C. Letellier, I. Sendi˝a-Nadal, E. Bianco-Martinez & M. S. Baptista
A symbolic network-based nonlinear theory for dynamical systems observability
Scientific Reports, 8, 3785, 2018.
When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the system exponentially increases with its dimension, the observability becomes a computationally prohibitive task. Our approach consists in computing the observability coefficients from a symbolic Jacobian matrix whose elements encode the linear, nonlinear polynomial or rational nature of the interaction among the variables. The novelty we introduce in this paper, required for treating large-dimensional systems, is to identify from the symbolic Jacobian matrix the minimal set of variables (together with their time derivatives) candidate to be measured for completing the state space reconstruction. Then symbolic observability coefficients are computed from the symbolic observability matrix. Our results are in agreement with the analytical computations, evidencing the correctness of our approach. Its application to efficiently exploring the dynamics of real world complex systems such as power grids, socioeconomic networks or biological networks is quite promising.
C. Letellier, S. Mangiarotti, I. Sendi˝a-Nadal & O. E. R÷ssler
Topological characterization versus synchronization for assessing (or not) dynamical equivalence
Chaos, 28, 045107, 2018. Online
Model validation from experimental data is an important and not trivial topic which is too often reduced to a simple visual inspection of the state portrait spanned by the variables of the system. Synchronization was suggested as a possible technique for model validation. By means of a topological analysis, we revisited this concept with the help of an abstract chemical reaction system and data from two electrodissolution experiments conducted by Jack Hudson’s group. The fact that it was possible to synchronize topologically different global models led us to conclude that synchronization is not a recommendable technique for model validation. A short historical preamble evokes Jack Hudson’s early career in interaction with Otto E. R÷ssler.
C. Letellier, I. Sendina-Nadal & L. A. Aguirre
A nonlinear graph-based theory for dynamical network observability
Physical Review E, 98, 020303(R), 2018. Online
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its d variables, an infeasible task for high dimensional systems due to practical limitations. However the network dynamics might be observable from a reduced set of measured variables but how to reliably identify the minimum set of variables providing full observability still remains an unsolved problem. In order to tackle this issue from the Jacobian matrix of the governing equations, we construct a pruned fluence graph in which the nodes are the state variables and the links represent only the linear dynamical interdependences after having ignored the nonlinear ones. From this graph, we identify the largest connected subgraphs with no outgoing links in which every node can be reached from any other node in the subgraph. In each one of them, at least one node must be measured to correctly monitor the state of the system in a d-dimensional reconstructed space. Our procedure is here tested by investigating large-dimensional reaction networks. Our results are validated by comparing them with the determinant of the observability matrix which provides a rigorous assessment of the system’s observability.
L. A. Aguirre, L. L. Portes & C. Letellier
Structural, Dynamical and Symbolic Observability : From Dynamical Systems to Networks
PLoS ONE, 13 (10), e0206180, 2018. On line
Abstract Classical definitions of observability classify a system as either being observable or not. Observability has been recognized as an important feature to study complex networks, and as for dynamical systems the focus has been on determining conditions for a network to be observable. About twenty years ago continuous measures of observability for nonlinear dynamical systems started to be used. In this paper various aspects of observability that are established for dynamical systems will be investigated in the context of networks. In particular it will be discussed in which ways simple networks can be ranked in terms of observability using continuous measures of such a property. Also it is pointed out that the analysis of the network topology is typically not sufficient for observability purposes, since both the dynamics and the coupling of such nodes play a vital role. Some of the main ideas are illustrated by means of numerical simulations.
C. Draghi, F. Denis, A. TolÚdano & C. Letellier
Parameter identification of a model for prostate cancer treated by intermittent therapy,
Journal of Theoretical Biology, 461, 117-132, 2019. Online 5 October 2018
Adenocarcinoma is the most frequent cancer affecting the prostate walnut-size gland in the male reproductive system. Such cancer may have a very slow progression or may be associated with a “dark prognosis” when tumor cells are spreading very quickly. Prostate cancers have the particular properties to be marked by the level of prostate specific antigen (PSA) in blood which allows to follow its evolution. At least in its first phase, prostate adenocarcinoma is most often hormone-dependent and, consequently, hormone therapy is a possible treatment. Since few years, hormone therapy started to be provided intermittently for improving patient’s quality of life. Today, durations of on- and off-treatment periods are still chosen empirically, most likely explaining why there is no clear benefit from the survival point of view. We therefore developed a model for describing the interaction between the tumor environment, the PSA produced by hormone-dependent and hormone-independent tumor cells, respectively, and the level of androgens. Model parameters were identified using a genetic algorithm applied to the PSA time series measured in a few patients who initially received prostatectomy and were then treated by intermittent hormone therapy (LHRH analogs and anti-androgen). The measured PSA time series is quite correctly reproduced by free runs over the whole follow-up. Model parameter values allow for distinguishing different types of patient (age and Gleason score) meaning that the model can be individualized. We thus showed that the long-term evolution of the cancer can be affected by durations of on- and off-treatment periods.
F. Denis, B. Koontz & C. Letellier
Application and benefits of web-mediated symptom reporting for patients undergoing immunotherapy : A clinical example
Case Report in Oncology, 11, 763-768, 2018. Online
Two randomized studies of symptom monitoring during chemotherapy or during second line treatment and follow-up via web-based patient-reported outcomes (PROs) was previously demonstrated to lengthen survival. We are presenting here a patient with advanced and re-current lung cancer who was followed for 4 years by PROs for relapse and adverse events detection. We report how the web-mediated follow-up helped to detect dangerous pulmonary embolism, relapse and pseudo-progression to immunotherapy by self-reported symptom tracking and specific algorithms triggering notifications to medical team, allowing early man-agement of events. We particularly describe how a discordance between objective clinical im-provement under immunotherapy assessed by the application allowed to detect pseudo-pro-gression on imaging and allowed maintenance of the treatment during more than 1-year, alt-hough imaging report could have led to stop an effective therapy. The progression observed in the routine imaging was indeed in clear contradiction with improvements in patient’s global status as assessed by the reduced PRO-score computed from patient self-reported symptoms. The ability of e-health tools based on symptoms reporting for tumor response assessment should be assessed in trials to help physician in decision of stopping or continuing therapy.
S. Mangiarotti, I. Sendi˝a-Nadal & Christophe Letellier
Using global modeling to unveil hidden couplings in small network motifs
Chaos, 28, 123110, 2018. Online
AbstractOne of the main tasks in network theory is to infer relations among interacting elements. We propose global modeling as a tool to detect links between nodes and their nature. Various situations using small network motifs are investigated under the assumption that the variable to be measured at each node provides full observability when isolated. Such a choice ensures no intrinsic difficulties for getting a global model in the coupled situation. As a first step toward unveiling the coupling function in larger network motifs, we consider three different scenarios involving R÷ssler systems diffusively coupled, in a couple or embedded in a network, or parametrically forced. We show that the global modeling is able to determine not only the existence of an interaction but also its functional form, to retrieve the dynamics of the whole system, and to extract the equations governing the single node dynamics as if it was isolated.