Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories

Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are important because they may provide simple non-supersymmetric examples of the AdS/CFT correspondence. For instance, it seems natural to conjecture that $O(N)_{-k}\times O(N)_k$ Chern-Simons theory coupled to Majorana fermions transforming in a bi-vector representation may be dual to pure Einstein gravity with a small negative cosmological constant in the "M-theory" limit where $k=1$ and $N$ is large. While it is extremely difficult to directly study such bifundamental theories when $k=1$ or even at strong 't Hooft coupling $\lambda=\frac{N}{k}$, it is possible to calculate physical quantities to all orders in $\lambda$ in a $U(M)_{k_M} \times U(N)_{k_N}$ theory, in the limit $M \ll N$, in an $M/N$ expansion. To illustrate this, we calculate the anomalous dimension of the primary operator $\bar{\psi}{\psi}$, to first order in $M/N$, to all orders in $\lambda_M=\frac{N}{k_M}$, but with $\lambda_N=\frac{N}{k_N}=0$. We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.Comment: 16 pages; v5: added correction

Can Polarised Drell-Yan Shed More Light On The Proton Spin?

We analyse polarised Drell-Yan process using the factorisation method and derive operator definitions for polarised parton distribution functions. We demonstrate that a factorisation analogous to that in the unpolarised Drell-Yan case holds in this process. We study the leading order gluonic contribution to the first moment of polarised Drell-Yan function and show that it is consistent with results obtained from polarised deep inelastic scattering.Comment: 12 page

Metal System for Chemical Reactions and for Studying Properties of Gases and Liquids

An all-metal system, made of copper, is herein described. It is suitable for working with those chemicals which do not attack copper. In particular it has been found very useful in the purification of BF3 and B(CH3)3. Some important features of such a system are (1) a complete absence of contaminants; (2) reactions may be carried out up to 500°C; (3) pressures up to several hundred pounds per square inch may be used; (4) flow of gases from very low to very high pressures may be easily controlled; (5) the system is very rugged. This latter point is particularly desirable where noxious or inflammable gases (such as B(CH3)3) are used. A method is also described whereby gases from sealed-off containers under either high or low pressures may be easily retrieved without introducing impurities. Other important advantages of such a system are mentioned in the text

Self-organization via active exploration in robotic applications

We describe a neural network based robotic system. Unlike traditional robotic systems, our approach focussed on non-stationary problems. We indicate that self-organization capability is necessary for any system to operate successfully in a non-stationary environment. We suggest that self-organization should be based on an active exploration process. We investigated neural architectures having novelty sensitivity, selective attention, reinforcement learning, habit formation, flexible criteria categorization properties and analyzed the resulting behavior (consisting of an intelligent initiation of exploration) by computer simulations. While various computer vision researchers acknowledged recently the importance of active processes (Swain and Stricker, 1991), the proposed approaches within the new framework still suffer from a lack of self-organization (Aloimonos and Bandyopadhyay, 1987; Bajcsy, 1988). A self-organizing, neural network based robot (MAVIN) has been recently proposed (Baloch and Waxman, 1991). This robot has the capability of position, size rotation invariant pattern categorization, recognition and pavlovian conditioning. Our robot does not have initially invariant processing properties. The reason for this is the emphasis we put on active exploration. We maintain the point of view that such invariant properties emerge from an internalization of exploratory sensory-motor activity. Rather than coding the equilibria of such mental capabilities, we are seeking to capture its dynamics to understand on the one hand how the emergence of such invariances is possible and on the other hand the dynamics that lead to these invariances. The second point is crucial for an adaptive robot to acquire new invariances in non-stationary environments, as demonstrated by the inverting glass experiments of Helmholtz. We will introduce Pavlovian conditioning circuits in our future work for the precise objective of achieving the generation, coordination, and internalization of sequence of actions

Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan \textit{et al}, in which recovery from a single erasure is considered. By studying the Generalized Hamming Weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Tur\'an graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from $2$ erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.Comment: 14 pages, 3 figures, Updated for improved readabilit