724 research outputs found
Random arrangements for lattice designs
From 1936 onwards Yates (11, 12, 13, 14, 15, 16)has introduced a series of incomplete block designs; the purpose of the designs was to segregate the variation within the complete blocks into that due to differences between and that within the incomplete blocks and at the same time to retain the advantages of the randomized complete blocks. The complete block was divided into incomplete blocks, each containing a portion of the total number of the treatments compared, in such a way that the differences between incomplete blocks could be eliminated from the treatment comparisons.https://lib.dr.iastate.edu/specialreports/1003/thumbnail.jp
A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
Continuing our development of a mathematical theory of stochastic
microlensing, we study the random shear and expected number of random lensed
images of different types. In particular, we characterize the first three
leading terms in the asymptotic expression of the joint probability density
function (p.d.f.) of the random shear tensor at a general point in the lens
plane due to point masses in the limit of an infinite number of stars. Up to
this order, the p.d.f. depends on the magnitude of the shear tensor, the
optical depth, and the mean number of stars through a combination of radial
position and the stars' masses. As a consequence, the p.d.f.s of the shear
components are seen to converge, in the limit of an infinite number of stars,
to shifted Cauchy distributions, which shows that the shear components have
heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the
limit of an infinite number of stars is also presented. Extending to general
random distributions of the lenses, we employ the Kac-Rice formula and Morse
theory to deduce general formulas for the expected total number of images and
the expected number of saddle images. We further generalize these results by
considering random sources defined on a countable compact covering of the light
source plane. This is done to introduce the notion of {\it global} expected
number of positive parity images due to a general lensing map. Applying the
result to microlensing, we calculate the asymptotic global expected number of
minimum images in the limit of an infinite number of stars, where the stars are
uniformly distributed. This global expectation is bounded, while the global
expected number of images and the global expected number of saddle images
diverge as the order of the number of stars.Comment: To appear in JM
Effectiveness of selection based on variability uncomplicated by heterotic effects
Effectiveness of selection based on variability uncomplicated by heterotic effect
Regularity of higher codimension area minimizing integral currents
This lecture notes are an expanded version of the course given at the
ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa,
September 30th - October 30th 2013. The lectures aim to explain the main steps
of a new proof of the partial regularity of area minimizing integer rectifiable
currents in higher codimension, due originally to F. Almgren, which is
contained in a series of papers in collaboration with C. De Lellis (University
of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real
Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L.
Ambrosio Ed., Edizioni SNS (CRM Series
Predicting the effects of climate change on water yield and forest production in the northeastern United States
Rapid and simultaneous changes in temperature, precipitation and the atmospheric concentration of CO2 are predicted to occur over the next century. Simple, well-validated models of ecosystem function are required to predict the effects of these changes. This paper describes an improved version of a forest carbon and water balance model (PnET-II) and the application of the model to predict stand- and regional-level effects of changes in temperature, precipitation and atmospheric CO2 concentration. PnET-II is a simple, generalized, monthly time-step model of water and carbon balances (gross and net) driven by nitrogen availability as expressed through foliar N concentration. Improvements from the original model include a complete carbon balance and improvements in the prediction of canopy phenology, as well as in the computation of canopy structure and photosynthesis. The model was parameterized and run for 4 forest/site combinations and validated against available data for water yield, gross and net carbon exchange and biomass production. The validation exercise suggests that the determination of actual water availability to stands and the occurrence or non-occurrence of soil-based water stress are critical to accurate modeling of forest net primary production (NPP) and net ecosystem production (NEP). The model was then run for the entire NewEngland/New York (USA) region using a 1 km resolution geographic information system. Predicted long-term NEP ranged from -85 to +275 g C m-2 yr-1 for the 4 forest/site combinations, and from -150 to 350 g C m-2 yr-1 for the region, with a regional average of 76 g C m-2 yr-1. A combination of increased temperature (+6*C), decreased precipitation (-15%) and increased water use efficiency (2x, due to doubling of CO2) resulted generally in increases in NPP and decreases in water yield over the region
On the Conduct of an Investigation
12 pages, 1 article*On the Conduct of an Investigation* (Federer, E. H.; Federer, W. T.) 12 page
The enclosure method for the heat equation
This paper shows how the enclosure method which was originally introduced for
elliptic equations can be applied to inverse initial boundary value problems
for parabolic equations. For the purpose a prototype of inverse initial
boundary value problems whose governing equation is the heat equation is
considered. An explicit method to extract an approximation of the value of the
support function at a given direction of unknown discontinuity embedded in a
heat conductive body from the temperature for a suitable heat flux on the
lateral boundary for a fixed observation time is given.Comment: 12pages. This is the final versio
A Theorem on the origin of Phase Transitions
For physical systems described by smooth, finite-range and confining
microscopic interaction potentials V with continuously varying coordinates, we
announce and outline the proof of a theorem that establishes that unless the
equipotential hypersurfaces of configuration space \Sigma_v ={(q_1,...,q_N)\in
R^N | V(q_1,...,q_N) = v}, v \in R, change topology at some v_c in a given
interval [v_0, v_1] of values v of V, the Helmoltz free energy must be at least
twice differentiable in the corresponding interval of inverse temperature
(\beta(v_0), \beta(v_1)) also in the N -> \infty and the
{\Sigma_v}_{v > v_c}, which is the consequence of the existence of critical
points of V on \Sigma_{v=v_c}, that is points where \nabla V=0.Comment: 10 pages, Statistical Mechanics, Phase Transitions, General Theory.
Phys. Rev. Lett., in pres
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