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Showing 1 to 20 of 34 for “"Minimizer"”.
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Minimizer-space computation
… handle the data arises. One such concept is minimizers, which are genomic substrings that allow for reduced representations of larger DNA sequences. In this thesis, we introduce minimizer-space computation as a new algorithmic paradigm for DNA sequence analysis. Instead of DNA nucleotides, we …
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Edge length minimizing polyhedra
… is shown to minimize over the same families. The minimizer of Aberth's Problem cannot have all equal-area faces; similarly, for Melzak's Problem, the minimizer cannot be an equal-faced polyhedron with 10 or more faces. For the minimizing object in both Aberth's Problem and Melzak's Problem, the …
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Regularity of Neumann solutions to an elliptic free boundary problem
… We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. These results include up-to-the boundary gradient estimates on harmonic functions with Neumann boundary conditions on convex domains. The main result is that the minimizer u is …
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Non-parametric hypersurfaces of prescribed mean curvature in H n x R
… given.We establish existence and uniqueness of a minimizer u to J. Furthermore, we prove height bounds for u if $varphi in LI(Omega)$. The interior regularity of the minimizer is proved via regularity theory of rectifiable $lambda$-minimizing currents from geometric measure theory up to dimension …
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Geometric variational problems with cross-sectional constraints
… area. We conclude that, up to a translation, the minimizer exists and is invariant under revolution. In Chapter 4, as a specific case of the problem in Chapter 2, the minimizing surface bounded by two parallel circles of the same size is studied carefully. We conclude that such an area minimizing …
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A variational formulation of a floating body
… appropriate function space in which we seek a minimizer and show existence in the static case under certain assumptions. Furthermore, making use of the Isoperimetric inequality we show that the contact set of a minimizer between fluid and body consists of finitely many components. Here, the …
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Boundary Properties for Almost-Minimizers of the Relative Perimeter
… concerning the boundary regularity for almost-minimizers of the relative perimeter in A. An almost-minimizer of the relative perimeter in A is a measurable set E that minimizes the perimeter functional P(E;A), roughly speaking the (n-1)-area of the boundary of E in A, among local competitors …
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Scalable sketching and indexing algorithms for large biological datasets
… analysis. Secondly, we introduce the concept of minimizer-space sequencing data analysis, where a set of minimizers, rather than DNA nucleotides, are the atomic tokens of the alphabet. We propose that minimizer-space representations can be seamlessly applied to the problem of genome assembly, the …
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Variational Methods for Nonlinear Partial Differential Equations
… results discussed is the existence theorem for minimizer of functionals for the case of fixed boundary problems. This theorem assumes coercivity and lower semicontinuity conditions of the functional and the energy functional is defined over subsets of Sobolev spaces. After that, the technical …
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Rotating Nonlinear States in Gross-Pitaevskii Equations
… symmetric solutions, one of which is a local minimizer and the other is a mountain pass type critical point of the associated energy, both with prescribed mass and angular momentum. We also establish that the local minimizer is orbitally stable, while the mountain pass type solution is …
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On two problems related to the Laplace operator
… and results of symmetry breaking for the minimizer.
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Calibration of Option Pricing in Reproducing Kernel Hilbert Space
… of the options. We discuss the existence of the minimizer by using regu- larized reproducing kernel method and show that the regularizer resolves the numerical instability of the calibration problem. Finally, we apply our studied method to data sets of index options by simulation tests and …
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Travelling wave solutions of the heat equation in an unbounded cylinder with a non-linear boundary condition
… specifically, a weak solution is found as the minimizer of a constrained minimization problem posed in a weighted Sobolev space. Due to underlying domain $RimesOmega$ being unbounded, this problem suffers from a lack of compactness. The problem is solved using a suitable approximation.
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The nonlinear differential semblance algorithm for plane waves in layered media
… algorithms may successfully approximate a global minimizer from a crude initial guess for typical band-limited data.
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Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations
… space. The existence and uniqueness of the minimizer for the cost functional is proved. Error estimates in a weighted 𝐻⁻¹-norm, 𝐿²-norm and 𝐿¹-norm for the numerical solution are derived. Numerical examples will be given to show features of this numerical method.
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Mappings Between Annuli of Smallest p-Harmonic Energy
… $\A^* = \A(r_*, R_*)$, we seek the traction-free minimizer of the $p$-harmonic energy among homeomorphisms in Sobolev class $W^{1, p}(\A, \A^*)$. For such a mapping, the $p$-harmonic energy is defined by \begin{equation*}</p> <p>\mathcal{E}_p[h] = \int\limits_{\A} |Dh(x)|^p dx</p> …
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Shape optimization of a floating body
… Using direct methods we prove the existence of a minimizer of the penalized problem. Moreover, we show that the minimizer is bounded and subharmonic. By a construction of two appropriate comparison functions we get equivalence of the original and the penalized problem provided we have chosen …
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Optimization by Gaussian smoothing with application to geometric alignment
… effect and follow the continuous path of the minimizer, eventually towards a minimum of the objective function. Empirically, people have observed that the minimum found this way has high chance to be the global minimum. Despite its empirical success, there has been little theoretical …
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Explicit Regularization for Overparameterized Models
… RMD provably converges to a point “close” to a minimizer of the regularized objective. Additionally, RMD is computationally efficient and imposes virtually no overhead to standard gradient descent. We observe that RMD is remarkably robust and consistent compared to gradient descent with weight …
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Variational methods in nonsmooth analysis and quasilinear equations
… 2 we look for assumptions, under which local minimizers for functionals of the Calculus of Variations in a weak topology are also local minimizers in a strong topology, while in Chapter 3 we give an application of the results of Chapter 2. We prove for a certain class of quasilinear equations …
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