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DOI: 10.1007/s00526-003-0210-4
, 2003
"... Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of sol ..."
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Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity
by an NSERC Discovery Grant.
, 2014
"... We study Ginzburg–Landau equations for a complex vector order parameter Ψ = (ψ+, ψ−) ∈ C2. We consider the Dirichlet problem in the disk in R2 with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find that t ..."
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We study Ginzburg–Landau equations for a complex vector order parameter Ψ = (ψ+, ψ−) ∈ C2. We consider the Dirichlet problem in the disk in R2 with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find
Nuclear Physics B Proceedings Supplement – preprint (2014) 1–42 Nuclear Physics B Proceedings Supplement Universal Aspects of QCD-like 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 QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe th ..."
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the phase diagram of two-color 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.
0 QUANTITATIVE UNIFORM IN TIME CHAOS PROPAGATION FOR BOLTZMANN COLLISION PROCESSES
, 2010
"... ar ..."
RICE UNIVERSITY Regime Change: Sampling Rate vs. Bit-Depth in Compressive Sensing
, 2011
"... The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated 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 analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated 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 sam-pling rates is quantization, i.e., higher bit-depths 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 bit-depths 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 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement
Results 1 - 10
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