Characterisation of the x-index and the rec-index

Axiomatic characterisation of a bibliometric index provides insight into the properties that the index satisfies and facilitates the comparison of different indices. A geometric generalisation of the h-index, called the x-index, has recently been proposed to address some of the problems with the h-index, in particular, the fact that it is not scale invariant, i.e., multiplying the number of citations of each publication by a positive constant may change the relative ranking of two researchers. While the square of the h-index is the area of the largest square under the citation curve of a researcher, the square of the x-index, which we call the rec-index (or rectangle-index), is the area of the largest rectangle under the citation curve. Our main contribution here is to provide a characterisation of the rec-index via three properties: monotonicity, uniform citation and uniform equivalence. Monotonicity is a natural property that we would expect any bibliometric index to satisfy, while the other two properties constrain the value of the rec-index to be the area of the largest rectangle under the citation curve. The rec-index also allows us to distinguish between in uential researchers who have relatively few, but highly-cited, publications and prolific researchers who have many, but less-cited, publications

Measure Theory in Noncommutative Spaces

The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG

Coherent random permutations with record statistics

Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are conditionally uniform given the counts of upper and lower records. This family interpolates between two versions of Ewens' distribution. We discuss characterisations of the conditionally uniform permutations, their asymptotic properties, constructions and relations to random partitions.Comment: 17 page

Scattering theory for a class of non-selfadjoint extensions of symmetric operators

This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices. On the basis of these formulae, we are able to construct wave operators and derive a new representation for the scattering matrix for pairs of such extensions in both self-adjoint and non-self-adjoint situations.Comment: 32 pages; This is the continuation of arXiv:1703.06220 (and formerly contained in v1); this version is as accepted by the journal (Operator Theory: Advances and Applications

Academic and demographic characteristics as predictors of scholarly productivity in the Israeli academia

In this study we investigated the influence of various researchers' characteristics, such as faculty, department, gender and seniority, on their scholarly productivity. A quantitative research was conducted with 601 professors with tenure from two leading Israeli universities, in order to construct a comprehensive model for assessment and prediction of the scholarly productivity. We found a great variability in seniority and productivity of the examined professors. In addition, a multivariate linear regression showed significant differences between the examined faculties. The faculty of Life Sciences was the most scholarly productive, while Social Sciences was the least scholarly productive faculty. Overall, there was a positive influence of academic seniority on scholarly productivity, however, scholars with over twenty years of seniority appeared to be less productive than those with the middle level seniority. One of the most interesting findings was gender differences of the scholarly productivity distribution. Contrary to the past research, we found that women were more productive than men. This is a first large-scale quantitative research of senior scholars in Israel which sheds some light on the productivity evaluation and its influence factors in the Israeli academia

Path integration over closed loops and Gutzwiller's trace formula

In 1967 M.C. Gutzwiller succeeded to derive the semiclassical expression of the quantum energy density of systems exhibiting a chaotic Hamiltonian dynamics in the classical limit. The result is known as the Gutzwiller trace formula. The scope of this review is to present in a self-contained way recent developments in functional determinant theory allowing to revisit the Gutzwiller trace formula in the spirit of field theory. The field theoretic setup permits to work explicitly at every step of the derivation of the trace formula with invariant quantities of classical periodic orbits. R. Forman's theory of functional determinants of linear, non singular elliptic operators yields the expression of quantum quadratic fluctuations around classical periodic orbits directly in terms of the monodromy matrix of the periodic orbits. The phase factor associated to quadratic fluctuations, the Maslov phase, is shown to be specified by the Morse index for closed extremals, also known as Conley and Zehnder index.Comment: Preprint, revised version 132 pages in pdf format. Comments welcom

Chaotic Time Series Analysis in Economics: Balance and Perspectives

To show that a mathematical model exhibits chaotic behaviour does not prove that chaos is also present in the corresponding data. To convincingly show that a system behaves chaotically, chaos has to be identified directly from the data. From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests test are developed to investigate the basic features of chaotic phenomena: nonlinearity, fractal attractor, and sensitivity to initial conditions. The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in the data. More specifically, our attention will be devoted to reviewing the results reached by the application of these techniques to economic and financial time series and to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.Economic dynamics, nonlinearity, tests for chaos, chaos

Generation and Application of Ultrashort Laser Pulses in Attosecond Science

In this thesis, I describe the development of a sub-4 fs few-cycle laser system at Imperial College London used to generate and characterise the first single attosecond (1 as = 10-18s) pulses in the UK. Phase-stabilised few-cycle laser pulses were generated using a hollow fibre system with a chirped mirror compression setup. The pulse was fully characterised using frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric field reconstruction in a spatially encoded filter arrangement (SEA-F-SPIDER). A pulse duration of 3.5 fs was measured with an argon filled hollow fibre. These phase stabilised Infra-Red (IR) pulses were used to generate a continuous spectrum of high harmonics in the Extreme Ultraviolet (XUV) originating from a single half-cycle of the driving field. Using subsequent spectral filtering, a single attosecond pulse was generated. The isolated XUV pulse was characterised using an atomic streaking camera and a pulse duration of ~260 as was retrieved using FROG for complete reconstruction of attosecond bursts (FROG-CRAB). In an experiment conducted at the Rutherford Appleton Laboratory, high harmonics were generated using a two-colour field with an energetic beam at 1300nm and a weak second harmonic orthogonally polarized to the fundamental. By changing the phase between the two fields, a deep modulation of the harmonic yield is seen and an enhancement of one order of magnitude compared to the single colour field with the same energy is observed