11,963 research outputs found
Intersection Rules and Open Branes
A general rule determining how extremal branes can intersect in a
configuration with zero binding energy is presented. It is derived in a model
independent way and without explicit use of supersymmetry, solving a set of
classical equations of motion. When specializing to M and type II theories, it
is shown that some intersection rules can be consistently interpreted as
boundary rules for open branes ending on other branes.Comment: 12 pages, Latex, uses crckapb.sty. To appear in the proceedings of
the Cargese '97 summer schoo
Linear And Nonlinear Arabesques: A Study Of Closed Chains Of Negative 2-Element Circuits
In this paper we consider a family of dynamical systems that we call
"arabesques", defined as closed chains of 2-element negative circuits. An
-dimensional arabesque system has 2-element circuits, but in addition,
it displays by construction, two -element circuits which are both positive
vs one positive and one negative, depending on the parity (even or odd) of the
dimension . In view of the absence of diagonal terms in their Jacobian
matrices, all these dynamical systems are conservative and consequently, they
can not possess any attractor. First, we analyze a linear variant of them which
we call "arabesque 0" or for short "A0". For increasing dimensions, the
trajectories are increasingly complex open tori. Next, we inserted a single
cubic nonlinearity that does not affect the signs of its circuits (that we call
"arabesque 1" or for short "A1"). These systems have three steady states,
whatever the dimension is, in agreement with the order of the nonlinearity. All
three are unstable, as there can not be any attractor in their state-space. The
3D variant (that we call for short "A1\_3D") has been analyzed in some detail
and found to display a complex mixed set of quasi-periodic and chaotic
trajectories. Inserting cubic nonlinearities (one per equation) in the same
way as above, we generate systems "A2\_D". A2\_3D behaves essentially as
A1\_3D, in agreement with the fact that the signs of the circuits remain
identical. A2\_4D, as well as other arabesque systems with even dimension, has
two positive -circuits and nine steady states. Finally, we investigate and
compare the complex dynamics of this family of systems in terms of their
symmetries.Comment: 22 pages, 12 figures, accepted for publication at Int. J. Bif. Chao
Mathematical Foundations for a Compositional Distributional Model of Meaning
We propose a mathematical framework for a unification of the distributional
theory of meaning in terms of vector space models, and a compositional theory
for grammatical types, for which we rely on the algebra of Pregroups,
introduced by Lambek. This mathematical framework enables us to compute the
meaning of a well-typed sentence from the meanings of its constituents.
Concretely, the type reductions of Pregroups are `lifted' to morphisms in a
category, a procedure that transforms meanings of constituents into a meaning
of the (well-typed) whole. Importantly, meanings of whole sentences live in a
single space, independent of the grammatical structure of the sentence. Hence
the inner-product can be used to compare meanings of arbitrary sentences, as it
is for comparing the meanings of words in the distributional model. The
mathematical structure we employ admits a purely diagrammatic calculus which
exposes how the information flows between the words in a sentence in order to
make up the meaning of the whole sentence. A variation of our `categorical
model' which involves constraining the scalars of the vector spaces to the
semiring of Booleans results in a Montague-style Boolean-valued semantics.Comment: to appea
A Polynomial Translation of pi-calculus FCPs to Safe Petri Nets
We develop a polynomial translation from finite control pi-calculus processes
to safe low-level Petri nets. To our knowledge, this is the first such
translation. It is natural in that there is a close correspondence between the
control flows, enjoys a bisimulation result, and is suitable for practical
model checking.Comment: To appear in special issue on best papers of CONCUR'12 of Logical
Methods in Computer Scienc
The two-dimensional Kolmogorov-Smirnov test
Goodness-of-fit statistics measure the compatibility of random samples against some theoretical
probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a
non-parametric statistic for comparing two empirical distributions which defines the largest absolute
difference between the two cumulative distribution functions as a measure of disagreement.
Adapting this test to more than one dimension is a challenge because there are 2d −1 independent
ways of defining a cumulative distribution function when d dimensions are involved. In this paper
three variations on the Kolmogorov-Smirnov test for multi-dimensional data sets are surveyed:
Peacock’s test [1] that computes in O(n3); Fasano and Franceschini’s test [2] that computes in
O(n2); Cooke’s test that computes in O(n2).
We prove that Cooke’s algorithm runs in O(n2), contrary to his claims that it runs in O(nlgn).
We also compare these algorithms with ROOT’s version of the Kolmogorov-Smirnov test
Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics
Parallel sorting of orbital angular momentum (OAM) and polarization has
recently acquired paramount importance and interest in a wide range of fields
ranging from telecommunications to high-dimensional quantum cryptography. Due
to their inherently polarization-sensitive optical response, optical elements
acting on the geometric phase prove to be useful for processing structured
light beams with orthogonal polarization states by means of a single optical
platform. In this work, we present the design, fabrication and test of a
Pancharatnam-Berry optical element in silicon implementing a log-pol optical
transformation at 1310 nm for the realization of an OAM sorter based on the
conformal mapping between angular and linear momentum states. The metasurface
is realized in the form of continuously-variant subwavelength gratings,
providing high-resolution in the definition of the phase pattern. A hybrid
device is fabricated assembling the metasurface for the geometric phase control
with multi-level diffractive optics for the polarization-independent
manipulation of the dynamic phase. The optical characterization confirms the
capability to sort orbital angular momentum and circular polarization at the
same time.Comment: 15 pages, 10 figure
- …