3,290 research outputs found
Locating the Source of Diffusion in Large-Scale Networks
How can we localize the source of diffusion in a complex network? Due to the
tremendous size of many real networks--such as the Internet or the human social
graph--it is usually infeasible to observe the state of all nodes in a network.
We show that it is fundamentally possible to estimate the location of the
source from measurements collected by sparsely-placed observers. We present a
strategy that is optimal for arbitrary trees, achieving maximum probability of
correct localization. We describe efficient implementations with complexity
O(N^{\alpha}), where \alpha=1 for arbitrary trees, and \alpha=3 for arbitrary
graphs. In the context of several case studies, we determine how localization
accuracy is affected by various system parameters, including the structure of
the network, the density of observers, and the number of observed cascades.Comment: To appear in Physical Review Letters. Includes pre-print of main
paper, and supplementary materia
Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization
A versatile method is described for the practical computation of the discrete
Fourier transforms (DFT) of a continuous function given by its values
at the points of a uniform grid generated by conjugacy classes
of elements of finite adjoint order in the fundamental region of
compact semisimple Lie groups. The present implementation of the method is for
the groups SU(2), when is reduced to a one-dimensional segment, and for
in multidimensional cases. This simplest case
turns out to result in a transform known as discrete cosine transform (DCT),
which is often considered to be simply a specific type of the standard DFT.
Here we show that the DCT is very different from the standard DFT when the
properties of the continuous extensions of these two discrete transforms from
the discrete grid points to all points are
considered. (A) Unlike the continuous extension of the DFT, the continuous
extension of (the inverse) DCT, called CEDCT, closely approximates
between the grid points . (B) For increasing , the derivative of CEDCT
converges to the derivative of . And (C), for CEDCT the principle of
locality is valid. Finally, we use the continuous extension of 2-dimensional
DCT to illustrate its potential for interpolation, as well as for the data
compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's
Repor
Gamow-Teller strength distributions for nuclei in pre-supernova stellar cores
Electron-capture and -decay of nuclei in the core of massive stars
play an important role in the stages leading to a type II supernova explosion.
Nuclei in the f-p shell are particularly important for these reactions in the
post Silicon-burning stage of a presupernova star. In this paper, we
characterise the energy distribution of the Gamow-Teller Giant Resonance (GTGR)
for mid-fp-shell nuclei in terms of a few shape parameters, using data obtained
from high energy, forward scattering (p,n) and (n,p) reactions. The energy of
the GTGR centroid is further generalised as function of nuclear
properties like mass number, isospin and other shell model properties of the
nucleus. Since a large fraction of the GT strength lies in the GTGR region, and
the GTGR is accessible for weak transitions taking place at energies relevant
to the cores of presupernova and collapsing stars, our results are relevant to
the study of important -capture and -decay rates of arbitrary,
neutron-rich, f-p shell nuclei in stellar cores. Using the observed GTGR and
Isobaric Analog States (IAS) energy systematics we compare the coupling
coefficients in the Bohr-Mottelson two particle interaction Hamiltonian for
different regions of the Isotope Table.Comment: Revtex, 28 pages +7 figures (PostScript Figures, uuencoded, filename:
Sutfigs.uu). If you have difficulty printing the figures, please contact
[email protected]. Accepted for publication in Phys. Rev. C, Nov 01,
199
Vector quantization of image subbands: a survey
Subband and wavelet decompositions are powerful tools in image coding because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting, which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization (VQ) provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988, a growing body of research has examined the use of VQ for subband/wavelet transform coefficients. We present a survey of these methods
Assessing Digital Surface Models by Verifying Shadows: A Sensor Network Approach
We propose to use wireless sensor networks to assess the accuracy and application of Digital Surface Models (DSM) for the study of shadowing and solar radiation over the built environment. Using the ability of sensor network data to provide information about solar radiation and predicting the exact time of the day that the Sun starts radiating a sensor, a comparative study and statistical analysis can be undertaken in order to evaluate the accuracy of the DSM for shadowing and radiation studies using image processing techniques. Two DSMs of the EPFL campus with different cell resolutions (1 meter and 0.5 meters), considering only information about ground, buildings with vertical walls and trees, are constructed step by step and employed. Three DSMs of the same campus with a cell resolution of 1 meter derived from raw LIDAR data and common interpolation techniques, such as Triangulated Irregular Network (TIN), kriging, Inverse Distance Weighting (IDW), are also used for comparison
Practical solution to the Monte Carlo sign problem: Realistic calculations of 54Fe
We present a practical solution to the "sign problem" in the auxiliary field
Monte Carlo approach to the nuclear shell model. The method is based on
extrapolation from a continuous family of problem-free Hamiltonians. To
demonstrate the resultant ability to treat large shell-model problems, we
present results for 54Fe in the full fp-shell basis using the Brown-Richter
interaction. We find the Gamow-Teller beta^+ strength to be quenched by 58%
relative to the single-particle estimate, in better agreement with experiment
than previous estimates based on truncated bases.Comment: 11 pages + 2 figures (not included
Complete 0 hbar omega calculations of Gamow-Teller strengths for nuclei in the iron region
Gamow-Teller strengths for selected nuclei in the iron region (A~56) have
been investigated via shell-model Monte Carlo calculations with realistic
interactions in the complete fp basis. Results for all cases show significant
quenching relative to single-particle estimates, in quantitative agreement with
(n,p) data. The J=1,T=0 residual interaction and the f_{7/2}-f_{5/2} spin-orbit
splitting are shown to play major roles in the quenching mechanism. Calculated
B(E2, 2^+_1 -> 0^+_1) values are in fair agreement with experiment using
effective charges of e_p=1.1e and e_n=0.1e.Comment: 13 pages + 1 postscript file, Caltech preprint MAP-16
Electron capture on iron group nuclei
We present Gamow-Teller strength distributions from shell model Monte Carlo
studies of fp-shell nuclei that may play an important role in the pre-collapse
evolution of supernovae. We then use these strength distributions to calculate
the electron-capture cross sections and rates in the zero-momentum transfer
limit. We also discuss the thermal behavior of the cross sections. We find
large differences in these cross sections and rates when compared to the naive
single-particle estimates. These differences need to be taken into account for
improved modeling of the early stages of type II supernova evolution
Gamow-Teller strength distributions in fp-shell nuclei
We use the shell model Monte Carlo method to calculate complete 0f1p-shell
response functions for Gamow-Teller (GT) operators and obtain the corresponding
strength distributions using a Maximum Entropy technique. The approach is
validated against direct diagonalization for 48Ti. Calculated GT strength
distributions agree well with data from (n,p) and (p,n) reactions for nuclei
with A=48-64. We also calculate the temperature evolution of the GT+
distributions for representative nuclei and find that the GT+ distributions
broaden and the centroids shift to lower energies with increasing temperature
Nuclear Polarization of Molecular Hydrogen Recombined on a Non-metallic Surface
The nuclear polarization of molecules formed by recombination
of nuclear polarized H atoms on the surface of a storage cell initially coated
with a silicon-based polymer has been measured by using the longitudinal
double-spin asymmetry in deep-inelastic positron-proton scattering. The
molecules are found to have a substantial nuclear polarization, which is
evidence that initially polarized atoms retain their nuclear polarization when
absorbed on this type of surfac
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