Central extensions of classical and quantum q-Viraroso algebras

We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions, we solve them, both in the classical and in the quantum case (for sl(2)). We find that the consistent central extensions are much more general that those found previously in the literature.Comment: Latex2e, needs amsfonts and amssymb package

Deformed W_N algebras from elliptic sl(N) algebras

We extend to the sl(N) case the results that we previously obtained on the construction of W_{q,p} algebras from the elliptic algebra A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining q-deformations of the W_N algebra, are constructed. The operators t(z) also close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N algebras depending on the parity of h, characterizing the exchange structures at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page

From quantum to elliptic algebras

It is shown that the elliptic algebra ${\cal A}_{q,p}(\hat{sl}(2)_c)$ at the critical level c=-2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m integer, they commute when in addition p=q^{2k} for k integer non-zero, and they belong to the center of ${\cal A}_{q,p}(\hat{sl}(2)_c)$ when k is odd. The Poisson structures obtained for t(z) in these classical limits contain the q-deformed Virasoro algebra, characterizing the structures at generic values of p, q and m as new ${\cal W}_{q,p}(sl(2))$ algebras.Comment: LaTeX2e Document - packages subeqn,amsfont

Universal construction of W_{p,q} algebras

We present a direct construction of abstract generators for q-deformed W_N algebras. This procedure hinges upon a twisted trace formula for the elliptic algebra A_{q,p}(sl(N)_c) generalizing the previously known formulae for quantum groups.Comment: packages amsfonts, amssym

RNA interference approaches for treatment of HIV-1 infection.

HIV/AIDS is a chronic and debilitating disease that cannot be cured with current antiretroviral drugs. While combinatorial antiretroviral therapy (cART) can potently suppress HIV-1 replication and delay the onset of AIDS, viral mutagenesis often leads to viral escape from multiple drugs. In addition to the pharmacological agents that comprise cART drug cocktails, new biological therapeutics are reaching the clinic. These include gene-based therapies that utilize RNA interference (RNAi) to silence the expression of viral or host mRNA targets that are required for HIV-1 infection and/or replication. RNAi allows sequence-specific design to compensate for viral mutants and natural variants, thereby drastically expanding the number of therapeutic targets beyond the capabilities of cART. Recent advances in clinical and preclinical studies have demonstrated the promise of RNAi therapeutics, reinforcing the concept that RNAi-based agents might offer a safe, effective, and more durable approach for the treatment of HIV/AIDS. Nevertheless, there are challenges that must be overcome in order for RNAi therapeutics to reach their clinical potential. These include the refinement of strategies for delivery and to reduce the risk of mutational escape. In this review, we provide an overview of RNAi-based therapies for HIV-1, examine a variety of combinatorial RNAi strategies, and discuss approaches for ex vivo delivery and in vivo delivery

Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space

We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u) = - \int_{\rr^d} K(x,y) (u(y)-u(x)) \, dy. Here we consider a kernel $K(x,y)=\psi (y-a(x))+\psi(x-a(y))$ where $\psi$ is a bounded, nonnegative function supported in the unit ball and $a$ means a diffeomorphism on \rr^d. A simple example being a linear function $a(x)= Ax$. The upper and lower bounds that we obtain are given in terms of the Jacobian of $a$ and the integral of $\psi$. Indeed, in the linear case $a(x) = Ax$ we obtain an explicit expression for the first eigenvalue in the whole \rr^d and it is positive when the the determinant of the matrix $A$ is different from one. As an application of our results, we observe that, when the first eigenvalue is positive, there is an exponential decay for the solutions to the associated evolution problem. As a tool to obtain the result, we also study the behaviour of the principal eigenvalue of the nonlocal Dirichlet problem in the ball $B_R$ and prove that it converges to the first eigenvalue in the whole space as $R\to \infty$

Urban structure and growth

Most economic activity occurs in cities. This creates a tension between local increasing returns, implied by the existence of cities, and aggregate constant returns, implied by balanced growth. To address this tension, we develop a theory of economic growth in an urban environment. We show how the urban structure is the margin that eliminates local increasing returns to yield constant returns to scale in the aggregate, thereby implying a city size distribution that is well described by a power distribution with coefficient one: Zipf's Law. Under strong assumptions our theory produces Zipf's Law exactly. More generally, it produces the systematic deviations from Zipf's Law observed in the data, namely, the underrepresentation of small cities and the absence of very large ones. In these cases, the model identifies the standard deviation of industry productivity shocks as the key element determining dispersion in the city size distribution. We present evidence that the dispersion of city sizes is consistent with the dispersion of productivity shocks in the data.

An ultra-compact low temperature scanning probe microscope for magnetic fields above 30 T

We present the design of a highly compact High Field Scanning Probe Microscope (HF-SPM) for operation at cryogenic temperatures in an extremely high magnetic field, provided by a water-cooled Bitter magnet able to reach 38 T. The HF-SPM is 14 mm in diameter: an Attocube nano-positioner controls the coarse approach of a piezo resistive AFM cantilever to a scanned sample. The Bitter magnet constitutes an extreme environment for SPM due to the high level of vibrational noise; the Bitter magnet noise at frequencies up to 300 kHz is characterized and noise mitigation methods are described. The performance of the HF-SPM is demonstrated by topographic imaging and noise measurements at up to 30 T. Additionally, the use of the SPM as a three-dimensional dilatometer for magnetostriction measurements is demonstrated via measurements on a magnetically frustrated spinel sample.Comment: 6 pages, 5 figure

Deformed Double Yangian Structures

Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N)) are defined for any N, extending the previously known case of N=2. They realise deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras A_qp(sl(N)), these algebras contain subalgebras at critical values of the central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations are derived for their abstract generators.Comment: 16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarra