Functional observability and subspace reconstruction in nonlinear systems

in Physical Review Research (2022), 4

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time- ordered data, with applications in many disciplines such as physics, biology, finance, and engineering ... [more ▼]

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time- ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are often low dimensional or even univariate, thus requiring embedding methods to reconstruct the original system’s state space. The observability of a system establishes fundamental conditions under which such reconstruction is possible. However, complete observability is too restrictive in applications where reconstructing the entire state space is not necessary and only a specific subspace is relevant. Here, we establish the theoretic condition to reconstruct a nonlinear functional of state variables from measurement processes, generalizing the concept of functional observability to nonlinear systems. When the functional observability condition holds, we show how to construct a map from the embedding space to the desired functional of state variables, characterizing the quality of such reconstruction. The theoretical results are then illustrated numerically using chaotic systems with contrasting observability properties. By exploring the presence of functionally unobservable regions in embedded attractors, we also apply our theory for the early warning of seizure-like events in simulated and empirical data. The studies demonstrate that the proposed functional observability condition can be assessed a priori to guide time-series analysis and experimental design for the dynamical characterization of complex systems. [less ▲]

Initialisation of Deep Brain Stimulation Parameters with Multi-objective Optimisation Using Imaging Data

in Bildverarbeitung für die Medizin 2022 (2022)

Following the deep brain stimulation (DBS) surgery, the stimulation parameters are manually tuned to reduce symptoms. This procedure can be timeconsuming, especially with directional leads. We propose an ... [more ▼]

Following the deep brain stimulation (DBS) surgery, the stimulation parameters are manually tuned to reduce symptoms. This procedure can be timeconsuming, especially with directional leads. We propose an automated methodology to initialise contact configurations using imaging techniques. The goal is to maximise the electric field on the target while minimising the spillover, and the electric field on regions of avoidance. By superposing pre-computed electric fields, we solve the optimisation problem in less than a minute, much more efficient compared to finite element methods. Our method offers a robust and rapid solution, and it is expected to considerably reduce the time required for manual parameter tuning. [less ▲]

Buffering variability in cell regulation motifs close to criticality

in Physical Review. E. (2022)

Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to ... [more ▼]

Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer system variability, hampering noise-induced regime shifts. Our analysis also shows that, in the considered cooperativity range, impending regime shifts can be generically detected by statistical early warning signals from distributional data. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality. [less ▲]

Model-based assessment of COVID-19 epidemic dynamics by wastewater analysis

in Science of the Total Environment (2022), 827

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective ... [more ▼]

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective approach for epidemic monitoring and the development of an effective warning system. However, its quantitative link to the epidemic status and the stages of outbreak is still elusive. Modelling is thus crucial to address these challenges. In this study, we present a novel mechanistic model-based approach to reconstruct the complete epidemic dynamics from SARS-CoV-2 viral load in wastewater. Our approach integrates noisy wastewater data and daily case numbers into a dynamical epidemiological model. As demonstrated for various regions and sampling protocols, it quantifies the case numbers, provides epidemic indicators and accurately infers future epidemic trends. Following its quantitative analysis, we also provide recommendations for wastewater data standards and for their use as warning indicators against new infection waves. In situations of reduced testing capacity, our modelling approach can enhance the surveillance of wastewater for early epidemic prediction and robust and cost-effective real-time monitoring of local COVID-19 dynamics. [less ▲]

Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere

in Communications Physics (2021), 4

From the flashing of fireflies to autonomous robot swarms, synchronization phenomena are ubiquitous in nature and technology. They are commonly described by the Kuramoto model that, in this paper, we ... [more ▼]

From the flashing of fireflies to autonomous robot swarms, synchronization phenomena are ubiquitous in nature and technology. They are commonly described by the Kuramoto model that, in this paper, we generalise to networks over n-dimensional spheres. We show that, for almost all initial conditions, the sphere model converges to a set with small diameter if the model parameters satisfy a given bound. Moreover, for even n, a special case of the generalized model can achieve phase synchronization with nonidentical frequency parameters. These results contrast with the standard n = 1 Kuramoto model, which is multistable (i.e., has multiple equilibria), and converges to phase synchronization only if the frequency parameters are identical. Hence, this paper shows that the generalized network Kuramoto models for n ≥ 2 displays more coherent and predictable behavior than the standard n = 1 model, a desirable property both in flocks of animals and for robot control. [less ▲]

Dynamical SPQEIR model assesses the effectiveness of non-pharmaceutical interventions against COVID-19 epidemic outbreaks.

in PloS one (2021), 16(5), 0252019

Against the current COVID-19 pandemic, governments worldwide have devised a variety of non-pharmaceutical interventions to mitigate it. However, it is generally difficult to estimate the joint impact of ... [more ▼]

Against the current COVID-19 pandemic, governments worldwide have devised a variety of non-pharmaceutical interventions to mitigate it. However, it is generally difficult to estimate the joint impact of different control strategies. In this paper, we tackle this question with an extended epidemic SEIR model, informed by a socio-political classification of different interventions. First, we inquire the conceptual effect of mitigation parameters on the infection curve. Then, we illustrate the potential of our model to reproduce and explain empirical data from a number of countries, to perform cross-country comparisons. This gives information on the best synergies of interventions to control epidemic outbreaks while minimising impact on socio-economic needs. For instance, our results suggest that, while rapid and strong lockdown is an effective pandemic mitigation measure, a combination of social distancing and early contact tracing can achieve similar mitigation synergistically, while keeping lower isolation rates. This quantitative understanding can support the establishment of mid- and long-term interventions, to prepare containment strategies against further outbreaks. This paper also provides an online tool that allows researchers and decision makers to interactively simulate diverse scenarios with our model. [less ▲]

FastField: An Open-Source Toolbox for Efficient Approximation of Deep Brain Stimulation Electric Fields

in NeuroImage (2020)

Deep brain stimulation (DBS) is a surgical therapy to alleviate symptoms of certain brain disorders by electrically modulating neural tissues. Computational models predicting electric fields and volumes ... [more ▼]

Deep brain stimulation (DBS) is a surgical therapy to alleviate symptoms of certain brain disorders by electrically modulating neural tissues. Computational models predicting electric fields and volumes of tissue activated are key for efficient parameter tuning and network analysis. Currently, we lack efficient and flexible software implementations supporting complex electrode geometries and stimulation settings. Available tools are either too slow (e.g. finite element method–FEM), or too simple, with limited applicability to basic use-cases. This paper introduces FastField, an efficient open-source toolbox for DBS electric field and VTA approximations. It computes scalable e-field approximations based on the principle of superposition, and VTA activation models from pulse width and axon diameter. In benchmarks and case studies, FastField is solved in about 0.2s, ~ 1000 times faster than using FEM. Moreover, it is almost as accurate as using FEM: average Dice overlap of 92%, which is around typical noise levels found in clinical data. Hence, FastField has the potential to foster efficient optimization studies and to support clinical applications [less ▲]

Assessing suppression strategies against epidemicoutbreaks like COVID-19: the SPQEIR model

E-print/Working paper (2020)

The current COVID-19 outbreak represents a most serious challenge for societies worldwide. It isendangering the health of millions of people, and resulting in severe socioeconomic challenges dueto lock ... [more ▼]

The current COVID-19 outbreak represents a most serious challenge for societies worldwide. It isendangering the health of millions of people, and resulting in severe socioeconomic challenges dueto lock-down measures. Governments worldwide aim to devise exit strategies to revive the economywhile keeping the pandemic under control. The problem is that the effects of distinct measures arenot well quantified. This paper compares several suppression approaches and potential exit strategiesusing a new extended epidemic SEIR model. It concludes that while rapid and strong lock-down isan effective pandemic suppression measure, a combination of other strategies such as social distanc-ing, active protection and removal can achieve similar suppression synergistically. This quantitativeunderstanding will support the establishment of mid- and long-term interventions. Finally, the paperprovides an online tool that allows researchers and decision makers to interactively simulate diversescenarios with our model. [less ▲]

Dynamical strategies for obstacle avoidance during Dictyostelium discoideum aggregation: a Multi-agent system model

E-print/Working paper (2019)

Chemotaxis, the movement of an organism in response to a chemical stimulus, is a typical feature of many microbiological systems. In particular, the social amoeba Disctyostelium discoideum is widely used ... [more ▼]

Chemotaxis, the movement of an organism in response to a chemical stimulus, is a typical feature of many microbiological systems. In particular, the social amoeba Disctyostelium discoideum is widely used as a model organism, but it is not still clear how it behaves in heterogeneous environments. A few models focused on mechanical features have already addressed the question; however, we propose that phenomenological models focusing on the dynamics may provide new meaningful data. Consequently, by means of a specific Multi-agent system model, we studied the dynamical features emerging from complex social interactions among individuals belonging to amoeboids colonies. After defining an appropriate metric to perform meaningful measurements, we found that: a) obstacles play the role of local topological perturbation, as they alter the flux of chemical signals; b) that obstacle that physically block the cellular motion as well as the chemicals elicit dynamical evolutions that are not statistically distinguishable from the case where obstacles that do not interfere physically with said motion; c) that fluctuations of the dynamics can lead to better exploration of the physical space, thus preventing multiple stable aggregates. From previous results, we may speculate about the fact that chemotactic cells, in many cases, can avoid obstacles by simply following the altered chemical gradient: social interactions seem to be sufficient to guarantee the aggregation of the whole colony past numerous obstacles. It is then unlikely that cells have developed special mechanisms to cope with the presence of topological perturbation sources. Nevertheless, we suggest that further studies can provide better understanding and that, in order to gain deeper knowledge, mechanical models should be coupled with phenomenological, system-oriented ones. [less ▲]