64,710 research outputs found
Convergence of the restricted Nelder-Mead algorithm in two dimensions
The Nelder-Mead algorithm, a longstanding direct search method for
unconstrained optimization published in 1965, is designed to minimize a
scalar-valued function f of n real variables using only function values,
without any derivative information. Each Nelder-Mead iteration is associated
with a nondegenerate simplex defined by n+1 vertices and their function values;
a typical iteration produces a new simplex by replacing the worst vertex by a
new point. Despite the method's widespread use, theoretical results have been
limited: for strictly convex objective functions of one variable with bounded
level sets, the algorithm always converges to the minimizer; for such functions
of two variables, the diameter of the simplex converges to zero, but examples
constructed by McKinnon show that the algorithm may converge to a nonminimizing
point.
This paper considers the restricted Nelder-Mead algorithm, a variant that
does not allow expansion steps. In two dimensions we show that, for any
nondegenerate starting simplex and any twice-continuously differentiable
function with positive definite Hessian and bounded level sets, the algorithm
always converges to the minimizer. The proof is based on treating the method as
a discrete dynamical system, and relies on several techniques that are
non-standard in convergence proofs for unconstrained optimization.Comment: 27 page
Biological effects of prolonged expoure of small animals to unusual gaseous environments semiannual report, 1 sep. 1964 - 28 feb. 1965
Biological effect of prolonged exposure of man and small animals to pure oxygen and helium - oxygen environmen
The impact of water on free-falling bodies
Report discussed measures to cushion impact on body falling into water. Heavy loads are generated by impact and by pressures of water cavity collapsing onto the body
Current Approaches to HR Strategies: Inside-Out vs. Outside-In
In an effort to determine the best practices with regard to Human Resource (HR) strategies, we conducted interviews with HR executives knowledgeable about their HR strategies from 20 companies, and gathered archival materials such as the HR strategy documents from 9 of the companies. We found that the content, process, and evaluation of the HR strategies can each be classified as focusing primarily on the HR function, the people of the firm, or the business. We provide some examples of ways that firms can move from an HR focused to a business-focused HR strategy
Recommended from our members
Organic components in interplanetary dust particles and their implications for the synthesis of cometary organics
A comparison of the excess mass around CFHTLenS galaxy-pairs to predictions from a semi-analytic model using galaxy-galaxy-galaxy lensing
The matter environment of galaxies is connected to the physics of galaxy
formation and evolution. Utilising galaxy-galaxy-galaxy lensing as a direct
probe, we map out the distribution of correlated surface mass-density around
galaxy pairs for different lens separations in the Canada-France-Hawaii
Telescope Lensing Survey (CFHTLenS). We compare, for the first time, these
so-called excess mass maps to predictions provided by a recent semi-analytic
model, which is implanted within the dark-matter Millennium Simulation. We
analyse galaxies with stellar masses between in
two photometric redshift bins, for lens redshifts , focusing on
pairs inside groups and clusters. To allow us a better interpretation of the
maps, we discuss the impact of chance pairs, i.e., galaxy pairs that appear
close to each other in projection only. Our tests with synthetic data
demonstrate that the patterns observed in the maps are essentially produced by
correlated pairs that are close in redshift ().
We also verify the excellent accuracy of the map estimators. In an application
to the galaxy samples in the CFHTLenS, we obtain a
significant detection of the excess mass and an overall good agreement with the
galaxy model predictions. There are, however, a few localised spots in the maps
where the observational data disagrees with the model predictions on a
confidence level. Although we have no strong indications for
systematic errors in the maps, this disagreement may be related to the residual
B-mode pattern observed in the average of all maps. Alternatively, misaligned
galaxy pairs inside dark matter halos or lensing by a misaligned distribution
of the intra-cluster gas might also cause the unanticipated bulge in the
distribution of the excess mass between lens pairs.Comment: 21 pages, 12 figures; abridged abstract; revised version for A&A
after addressing all comments by the refere
A probability-conserving cross-section biasing mechanism for variance reduction in Monte Carlo particle transport calculations
In Monte Carlo particle transport codes, it is often important to adjust
reaction cross sections to reduce the variance of calculations of relatively
rare events, in a technique known as non-analogous Monte Carlo. We present the
theory and sample code for a Geant4 process which allows the cross section of a
G4VDiscreteProcess to be scaled, while adjusting track weights so as to
mitigate the effects of altered primary beam depletion induced by the cross
section change. This makes it possible to increase the cross section of nuclear
reactions by factors exceeding 10^4 (in appropriate cases), without distorting
the results of energy deposition calculations or coincidence rates. The
procedure is also valid for bias factors less than unity, which is useful, for
example, in problems that involve computation of particle penetration deep into
a target, such as occurs in atmospheric showers or in shielding
Basins of attraction in forced systems with time-varying dissipation
We consider dissipative periodically forced systems and investigate cases in
which having information as to how the system behaves for constant dissipation
may be used when dissipation varies in time before settling at a constant final
value. First, we consider situations where one is interested in the basins of
attraction for damping coefficients varying linearly between two given values
over many different time intervals: we outline a method to reduce the
computation time required to estimate numerically the relative areas of the
basins and discuss its range of applicability. Second, we observe that
sometimes very slight changes in the time interval may produce abrupt large
variations in the relative areas of the basins of attraction of the surviving
attractors: we show how comparing the contracted phase space at a time after
the final value of dissipation has been reached with the basins of attraction
corresponding to that value of constant dissipation can explain the presence of
such variations. Both procedures are illustrated by application to a pendulum
with periodically oscillating support.Comment: 16 pages, 13 figures, 7 table
Reaction of the chick to one atmosphere of oxygen
Experiment to determine chicken reaction to 100 percent oxygen at atmospheric pressur
- …