14,927 research outputs found
Categorifying the Knizhnik-Zamolodchikov Connection via an Infinitesimal 2-Yang-Baxter Operator in the String Lie-2-Algebra
We construct a flat (and fake-flat) 2-connection in the configuration space
of indistinguishable particles in the complex plane, which categorifies the
-Knizhnik-Zamolodchikov connection obtained from the adjoint
representation of . This will be done by considering the adjoint
categorical representation of the string Lie 2-algebra and the notion of an
infinitesimal 2-Yang-Baxter operator in a differential crossed module.
Specifically, we find an infinitesimal 2-Yang-Baxter operator in the string Lie
2-algebra, proving that any (strict) categorical representation of the string
Lie-2-algebra, in a chain-complex of vector spaces, yields a flat and (fake
flat) 2-connection in the configuration space, categorifying the
-Knizhnik-Zamolodchikov connection. We will give very detailed
explanation of all concepts involved, in particular discussing the relevant
theory of 2-connections and their two dimensional holonomy, in the specific
case of 2-groups derived from chain complexes of vector spaces.Comment: The main result was considerably sharpened. Title, abstract and
introduction updated. 50 page
Massive MIMO Full-Duplex Relaying with Optimal Power Allocation for Independent Multipairs
With the help of an in-band full-duplex relay station, it is possible to
simultaneously transmit and receive signals from multiple users. The
performance of such system can be greatly increased when the relay station is
equipped with a large number of antennas on both transmitter and receiver
sides. In this paper, we exploit the use of massive arrays to effectively
suppress the loopback interference (LI) of a decode-and-forward relay (DF) and
evaluate the performance of the end-to-end (e2e) transmission. This paper
assumes imperfect channel state information is available at the relay and
designs a minimum mean-square error (MMSE) filter to mitigate the interference.
Subsequently, we adopt zero-forcing (ZF) filters for both detection and
beamforming. The performance of such system is evaluated in terms of bit error
rate (BER) at both relay and destinations, and an optimal choice for the
transmission power at the relay is shown. We then propose a complexity
efficient optimal power allocation (OPA) algorithm that, using the channel
statistics, computes the minimum power that satisfies the rate constraints of
each pair. The results obtained via simulation show that when both MMSE
filtering and OPA method are used, better values for the energy efficiency are
attained.Comment: Accepted to the 16th IEEE International Workshop on Signal Processing
Advances in Wireless Communications - SPAWC, Stockholm, Sweden 201
Infinitesimal 2-braidings and differential crossed modules
We categorify the notion of an infinitesimal braiding in a linear strict
symmetric monoidal category, leading to the notion of a (strict) infinitesimal
2-braiding in a linear symmetric strict monoidal 2-category. We describe the
associated categorification of the 4-term relation, leading to six categorified
relations. We prove that any infinitesimal 2-braiding gives rise to a flat and
fake flat 2-connection in the configuration space of particles in the
complex plane, hence to a categorification of the Knizhnik-Zamolodchikov
connection. We discuss infinitesimal 2-braidings in a 2-category naturally
assigned to every differential crossed module, leading to the notion of a
quasi-invariant tensor in a differential crossed module. Finally we prove that
quasi-invariant tensors exist in the differential crossed module associated to
the String Lie-2-algebra.Comment: v3 - the introduction has been expanded, overall improvements in the
presentation. Final version, to appear in Adv. Mat
A Spitzer Study of Interacting Luminous and Ultra-Luminous Infrared Galaxies
We conducted a Spitzer Space Telescope survey of 28 Luminous (11 <
log(LIR/L_odot) < 12, LIRGs) and Ultra-Luminous Infrared Galaxies
(log(LIR/L_odot) > 12, ULIRGs). Many of these galaxies are found in pairs or
associations and are powered by either nuclear activity or starformation
(Sanders & Mirabel 1996). Our main goal is to understand the relative
importance of starbursts and AGNs in interacting systems. Is the frequency of
AGN and starbursts in these interacting galaxies related to their luminosities?
What is the importance of the merger stage and the frequency of AGNs? We
present our conclusions and diagnostic diagrams based in the observed near
infrared lines and compare to studies based solely in optical data.Comment: 3 pages, 2 figures, to appear in the Spectral Energy Distribution of
Galaxies (SED2011) conference proceedings, Preston, UK, 201
Schwarzschild -singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
In this paper we will study the complete equations of motion for a ghost free
quadratic curvature infinite derivative gravity. We will argue that within the
scale of non-locality, Schwarzschild-type singular metric solution is not {\it
permissible}. Therefore, Schwarzschild-type vacuum solution which is a
prediction in Einstein-Hilbert gravity may {\it not} persist within the region
of non-locality. We will also show that just quadratic curvature gravity,
without infinite derivatives, always allows Schwarzschild-type singular metric
solution.Comment: 10 pages, title changed, discussion added, references updated,
version accepted in PR
Alignment of velocity fields for video surveillance
Velocity fields play an important role in surveillance since they describe typical motion behaviors of video objects (e.g., pedestrians) in the scene. This paper presents an algorithm for the alignment of velocity fields acquired by different cameras, at different time intervals, from different viewpoints. Velocity fields are aligned using a warping function which maps corresponding points and vectors in both fields. The warping parameters are estimated by minimizing a non-linear least squares energy. Experimental tests show that the proposed model is able to compensate significant misalignments, including translation, rotation and scaling
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