2,623 research outputs found
The key role of off-axis singularities in free-space vortex transmutation
We experimentally demonstrate the generation of off-axis phase singularities
in a vortex transmutation process induced by the breaking of rotational
symmetry. The process takes place in free space by launching a highly-charged
vortex, owning full rotational symmetry, into a linear thin diffractive element
presenting discrete rotational symmetry. It is shown that off-axis phase
singularities follow straight dark rays bifurcating from the symmetry axis.
This phenomenon may provide new routes towards the spatial control of multiple
phase singularities for applications in atom trapping and particle
manipulation.Comment: 4 pages, 4 figures, to appear in Applied Physics B: Lasers and Optic
Optimal trading using signals
In this paper we propose a mathematical framework to address the uncertainty
emergingwhen the designer of a trading algorithm uses a threshold on a signal
as a control. We rely ona theorem by Benveniste and Priouret to deduce our
Inventory Asymptotic Behaviour (IAB)Theorem giving the full distribution of the
inventory at any point in time for a well formulatedtime continuous version of
the trading algorithm.Since this is the first time a paper proposes to address
the uncertainty linked to the use of athreshold on a signal for trading, we
give some structural elements about the kind of signals thatare using in
execution. Then we show how to control this uncertainty for a given cost
function.There is no closed form solution to this control, hence we propose
several approximation schemesand compare their performances.Moreover, we
explain how to apply the IAB Theorem to any trading algorithm drivenby a
trading speed. It is not needed to control the uncertainty due to the
thresholding of asignal to exploit the IAB Theorem; it can be applied ex-post
to any traditional trading algorithm.Comment: 21 pages, 5 figur
Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media
We determine the functional behavior near the discrete rotational symmetry
axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that
these solutions present a central phase singularity whose charge is restricted
by symmetry arguments. Consequently, we demonstrate that the existence of
high-charged discrete vortices is related to the presence of other off-axis
phase singularities, whose positions and charges are also restricted by
symmetry arguments. To illustrate our theoretical results, we offer two
numerical examples of high-charged discrete vortices in photonic crystal fibers
showing hexagonal discrete rotational invariance.Comment: 6 pages, 2 figure
Effects of two tillage techniques on soil macroporosity in sub-humid environment.
Postprint (published version
Vorticity cutoff in nonlinear photonic crystals
Using group theory arguments, we demonstrate that, unlike in homogeneous
media, no symmetric vortices of arbitrary order can be generated in
two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry.
The only condition needed is that the non-linearity term exclusively depends on
the modulus of the field. In the particular case of 2D periodic systems, such
as nonlinear photonic crystals or Bose-Einstein condensates in periodic
potentials, it is shown that the realization of discrete symmetry forbids the
existence of symmetric vortex solutions with vorticity higher than two.Comment: 4 pages, 5 figures; minor changes in address and reference
Vortex transmutation
Using group theory arguments and numerical simulations, we demonstrate the
possibility of changing the vorticity or topological charge of an individual
vortex by means of the action of a system possessing a discrete rotational
symmetry of finite order. We establish on theoretical grounds a "transmutation
pass rule'' determining the conditions for this phenomenon to occur and
numerically analize it in the context of two-dimensional optical lattices or,
equivalently, in that of Bose-Einstein condensates in periodic potentials.Comment: 4 pages, 4 figure
Photonic Nambu-Goldstone bosons
We predict the existence of a Nambu-Goldstone excitation in the propagation of light in nonlinear
periodic lattices. We use methods of condensed matter physics that emphasize the peculiarities
stemming from the interplay between the nonlinearity and the lattice periodicity. By means of
nonlinear Bloch and Wannier functions we provide an explicit construction of the effective free
energy of the system, valid for long-range, or, equivalently, low-energy excitations around Bloch
solutions. Using then Landau mean field theory for phase transitions we determine the possible
stable ground states of the optical system and their stability conditions. Low energy excitations
above a stable ground state are fully controlled by the U(1) phase of the optical field, which appear
as a Nambu-Goldstone boson, analogous to those predicted in condenser matter and particle physics
systems. We support these results by numerical simulations both for spatially periodic and finite
nonlinear Bloch wave solutions. We demonstrate how finite-sized nonlinear Bloch light structures
embedded in a linear periodic lattice act as tunable metawaveguides for the phase Nambu-Goldstone waves.Ciencias Experimentale
openWAR: An Open Source System for Evaluating Overall Player Performance in Major League Baseball
Within baseball analytics, there is substantial interest in comprehensive
statistics intended to capture overall player performance. One such measure is
Wins Above Replacement (WAR), which aggregates the contributions of a player in
each facet of the game: hitting, pitching, baserunning, and fielding. However,
current versions of WAR depend upon proprietary data, ad hoc methodology, and
opaque calculations. We propose a competitive aggregate measure, openWAR, that
is based upon public data and methodology with greater rigor and transparency.
We discuss a principled standard for the nebulous concept of a "replacement"
player. Finally, we use simulation-based techniques to provide interval
estimates for our openWAR measure.Comment: 27 pages including supplemen
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