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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola
Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola
Dartmouth Scholarship
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We …
Building Graphs From Colored Trees, Rachel M. Esselstein, Peter Winkler
Building Graphs From Colored Trees, Rachel M. Esselstein, Peter Winkler
Dartmouth Scholarship
We will explore the computational complexity of satisfying certain sets of neighborhood conditions in graphs with various properties. More precisely, fix a radius $\rho$ and let $N(G)$ be the set of isomorphism classes of $\rho$-neighborhoods of vertices of $G$ where $G$ is a graph whose vertices are colored (not necessarily properly) by colors from a fixed finite palette. The root of the neighborhood will be the unique vertex at the "center" of the graph. Given a set S of colored graphs with a unique root, when is there a graph G with N (G) = S? Or N (G) ⊂ …
An Exponentially Convergent Nonpolynomial Finite Element Method For Time-Harmonic Scattering From Polygons, A. H. Barnett, T. Betcke
An Exponentially Convergent Nonpolynomial Finite Element Method For Time-Harmonic Scattering From Polygons, A. H. Barnett, T. Betcke
Dartmouth Scholarship
In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination …
Results From Electrostatic Calibrations For Measuring The Casimir Force In The Cylinder-Plane Geometry, Q. Wei, D. A. R. Dalvit, F. C. Lombardo, F. D. Mazzitelli, R. Onofrio
Results From Electrostatic Calibrations For Measuring The Casimir Force In The Cylinder-Plane Geometry, Q. Wei, D. A. R. Dalvit, F. C. Lombardo, F. D. Mazzitelli, R. Onofrio
Dartmouth Scholarship
We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurements performed in the parallel-plane configuration, showing that the dependence on distance of the minimizing potential, if present …
Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp
Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp
Dartmouth Scholarship
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool …
The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott D. Pauls
The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott D. Pauls
Dartmouth Scholarship
In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C 2 complete em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16], …
Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, James M. Hughes, Daniel J. Graham, Daniel N. Rockmore
Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, James M. Hughes, Daniel J. Graham, Daniel N. Rockmore
Dartmouth Scholarship
Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison …