A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials

We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict the asymptotic formulae for moments of derivatives of L-functions which arise in number theory. Each formula gives the leading constant of the asymptotic in terms of determinants of hypergeometric functions. We find a differential recurrence relation between these determinants which allows the rapid computation of the (k+1)-st constant in terms of the k-th and (k-1)-st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of \tau-functions associated with Painlev\'e differential equations

Knowledge industry survival strategy (KISS): fundamental principles and interoperability requirements for domain specific modeling languages.

Domain Specific Languages are raising the level of abstraction of software specifications and of knowledge represen-tation in general. When DSLs are used to formalize the results of domain analysis, the result is a clean separation of concerns in the problem space. This is a major advance over aspect oriented programming, where separation of concerns is only achieved in the solution space. However, the level of interoperability between current DSL tools is comparable to the level of interoperability between CASE tools in the 90s. To increase the popularity of DSL based approaches, this needs to change. Software development has become highly decentralized, and an assumption that all parties in a global software supply chain will use identical tooling is simply not realistic. As a result today's software supply chains are much less automated than supply chains in other, more mature industries. The KISS series of workshops is used to incrementally establish a consensus on the fundamental principles that underpin the use of DSLs, and to improve DSL tool interoperability

Small values of signed harmonic sums

For every \u3c4 08R and every integer N, let mN(\u3c4) be the minimum of the distance of \u3c4 from the sums 11n=1Nsn/n, where s1,\u2026,sn 08 121,+1. We prove that mN(\u3c4

A recursion formula for moments of derivatives of random matrix polynomials

We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O−(2N). These averages are used to predict the asymptotic formulae for moments of derivatives of L-functions which arise in number theory. Each formula gives the leading constant of the asymptotic in terms of determinants of hypergeometric functions. We find a differential recurrence relation between these determinants that allows the rapid computation of the (k+1)st constant in terms of the kth and (k−1)st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of τ-functions associated with Painlevé differential equations

A conjectural extension of Hecke’s converse theorem

We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses

Pinus mugo essential oil impairs STAT3 activation through oxidative stress and induces apoptosis in prostate cancer cells

Essential oils (EOs) and their components have been reported to possess anticancer properties and to increase the sensitivity of cancer cells to chemotherapy. The aim of this work was to select EOs able to downregulate STAT3 signaling using Western blot and RT-PCR analyses. The molecular mechanism of anti-STAT3 activity was evaluated through spectrophotometric and fluorometric analyses, and the biological effect of STAT3 inhibition was analyzed by flow cytometry and wound healing assay. Herein, Pinus mugo EO (PMEO) is identified as an inhibitor of constitutive STAT3 phosphorylation in human prostate cancer cells, DU145. The down-modulation of the STAT3 signaling cascade decreased the expression of anti-proliferative as well as anti-apoptotic genes and proteins, leading to the inhibition of cell migration and apoptotic cell death. PMEO treatment induced a rapid drop in glutathione (GSH) levels and an increase in reactive oxygen species (ROS) concentration, resulting in mild oxidative stress. Pretreatment of cells with N-acetyl-cysteine (NAC), a cell-permeable ROS scavenger, reverted the inhibitory action of PMEO on STAT3 phosphorylation. Moreover, combination therapy revealed that PMEO treatment displayed synergism with cisplatin in inducing the cytotoxic effect. Overall, our data highlight the importance of STAT3 signaling in PMEO cytotoxic activity, as well as the possibility of developing adjuvant therapy or sensitizing cancer cells to conventional chemotherapy

An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.Comment: 4 pages, 5 figures, 3 table

Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems

A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view, the two phases are characterized by two distinct single-particle motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous diffusion is observed up to a time $\tau$ that increases linearly with $N$. Therefore, the finite particle number acts like a white noise source for the system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review