Construction of irreducible polynomials through rational transformations

Let $\mathbb F_q$ be the finite field with $q$ elements, where $q$ is a power of a prime. We discuss recursive methods for constructing irreducible polynomials over $\mathbb F_q$ of high degree using rational transformations. In particular, given a divisor $D>2$ of $q+1$ and an irreducible polynomial $f\in \mathbb F_{q}[x]$ of degree $n$ such that $n$ is even or $D\not \equiv 2\pmod 4$, we show how to obtain from $f$ a sequence $\{f_i\}_{i\ge 0}$ of irreducible polynomials over $\mathbb F_q$ with $\mathrm{deg}(f_i)=n\cdot D^{i}$.Comment: 21 pages; comments are welcome

Organizing the innovation process : complementarities in innovation networking

This paper contributes to the developing literature on complementarities in organizational design. We test for the existence of complementarities in the use of external networking between stages of the innovation process in a sample of UK and German manufacturing plants. Our evidence suggests some differences between the UK and Germany in terms of the optimal combination of innovation activities in which to implement external networking. Broadly, there is more evidence of complementarities in the case of Germany, with the exception of the product engineering stage. By contrast, the UK exhibits generally strong evidence of substitutability in external networking in different stages, except between the identification of new products and product design and development stages. These findings suggest that previous studies indicating strong complementarity between internal and external knowledge sources have provided only part of the picture of the strategic dilemmas facing firms

Robust functional principal components: A projection-pursuit approach

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simulation study under different contamination schemes.Comment: Published in at http://dx.doi.org/10.1214/11-AOS923 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Vehicular Inter-Networking via Named Data

In this paper we apply the Named Data Networking, a newly proposed Internet architecture, to networking vehicles on the run. Our initial design, dubbed V-NDN, illustrates NDN's promising potential in providing a unifying architecture that enables networking among all computing devices independent from whether they are connected through wired infrastructure, ad hoc, or intermittent DTN. This paper describes the prototype implementation of V-NDN and its preliminary performance assessment

Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms

Generation of energetic (hot) electrons is an intrinsic property of any plasmonic nanostructure under illumination. Simultaneously, a striking advantage of metal nanocrystals over semiconductors lies in their very large absorption cross sections. Therefore, metal nanostructures with strong and tailored plasmonic resonances are very attractive for photocatalytic applications. However, the central questions regarding plasmonic hot electrons are how to quantify and extract the optically-excited energetic electrons in a nanocrystal. We develop a theory describing the generation rates and the energy-distributions of hot electrons in nanocrystals with various geometries. In our theory, hot electrons are generated owing to surfaces and hot spots. The formalism predicts that large optically-excited nanocrystals show the excitation of mostly low-energy Drude electrons, whereas plasmons in small nanocrystals involve mostly hot electrons. The energy distributions of electrons in an optically-excited nanocrystal show how the quantum many-body state in small particles evolves towards the classical state described by the Drude model when increasing nanocrystal size. We show that the rate of surface decay of plasmons in nanocrystals is directly related to the rate of generation of hot electrons. Based on a detailed many-body theory involving kinetic coefficients, we formulate a simple scheme describing the plasmon's dephasing. In most nanocrystals, the main decay mechanism of a plasmon is the Drude friction-like process and the secondary path comes from generation of hot electrons due to surfaces and electromagnetic hot spots. This latter path strongly depends on the size, shape and material of the nanocrystal, correspondingly affecting its efficiency of hot-electron production. The results in the paper can be used to guide the design of plasmonic nanomaterials for photochemistry and photodetectors.Comment: 90 pages, 21 figures, including Supplementary Informatio