5,575 research outputs found
Crystallization of random trigonometric polynomials
We give a precise measure of the rate at which repeated differentiation of a
random trigonometric polynomial causes the roots of the function to approach
equal spacing. This can be viewed as a toy model of crystallization in one
dimension. In particular we determine the asymptotics of the distribution of
the roots around the crystalline configuration and find that the distribution
is not Gaussian.Comment: 10 pages, 3 figure
System impacts of solar dynamic and growth power systems on space station
Concepts for the 1990's space station envision an initial operational capability with electrical power output requirements of approximately 75 kW and growth power requirements in the range of 300 kW over a period of a few years. Photovoltaic and solar dynamic power generation techniques are contenders for supplying this power to the space station. A study was performed to identify growth power subsystem impacts on other space station subsystems. Subsystem interactions that might suggest early design changes for the space station were emphasized. Quantitative analyses of the effects of power subsystem mass and projected area on space station controllability and reboost requirements were conducted for a range of growth station configurations. Impacts on space station structural dynamics as a function of power subsystem growth were also considered
Autocorrelation of Random Matrix Polynomials
We calculate the autocorrelation functions (or shifted moments) of the
characteristic polynomials of matrices drawn uniformly with respect to Haar
measure from the groups U(N), O(2N) and USp(2N). In each case the result can be
expressed in three equivalent forms: as a determinant sum (and hence in terms
of symmetric polynomials), as a combinatorial sum, and as a multiple contour
integral. These formulae are analogous to those previously obtained for the
Gaussian ensembles of Random Matrix Theory, but in this case are identities for
any size of matrix, rather than large-matrix asymptotic approximations. They
also mirror exactly autocorrelation formulae conjectured to hold for
L-functions in a companion paper. This then provides further evidence in
support of the connection between Random Matrix Theory and the theory of
L-functions
W. D. Farmer to H. R. Miller (1 March 1863)
Update on the health of a horsehttps://egrove.olemiss.edu/ciwar_corresp/1588/thumbnail.jp
Random polynomials, random matrices, and -functions
We show that the Circular Orthogonal Ensemble of random matrices arises
naturally from a family of random polynomials. This sheds light on the
appearance of random matrix statistics in the zeros of the Riemann
zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit
Plasma density measurements using chirped pulse broad-band Raman amplification
Stimulated Raman backscattering is used as a non-destructive method to determine the density of plasma media at localized positions in space and time. By colliding two counter-propagating, ultra-short laser pulses with a spectral bandwidth larger than twice the plasma frequency, amplification occurs at the Stokes wavelengths, which results in regions of gain and loss separated by twice the plasma frequency, from which the plasma density can be deduced. By varying the relative delay between the laser pulses, and therefore the position and timing of the interaction, the spatio-temporal distribution of the plasma density can be mapped out
An FTIR spectrometer for remote measurements of atmospheric composition
The JPL IV interferometer, and infrared Michelson interferometer, was built specifically for recording high resolution solar absorption spectra from remote ground-based sites, aircraft and from stratospheric balloons. The instrument is double-passed, with one fixed and one moving corner reflector, allowing up to 200-cm of optical path difference (corresponding to an unapodised spectral resolution of 0.003/cm). The carriage which holds the moving reflector is driven by a flexible nut riding on a lead screw. This arrangement, together with the double-passed optical scheme, makes the instrument resistant to the effects of mechanical distortion and shock. The spectral range of the instrument is covered by two liquid nitrogen-cooled detectors: an InSb photodiode is used for the shorter wavelengths (1.85 to 5.5 microns, 1,800 to 5,500/cm) and a HgCdTe photoconductor for the range (5.5 to 15 microns, 650 to 1,800/cm). For a single spectrum of 0.01/cm resolution, which requires a scan time of 105 seconds, the signal/noise ratio is typically 800:1 over the entire wavelength range
Statistical theory of the continuous double auction
Most modern financial markets use a continuous double auction mechanism to
store and match orders and facilitate trading. In this paper we develop a
microscopic dynamical statistical model for the continuous double auction under
the assumption of IID random order flow, and analyze it using simulation,
dimensional analysis, and theoretical tools based on mean field approximations.
The model makes testable predictions for basic properties of markets, such as
price volatility, the depth of stored supply and demand vs. price, the bid-ask
spread, the price impact function, and the time and probability of filling
orders. These predictions are based on properties of order flow and the limit
order book, such as share volume of market and limit orders, cancellations,
typical order size, and tick size. Because these quantities can all be measured
directly there are no free parameters. We show that the order size, which can
be cast as a nondimensional granularity parameter, is in most cases a more
significant determinant of market behavior than tick size. We also provide an
explanation for the observed highly concave nature of the price impact
function. On a broader level, this work suggests how stochastic models based on
zero-intelligence agents may be useful to probe the structure of market
institutions. Like the model of perfect rationality, a stochastic-zero
intelligence model can be used to make strong predictions based on a compact
set of assumptions, even if these assumptions are not fully believable.Comment: 36 pages, 40 figures, RevTex4, submitted to Quantitative Financ
A Universal Machine for Biform Theory Graphs
Broadly speaking, there are two kinds of semantics-aware assistant systems
for mathematics: proof assistants express the semantic in logic and emphasize
deduction, and computer algebra systems express the semantics in programming
languages and emphasize computation. Combining the complementary strengths of
both approaches while mending their complementary weaknesses has been an
important goal of the mechanized mathematics community for some time. We pick
up on the idea of biform theories and interpret it in the MMTt/OMDoc framework
which introduced the foundations-as-theories approach, and can thus represent
both logics and programming languages as theories. This yields a formal,
modular framework of biform theory graphs which mixes specifications and
implementations sharing the module system and typing information. We present
automated knowledge management work flows that interface to existing
specification/programming tools and enable an OpenMath Machine, that
operationalizes biform theories, evaluating expressions by exhaustively
applying the implementations of the respective operators. We evaluate the new
biform framework by adding implementations to the OpenMath standard content
dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final
publication is available at http://link.springer.com
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