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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Topological Structures In The Equities Market Network, Gregory Leibon, Scott Pauls, Daniel Rockmore, Robert Savell
Topological Structures In The Equities Market Network, Gregory Leibon, Scott Pauls, Daniel Rockmore, Robert Savell
Dartmouth Scholarship
We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on “partition decoupled null models,” a new class of null models that incorporate the interaction of clustered partitions into a random model and generalize the Gaussian ensemble. As an application, we analyze a correlation matrix derived from 4 years of close prices of equities in the New York Stock Exchange (NYSE) and National Association of Securities Dealers Automated Quotation (NASDAQ). In this example, we expose (i) a natural structure composed of 2 interacting partitions of …
A Sharp Bound For The Reconstruction Of Partitions, Vincent Vatter
A Sharp Bound For The Reconstruction Of Partitions, Vincent Vatter
Dartmouth Scholarship
Answer in g a question of Cameron, Pretzel and Siemons proved that every integer partition of n >= 2(k + 3) (k + 1) can be reconstructed from its set of k-deletions. We describe a new reconstruction algorithm that lowers this bound to n >= k(2) + 2k and present examples showing that this bound is best possible.
Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb
Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb
Dartmouth Scholarship
Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum …