Tractable theories for the synthesis of neural networks

The Radius of Direct attraction of a discrete neural network is a measure of stability of the network. it is known that Hopfield networks designed using Hebb's Rule have a radius of direct attraction of Omega(n/p) where n is the size of the input patterns and p is the number of them. This lower bound is tight if p is no larger than 4. We construct a family of such networks with radius of direct attraction Omega(n/root plog p), for any p greater than or equal to 5. The techniques used to prove the result led us to the first polynomial-time algorithm for designing a neural network with maximum radius of direct attraction around arbitrary input patterns. The optimal synaptic matrix is computed using the ellipsoid method of linear programming in conjunction with an efficient separation oracle. Restrictions of symmetry and non-negative diagonal entries in the synaptic matrix can be accommodated within this scheme.

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Supersymmetric Chern-Simons theories with vector matter

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N = 2 supersymmetric model (with one chiral field) for all values of the `t Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.

Renormalization of noncommutative quantum field theories

We report on a comprehensive analysis of the renormalization of noncommutative phi(4) scalar field theories on the Groenewold-Moyal plane. These scalar field theories are twisted Poincare invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative Lehmann-Symanzik-Zimmermann formalism. DOI: 10.1103/PhysRevD.87.064014

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Spontaneous Lorentz violation in gauge theories

Frohlich, Morchio and Strocchi long ago proved that the Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where the consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected ``Sky'' group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These Abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.

Formal Synthesis of Actin Binding Macrolide Rhizopodin

Formal synthesis, of an actin binding macrolide rhizopodin was achieved in 19 longest linear steps. The key features of the synthesis include a stereoselective Mukaiyama aldol reaction, dual role of a Nagao auxiliary (first, as a chiral auxiliary of choice for installing hydroxy centers and, later, as an acylating agent to form an amide bond with an amino alcohol), late stage oxazole formation, and Stille coupling reactions.

Evaluating competing theories of street entrepreneurship

Conventionally, street entrepreneurs were either seen as a residue from a pre-modern era that is gradually disappearing (modernisation theory), or an endeavour into which marginalised populations are driven out of necessity in the absence of alternative ways of securing a livelihood (structuralist theory). In recent years, however, participa-tioninstreetentrepreneurshiphas beenre-read eitherasa rationaleconomicchoice(neo-liberal theory) or as conducted for cultural reasons (post-modern theory). The aim of this paper is to evaluate critically these competing explanations for participation in street entrepreneurship. To do this, face-to-face interviews were conducted with 871 street entrepreneurs in the Indian city of Bangalore during 2010 concerning their reasons for participation in street entrepreneurship. The finding is that no one explanation suffices. Some 12 % explain their participation in street entrepreneurship as necessity-driven, 15 % as traditional ancestral activity, 56 % as a rational economic choice and 17 % as pursued for social or lifestyle reasons. The outcome is a call to combine these previously rival explanations in order to develop a richer and more nuanced theorisation of the multifarious motives for street entrepreneurship in emerging market economies.

Unexpected mechanism for formal 2+2] cycloadditions of metallacyclocumulenes

The formation of radialene complex 6M proceeds through a three-membered metallacyclopropene complex 7M, contrary to the prevailing notion of simple dimerization of metallacyclocumulene 1M. The 1M-7M equilibrium, which is predominantly governed by the size-dependent ligand binding of the metal atoms, plays a decisive role in the chemistry of Cp2M-ligand complexes. This size dependency is further fine-tuned by the substituents on the substrates and helps in exploiting these classes of metallacycles to generate new chemistry.

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 1] and arXiv:1310.6659 2] a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926 3]. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the R-2 case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

Enantiospecific Formal Total Synthesis of Iriomoteolide 3a

A formal total synthesis of the marine macrolide iriomoteolide3a is described. Salient features of the synthesis include the elaboration of a -keto phosphonate derived from D-(-)-tartaric acid and the extension of a chiral butyrolactone derived from L-glutamic acid. Ring-closing metathesis is employed to construct the macrolactone core of the natural product.

Using formal reasoning on a model of tasks for FreeRTOS

FreeRTOS is an open-source real-time microkernel that has a wide community of users. We present the formal specification of the behaviour of the task part of FreeRTOS that deals with the creation, management, and scheduling of tasks using priority-based preemption. Our model is written in the Z notation, and we verify its consistency using the Z/Eves theorem prover. This includes a precise statement of the preconditions for all API commands. This task model forms the basis for three dimensions of further work: (a) the modelling of the rest of the behaviour of queues, time, mutex, and interrupts in FreeRTOS; (b) refinement of the models to code to produce a verified implementation; and (c) extension of the behaviour of FreeRTOS to multi-core architectures. We propose all three dimensions as benchmark challenge problems for Hoare's Verified Software Initiative.

A Grassmann path from AdS(3) to flat space

We show that interpreting the inverse AdS(3) radius 1/l as a Grassmann variable results in a formal map from gravity in AdS(3) to gravity in flat space. The underlying reason for this is the fact that ISO(2, 1) is the Inonu-Wigner contraction of SO(2, 2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS(3) maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.

Organocatalytic Enantioselective Formal C(sp(2))-H Alkylation

An organocatalytic enantioselective formal C(sp(2))-H alkylation is reported. This alkylative desymmetrization of prochiral 2,2-disubstituted cyclopentene-1,3-dione is catalyzed by a bifunctional tertiary aminourea derivative, utilizes air-stable and inexpensive nitroalkanes as the alkylating agents, and delivers synthetically versatile five-membered carbocycles containing an all-carbon quaternary stereogenic center remote from the reaction site in excellent enantioselectivity.