The agrin gene codes for a family of basal lamina proteins that differ in function and distribution

We isolated two cDNAs that encode isoforms of agrin, the basal lamina protein that mediates the motor neuron-induced aggregation of acetylcholine receptors on muscle fibers at the neuromuscular junction. Both proteins are the result of alternative splicing of the product of the agrin gene, but, unlike agrin, they are inactive in standard acetylcholine receptor aggregation assays. They lack one (agrin-related protein 1) or two (agrin-related protein 2) regions in agrin that are required for its activity. Expression studies provide evidence that both proteins are present in the nervous system and muscle and that, in muscle, myofibers and Schwann cells synthesize the agrin-related proteins while the axon terminals of motor neurons are the sole source of agrin

The Computational Power of Optimization in Online Learning

We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point in time. In this setting, we give a novel online algorithm that attains vanishing regret with respect to $N$ experts in total $\widetilde{O}(\sqrt{N})$ computation time. We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is $\widetilde{\Theta}(N)$. These results demonstrate an exponential gap between the power of optimization in online learning and its power in statistical learning: in the latter, an optimization oracle---i.e., an efficient empirical risk minimizer---allows to learn a finite hypothesis class of size $N$ in time $O(\log{N})$. We also study the implications of our results to learning in repeated zero-sum games, in a setting where the players have access to oracles that compute, in constant time, their best-response to any mixed strategy of their opponent. We show that the runtime required for approximating the minimax value of the game in this setting is $\widetilde{\Theta}(\sqrt{N})$, yielding again a quadratic improvement upon the oracle-free setting, where $\widetilde{\Theta}(N)$ is known to be tight

On the constitution of sodium at higher densities

Using density functional theory the atomic and electronic structure of sodium are predicted to depart substantially from those expected of simple metals for $r_s 130$ GPa). Newly-predicted phases include those with low structural symmetry, semi-metallic electronic properties (including zero-gap semiconducting limiting behavior), unconventional valence charge density distributions, and even those that raise the possibility of superconductivity, all at currently achievable pressures. Important differences emerge between sodium and lithium at high densities, and these are attributable to corresponding differences in their respective cores.Comment: 13 pages; 3 figure

Similarities between the Hubbard and Periodic Anderson Models at Finite Temperatures

The single band Hubbard and the two band Periodic Anderson Hamiltonians have traditionally been applied to rather different physical problems - the Mott transition and itinerant magnetism, and Kondo singlet formation and scattering off localized magnetic states, respectively. In this paper, we compare the magnetic and charge correlations, and spectral functions, of the two systems. We show quantitatively that they exhibit remarkably similar behavior, including a nearly identical topology of the finite temperature phase diagrams at half-filling. We address potential implications of this for theories of the rare earth ``volume collapse'' transition.Comment: 4 pages (RevTeX) including 4 figures in 7 eps files; as to appear in Phys. Rev. Let

Pairing Correlations on t-U-J Ladders

Pairing correlations on generalized t-U-J two-leg ladders are reported. We find that the pairing correlations on the usual t-U Hubbard ladder are significantly enhanced by the addition of a nearest-neighbor exchange interaction J. Likewise, these correlations are also enhanced for the t-J model when the onsite Coulomb interaction is reduced from infinity. Moreover, the pairing correlations are larger on a t-U-J ladder than on a t-Jeff ladder in which Jeff has been adjusted so that the two models have the same spin gap at half-filling. This enhancement of the pairing correlations is associated with an increase in the pair-binding energy and the pair mobility in the t-U-J model and point to the importance of the charge transfer nature of the cuprate systems

Phase separation and valence instabilities in cuprate superconductors. Effective one-band model approach

We study the Cu-O valence instability (VI) and the related phase separation (PS) driven by Cu-O nearest-neighbor repulsion $U_{pd}$, using an effective extended one-band Hubbard model ($H_{eff}$) obtained from the extended three-bandHubbard model, through an appropriate low-energy reduction. $H_{eff}$ is solved by exact diagonalization of a square cluster with 10 unit cells and also within a slave-boson mean-field theory. Its parameters depend on doping for $U_{pd}\neq 0$ or on-site O repulsion $U_p\neq 0$. The results using both techniques coincide in that there is neither VI nor PS for doping levels $x<0.5$ if $U_{pd}\lesssim 2$ eV. The PS region begins for $U_{pd}\gtrsim 2$ eV at large doping $x>0.6$ and increases with increasing $U_{pd}$. The PS also increases with increasing on-site Cu repulsion $U_d$.Comment: 16 pages and 10 figures in postscript format, compressed with uufile

Low-frequency incommensurate magnetic response in strongly correlated systems

It is shown that in the t-J model of Cu-O planes at low frequencies the dynamic spin structure factor is peaked at incommensurate wave vectors (1/2+-delta,1/2)$, (1/2,1/2+-delta). The incommensurability is connected with the momentum dependencies of the magnon frequency and damping near the antiferromagnetic wave vector. The behavior of the incommensurate peaks is similar to that observed in La_{2-x}(Ba,Sr)_xCuO_{4+y} and YBa_2Cu_3O_{7-y}: for hole concentrations 0.02<x<=0.12 we find that delta is nearly proportional to x, while for x>0.12 it tends to saturation. The incommensurability disappears with increasing temperature. Generally the incommensurate magnetic response is not accompanied by an inhomogeneity of the carrier density.Comment: 4 pages, 4 figure

Dynamical Mean-Field Theory and Its Applications to Real Materials

Dynamical mean-field theory (DMFT) is a non-perturbative technique for the investigation of correlated electron systems. Its combination with the local density approximation (LDA) has recently led to a material-specific computational scheme for the ab initio investigation of correlated electron materials. The set-up of this approach and its application to materials such as (Sr,Ca)VO_3, V_2O_3, and Cerium is discussed. The calculated spectra are compared with the spectroscopically measured electronic excitation spectra. The surprising similarity between the spectra of the single-impurity Anderson model and of correlated bulk materials is also addressed.Comment: 20 pages, 9 figures, invited paper for the JPSJ Special Issue "Kondo Effect - 40 Years after the Discovery"; final version, references adde

Quantum Monte Carlo Study of Hole Binding and Pairing Correlations in the Three-Band Hubbard Model

We simulated the 3-band Hubbard model using the Constrained Path Monte Carlo (CPMC) method in search for a possible superconducting ground state. The CPMC is a ground state method which is free of the exponential scaling of computing time with system size. We calculated the binding energy of a pair of holes for systems up to $6 \times 4$ unit cells. We also studied the pairing correlation functions versus distance for both the d-wave and extended s-wave channels in systems up to $6 \times 6$. We found that holes bind for a wide range of parameters and that the binding increased as the system size is increased. However, the pairing correlation functions decay quickly with distance. For the extended s channel, we found that as the Coulomb interaction $U_d$ on the Cu sites is increased, the long-range part of the correlation functions is suppressed and fluctuates around zero. For the $d_{x^2 - y^2}$ channel, we found that the correlations decay rapidly with distance towards a small positive value. However, this value becomes smaller as the interaction $U_d$ or the system size is increased.Comment: 21 pages, 13 Postscript figures, Submitted to Phys. Rev.