568 research outputs found
The solution of multi-scale partial differential equations using wavelets
Wavelets are a powerful new mathematical tool which offers the possibility to
treat in a natural way quantities characterized by several length scales. In
this article we will show how wavelets can be used to solve partial
differential equations which exhibit widely varying length scales and which are
therefore hardly accessible by other numerical methods. As a benchmark
calculation we solve Poisson's equation for a 3-dimensional Uranium dimer. The
length scales of the charge distribution vary by 4 orders of magnitude in this
case. Using lifted interpolating wavelets the number of iterations is
independent of the maximal resolution and the computational effort therefore
scales strictly linearly with respect to the size of the system
Linear Scaling Solution of the Coulomb problem using wavelets
The Coulomb problem for continuous charge distributions is a central problem
in physics. Powerful methods, that scale linearly with system size and that
allow us to use different resolutions in different regions of space are
therefore highly desirable. Using wavelet based Multi Resolution Analysis we
derive for the first time a method which has these properties. The power and
accuracy of the method is illustrated by applying it to the calculation of of
the electrostatic potential of a full three-dimensional all-electron Uranium
dimer
Gender identity and breast cancer campaigns
Concerning itself with understanding how marketing methods and tools can be of benefit to healthcare professionals, health marketing is an area of research that has grown substantially in recent years. Of much interest to the sector is whether awareness campaigns are effective in increasing the public’s perceived vulnerability to any given disease
Representation theory for high-rate multiple-antenna code design
Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We, therefore, also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels
How Numerical Cognition Explains Ambiguity Aversion
Consumers generally prefer precise probabilities or outcomes over imprecise ranges with the same expected value, a bias known as ‘ambiguity aversion.’ We argue that two elementary principles of numerical cognition explain great heterogeneity in this bias, affecting consumer choices in many domains where options are characterized by varying levels of uncertainty (e.g., lotteries, discounts, investment products, vaccines, etc.). The first principle, the ‘compression effect,’ stipulates that consumers’ mental number lines are increasingly compressed at greater number magnitudes. This alone suffices to predict ambiguity aversion as it causes a midpoint (e.g., 60) compared to its lower bound (e.g., $20). Furthermore, as the compression effect distorts the mental number line especially at lower numbers, it follows that ambiguity aversion should decrease around greater numbers. The second principle, the ‘left-digit effect’ causes a range’s relative attractiveness to decrease (increase) disproportionately with every left-digit transition in its lower (upper) bound, thus increasing (decreasing) ambiguity aversion. Due to the overall compression effect, the impact of the left-digit effect increases at greater numbers. We present 34 experiments (N = 10634), to support the theory’s predictions and wide applicability
Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices
In this paper, we extend our analysis of lattice systems using the wavelet
transform to systems for which exact enumeration is impractical. For such
systems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm,
which hierarchically coarse-grains a lattice model by computing the probability
distribution for successively larger block spins. We demonstrate that although
the method perturbs the system by changing its Hamiltonian and by allowing
block spins to take on values not permitted for individual spins, the results
obtained agree with the analytical results in the preceding paper, and
``converge'' to exact results obtained in the absence of coarse-graining.
Additionally, we show that the decorrelation time for the WAMC is no worse than
that of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed
from data performed in several short simulations to estimate the results that
would be obtained from the original simulation. Although the algorithm is not
asymptotically faster than traditional MMC, because of its hierarchical design,
the new algorithm executes several orders of magnitude faster than a full
simulation of the original problem. Consequently, the new method allows for
rapid analysis of a phase diagram, allowing computational time to be focused on
regions near phase transitions.Comment: 11 pages plus 7 figures in PNG format (downloadable separately
Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations
We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators
Gender identity and breast cancer campaigns
Concerning itself with understanding how marketing methods
and tools can be of benefit to healthcare professionals, health
marketing is an area of research that has grown substantially in
recent years. Of much interest to the sector is whether awareness
campaigns are effective in increasing the public’s perceived
vulnerability to any given disease
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