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 people’s 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 $B\to K^*\ell^+\ell^-$ and a measurement of the branching fraction for the related process $B\to K\ell^+\ell^-$, where $\ell^+\ell^-$ is either an $e^+e^-$ or $\mu^+\mu^-$ 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 $123\times 10^6$ $\Upsilon(4S)\to B\bar{B}$ decays collected with the Babar detector at the PEP-II $e^+e^-$ storage ring. Averaging over $K^{(*)}$ isospin and lepton flavor, we obtain the branching fractions ${\mathcal B}(B\to K\ell^+\ell^-)=(0.65^{+0.14}_{-0.13}\pm 0.04)\times 10^{-6}$ and ${\mathcal B}(B\to K^*\ell^+\ell^-)=(0.88^{+0.33}_{-0.29}\pm 0.10)\times 10^{-6}$, where the uncertainties are statistical and systematic, respectively. The significance of the $B\to K\ell^+\ell^-$ signal is over $8\sigma$, while for $B\to K^*\ell^+\ell^-$ it is $3.3\sigma$.Comment: 7 pages, 2 postscript figues, submitted to Phys. Rev. Let

Measurement of Branching Fraction and Dalitz Distribution for B0->D(*)+/- K0 pi-/+ Decays

We present measurements of the branching fractions for the three-body decays B0 -> D(*)-/+ K0 pi^+/-$and their resonant submodes$B0 -> D(*)-/+ K*+/- using a sample of approximately 88 million BBbar pairs collected by the BABAR detector at the PEP-II asymmetric energy storage ring. We measure: B(B0->D-/+ K0 pi+/-)=(4.9 +/- 0.7(stat) +/- 0.5 (syst)) 10^{-4} B(B0->D*-/+ K0 pi+/-)=(3.0 +/- 0.7(stat) +/- 0.3 (syst)) 10^{-4} B(B0->D-/+ K*+/-)=(4.6 +/- 0.6(stat) +/- 0.5 (syst)) 10^{-4} B(B0->D*-/+ K*+/-)=(3.2 +/- 0.6(stat) +/- 0.3 (syst)) 10^{-4} From these measurements we determine the fractions of resonant events to be : f(B0-> D-/+ K*+/-) = 0.63 +/- 0.08(stat) +/- 0.04(syst) f(B0-> D*-/+ K*+/-) = 0.72 +/- 0.14(stat) +/- 0.05(syst)Comment: 7 pages, 3 figures submitted to Phys. Rev. Let