1,720,989 research outputs found
Electrokinetic Lattice Boltzmann Solver Coupled to Molecular Dynamics: Application to Polymer Translocation
Full text linkWe have developed a theoretical and computational approach to deal with systems that involve a disparate range of spatiotemporal scales, such as those composed of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multicomponent Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multicomponent description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. Lastly, we discuss the advantages and complexities of the approach
Distributed control of multi-vehicle systems using modular architectures
No full textDiese Dissertation präsentiert neue Ergebnisse zur kooperativen Regelung von Fahrzeugen.
Modulare Architekturen werden untersucht, die aus Netzwerken vereinfachter Modelle und komplexer Fahrzeuge bestehen, die die von diesen vereinfachten Modellen erzeugten Trajektorien verfolgen.
Dissipativitätstheorie und \textit{integral quadratic constraints} werden verwendet, um hinreichende Bedingungen für Stabilität und Regelgüte zu finden, die höchstens linear mit der Netzwerkgröße skalieren.
Konvexe und nicht-konvexe Interaktionen zwischen Fahrzeugen werden im Zusammenhang mit einem \textit{source-seeking} Problem betrachtet, bei dem Fahrzeuge das Minimum eines externen Skalarfelds lokalisieren müssen.
Experimente mit Quadrotoren und Simulationsstudien veranschaulichen die Ergebnisse.This thesis presents results on cooperative control of vehicles by studying modular architectures consisting of networks of simplified models and complex vehicles tracking the trajectories generated by these simplified models. Convex intervehicle interactions from formation control and non-convex inter-vehicle interactions emerging from flocking dynamics are studied within the context of a source-seeking problem, where vehicles are required to locate the minimum of an external scalar field. The main analysis tools are dissipativity theory and integral quadratic
constraints while the experimental results are with quadrotors
Convergence properties of natural gradient descent for minimizing KL divergence
No full textThe Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is
often performed over the probability simplex, where the choice of parameterization significantly impacts convergence. In this work, we study the problem of minimizing the KL divergence and analyze the behavior of gradient-based optimization algorithms under two dual coordinate systems within the framework of information geometry− the exponential
family (θ coordinates) and the mixture family (η coordinates). We compare Euclidean gradient descent (GD) in these coordinates with the coordinate-invariant natural gradient
descent (NGD), where the natural gradient is a Riemannian gradient that incorporates the intrinsic geometry of the underlying statistical model. In continuous time, we prove that
the convergence rates of GD in the θ and η coordinates provide lower and upper bounds, respectively, on the convergence rate of NGD. Moreover, under affine reparameterizations
of the dual coordinates, the convergence rates of GD in η and θ coordinates can be scaled to 2c and 2 c , respectively, for any c > 0, while NGD maintains a fixed convergence rate of
2, remaining invariant to such transformations and sandwiched between them. Although this suggests that NGD may not exhibit uniformly superior convergence in continuous time,
we demonstrate that its advantages become pronounced in discrete time, where it achieves faster convergence and greater robustness to noise, outperforming GD. Our analysis hinges on bounding the spectrum and condition number of the Hessian of the KL divergence at the optimum, which coincides with the Fisher information matrix
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Robust Performance Analysis of Source-Seeking Dynamics with Integral Quadratic Constraints
No full textWe analyze the performance of source-seeking dynamics involving vehicles embedded in an underlying scalar field with gradient based forcing terms. We leverage the recently developed framework of α-integral quadratic constraints (IQCs) to obtain convergence rate estimates. We first present the hard Zames-Falb (ZF) α-IQCs involving general non-causal multipliers and show that a parameterization of the ZF multiplier, suggested in the literature for the standard version of the ZF IQCs, can be adapted to the α-IQCs setting. Owing to the time-domain arguments, we can seamlessly extend these results to linear parameter varying (LPV) vehicles possibly opening the doors to non-linear vehicle models with quasi-LPV representations. We illustrate the theoretical results on a linear time invariant (LTI) model of a quadrotor, a non-minimum phase LTI example and an LPV example of a quadrotor with two modes which show a clear benefit of using general non-causal dynamic multipliers to drastically reduce conservatism
Wasserstein KL-divergence for Gaussian distributions
No full textWe introduce a new version of the KL-divergence for Gaussian distributions which is based onWasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space Rn. In particular, we can evaluate the WKLdivergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points
Wasserstein KL-divergence for Gaussian distributions
No full textWe introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space {R}^n. In particular, we can evaluate the WKL-divergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points
Code for Paper: Distributed Control of Heterogeneous Networks of Vehicles with Positive Systems Theory and Generalized H2 Norm
No full textThere is a considerable body of literature analyzing large scale networks of interconnected systems with simple dynamics. For interconnections of vehicles with complex dynamics, it is commonly suggested to design controllers locally at agents so that agents track the trajectories generated by simplified dynamics. We analyze the performance of such a decoupled control architecture by considering the l∞ norm of the local tracking error. This allows us to quantify the deviation of the actual system from the simplified system and either provide a justification for the decoupled architecture or show a need to consider instead a coupled architecture. Specifically, we consider first-order protocols as the interaction mechanism among agents and general discrete-time Linear Time-Invariant (LTI) dynamics as agent models which track the trajectories generated by the first-order protocols. For the analysis and synthesis of first-order protocols, we do not assume a priori knowledge of the connectivity of the graph or the spectrum of the Laplacian matrix, but use results on positive systems to obtain conditions that can scale linearly with network size. We provide bounds on the loss in performance due to imperfect tracking of first order dynamics by higher order agent dynamics and due to disturbances acting locally on agents. Numerical simulations involving generic second order vehicle models with damping illustrate the applicability of the results
Distributed Control of Heterogeneous Networks of Vehicles with Positive Systems Theory and Generalized H₂Norm
No full textFor interconnections of vehicles with complex dynamics, it is commonly suggested to design controllers locally at agents so that agents track the trajectories generated by simplified dynamics. We analyze the performance of such a decoupled control architecture by considering the l∞ norm of the local tracking error, which allows to quantify the deviation of the actual system from the simplified system and either provide a justification for the decoupled architecture or show a need to consider instead a coupled architecture. Specifically, we consider first-order protocols as the interaction mechanism among agents and general discrete-time Linear Time-Invariant (LTI) dynamics as agent models which track the trajectories generated by the first-order protocols. For the analysis and synthesis of first-order protocols, we do not assume a priori knowledge of the connectivity of the graph or the spectrum of the Laplacian matrix, but use results on positive systems to obtain conditions that can scale linearly with network size. We provide bounds on the loss in performance due to imperfect tracking of first order dynamics by higher order agent dynamics and due to disturbances acting locally on agents. Numerical simulations involving generic second order vehicle models with damping illustrate the applicability of the results
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