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Simplex Partitioning via Exponential Clocks and the Multiway Cut Problem (Extended Abstract)
, 2013
"... The MultiwayCut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called terminals. This problem is NPhard and there is a well known geometric relaxation in which the graph is embedded i ..."
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into a high dimensional simplex. Rounding a solution to the geometric relaxation is equivalent to partitioning the simplex. We present a novel simplex partitioning algorithm which is based on competing exponential clocks and distortion. Unlike previous methods, it utilizes cuts that are not parallel
Simplices, frames and questions about reality Simplices, frames and questions about reality Filosofie licentiatavhandling
"... Att presenteras den 14 september 2009, kl. 13.15, rum 306, hus 6, Matematiska institutionen, Stockholms universitet, Kräftriket. The two included papers are Incomplete KochenSpecker coloring and The frame function, on average. Abstract This thesis is centered around mathematical structures of fund ..."
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of Hermitian matrices of unit trace also enables us to state the existence problem as one that concerns the shape of the convex body of density matrices mentioned in section 1.2: is it possible to inscribe a regular simplex with N 2 corners in this body? The task is not trivial; whereas the outsphere on which
CERTIFICATE OF APPROVAL
, 2014
"... Treatment plan optimization for rotatingshield brachytherapy ..."
RICE UNIVERSITY Regime Change: Sampling Rate vs. BitDepth in Compressive Sensing
, 2011
"... The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of t ..."
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The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bitdepths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bitdepths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1bit CS framework leads us to scenarios where it may be more appropriate to reduce bitdepth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signaltonoise ratio (SNR). In the measurement
Nuclear Physics B Proceedings Supplement – preprint (2014) 1–42 Nuclear Physics B Proceedings Supplement Universal Aspects of QCDlike TheoriesI
"... In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCDlike theories. As an example for flavor dynamics I discuss a quarkhadron model to describe th ..."
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In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCDlike theories. As an example for flavor dynamics I discuss a quarkhadron model to describe the phase diagram of twocolor QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2 + 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.
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, 2014
"... This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has ..."
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This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has
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, 2010
"... In this thesis, two sets of experimental studies in bosonic and fermionic gases are described. In the first part of the thesis, itinerant ferromagnetism was studied in a strongly interacting Fermi gas of ultracold atoms. The observation of nonmonotonic behavior of lifetime, kinetic energy, and size ..."
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In this thesis, two sets of experimental studies in bosonic and fermionic gases are described. In the first part of the thesis, itinerant ferromagnetism was studied in a strongly interacting Fermi gas of ultracold atoms. The observation of nonmonotonic behavior of lifetime, kinetic energy, and size for increasing repulsive interactions provides strong evidence for a phase transition to a ferromagnetic state. Our observations imply that itinerant ferromagnetism of delocalized fermions is possible without lattice and band structure, and our data validate the most basic model for ferromagnetism introduced by Stoner. In the second part of the thesis, the coherence properties of a BoseEinstein condensate (BEC) was studied in a radio frequency induced doublewell potential implemented on a microfabricated atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial