruction from umbrella samples using Gaussian process regression

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.

Free energy surface reconstruction from umbrella samples using Gaussian process regression II: Multiple collective variables

We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive allows the concurrent use of histograms and free energy gradients and can easily be extended to include further data. In Part I we review the necessary theory and test the method for one collective variable. We demonstrate improved performance with respect to the weighted histogram analysis method and obtain meaningful error bars without any significant additional computation. In Part II we consider the case of multiple collective variables and compare to a reconstruction using least squares fitting of radial basis functions. We find substantial improvements in the regimes of spatially sparse data or short sampling trajectories. A software implementation is made available on www.libatoms.org.

Network reconstruction using knock-out and over-expression data

This paper outlines necessary and sufficient conditions for network reconstruction of linear, time-invariant systems using data from either knock-out or over-expression experiments. These structural system perturbations, which are common in biological experiments, can be formulated as unknown system inputs, allowing the network topology and dynamics to be found. We assume that only partial state measurements are available and propose an algorithm that can reconstruct the network at the level of the measured states using either time-series or steady-state data. A simulated example illustrates how the algorithm successfully reconstructs a network from data. © 2013 EUCA.

Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling

An approach of rapid hologram generation for the realistic three-dimensional (3-D) image reconstruction based on the angular tiling concept is proposed, using a new graphic rendering approach integrated with a previously developed layer-based method for hologram calculation. A 3-D object is simplified as layered cross-sectional images perpendicular to a chosen viewing direction, and our graphics rendering approach allows the incorporation of clear depth cues, occlusion, and shading in the generated holograms for angular tiling. The combination of these techniques together with parallel computing reduces the computation time of a single-view hologram for a 3-D image of extended graphics array resolution to 176 ms using a single consumer graphics processing unit card. © 2014 SPIE and IS and T.