Searching for Apery-Style Miracles [Using, Inter-Alia, the Amazing Almkvist-Zeilberger Algorithm]

Roger Apery's seminal method for proving irrationality is "turned on its head" and taught to computers, enabling a one second redux of the original proof of zeta(3), and many new irrationality proofs of many new constants, alas, none of them is both famous and not-yet-proved-irrational.Comment: 16 pages. Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, May 2014, and this arxiv.org. Accompanied my Maple package NesApery, available from http://www.math.rutgers.edu/~zeilberg/tokhniot/NesAper

Molecular principles underlying dual RNA specificity in the Drosophila SNF protein

The first RNA recognition motif of the Drosophila SNF protein is an example of an RNA binding protein with multi-specificity. It binds different RNA hairpin loops in spliceosomal U1 or U2 small nuclear RNAs, and only in the latter case requires the auxiliary U2A′ protein. Here we investigate its functions by crystal structures of SNF alone and bound to U1 stem-loop II, U2A′ or U2 stem-loop IV and U2A′, SNF dynamics from NMR spectroscopy, and structure-guided mutagenesis in binding studies. We find that different loop-closing base pairs and a nucleotide exchange at the tips of the loops contribute to differential SNF affinity for the RNAs. U2A′ immobilizes SNF and RNA residues to restore U2 stem-loop IV binding affinity, while U1 stem-loop II binding does not require such adjustments. Our findings show how U2A′ can modulate RNA specificity of SNF without changing SNF conformation or relying on direct RNA contacts

Dynamics of spin 1/2 quantum plasmas

The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron--ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out.Comment: 4 pages, 2 figures, to appear in Physical Review Letter

Graviton mediated photon-photon scattering in general relativity

In this paper we consider photon-photon scattering due to self-induced gravitational perturbations on a Minkowski background. We focus on four-wave interaction between plane waves with weakly space and time dependent amplitudes, since interaction involving a fewer number of waves is excluded by energy-momentum conservation. The Einstein-Maxwell system is solved perturbatively to third order in the field amplitudes and the coupling coefficients are found for arbitrary polarizations in the center of mass system. Comparisons with calculations based on quantum field theoretical methods are made, and the small discrepances are explained.Comment: 5 pages, 3 figure

Diplomats or Defendants? Defining the Future of Head-of-State Immunity

Fluorescence nanoscopy provides means to discernthe finer details of protein localization and interaction in cells by offeringan order of magnitude higher resolution than conventional optical imagingtechniques. However, these super resolution techniques put higher demands onthe optical system as well as on the fluorescent probes, making multicolorfluorescence nanoscopy a challenging task. Here we present a new and simpleprocedure which exploits the photostability and excitation spectra of dyes toincrease the number of simultaneous recordable targets in STED nanoscopy. Weuse this procedure to demonstrate four color STED imaging of platelets with ≤40 nm resolution and low crosstalk. Platelets can selectively store, sequesterand release a multitude of different proteins, and in a manner specific fordifferent physiological and disease states. By applying multicolor nanoscopy tostudy platelets, we can achieve spatial mapping of the protein organizationwith a high resolution, for multiple proteins at the same time and in the samecell. This provides a means to identify specific platelet activation states fordiagnostic purposes and to understand the underlying protein storage andrelease mechanisms. We studied the organization of the pro- and anti-angiogenicproteins VEGF and PF-4 together with fibrinogen and filamentous actin, andfound distinct features in their respective protein localization. Further,colocalization analysis revealed only minor overlap between the proteins VEGFand PF-4 indicating that they have separate storage and release mechanisms,corresponding well with their opposite rules as pro- and anti-angiogenicproteins, respectively.Updated from "Submitted" to "Published". QC 20140630</p

The Complex Langevin method: When can it be trusted?

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and minor corrections added, to appear in PR

A possibility to measure elastic photon--photon scattering in vacuum

Photon--photon scattering in vacuum due to the interaction with virtual electron-positron pairs is a consequence of quantum electrodynamics. A way for detecting this phenomenon has been devised based on interacting modes generated in microwave waveguides or cavities [G. Brodin, M. Marklund and L. Stenflo, Phys. Rev. Lett. \textbf{87} 171801 (2001)]. Here we materialize these ideas, suggest a concrete cavity geometry, make quantitative estimates and propose experimental details. It is found that detection of photon-photon scattering can be within the reach of present day technology.Comment: 7 pages, 3 figure