1,377 research outputs found
Efficient long division via Montgomery multiply
We present a novel right-to-left long division algorithm based on the
Montgomery modular multiply, consisting of separate highly efficient loops with
simply carry structure for computing first the remainder (x mod q) and then the
quotient floor(x/q). These loops are ideally suited for the case where x
occupies many more machine words than the divide modulus q, and are strictly
linear time in the "bitsize ratio" lg(x)/lg(q). For the paradigmatic
performance test of multiword dividend and single 64-bit-word divisor,
exploitation of the inherent data-parallelism of the algorithm effectively
mitigates the long latency of hardware integer MUL operations, as a result of
which we are able to achieve respective costs for remainder-only and full-DIV
(remainder and quotient) of 6 and 12.5 cycles per dividend word on the Intel
Core 2 implementation of the x86_64 architecture, in single-threaded execution
mode. We further describe a simple "bit-doubling modular inversion" scheme,
which allows the entire iterative computation of the mod-inverse required by
the Montgomery multiply at arbitrarily large precision to be performed with
cost less than that of a single Newtonian iteration performed at the full
precision of the final result. We also show how the Montgomery-multiply-based
powering can be efficiently used in Mersenne and Fermat-number trial
factorization via direct computation of a modular inverse power of 2, without
any need for explicit radix-mod scalings.Comment: 23 pages; 8 tables v2: Tweak formatting, pagecount -= 2. v3: Fix
incorrect powers of R in formulae [7] and [11] v4: Add Eldridge & Walter ref.
v5: Clarify relation between Algos A/A',D and Hensel-div; clarify
true-quotient mechanics; Add Haswell timings, refs to Agner Fog timings pdf
and GMP asm-timings ref-page. v6: Remove stray +bw in MULL line of Algo D
listing; add note re byte-LUT for qinv_
Long's Vortex Revisited
The conical self-similar vortex solution of Long (1961) is reconsidered, with
a view toward understanding what, if any, relationship exists between Long's
solution and the more-recent similarity solutions of Mayer and Powell (1992),
which are a rotational-flow analogue of the Falkner-Skan boundary-layer flows,
describing a self-similar axisymmetric vortex embedded in an external stream
whose axial velocity varies as a power law in the axial (z) coordinate, with
phi=r/z^n being the radial similarity coordinate and n the core growth rate
parameter. We show that, when certain ostensible differences in the
formulations and radial scalings are properly accounted for, the Long and
Mayer-Powell flows in fact satisfy the same system of coupled ordinary
differential equations, subject to different kinds of outer-boundary
conditions, and with Long's equations a special case corresponding to conical
vortex core growth, n=1 with outer axial velocity field decelerating in a 1/z
fashion, which implies a severe adverse pressure gradient. For pressure
gradients this adverse Mayer and Powell were unable to find any
leading-edge-type vortex flow solutions which satisfy a basic physicality
criterion based on monotonicity of the total-pressure profile of the flow, and
it is shown that Long's solutions also violate this criterion, in an extreme
fashion. Despite their apparent nonphysicality, the fact that Long's solutions
fit into a more general similarity framework means that nonconical analogues of
these flows should exist. The far-field asymptotics of these generalized
solutions are derived and used as the basis for a hybrid spectral-numerical
solution of the generalized similarity equations, which reveal the existence of
solutions for more modestly adverse pressure gradients than those in Long's
case, and which do satisfy the above physicality criterion.Comment: 30 pages, including 16 figure
Similarity models for viscous vortex cores
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76178/1/AIAA-1990-592-491.pd
Measurement of p + d -> 3He + eta in S(11) Resonance
We have measured the reaction p + d -> 3He + eta at a proton beam energy of
980 MeV, which is 88.5 MeV above threshold using the new ``germanium wall''
detector system. A missing--mass resolution of the detector system of 2.6% was
achieved. The angular distribution of the meson is forward peaked. We found a
total cross section of (573 +- 83(stat.) +- 69(syst.))nb. The excitation
function for the present reaction is described by a Breit Wigner form with
parameters from photoproduction.Comment: 8 pages, 2 figures, corrected typos in heade
30 days wild: development and evaluation of a large-scale nature engagement campaign to improve well-being
There is a need to increase peopleâs engagement with and connection to nature, both for human well-being and the conservation of nature itself. In order to suggest ways for people to engage with nature and create a wider social context to normalise nature engagement, The Wildlife Trusts developed a mass engagement campaign, 30 Days Wild. The campaign asked people to engage with nature every day for a month. 12,400 people signed up for 30 Days Wild via an online sign-up with an estimated 18,500 taking part overall, resulting in an estimated 300,000 engagements with nature by participants. Samples of those taking part were found to have sustained increases in happiness, health, connection to nature and pro-nature behaviours. With the improvement in health being predicted by the improvement in happiness, this relationship was mediated by the change in connection to nature
Coordinated optimization of visual cortical maps (II) Numerical studies
It is an attractive hypothesis that the spatial structure of visual cortical
architecture can be explained by the coordinated optimization of multiple
visual cortical maps representing orientation preference (OP), ocular dominance
(OD), spatial frequency, or direction preference. In part (I) of this study we
defined a class of analytically tractable coordinated optimization models and
solved representative examples in which a spatially complex organization of the
orientation preference map is induced by inter-map interactions. We found that
attractor solutions near symmetry breaking threshold predict a highly ordered
map layout and require a substantial OD bias for OP pinwheel stabilization.
Here we examine in numerical simulations whether such models exhibit
biologically more realistic spatially irregular solutions at a finite distance
from threshold and when transients towards attractor states are considered. We
also examine whether model behavior qualitatively changes when the spatial
periodicities of the two maps are detuned and when considering more than 2
feature dimensions. Our numerical results support the view that neither minimal
energy states nor intermediate transient states of our coordinated optimization
models successfully explain the spatially irregular architecture of the visual
cortex. We discuss several alternative scenarios and additional factors that
may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with
arXiv:1102.335
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Measurement of the Branching Fraction for B- --> D0 K*-
We present a measurement of the branching fraction for the decay B- --> D0
K*- using a sample of approximately 86 million BBbar pairs collected by the
BaBar detector from e+e- collisions near the Y(4S) resonance. The D0 is
detected through its decays to K- pi+, K- pi+ pi0 and K- pi+ pi- pi+, and the
K*- through its decay to K0S pi-. We measure the branching fraction to be
B.F.(B- --> D0 K*-)= (6.3 +/- 0.7(stat.) +/- 0.5(syst.)) x 10^{-4}.Comment: 7 pages, 1 postscript figure, submitted to Phys. Rev. D (Rapid
Communications
Evidence for the Rare Decay B -> K*ll and Measurement of the B -> Kll Branching Fraction
We present evidence for the flavor-changing neutral current decay and a measurement of the branching fraction for the related
process , where is either an or
pair. These decays are highly suppressed in the Standard Model,
and they are sensitive to contributions from new particles in the intermediate
state. The data sample comprises
decays collected with the Babar detector at the PEP-II storage ring.
Averaging over isospin and lepton flavor, we obtain the branching
fractions and , where the
uncertainties are statistical and systematic, respectively. The significance of
the signal is over , while for it is .Comment: 7 pages, 2 postscript figues, submitted to Phys. Rev. Let
Measurement of the quasi-elastic axial vector mass in neutrino-oxygen interactions
The weak nucleon axial-vector form factor for quasi-elastic interactions is
determined using neutrino interaction data from the K2K Scintillating Fiber
detector in the neutrino beam at KEK. More than 12,000 events are analyzed, of
which half are charged-current quasi-elastic interactions nu-mu n to mu- p
occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for
oxygen and assume the form factor is approximately a dipole with one parameter,
the axial vector mass M_A, and fit to the shape of the distribution of the
square of the momentum transfer from the nucleon to the nucleus. Our best fit
result for M_A = 1.20 \pm 0.12 GeV. Furthermore, this analysis includes updated
vector form factors from recent electron scattering experiments and a
discussion of the effects of the nucleon momentum on the shape of the fitted
distributions.Comment: 14 pages, 10 figures, 6 table
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