Canonical lossless state-space systems: Staircase forms and the Schur algorithm

A new finite atlas of overlapping balanced canonical forms for multivariate discrete-time lossless systems is presented. The canonical forms have the property that the controllability matrix is positive upper triangular up to a suitable permutation of its columns. This is a generalization of a similar balanced canonical form for continuous-time lossless systems. It is shown that this atlas is in fact a finite sub-atlas of the infinite atlas of overlapping balanced canonical forms for lossless systems that is associated with the tangential Schur algorithm; such canonical forms satisfy certain interpolation conditions on a corresponding sequence of lossless transfer matrices. The connection between these balanced canonical forms for lossless systems and the tangential Schur algorithm for lossless systems is a generalization of the same connection in the SISO case that was noted before. The results are directly applicable to obtain a finite sub-atlas of multivariate input-normal canonical forms for stable linear systems of given fixed order, which is minimal in the sense that no chart can be left out of the atlas without losing the property that the atlas covers the manifold

Parametrization of matrix-valued lossless functions based on boundary interpolation

International audienceThis paper is concerned with parametrization issues for rational lossless matrix valued functions. In the same vein as previous works, interpolation theory with metric constraints is used to ensure the lossless property. We consider here boundary interpolation and provide a new parametrization of balanced canonical forms in which the parameters are angular derivatives. We finally investigate the possibility to parametrize orthogonal wavelets with vanishing moments using these results

Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm

In this report, the connections are investigated between two different approaches towards the parametrization of multivariable stable all-pass systems in discrete-time. The first approach involves the tangential Schur algorithm, which employs linear fractional transformations. It stems from the theory of reproducing kernel Hilbert spaces and enables the direct construction of overlapping local parametrizations using Schur parameters and interpolation points. The second approach proceeds in terms of state-space realizations. In the scalar case, a balanced canonical form exists that can also be parametrized by Schur parameters. This canonical form can be constructed recursively, using unitary matrix operations. Here, this procedure is generalized to the multivariable case by establishing the connections with the first approach. It gives rise to balanced realizations and overlapping canonical forms directly in terms of the parameters used in the tangential Schur algorithm

Lossless scalar functions: boundary interpolation, Schur algorithm and Ober's canonical form

International audienceIn Ober (1987) a balanced canonical form for continuous-time lossless systems was presented. This form has a tridiagonal dynamical matrix A and the useful property that the corresponding controllability matrix K is upper triangular. In this paper, a connection is established between Ober's canonical form and a Schur algorithm builts from angular derivative interpolation conditions. It provides a new interpretation of the parameters in Ober's form, as interpolation values at infinity, and a recursive construction of the balanced realization

Continuous-time lossless systems, boundary interpolation and pivot structures

International audienceBalanced realizations of lossless systems can be generated from the tangential Schur algorithm using linear fractional transformations. In discrete-time, canonical forms with pivot structures are obtained by interpolation at in finity. In continuous-time case interpolation at infi nity is on the stability boundary, leading to an angular derivative interpolation problem. In the scalar case, the balanced canonical form of Ober can be recovered in this way. Here we generalize to the multivariable case. It is shown that boundary interpolation can be regarded as a limit of classical interpolation with interpolation points tending to the imaginary axis. Some pivot structures can be generated, but no complete atlas is obtained. However, for input normal pairs an atlas of admissible pivot structures can be generated in a closely related way

Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm

In this paper, the connections are investigated between two different approaches towards the parametrization of multivariable stable all-pass systems in discrete-time. The first approach involves the tangential Schur algorithm, which employs linear fractional transformations. It stems from the theory of reproducing kernel Hilbert spaces and enables the direct construction of overlapping local parametrizations using Schur parameters and interpolation points. The second approach proceeds in terms of state-space realizations. In the scalar case, a balanced canonical form exists that can also be parametrized by Schur parameters. This canonical form can be constructed recursively, using unitary matrix operations. Here, this procedure is generalized to the multivariable case by establishing the connections with the first approach. It gives rise to balanced realizations and overlapping canonical forms directly in terms of the parameters used in the tangential Schur algorithm

Application of transfer learning to predict drug-induced human in vivo gene expression changes using rat in vitro and in vivo data

The liver is the primary site for the metabolism and detoxification of many compounds, including pharmaceuticals. Consequently, it is also the primary location for many adverse reactions. As the liver is not readily accessible for sampling in humans; rodent or cell line models are often used to evaluate potential toxic effects of a novel compound or candidate drug. However, relating the results of animal and in vitro studies to relevant clinical outcomes for the human in vivo situation still proves challenging. In this study, we incorporate principles of transfer learning within a deep artificial neural network allowing us to leverage the relative abundance of rat in vitro and in vivo exposure data from the Open TG-GATEs data set to train a model to predict the expected pattern of human in vivo gene expression following an exposure given measured human in vitro gene expression. We show that domain adaptation has been successfully achieved, with the rat and human in vitro data no longer being separable in the common latent space generated by the network. The network produces physiologically plausible predictions of human in vivo gene expression pattern following an exposure to a previously unseen compound. Moreover, we show the integration of the human in vitro data in the training of the domain adaptation network significantly improves the temporal accuracy of the predicted rat in vivo gene expression pattern following an exposure to a previously unseen compound. In this way, we demonstrate the improvements in prediction accuracy that can be achieved by combining data from distinct domains.</p

Application of transfer learning to predict drug-induced human in vivo gene expression changes using rat in vitro and in vivo data

The liver is the primary site for the metabolism and detoxification of many compounds, including pharmaceuticals. Consequently, it is also the primary location for many adverse reactions. As the liver is not readily accessible for sampling in humans; rodent or cell line models are often used to evaluate potential toxic effects of a novel compound or candidate drug. However, relating the results of animal and in vitro studies to relevant clinical outcomes for the human in vivo situation still proves challenging. In this study, we incorporate principles of transfer learning within a deep artificial neural network allowing us to leverage the relative abundance of rat in vitro and in vivo exposure data from the Open TG-GATEs data set to train a model to predict the expected pattern of human in vivo gene expression following an exposure given measured human in vitro gene expression. We show that domain adaptation has been successfully achieved, with the rat and human in vitro data no longer being separable in the common latent space generated by the network. The network produces physiologically plausible predictions of human in vivo gene expression pattern following an exposure to a previously unseen compound. Moreover, we show the integration of the human in vitro data in the training of the domain adaptation network significantly improves the temporal accuracy of the predicted rat in vivo gene expression pattern following an exposure to a previously unseen compound. In this way, we demonstrate the improvements in prediction accuracy that can be achieved by combining data from distinct domains.</p

A computational model of postprandial adipose tissue lipid metabolism derived using human arteriovenous stable isotope tracer data

Given the association of disturbances in non-esterified fatty acid (NEFA) metabolism with the development of Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, computational models of glucose-insulin dynamics have been extended to account for the interplay with NEFA. In this study, we use arteriovenous measurement across the subcutaneous adipose tissue during a mixed meal challenge test to evaluate the performance and underlying assumptions of three existing models of adipose tissue metabolism and construct a new, refined model of adipose tissue metabolism. Our model introduces new terms, explicitly accounting for the conversion of glucose to glyceraldehye-3-phosphate, the postprandial influx of glycerol into the adipose tissue, and several physiologically relevant delays in insulin signalling in order to better describe the measured adipose tissues fluxes. We then applied our refined model to human adipose tissue flux data collected before and after a diet intervention as part of the Yoyo study, to quantify the effects of caloric restriction on postprandial adipose tissue metabolism. Significant increases were observed in the model parameters describing the rate of uptake and release of both glycerol and NEFA. Additionally, decreases in the model’s delay in insulin signalling parameters indicates there is an improvement in adipose tissue insulin sensitivity following caloric restriction.</p