23,301 research outputs found
Stopping time signatures for some algorithms in cryptography
We consider the normalized distribution of the overall running times of some
cryptographic algorithms, and what information they reveal about the
algorithms. Recent work of Deift, Menon, Olver, Pfrang, and Trogdon has shown
that certain numerical algorithms applied to large random matrices exhibit a
characteristic distribution of running times, which depends only on the
algorithm but are independent of the choice of probability distributions for
the matrices. Different algorithms often exhibit different running time
distributions, and so the histograms for these running time distributions
provide a time-signature for the algorithms, making it possible, in many cases,
to distinguish one algorithm from another. In this paper we extend this
analysis to cryptographic algorithms, and present examples of such algorithms
with time-signatures that are indistinguishable, and others with
time-signatures that are clearly distinct.Comment: 20 page
Embedded density functional theory for covalently bonded and strongly interacting subsystems
Embedded density functional theory (e-DFT) is used to describe the electronic structure of strongly interacting molecular subsystems. We present a general implementation of the Exact Embedding (EE) method [J. Chem. Phys. 133, 084103 (2010)] to calculate the large contributions of the nonadditive kinetic potential (NAKP) in such applications. Potential energy curves are computed for the dissociation of Li^+–Be, CH_3–CF_3, and hydrogen-bonded water clusters, and e-DFT results obtained using the EE method are compared with those obtained using approximate kinetic energy functionals. In all cases, the EE method preserves excellent agreement with reference Kohn–Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures. We also demonstrate an accurate pairwise approximation to the NAKP that allows for efficient parallelization of the EE method in large systems; benchmark calculations on molecular crystals reveal ideal, size-independent scaling of wall-clock time with increasing system size
The Radius of the Proton: Size Does Matter
The measurement by Pohl et al. [1] of the 2S_1/2^F=1 to 2P_3/2^F=2 transition
in muonic hydrogen and the subsequent analysis has led to a conclusion that the
rms charge radius of the proton differs from the accepted (CODATA [2]) value by
approximately 4%, leading to a 4.9 s.d. discrepancy. We investigate the muonic
hydrogen spectrum relevant to this transition using bound-state QED with Dirac
wave-functions and comment on the extent to which the perturbation-theory
analysis which leads to the above conclusion can be confirmed.Comment: Delayed arXiv submission. To appear in 'Proceedings of T(R)OPICALQCD
2010' (September 26 - October 1, 2010). 7 pages, 1 figure. Superseded by
arXiv:1104.297
Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results
We compute the pointwise asymptotics of orthogonal polynomials with respect
to a general class of pure point measures supported on finite sets as both the
number of nodes of the measure and also the degree of the orthogonal
polynomials become large. The class of orthogonal polynomials we consider
includes as special cases the Krawtchouk and Hahn classical discrete orthogonal
polynomials, but is far more general. In particular, we consider nodes that are
not necessarily equally spaced. The asymptotic results are given with error
bound for all points in the complex plane except for a finite union of discs of
arbitrarily small but fixed radii. These exceptional discs are the
neighborhoods of the so-called band edges of the associated equilibrium
measure. As applications, we prove universality results for correlation
functions of a general class of discrete orthogonal polynomial ensembles, and
in particular we deduce asymptotic formulae with error bound for certain
statistics relevant in the random tiling of a hexagon with rhombus-shaped
tiles.
The discrete orthogonal polynomials are characterized in terms of a a
Riemann-Hilbert problem formulated for a meromorphic matrix with certain pole
conditions. By extending the methods of [17, 22], we suggest a general and
unifying approach to handle Riemann-Hilbert problems in the situation when
poles of the unknown matrix are accumulating on some set in the asymptotic
limit of interest.Comment: 28 pages, 7 figure
Exact nonadditive kinetic potentials for embedded density functional theory
We describe an embedded density functional theory (DFT) protocol in which the nonadditive kinetic energy component of the embedding potential is treated exactly. At each iteration of the Kohn–Sham equations for constrained electron density, the Zhao–Morrison–Parr constrained search method for constructing Kohn–Sham orbitals is combined with the King-Handy expression for the exact kinetic potential. We use this formally exact embedding protocol to calculate ionization energies for a series of three- and four-electron atomic systems, and the results are compared to embedded DFT calculations that utilize the Thomas–Fermi (TF) and the Thomas–Fermi–von Weisacker approximations to the kinetic energy functional. These calculations illustrate the expected breakdown due to the TF approximation for the nonadditive kinetic potential, with errors of 30%–80% in the calculated ionization energies; by contrast, the exact protocol is found to be accurate and stable. To significantly improve the convergence of the new protocol, we introduce a density-based switching function to map between the exact nonadditive kinetic potential and the TF approximation in the region of the nuclear cusp, and we demonstrate that this approximation has little effect on the accuracy of the calculated ionization energies. Finally, we describe possible extensions of the exact protocol to perform accurate embedded DFT calculations in large systems with strongly overlapping subsystem densities
Nuclear Quasi-Elastic Electron Scattering Limits Nucleon Off-Mass Shell Properties
The use of quasi-elastic electron nucleus scattering is shown to provide
significant constraints on models of the proton electromagnetic form factor of
off-shell nucleons. Such models can be constructed to be consistent with
constraints from current conservation and low-energy theorems, while also
providing a contribution to the Lamb shift that might potentially resolve the
proton radius puzzle in muonic hydrogen. However, observations of quasi-elastic
scattering limit the overall strength of the off-shell form factors to values
that correspond to small contributions to the Lamb shift.Comment: 11 pages, 2 figures. Resubmission to improve the clarity, and correct
possible misconception
Density functional theory embedding for correlated wavefunctions: Improved methods for open-shell systems and transition metal complexes
Density functional theory (DFT) embedding provides a formally exact framework
for interfacing correlated wave-function theory (WFT) methods with lower-level
descriptions of electronic structure. Here, we report techniques to improve the
accuracy and stability of WFT-in-DFT embedding calculations. In particular, we
develop spin-dependent embedding potentials in both restricted and unrestricted
orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and
we develop an orbital-occupation-freezing technique to improve the convergence
of optimized effective potential (OEP) calculations that arise in the
evaluation of the embedding potential. The new techniques are demonstrated in
applications to the van-der-Waals-bound ethylene-propylene dimer and to the
hexaaquairon(II) transition-metal cation. Calculation of the dissociation curve
for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces
full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating
errors in the dispersion interactions due to conventional exchange-correlation
(XC) functionals while simultaneously avoiding errors due to subsystem
partitioning across covalent bonds. Application of WFT-in-DFT embedding to the
calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II)
cation reveals that the majority of the dependence on the DFT XC functional can
be eliminated by treating only the single transition-metal atom at the WFT
level; furthermore, these calculations demonstrate the substantial effects of
open-shell contributions to the embedding potential, and they suggest that
restricted open-shell WFT-in-DFT embedding provides better accuracy than
unrestricted open-shell WFT-in-DFT embedding due to the removal of spin
contamination.Comment: 11 pages, 5 figures, 2 table
Blue Crab target setting: final report
We have developed a hierarchy of target levels, designated to address sustainability, efficiency, and recovery scenarios. Targets were derived from: 1) reported catches and effort in the commercial fishery, 2) statistics from fishery-independent surveys, and 3) knowledge of the biology of blue crab. Targets that are recommended include population sizes, catches, and effort levels, as well as reference fishing mortality rates. They are intended to be conservative and risk-averse. (PDF contains 182 pages
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