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 27 for “"spectral gap"”.
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Quantitative studies and Hydrodynamical limits for interacting particle systems
… objective is to determine the scaling of the spectral gap, i.e. the relaxation rate, in terms of the number of the particles for a paradigmatic model describing heat transport, the chain of oscillators. The mathematical study of this model started at the end of $90$s and it is challenging due …
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Entire Function Majorants
… Rfn y for bounded functions f with a spectral gap at the origin.
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Statistical inference in networks: fundamental limits and efficient algorithms
… identify, and exactly matches without a constant gap when there is a single community or two equal-sized communities. However, if the community sizes are sublinear in the total number of vertices, the guarantee is far from the information limit. We conjecture that our algorithm achieves the …
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Discrepancy Inequalities in Graphs and Their Applications
<p>Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy …
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Spectral analysis in bipartite biregular graphs and community detection
This thesis concerns to spectral gap of random regular graphs and consists of two main con- tributions. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for the non trivial eigenvalues of its adjacency operator, proving Alon's …
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Half-bound states of a one-dimensional Dirac system: their effect on the Titchmarsh-Weyl M([lambda])-function and the scattering matrix
… as a corollary, we deduce the behavior of the spectral function near the spectral gap endpoints. Further, we establish community of the S-matrix in momentum space and prove the Levinson theorem as a corollary to this analysis. We also obtain explicit asymptotics of the S-matrix for power-law …
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Improved Tools for Local Hamiltonians
… structured setting where the Hamiltonian has a spectral gap and spatial locality. This setting is widely studied using approximate ground space projectors (AGSPs). In chapter 1 we give an improved analysis of AGSPs in the setting of local Hamiltonians with a degenerate ground space. This implies …
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Eigenvalue Spacings of Transition Matrices Associated to Directed Graphs
This thesis develops new spectral techniques to analyze the convergence behaviour of finite, discrete-time, time-homogeneous Markov chains and explores their applications to directed graphs. We derive an explicit expression for the error term in the convergence theorem in terms of the eigenvalues …
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Generalized phononic networks : of length scales, symmetry breaking and (non) locality : "controlling complexity through simplicity"
… which possesses multiple complete in-plane spectral gaps totaling over 100% in normalized gap size to a phononic metamaterial which exhibits a single complete in-plane spectral gap of 102% and a complete spectral gap of 88%, both significant advancements over the state of the art. This …
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Optimizing Quantum Annealing for Trapped Ions: Performance, Resources, and Noise Mitigation
… of the annealing Hamiltonian affects the minimum spectral gap that controls the annealing runtime. On the cost side, we show that retaining the native polynomial unconstrained binary optimization (PUBO) structure of combinatorial problems, rather than reducing them to the standard quadratic (QUBO) …
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EXPLORATIONS IN QUANTUM GRAVITY AND CONFORMAL BOOTSTRAP
… a new bound on the scaling dimension of the spectral gap. Chapter five is about the black hole information paradox. Using the replica trick for computing the entropy of Hawking radiation, we found a new saddle-point in the gravitational path integral. This saddle-point corresponds to a …
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Sequence-phase optimal (SPO) [d̳e̳l̳t̳a̳]B₀ field control for lipid suppression and homogeneity for brain magnetic resonance spectroscopic imaging
… the lipid-suppression phase, by widening the spectral gap between spatially separate lipid and metabolite regions, and then to narrow metabolite linewidth during readout, by brain-only [delta]B₀ homogenization. This sequence-phase-optimal (SPO) shimming approach is demonstrated on four …
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Computations and lower bounds for scl and the relative Gromov seminorm
… a new proof of a theorem of Heuer on a sharp spectral gap for right-angled Artin groups.
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Potential-based analysis of social, communication, and distributed networks
… by connecting the convergence time to the spectral gap of the adjacency matrices of underlying dynamics. This not only allows us to improve the best known upper bound, but also removes the dependency of termination time from the dimension of the ambient space. The approach adopted here can …
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Qualitative and quantitative convergence results for randomised integration methods
… Markov chain Monte Carlo methods which satisfy a spectral gap condition and functions which do not need to have a finite second moment. We prove error bounds for the absolute mean error where the rate of convergence is optimal. Illustrative scenarios where our theory is applicable are the random …
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Thermostated Kac models
We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium canonical distribution in terms of the L2 norm, in relative entropy, and in the …
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Fine properties of stochastic evolution equations and their applications
… to the invariant measure and the existence of a spectral gap are also obtained. These results are first established for general stochastic evolution equations with strongly dissipative drift, e.g. stochastic reaction-diffusion equations, stochastic porous media equations and the stochastic …
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Optimizing Irreversible Perturbations of the Unadjusted Langevin Algorithm
… two competing objectives: maximizing the spectral gap of the continuous dynamics to accelerate convergence, and minimizing discretization error that drives estimation bias. Motivated by this, we introduce new criteria that jointly evaluate bias and efficiency, and we show how these …
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Case studies in quantum adiabatic optimization
… time of this algorithm is related to the minimum spectral gap of H(s) for s E (0, 11. We study such transverse field spin Hamiltonians using both analytic and numerical techniques. Our approach is example-based, that is, we study some specific choices for the problem Hamiltonian Hp which …
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Metal-insulator-insulator-metal plasmonic waveguides and devices
… and radiative (leaky) portions separated by a spectral gap at the light line. The leaky regime is further divided into antenna and reactive mode regions. Spatial dispersion effect on the SH mode yields a reduced wave vector in its dispersion curve and an increased propagation loss. The MIM …
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