Categorifying the sl(2,C)sl(2,C) 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 $n$ indistinguishable particles in the complex plane, which categorifies the $sl(2,C)$-Knizhnik-Zamolodchikov connection obtained from the adjoint representation of $sl(2,C)$. 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 $sl(2,C)$-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 $n$ 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 1/r1/r-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