Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 45 for “"Gradient Flow"”.
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Dynamics of Gradient Flow with Contrastive Learning
… an explicit bias. The implicit bias of the gradient descent is a likely candidate to explain this phenomena. Here, we investigate the gradient ow of the spectral contrastive loss and give a theoretical description of the learning dynamics.
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Pursuit-evasion and time-dependent gradient flow in singular spaces
… regularity theorem. Pursuit curves are downward gradient curves for the distance from a moving evader, that is, for a time-dependent gradient flow. We consider not only pursuit curves, but also more general time-dependent gradient flow.
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Convex Relaxations for Particle-Gradient Flow with Applications in Super-Resolution Single-Molecule Localization Microscopy
… datasets in mind, we discuss leveraging particle-gradient flow 1) for quantifying the accuracy of localization algorithms with and without ground truth and 2) as a basis for novel, model-driven localization algorithms with empirically robust performance. Using experimental data, we demonstrate …
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Optimal sensor placement
… to achieve this goal: the first one is based on gradient flow differential in which it provides the global optimal solution for the placement, and the second one is based on the evaluation of the Hessian matrix at the critical points. The optimal sensor/actuator location found using the gradient …
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Solitons and Volume Preserving Flow
… technique for obtaining static solutions is gradient flow. Gradient flow evolution is in a direction which never increases energy, leading to solutions which are local minima. Here, a modified version of gradient flow referred to as volume preserving flow is introduced. This flow is …
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Similarity in adverse pressure gradient turbulent flows
… generate increasingly adverse pressure gradient flow data for comparison with published data, to find similarities allowing categorization leading to improved flow prediction.
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The evolution equations for Dirac-harmonic Maps
This thesis investigates the gradient flow of Dirac-harmonic maps. Dirac-harmonic maps are critical points of an energy functional that is motivated from supersymmetric field theories. The critical points of this energy functional couple the equation for harmonic maps with spinor fields. At …
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The Ricci Flow on Spin Manifolds
… mass theorem. Finally, on such manifolds, Ricci flow is the gradient flow of said weighted ADM mass, for a natural choice of weight function. This yields a monotonicity formula for the weighted spinorial Dirichlet energy of a weighted Witten spinor along Ricci flow. This part is joint work with …
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Regularity and Numerics for stochastic p-Laplace and symmetric p-Stokes systems
… /> The p-Laplace system arises naturally as the gradient flow of the p-Dirichlet energy. Exactly the gradient flow structure enables improved energy estimates. Exploiting the energy estimates, we show advanced temporal regularity results for strong solutions in optimal function spaces. By optimal …
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Biharmonic maps
… the long-time existence and convergence of the gradient flow for the (intrinsic) biharmonic energy under suitable curvature or initial energy assumptions. Moreover we use the biharmonic energy to regularize the Dirichlet energy for maps from a Riemannian surface into a round sphere. Finally we …
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Learning and inference with Wasserstein metrics
… characterization of the diffusion as following a gradient flow in a space of probability densities endowed with a Wasserstein metric. Existing methods for computing this Wasserstein gradient flow rely on discretizing the underlying domain of the diffusion, prohibiting their application to problems …
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Some unsteady features of turbulent boundary layers
… steady free-stream, zero and favorable pressure gradient turbulent boundary layers, the unsteadiness in the form of turbulent fluctuations was investigated. Phase ensemble-averaged flow characteristics of a large amplitude periodic unsteady turbulent boundary layer was also investigated at a …
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Monopoles and Pin(2)-symmetry
… due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a spinc structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent …
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Tipping Points in Stochastically Perturbed Linear Filippov Systems
… the corresponding Euler-Lagrange equations and a gradient flow applied to the functional. We also prove an extension of Kramer's law to determine bounds for the expected tipping time. Using these methods, we determine the most probable transition path from a frozen state to an unfrozen state and …
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A Product Structure on Generating Family Cohomology for Legendrian Submanifolds
… μ2. To define the product, moduli spaces of gradient flow trees are constructed and shown to live as the 0-stratum of a compact smooth manifold with corners. These spaces consist of intersecting gradient trajectories of functions whose critical points correspond to Reeb chords of the …
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Anisotropic nonlinear PDE models and dynamical systems in biology
… existence of weak solutions of the macroscopic gradient flow. Results of numerical simulations of the discrete gradient flow illustrate the convergence to steady states, their non-uniqueness as well as their dependence on initial data and model parameters. Based on this model we propose an …
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Special gradient trajectories counted by simplex straightening
… tangent trajectories of a nowhere-vanishing gradient-like vector field on a manifold with boundary. And third, the Morse broken trajectory theorem relates the simplicial volume to the number of maximally broken trajectories of the gradient flow of a Morse--Smale function. Corollary: a Morse …
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Moduli spaces and cw structures arising from morse theory
… a Morse function on it. We consider the negative gradient flow of f. Suppose the flow satisfies transversality. This naturally defines the moduli spaces of flow lines and gives a stratication of M by its unstable manifolds. The gluing of broken flow lines can also be constructed.</p> <p>We prove …
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Accelerated algorithms for constrained optimization and control
… in the form of academic examples, power flow optimization and neural network optimization. We devote special attention to analyze a special case of neural network optimization, namely, linear neural network training problem, to understand the dynamics of nonconvex optimization governed by …
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