Divisive Normalization from Wilson-Cowan Dynamics

Divisive Normalization and the Wilson-Cowan equations are influential models of neural interaction and saturation [Carandini and Heeger Nat.Rev.Neurosci. 2012; Wilson and Cowan Kybernetik 1973]. However, they have not been analytically related yet. In this work we show that Divisive Normalization can be obtained from the Wilson-Cowan model. Specifically, assuming that Divisive Normalization is the steady state solution of the Wilson-Cowan differential equation, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson-Cowan kernel but also has a signal-dependent contribution. A standard stability analysis of a Wilson-Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability demonstrates the consistency of our steady state assumption, and is in line with the straightforward use of Divisive Normalization with time-varying stimuli. The proposed theory provides a physiological foundation (a relation to a dynamical network with fixed wiring among neurons) for the functional suggestions that have been done on the need of signal-dependent Divisive Normalization [e.g. in Coen-Cagli et al., PLoS Comp.Biol. 2012]. Moreover, this theory explains the modifications that had to be introduced ad-hoc in Gaussian kernels of Divisive Normalization in [Martinez et al. Front. Neurosci. 2019] to reproduce contrast responses. The proposed relation implies that the Wilson-Cowan dynamics also reproduces visual masking and subjective image distortion metrics, which up to now had been mainly explained via Divisive Normalization. Finally, this relation allows to apply to Divisive Normalization the methods which up to now had been developed for dynamical systems such as Wilson-Cowan networks

Estimation of source parameters using a non-Gaussian probability density function in a Bayesian framework

Source parameters represent key factors in seismic hazard assessment and understanding source physics of earthquakes. In addition to conventional grid search approach to estimate source parameters, other approaches have been used recently. This study uses a Bayesian framework, the Markov Chain Monte Carlo method, to estimate source parameters including uncertainty assessment with inter-parameter correlations. The Bayesian calculation method requires to select a probability density function for estimating likelihood and the function can infuence calculation reliability. While most studies use a normal distribution, we select an F-distribution due to its suitability for the data in ratio form. Using synthetic data and real observations from induced earthquakes in Oklahoma, we compare the calculation steps for spectral ftting and source parameter estimation using the two probability density functions. The sampling distribution and estimated parameters support the assumption that the F-distribution is well-suited for spectral ratio analysis. Results further show that a sampling distribution can efectively reveal trade-ofs and uncertainty among parameters. Sampling distribution trends also reveal data quality criteria that can be used to refne results

Computational and Robotic Models of Human Postural Control

Currently, no bipedal robot exhibits fully human-like characteristics in terms of its postural control and movement. Current biped robots move more slowly than humans and are much less stable. Humans utilize a variety of sensory systems to maintain balance, primary among them being the visual, vestibular and proprioceptive systems. A key finding of human postural control experiments has been that the integration of sensory information appears to be dynamically regulated to adapt to changing environmental conditions and the available sensory information, a process referred to as "sensory re-weighting." In contrast, in robotics, the emphasis has been on controlling the location of the center of pressure based on proprioception, with little use of vestibular signals (inertial sensing) and no use of vision. Joint-level PD control with only proprioceptive feedback forms the core of robot standing balance control. More advanced schemes have been proposed but not yet implemented. The multiple sensory sources used by humans to maintain balance allow for more complex sensorimotor strategies not seen in biped robots, and arguably contribute to robust human balance function across a variety of environments and perturbations. Our goal is to replicate this robust human balance behavior in robots.In this work, we review results exploring sensory re-weighting in humans, through a series of experimental protocols, and describe implementations of sensory re-weighting in simulation and on a robot

The Impact of Renewable Power Generation and Extreme Weather Events on the Stability and Resilience of AC Power Grids

Der erste Teil dieser Arbeit beschäftigt sich mit der Frage, welchen Einfluss kurzzeitige Schwankungen der erneuerbaren Energiequellen auf die synchrone Netzfrequenz haben. Zu diesem Zweck wird eine lineare Antworttheorie für stochastische Störungen von dynamischen Systemen auf Netzwerken hergeleitet. Anschließend wird diese Theorie verwendet, um den Einfluss von kurzfristigen Wind- und Sonnenschwankungen auf die Netzdynamik zu analysieren. Hierbei wird gezeigt, dass die Frequenzantwort des Netzes weitestgehend homogen ist, aber die Anfälligkeit für Leistungsschwankungen aufgrund von Leitungsverlusten entlang des Leistungsflusses zunimmt. Der zweite Teil der Arbeit befasst sich mit der Modellierung von netzbildenden Wechselrichterregelungen. Bislang existiert kein universelles Modell zur Beschreibung der kollektiven Dynamik solcher Systeme. Um dies zu erreichen, wird unter Ausnutzung der inhärenten Symmetrie des synchronen Betriebszustandes eine Normalform für netzbildende Akteure abgeleitet. Anschließend wird gezeigt, dass dieses Modell eine gute Annäherung an typische Wechselrichter-Dynamiken bietet, aber auch für eine datengesteuerte Modellierung gut geeignet ist. Der letzte Teil der Arbeit befasst sich mit der Analyse des Risikos von Stromausfällen, welche durch Hurrikans verursacht werden. Hohe Windgeschwindigkeiten verursachen häufig Schäden an der Übertragungsinfrastruktur, welche wiederum zu Überlastungen anderer Komponenten führen und damit eine Kaskade von Ausfällen im gesamten Netz auslösen können. Simulationen solcher Szenarien werden durch die Kombination eines meteorologischen Windmodells sowie eines Modells für kaskadierende Leitungsausfälle durchgeführt. Durch Monte-Carlo-Simulationen in einer synthetischen Nachbildung des texanischen Übertragungsnetzes können einzelne kritische Leitungen identifiziert werden, welche zu großflächigen Stromausfällen führen.The first part of this thesis addresses the question which impact short-term renewable fluctuations have on the synchronous grid frequency. For this purpose, a linear response theory for stochastic perturbations of networked dynamical systems is derived. This theory is then used to analyze the impact of short-term wind and solar fluctuations on the grid frequency. It is shown that while the network frequency response is mainly homogenous, the susceptibility to power fluctuations is increasing along the power flow due to transmission line losses. The second part of the thesis is concerned with modeling grid-forming inverter controls. So far there exists no universal model for studying the collective dynamics of such systems. By utilizing the inherent symmetry of the synchronous operating state, a normal form for grid-forming actors is derived. It is shown that this model provides a useful approximation of certain inverter control dynamics but is also well-suited for a data-driven modeling approach. The last part of the thesis deals with analyzing the risk of hurricane-induced power outages. High wind speeds often cause damage to transmission infrastructure which can lead to overloads of other components and thereby induce a cascade of failures spreading through the entire grid. Simulations of such scenarios are implemented by combining a meteorological wind field model with a model for cascading line failures. Using Monte Carlo simulations in a synthetic test case resembling the Texas transmission system, it is possible to identify critical lines that trigger large-scale power outages

Trajectory Deformations from Physical Human-Robot Interaction

Robots are finding new applications where physical interaction with a human is necessary: manufacturing, healthcare, and social tasks. Accordingly, the field of physical human-robot interaction (pHRI) has leveraged impedance control approaches, which support compliant interactions between human and robot. However, a limitation of traditional impedance control is that---despite provisions for the human to modify the robot's current trajectory---the human cannot affect the robot's future desired trajectory through pHRI. In this paper, we present an algorithm for physically interactive trajectory deformations which, when combined with impedance control, allows the human to modulate both the actual and desired trajectories of the robot. Unlike related works, our method explicitly deforms the future desired trajectory based on forces applied during pHRI, but does not require constant human guidance. We present our approach and verify that this method is compatible with traditional impedance control. Next, we use constrained optimization to derive the deformation shape. Finally, we describe an algorithm for real time implementation, and perform simulations to test the arbitration parameters. Experimental results demonstrate reduction in the human's effort and improvement in the movement quality when compared to pHRI with impedance control alone

HPC-enabling technologies for high-fidelity combustion simulations

With the increase in computational power in the last decade and the forthcoming Exascale supercomputers, a new horizon in computational modelling and simulation is envisioned in combustion science. Considering the multiscale and multiphysics characteristics of turbulent reacting flows, combustion simulations are considered as one of the most computationally demanding applications running on cutting-edge supercomputers. Exascale computing opens new frontiers for the simulation of combustion systems as more realistic conditions can be achieved with high-fidelity methods. However, an efficient use of these computing architectures requires methodologies that can exploit all levels of parallelism. The efficient utilization of the next generation of supercomputers needs to be considered from a global perspective, that is, involving physical modelling and numerical methods with methodologies based on High-Performance Computing (HPC) and hardware architectures. This review introduces recent developments in numerical methods for large-eddy simulations (LES) and direct-numerical simulations (DNS) to simulate combustion systems, with focus on the computational performance and algorithmic capabilities. Due to the broad scope, a first section is devoted to describe the fundamentals of turbulent combustion, which is followed by a general description of state-of-the-art computational strategies for solving these problems. These applications require advanced HPC approaches to exploit modern supercomputers, which is addressed in the third section. The increasing complexity of new computing architectures, with tightly coupled CPUs and GPUs, as well as high levels of parallelism, requires new parallel models and algorithms exposing the required level of concurrency. Advances in terms of dynamic load balancing, vectorization, GPU acceleration and mesh adaptation have permitted to achieve highly-efficient combustion simulations with data-driven methods in HPC environments. Therefore, dedicated sections covering the use of high-order methods for reacting flows, integration of detailed chemistry and two-phase flows are addressed. Final remarks and directions of future work are given at the end. }The research leading to these results has received funding from the European Union’s Horizon 2020 Programme under the CoEC project, grant agreement No. 952181 and the CoE RAISE project grant agreement no. 951733.Peer ReviewedPostprint (published version