4,256 research outputs found
Detecting bifurcation values at infinity of real polynomials
We present a new approach for estimating the set of bifurcation values at
infinity. This yields a significant shrinking of the number of coefficients in
the recent algorithm introduced by Jelonek and Kurdyka for reaching critical
values at infinity by rational arcs
Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians
The Projected Configuration Interaction (PCI) method starts from a collection
of mean-field wave functions, and builds up correlated wave functions of good
symmetry. It relies on the Generator Coordinator Method (GCM) techniques, but
it improves the past approaches by a very efficient method of selecting the
basis states. We use the same realistic Hamiltonians and model spaces as the
Configuration Interaction (CI) method, and compare the results with the full CI
calculations in the sd and pf shell. Examples of 24Mg, 28Si, 48Cr, 52Fe and
56Ni are discussed.Comment: 10 pages, 10 figures. Revised version. To be published in Physical
Review
Single-cycle gap soliton in a subwavelength structure
We demonstrate that a single sub-cycle optical pulse can be generated when a
pulse with a few optical cycles penetrates through resonant two-level dense
media with a subwavelength structure. The single-cycle gap soliton phenomenon
in the full Maxwell-Bloch equations without the frame of slowly varying
envelope and rotating wave approximations is observed. Our study shows that the
subwavelength structure can be used to suppress the frequency shift caused by
intrapulse four-wave mixing in continuous media and supports the formation of
single-cycle gap solitons even in the case when the structure period breaks the
Bragg condition. This suggests a way toward shortening high-intensity laser
fields to few- and even single-cycle pulse durations.Comment: 4 pages, 6 figure
Positivity and optimization for semi-algebraic functions
We describe algebraic certificates of positivity for functions belonging to a
finitely generated algebra of Borel measurable functions, with particular
emphasis to algebras generated by semi-algebraic functions. In which case the
standard global optimization problem with constraints given by elements of the
same algebra is reduced via a natural change of variables to the better
understood case of polynomial optimization. A collection of simple examples and
numerical experiments complement the theoretical parts of the article.Comment: 20 page
Photon scattering from strongly driven atomic ensembles
The second order correlation function for light emitted from a strongly and
near-resonantly driven dilute cloud of atoms is discussed. Because of the
strong driving, the fluorescence spectrum separates into distinct peaks, for
which the spectral properties can be defined individually. It is shown that the
second-order correlations for various combinations of photons from different
spectral lines exhibit bunching together with super- or sub-Poissonian photon
statistics, tunable by the choice of the detector positions. Additionally, a
Cauchy-Schwarz inequality is violated for photons emitted from particular
spectral bands. The emitted light intensity is proportional to the square of
the number of particles, and thus can potentially be intense. Three different
averaging procedures to model ensemble disorder are compared.Comment: 7 pages, 4 figure
One Table to Count Them All: Parallel Frequency Estimation on Single-Board Computers
Sketches are probabilistic data structures that can provide approximate
results within mathematically proven error bounds while using orders of
magnitude less memory than traditional approaches. They are tailored for
streaming data analysis on architectures even with limited memory such as
single-board computers that are widely exploited for IoT and edge computing.
Since these devices offer multiple cores, with efficient parallel sketching
schemes, they are able to manage high volumes of data streams. However, since
their caches are relatively small, a careful parallelization is required. In
this work, we focus on the frequency estimation problem and evaluate the
performance of a high-end server, a 4-core Raspberry Pi and an 8-core Odroid.
As a sketch, we employed the widely used Count-Min Sketch. To hash the stream
in parallel and in a cache-friendly way, we applied a novel tabulation approach
and rearranged the auxiliary tables into a single one. To parallelize the
process with performance, we modified the workflow and applied a form of
buffering between hash computations and sketch updates. Today, many
single-board computers have heterogeneous processors in which slow and fast
cores are equipped together. To utilize all these cores to their full
potential, we proposed a dynamic load-balancing mechanism which significantly
increased the performance of frequency estimation.Comment: 12 pages, 4 figures, 3 algorithms, 1 table, submitted to EuroPar'1
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