47,183 research outputs found

    Advances on Concept Drift Detection in Regression Tasks using Social Networks Theory

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    Mining data streams is one of the main studies in machine learning area due to its application in many knowledge areas. One of the major challenges on mining data streams is concept drift, which requires the learner to discard the current concept and adapt to a new one. Ensemble-based drift detection algorithms have been used successfully to the classification task but usually maintain a fixed size ensemble of learners running the risk of needlessly spending processing time and memory. In this paper we present improvements to the Scale-free Network Regressor (SFNR), a dynamic ensemble-based method for regression that employs social networks theory. In order to detect concept drifts SFNR uses the Adaptive Window (ADWIN) algorithm. Results show improvements in accuracy, especially in concept drift situations and better performance compared to other state-of-the-art algorithms in both real and synthetic data

    MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

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    We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number n and frequency omega in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field, ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfven wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfven eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of RSAE, the tunneling damping of TAE, as well as the polarization characteristics of KBAE and BAAE being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.Comment: 40 pages, 21 figure

    Decentralized projected Riemannian gradient method for smooth optimization on compact submanifolds

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    We consider the problem of decentralized nonconvex optimization over a compact submanifold, where each local agent's objective function defined by the local dataset is smooth. Leveraging the powerful tool of proximal smoothness, we establish local linear convergence of the projected gradient descent method with unit step size for solving the consensus problem over the compact manifold. This serves as the basis for analyzing decentralized algorithms on manifolds. Then, we propose two decentralized methods, namely the decentralized projected Riemannian gradient descent (DPRGD) and the decentralized projected Riemannian gradient tracking (DPRGT) methods. We establish their convergence rates of O(1/K)\mathcal{O}(1/\sqrt{K}) and O(1/K)\mathcal{O}(1/K), respectively, to reach a stationary point. To the best of our knowledge, DPRGT is the first decentralized algorithm to achieve exact convergence for solving decentralized optimization over a compact manifold. The key ingredients in the proof are the Lipschitz-type inequalities of the projection operator on the compact manifold and smooth functions on the manifold, which could be of independent interest. Finally, we demonstrate the effectiveness of our proposed methods compared to state-of-the-art ones through numerical experiments on eigenvalue problems and low-rank matrix completion.Comment: 32 page

    Formation control of robots in nonlinear two-dimensional potential

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    The formation control of multi-agent systems has garnered significant research attention in both theoretical and practical aspects over the past two decades. Despite this, the examination of how external environments impact swarm formation dynamics and the design of formation control algorithms for multi-agent systems in nonlinear external potentials have not been thoroughly explored. In this paper, we apply our theoretical formulation of the formation control algorithm to mobile robots operating in nonlinear external potentials. To validate the algorithm's effectiveness, we conducted experiments using real mobile robots. Furthermore, the results demonstrate the effectiveness of Dynamic Mode Decomposition in predicting the velocity of robots in unknown environments

    Heat kernel-based p-energy norms on metric measure spaces

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    We focus on heat kernel-based p-energy norms (1<p<\infty) on bounded and unbounded metric measure spaces, in particular, weak-monotonicity properties for different types of energies. Such properties are key to related studies, under which we generalise the convergence result of Bourgain-Brezis-Mironescu (BBM) for p\neq2. We establish the equivalence of various p-energy norms and weak-monotonicity properties when there admits a heat kernel satisfying the two-sided estimates. Using these equivalences, we verify various weak-monotonicity properties on nested fractals and their blowups. Immediate consequences are that, many classical results on p-energy norms hold for such bounded and unbounded fractals, including the BBM convergence and Gagliardo-Nirenberg inequality.Comment: 39 pages with 1 figur

    Can you hear your location on a manifold?

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    We introduce a variation on Kac's question, "Can one hear the shape of a drum?" Instead of trying to identify a compact manifold and its metric via its Laplace--Beltrami spectrum, we ask if it is possible to uniquely identify a point xx on the manifold, up to symmetry, from its pointwise counting function Nx(λ)=λjλej(x)2, N_x(\lambda) = \sum_{\lambda_j \leq \lambda} |e_j(x)|^2, where here Δgej=λj2ej\Delta_g e_j = -\lambda_j^2 e_j and eje_j form an orthonormal basis for L2(M)L^2(M). This problem has a physical interpretation. You are placed at an arbitrary location in a familiar room with your eyes closed. Can you identify your location in the room by clapping your hands once and listening to the resulting echos and reverberations? The main result of this paper provides an affirmative answer to this question for a generic class of metrics. We also probe the problem with a variety of simple examples, highlighting along the way helpful geometric invariants that can be pulled out of the pointwise counting function NxN_x.Comment: 26 pages, 1 figur

    First eigenvalue of embedded minimal surfaces in S3S^3

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    We prove that for an embedded minimal surface Σ\Sigma in S3S^3, the first eigenvalue of the Laplacian operator λ1\lambda_1 satisfies λ11+ϵg\lambda_1\geq 1+\epsilon_g, where ϵg>0\epsilon_g>0 is a constant depending only on the genus gg of Σ\Sigma. This improves previous result of Choi-Wang

    The Gravito-Maxwell equations of General Relativity in the local reference frame of a GR-noninertial observer

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    We show that the acceleration-difference of neighboring freefalling particles (= geodesic deviation) measured in the local reference frame of a noninertial observer in general relativity (GR) is not given by the Riemann tensor. With the gravito-electric field Eg of GR defined as the acceleration of freefalling quasi-static particles relative to the observer, divEg measured in the reference frame of a GR-noninertial observer is different from the curvature R00. We derive our exact, explicit, and simple gravito-Gauss law for divEg in our new reference frame of a GR-noninertial observer with his LONB (Local Ortho-Normal Basis ¯eˆa) and his LONB-connections (ωˆbˆa)ˆc in his time- and 3-directions: the sources of divEg are contributed by all fields including the GR-gravitational fields (Eg,Bg). In the reference frame of a GR-inertial observer our gravito-Gauss law coincides with with Einstein’s R00 equation, which does not have gravitational fields as sources. We derive the gravito-Ampère law for curlBg, the gravito-Faraday law for curlEg, and the law for divBg. The densities of energy, momentum, and momentum-flow of GR-gravitational fields (Eg,Bg) are local observables, but they depend on the observer with his local reference frame: if measured by a GR-inertial observer on his worldline in his frame of LONB con nections, these quantities are zero. For a GR-noninertial observer the sources of gravitational energy, momentum, and momentum-flow densities have the opposite sign from the electromagnetic and matter sources. The sources in the gravito-Gauss law contributed by gravitational energy and momentum-flow densities have a repulsive effect on the gravitational acceleration-difference of particles. This contributes to the accelerated expansion of our inhomogeneous Universe today.ISSN:0264-9381ISSN:1361-638

    Band width estimates with lower scalar curvature bounds

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    A band is a connected compact manifold X together with a decomposition ∂X = ∂−X t ∂+X where ∂±X are non-empty unions of boundary components. If X is equipped with a Riemannian metric, the pair (X, g) is called a Riemannian band and the width of (X, g) is defined to be the distance between ∂−X and ∂+X with respect to g. Following Gromov’s seminal work on metric inequalities with scalar curvature, the study of Riemannian bands with lower curvature bounds has been an active field of research in recent years, which led to several breakthroughs on longstanding open problems in positive scalar curvature geometry and to a better understanding of the positive mass theorem in general relativity In the first part of this thesis we combine ideas of Gromov and Cecchini-Zeidler and use the variational calculus surrounding so called µ-bubbles to establish a scalar and mean curvature comparison principle for Riemannian bands with the property that no closed embedded hypersurface which separates the two ends of the band admits a metric of positive scalar curvature. The model spaces we use for this comparison are warped product over scalar flat manifolds with log-concave warping functions. We employ ideas from surgery and bordism theory to deduce that, if Y is a closed orientable manifold which does not admit a metric of positive scalar curvature, dim(Y ) 6= 4 and Xn≤7 = Y ×[−1, 1], the width of X with respect to any Riemannian metric with scalar curvature ≥ n(n − 1) is bounded from above by 2π n. This solves, up to dimension 7, a conjecture due to Gromov in the orientable case. Furthermore, we adapt and extend our methods to show that, if Y is as before and Mn≤7 = Y × R, then M does not admit a metric of positive scalar curvature. This solves, up to dimension 7 a conjecture due to Rosenberg and Stolz in the orientable case. In the second part of this thesis we explore how these results transfer to the setting where the lower scalar curvature bound is replaced by a lower bound on the macroscopic scalar curvature of a Riemannian band. This curvature condition amounts to an upper bound on the volumes of all unit balls in the universal cover of the band. We introduce a new class of orientable manifolds we call filling enlargeable and prove: If Y is filling enlargeable, Xn = Y × [−1, 1] and g is a Riemannian metric on X with the property that the volumes of all unit balls in the universal cover of (X, g) are bounded from above by a small dimensional constant εn, then width(X, g) ≤ 1. Finally, we establish that whether or not a closed orientable manifold is filling enlargeable or not depends on the image of the fundamental class under the classifying map of the universal cover

    Experimental challenges for high-mass matter-wave interference with nanoparticles

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    We discuss recent advances towards matter-wave interference experiments with free beams of metallic and dielectric nanoparticles. They require a brilliant source, an efficient detection scheme and a coherent method to divide the de Broglie waves associated with these clusters: We describe an approach based on a magnetron sputtering source which ejects an intense cluster beam with a wide mass dispersion but a small velocity spread of 10%. The source is universal as it can be used with all conducting and many semiconducting or even insulating materials. Here we focus on metals and dielectrics with a low work function of the bulk and thus a low cluster ionization energy. This allows us to realize photoionization gratings as coherent matter-wave beam splitters and also to realize an efficient ionization detection scheme. These new methods are now combined in an upgraded Talbot-Lau interferometer with three 266 nm depletion gratings. We here describe the experimental boundary conditions and how to realize them in the lab. This next generation of near-field interferometers shall allow us to soon push the limits of matter-wave interference to masses up to 10 megadaltons.Comment: 10 pages, 5 figure