Suprema of Chaos Processes and the Restricted Isometry Property

We present a new bound for suprema of a special type of chaos process indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time‐frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sparsity s and the vector length n is m ? s log² s log² n. © 2014 Wiley Periodicals, Inc.     

On the Lamb vector and the hydrodynamic charge

This work is an attempt to test the concept of the hydrodynamic charge (analogous to the electric charge in electromagnetism) in the simple case of a coherent structure such as the Burgers vortex. We provide experimental measurements of both the so-called Lamb vector and its divergence (the charge) by two-dimensional particles images velocimetry. In addition, we perform a Helmholtz–Hodge decomposition of the Lamb vector in order to explore its topological features. We compare the charge with the well-known Q-criterion in order to assess its interest in detecting and characterizing coherent structure. Usefulness of this concept in studies of vortex dynamics is demonstrated.

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Activation of Sperm EGFR by Light Irradiation is Mediated by Reactive Oxygen Species

To acquire fertilization competence, spermatozoa must undergo several biochemical and motility changes in the female reproductive tract, collectively called capacitation. Actin polymerization and the development of hyperactivated motility (HAM) are part of the capacitation process. In a recent study, we showed that irradiation of human sperm with visible light stimulates HAM through a mechanism involving reactive‐oxygen‐species (ROS), Ca²⁺ influx, protein kinases A (PKA), and sarcoma protein kinase (Src). Here, we showed that this effect of light on HAM is mediated by ROS‐dependent activation of the epidermal growth factor receptor (EGFR). Interestingly, ROS‐mediated HAM even when the EGFR was activated by EGF, the physiological ligand of EGFR. Light irradiation stimulated ROS‐dependent actin polymerization, and this effect was abrogated by PBP10, a peptide which activates the actin‐severing protein, gelsolin, and causes actin‐depolymerization in human sperm. Light‐stimulated tyrosine phosphorylation of Src‐dependent gelsolin, resulting in enhanced HAM. Thus, light irradiation stimulates HAM through a mechanism involving Src‐mediated actin polymerization. Light‐stimulated HAM and in vitro‐fertilization (IVF) rate in mouse sperm, and these effects were mediated by ROS and EGFR. In conclusion, we show here that irradiation of sperm with visible light, enhances their fertilization capacity via a mechanism requiring ROS, EGFR and HAM.     

Evidence for a near-resonant charge transfer mechanism for double-stranded peptide nucleic acid

We present evidence for a near-resonant mechanism of charge transfer in short peptide nucleic acid (PNA) duplexes obtained through electrochemical, STM break junction (STM-BJ), and computational studies. A seven base pair (7-bp) PNA duplex with the sequence (TA)(3)-(XY)-(TA)(3) was studied, in which XY is a complementary nucleobase pair. The experiments showed that the heterogeneous charge transfer rate constant (k(0)) and the single-molecule conductance (σ) correlate with the oxidation potential of the purine base in the XY base pair. The electrochemical measurements showed that the enhancement of k(0) is independent, within experimental error, of which of the two PNA strands contains the purine base of the XY base pair. 7-bp PNA duplexes with one or two GC base pairs had similar measured k(0) and conductance values. While a simple superexchange model, previously used to rationalize charge transfer in single stranded PNA (Paul et al. J. Am. Chem. Soc. 2009, 131, 6498-6507), describes some of the experimental observations, the model does not explain the absence of an enhancement in the experimental k(0) and σ upon increasing the G content in the duplexes from one to two. Moreover, the superexchange model is not consistent with other studies (Paul et al. J. Phys. Chem. B 2010, 114, 14140), that showed a hopping charge transport mechanism is likely important for PNA duplexes longer than seven base pairs. A quantitative computational analysis shows that a near-resonant charge transfer regime, wherein a mix of superexchange and hopping mechanisms are expected to coexist, can rationalize all of the experimental results.     

NCIPLOT: a program for plotting non-covalent interaction regions

Non-covalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these non-covalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define non-covalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their van der Waals radii. We recently developed an alternative perspective, derived from the electronic density: the Non-Covalent Interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of non-covalent interactions is of great potential value. Here, we describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical, as well as promolecular, densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/~yang/software.htm.     

Obtaining fast error rates in nonconvex situations

We show that under mild assumptions on the learning problem, one can obtain a fast error rate for every reasonable fixed target function even if the base class is not convex. To that end, we show that in such cases the excess loss class satisfies a Bernstein type condition.     

Mixing of all orders of Lie groups actions

Summary We show that for Lie groups whose adjoint representation reflects their topology, mixing implies mixing of all orders. In particular we prove that mixing actions of a semisimple Lie group are mixing of all orders, answering a conjecture of B. Marcus.Oblatum 6-VIII-1990 & 4-IV-1991Sponsored in part by the Edmund Landau Center for research in Mathematical Analysis supported by the Minerva Foundation (Federal Republic of Germany)     

Automata and Square Complexes

We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reprove the theorem of Macedońska, Nekrashevych, Sushchansky, on the connection between bi-reversible automata and the commensurator of a regular tree.     

Empirical Processes with a Bounded Ψ 1 Diameter

We study the empirical process ${{\rm sup}_{f \in F}|N^{-1}\sum_{i=1}^{N}\,f^{2}(X_i)-\mathbb{E}f^{2}|}We study the empirical process sup_{f ? F}|N^-1?_i=1^N f²(X_i)-\mathbbEf²|{{\rm sup}_{f \in F}|N^{-1}\sum_{i=1}^{N}\,f^{2}(X_i)-\mathbb{E}f^{2}|}, where F is a class of mean-zero functions on a probability space (Ω, μ), and (X_i)_{i = 1}^N{(X_{i})_{i =1}^N} are selected independently according to μ.