17,026 research outputs found
Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
We prove an existence and uniqueness theorem for solutions of
multidimensional, time dependent, stochastic differential equations driven
simultaneously by a multidimensional fractional Brownian motion with Hurst
parameter H>1/2 and a multidimensional standard Brownian motion. The proof
relies on some a priori estimates, which are obtained using the methods of
fractional integration, and the classical Ito stochastic calculus. The
existence result is based on the Yamada-Watanabe theorem.Comment: 21 page
The mid-domain effect: It’s not just about space
Ecologists and biogeographers have long sought to understand how and why diversity varies across space. Up until the late 20th century, the dominant role of environmental gradients and historical processes in driving geographical species richness patterns went largely undisputed. However, almost 20 years ago, Colwell & Hurtt (1994) proposed a radical reappraisal of ecological gradient theory that called into question decades of empirical and theoretical research. That controversial idea was later termed the ‘the mid-domain effect’: the simple proposition that in the absence of environmental gradients, the random placement of species ranges within a bounded domain will give rise to greatest range overlap, and thus richness, at the center of the domain (Colwell & Lees, 2000) (Fig. 1a). The implication of this line of reasoning is that the conventional null model of equal species richness regardless of latitude, elevation or depth should be replaced by one where richness peaks at some midpoint in geographical space.
Our intention here is to draw attention to a neglected, yet important manifestation of the mid-domain effect, namely the application of mid-domain models (also referred to as geometric constraint models) to non-spatial domains. If individual species have ranges that exist not just in geographical space but also in environmental factors, such as temperature, rainfall, pH, productivity or disturbance, shouldn’t we also expect mid-domain richness peaks along non-spatial gradients? A mid-domain model applied to non-spatial gradients predicts the maximum potential richness for every value of an environmental factor. As with spatial mid-domain models, realized richness would probably be less, but the limits to richness are still predicted to be hump-shaped. Indeed, hump-shaped relationships emerge with remarkably high frequency across various non-spatial gradients. For instance, two of ecology’s most fundamental, albeit controversial theories – the productivity–diversity relationship and the intermediate disturbance hypothesis – predict mid-domain peaks in species richness. However, the potential of non-spatial mid-domain models has gone largely ignored
A 233 km Tunnel for Lepton and Hadron Colliders
A decade ago, a cost analysis was conducted to bore a 233 km circumference
Very Large Hadron Collider (VLHC) tunnel passing through Fermilab. Here we
outline implementations of , , and collider
rings in this tunnel using recent technological innovations. The 240 and 500
GeV colliders employ Crab Waist Crossings, ultra low emittance damped
bunches, short vertical IP focal lengths, superconducting RF, and low
coercivity, grain oriented silicon steel/concrete dipoles. Some details are
also provided for a high luminosity 240 GeV collider and 1.75 TeV
muon accelerator in a Fermilab site filler tunnel. The 40 TeV
collider uses the high intensity Fermilab source, exploits high cross
sections for production of high mass states, and uses 2 Tesla ultra
low carbon steel/YBCO superconducting magnets run with liquid neon. The 35 TeV
muon ring ramps the 2 Tesla superconducting magnets at 9 Hz every 0.4 seconds,
uses 250 GV of superconducting RF to accelerate muons from 1.75 to 17.5 TeV in
63 orbits with 71% survival, and mitigates neutrino radiation with phase
shifting, roller coaster motion in a FODO lattice.Comment: LaTex, 6 pages, 1 figure, Advanced Accelerator Concepts Workshop,
Austin, TX, 10-15 June 201
Standard Model Top Quark Asymmetry at the Fermilab Tevatron
Top quark pair production at proton-antiproton colliders is known to exhibit
a forward-backward asymmetry due to higher-order QCD effects. We explore how
this asymmetry might be studied at the Fermilab Tevatron, including how the
asymmetry depends on the kinematics of extra hard partons. We consider results
for top quark pair events with one and two additional hard jets. We further
note that a similar asymmetry, correlated with the presence of jets, arises in
specific models for parton showers in Monte Carlo simulations. We conclude that
the measurement of this asymmetry at the Tevatron will be challenging, but
important both for our understanding of QCD and for our efforts to model it.Comment: 26 p., 10 embedded figs., comment added, version to appear in PR
Kusuoka-Stroock gradient bounds for the solution of the filtering equation
© 2014 Elsevier Inc.We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [13,14,16,17], and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. It uses a pathwise representation of the perturbed semigroup following Ocone [22]. The estimates we derive have sharp small time asymptotics
Symmetric mixed states of qubits: local unitary stabilizers and entanglement classes
We classify, up to local unitary equivalence, local unitary stabilizer Lie
algebras for symmetric mixed states into six classes. These include the
stabilizer types of the Werner states, the GHZ state and its generalizations,
and Dicke states. For all but the zero algebra, we classify entanglement types
(local unitary equivalence classes) of symmetric mixed states that have those
stabilizers. We make use of the identification of symmetric density matrices
with polynomials in three variables with real coefficients and apply the
representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for
published versio
Algebraic structure of stochastic expansions and efficient simulation
We investigate the algebraic structure underlying the stochastic Taylor
solution expansion for stochastic differential systems.Our motivation is to
construct efficient integrators. These are approximations that generate strong
numerical integration schemes that are more accurate than the corresponding
stochastic Taylor approximation, independent of the governing vector fields and
to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is
one example. Herein we: show that the natural context to study stochastic
integrators and their properties is the convolution shuffle algebra of
endomorphisms; establish a new whole class of efficient integrators; and then
prove that, within this class, the sinhlog integrator generates the optimal
efficient stochastic integrator at all orders.Comment: 19 page
The improvement of aircraft specific range by periodic control
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76150/1/AIAA-1981-1748-116.pd
A Visual Environment for Real-Time Image Processing in Hardware (VERTIPH)
Real-time video processing is an image-processing application that is ideally suited to implementation on FPGAs. We discuss the strengths and weaknesses of a number of existing languages and hardware compilers that have been developed for specifying image processing algorithms on FPGAs. We propose VERTIPH, a new multiple-view visual language that avoids the weaknesses we identify. A VERTIPH design incorporates three different views, each tailored to a different aspect of the image processing system under development; an overall architectural view, a computational view, and a resource and scheduling view
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