On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.Comment: 33 pages; to appear in Mathematische Zeitschrift; v3 many minor updates including new title; v2 some cohomological arguments simplified; v1 is a revised version of the second half of arXiv:1408.4934v

Low Catalyst Loadings in Olefin Metathesis: Synthesis of Nitrogen Heterocycles by Ring-Closing Metathesis

A series of ruthenium catalysts have been screened under ring-closing metathesis (RCM) conditions to produce five-, six-, and seven-membered carbamate-protected cyclic amines. Many of these catalysts demonstrated excellent RCM activity and yields with as low as 500 ppm catalyst loadings. RCM of the five-membered carbamate series could be run neat, the six-membered carbamate series could be run at 1.0 M, and the seven-membered carbamate series worked best at 0.2−0.05 M

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

We calculate very long low- and high-temperature series for the susceptibility $\chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $\chi^{(5)}$ and six-particle contribution $\chi^{(6)}$. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150000 CPU hours on computer clusters. For $\chi^{(5)}$ 10000 terms of the series are calculated {\it modulo} a single prime, and have been used to find the linear ODE satisfied by $\chi^{(5)}$ {\it modulo} a prime. A diff-Pad\'e analysis of 2000 terms series for $\chi^{(5)}$ and $\chi^{(6)}$ confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the $n$-particle components of the susceptibility, up to a small set of ``additional'' singularities. We find the presence of singularities at $w=1/2$ for the linear ODE of $\chi^{(5)}$, and $w^2= 1/8$ for the ODE of $\chi^{(6)}$, which are {\it not} singularities of the ``physical'' $\chi^{(5)}$ and $\chi^{(6)},$ that is to say the series-solutions of the ODE's which are analytic at $w =0$. Furthermore, analysis of the long series for $\chi^{(5)}$ (and $\chi^{(6)}$) combined with the corresponding long series for the full susceptibility $\chi$ yields previously conjectured singularities in some $\chi^{(n)}$, $n \ge 7$. We also present a mechanism of resummation of the logarithmic singularities of the $\chi^{(n)}$ leading to the known power-law critical behaviour occurring in the full $\chi$, and perform a power spectrum analysis giving strong arguments in favor of the existence of a natural boundary for the full susceptibility $\chi$.Comment: 54 pages, 2 figure

Temporal–spectral signaling of sensory information and expectations in the cerebral processing of pain

The perception of pain is shaped by somatosensory information about threat. However, pain is also influenced by an individual's expectations. Such expectations can result in clinically relevant modulations and abnormalities of pain. In the brain, sensory information, expectations (predictions), and discrepancies thereof (prediction errors) are signaled by an extended network of brain areas which generate evoked potentials and oscillatory responses at different latencies and frequencies. However, a comprehensive picture of how evoked and oscillatory brain responses signal sensory information, predictions, and prediction errors in the processing of pain is lacking so far. Here, we therefore applied brief painful stimuli to 48 healthy human participants and independently modulated sensory information (stimulus intensity) and expectations of pain intensity while measuring brain activity using electroencephalography (EEG). Pain ratings confirmed that pain intensity was shaped by both sensory information and expectations. In contrast, Bayesian analyses revealed that stimulus-induced EEG responses at different latencies (the N1, N2, and P2 components) and frequencies (alpha, beta, and gamma oscillations) were shaped by sensory information but not by expectations. Expectations, however, shaped alpha and beta oscillations before the painful stimuli. These findings indicate that commonly analyzed EEG responses to painful stimuli are more involved in signaling sensory information than in signaling expectations or mismatches of sensory information and expectations. Moreover, they indicate that the effects of expectations on pain are served by brain mechanisms which differ from those conveying effects of sensory information on pain

Simultaneous detection of Brazilian isolates of grapevine viruses by TaqMan real-time RT-PCR.

The aim of this work was to evaluate the efficiency of real-time RT-PCR for detection of different isolates of ten important virus species that infect grapevines in Brazil: Grapevine leafroll-associated virus (GLRaV-1, -2, -3 and -5), Grapevine virus A (GVA), Grapevine virus B (GVB), Grapevine virus D (GVD), Grapevine rupestris stem pitting-associated virus (GRSPaV), Grapevine fleck virus (GFkV) and Grapevine fanleaf virus (GFLV). The reactions consisted of individual (simplex) and simultaneous (duplex) virus detections. Thirty six grapevine accessions, regenerated after thermotherapy and tissue culture treatments, have been analysed. All the above-mentioned viruses were sensitively detected in simplex reactions in samples infected with different virus isolates. Specifically to GLRaV-1 it was necessary to mix reagents refered by different sources to achieve the amplification. GVA, GRSPaV, GLRaV-2 and GLRaV-3 combined with GVB, GFLV, GFkV, GVD and GLRaV-5 were accurately detected in duplex trials. It was shown, that real-time RT-PCR (TaqMan) is able to efficiently detect different local virus species and isolates.Comunicação científica

Detecção por RT-PCR em Tempo Real e caracterização molecular do Grapevine virus D e Grapevine leafroll-associated virus 5 em videira.

O objetivo deste trabalho foi verificar a ocorrência destes dois vírus em videiras por meio de RT-PCR em Tempo Real, além de caracterizar molecularmente três dos isolados obtidos.Resumo

Competing phases in the high field phase diagram of (TMTSF)2_2ClO4_4

A model is presented for the high field phase diagram of (TMTSF)$_2$ClO$_4$, taking into account the anion ordering, which splits the Fermi surface in two bands. For strong enough field, the largest metal-SDW critical temperature corresponds to the N=0 phase, which originates from two intraband nesting processes. At lower temperature, the competition between these processes puts at disadvantage the N=0 phase vs. the N=1 phase, which is due to interband nesting. A first order transition takes then place from the N=0 to N=1 phase. We ascribe to this effect the experimentally observed phase diagrams.Comment: 5 pages, 3 figures (to appear in Phys. Rev. Lett.

Superconducting pairing and density-wave instabilities in quasi-one-dimensional conductors

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations and both intrachain and interchain repulsive interactions. d-wave superconductivity, which dominates over the spin-density-wave (SDW) phase at large nesting deviations, becomes unstable to the benefit of a triplet $f$-wave phase for a weak repulsive interchain backscattering term $g_1^\perp>0$, despite the persistence of dominant SDW correlations in the normal state. Antiferromagnetism becomes unstable against the formation of a charge-density-wave state when $g_1^\perp$ exceeds some critical value. While these features persist when both Umklapp processes and interchain forward scattering ($g_2^\perp$) are taken into account, the effect of $g_2^\perp$ alone is found to frustrate nearest-neighbor interchain $d$- and $f$-wave pairing and instead favor next-nearest-neighbor interchain singlet or triplet pairing. We argue that the close proximity of SDW and charge-density-wave phases, singlet d-wave and triplet $f$-wave superconducting phases in the theoretical phase diagram provides a possible explanation for recent puzzling experimental findings in the Bechgaard salts, including the coexistence of SDW and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase.Comment: 19 pages, 13 figure

Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model

We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$ of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$, versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ``Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ``connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of $\chi^{(3)}$ and $\chi^{(4)}$. We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the $n$-particle contributions $\chi^{(n)}$ and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc

New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.