We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud...
ISBN:
(纸本)9781713871088
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes.
We consider a class of random ergodic averages, containing averages along random non–integer sequences. For such averages, Cohen & Cuny obtained ∫ uniform universal pointwise convergence for functions in L2 with...
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We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using it...
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We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear optimization. We show the vertices of the Max k-Cut relaxation correspond to partitions of the data into at most k sets. We also show the vertices are attractive fixed points of iterated linear optimization. Each step of this iterative process solves a relaxation of the closest vertex problem and leads to a new clustering problem where the underlying clusters are more clearly defined. Our experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation leads to significantly better results when compared to randomized rounding.
Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, ...
Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this symmetry in terms of a (non-compact) group action, and we employ dimensional analysis and ideas from equivariant machine learning to provide a methodology for exactly units-equivariant machine learning: For any given learning task, we first construct a dimensionless version of its inputs using classic results from dimensional analysis and then perform inference in the dimensionless space. Our approach can be used to impose units equivariance across a broad range of machine learning methods that are equivariant to rotations and other groups. We discuss the in-sample and out-of-sample prediction accuracy gains one can obtain in contexts like symbolic regression and emulation, where symmetry is important. We illustrate our approach with simple numerical examples involving dynamical systems in physics and ecology.
Identification of drug target proteins is an important process in drug discovery and development. To perform predictions of large-scale drug-Target interactions, many computational methods have been proposed using the...
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The characteristic mode analysis (CMA) is formulated and implemented for the hydrodynamic volume integral equation (HDVIE) that is used to mathematically model electromagnetic field interactions and conduction current...
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ISBN:
(数字)9798350369908
ISBN:
(纸本)9798350369915
The characteristic mode analysis (CMA) is formulated and implemented for the hydrodynamic volume integral equation (HDVIE) that is used to mathematically model electromagnetic field interactions and conduction current dynamics on nanoantennas and nanoscatterers. The proposed method produces excitation-independent characteristic hydrodynamic currents and the corresponding modal significance curves, providing useful information that can be used to optimize the performance of a nanoantenna. Numerical results demonstrate the reliability and the applicability of the proposed approach.
The diagnosis of primary bone tumors is challenging, as the initial complaints are often non-specific. Early detection of bone cancer is crucial for a favorable prognosis. Incidentally, lesions may be found on radiogr...
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MSC Codes 65N22, 65K10, 65F45We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduc...
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Socio-spatial segregation is the physical separation of different social, economic, or demographic groups within a geographic space, often resulting in unequal access to resources, services, and opportunities. The lit...
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Software-defined networking(SDN)is a new paradigm that promises to change by breaking vertical integration,decoupling network control logic from the underlying routers and switches,promoting(logical)network control ce...
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Software-defined networking(SDN)is a new paradigm that promises to change by breaking vertical integration,decoupling network control logic from the underlying routers and switches,promoting(logical)network control centralization,and introducing network ***,the controller is similarly vulnerable to a“single point of failure”,an attacker can execute a distributed denial of service(DDoS)attack that invalidates the controller and compromises the network security in *** address the problem of DDoS traffic detection in SDN,a novel detection approach based on information entropy and deep neural network(DNN)is *** approach contains a DNN-based DDoS traffic detection module and an information-based entropy initial inspection *** initial inspection module detects the suspicious network traffic by computing the information entropy value of the data packet’s source and destination Internet Protocol(IP)addresses,and then identifies it using the DDoS detection module based on *** assaults were found when suspected irregular traffic was *** reveal that the algorithm recognizes DDoS activity at a rate of more than 99%,with a much better accuracy *** false alarm rate(FAR)is much lower than that of the information entropy-based detection ***,the proposed framework can shorten the detection time and improve the resource utilization efficiency.
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