This paper introduces a novel strategy for point force localization in the frequency domain, based on metamodeling techniques and independent of excitation level. More precisely, ability well-established techniques, such as Polynomial Chaos expansion or Universal Kriging, providing accurate surrogate models locating through an optimization procedure is evaluated. The proposed methodology applie...

Consider a finite irreducible Markov chain with invariant distribution π. We use the inner product induced by π and the associated heat operator to simplify and generalize some results related to graph partitioning and the small-set expansion problem. For example, Steurer showed a tight connection between the number of small eigenvalues of a graph’s Laplacian and the expansion of small sets in ...

– I construct a well-defined expansion in ǫ = 2− d for diffusion processes on smallworld networks. The technique permits one to calculate the average over disorder of moments of the Green’s function, and is used to calculate the average Green’s function and fluctuations to first non-leading order in ǫ, giving results which agree with numerics. This technique is also applicable to other problems...

A class of simple undirected graphs is small if it contains at most n!α labelled graphs with n vertices, for some constant α. We prove that for any constants c, ε > 0, the class of graphs with expansion bounded by the function f(r) = c 1/3−ε is small. Also, we show that the class of graphs with expansion bounded by 6 · 3 √ r log(r+e) is not small. We work with simple undirected graphs, without ...

Consider an irreducible reversible Markov chain on state space V , with |V | = n and invariant distribution π. Let 0 = λ1 ≤ λ2 ≤ · · ·λn ≤ 2 be the eigenvalues of its Laplacian operator. We give a simple spectral condition under which there exists a unit vector f ∈ L(V, π) with ‖f‖1 ≤ δ and 〈f, Lf〉 ≤ . (Using a standard Cheeger inequality, this implies the existence of a set S ⊆ V with measure ...

We consider the problem of testing small set expansion for general graphs. A graph G is a (k, φ)expander if every subset of volume at most k has conductance at least φ. Small set expansion has recently received significant attention due to its close connection to the unique games conjecture, the local graph partitioning algorithms and locally testable codes. We give testers with two-sided error...

In this dissertation, we study the Karhunen-Loève (KL) expansion and the exact L small ball probability for Gaussian processes. The exact L small ball probability is connected to the Laplace transform of the Gaussian process via Sytaja Tauberian theorem. Using this technique, we solved the problem of finding the exact L small ball estimates for the Slepian process S(t) defined as S(t) = W (t+a)...