Guide to the Chateau Benoit Collection

This collection is comprised of a large variety of publications, documents, photographs, books, and other materials from Fred and Mary Benoit’s time as owners of Chateau Benoit

Benoit Mandelbrot 1924 -2010: A Greek among Romans

In this brief note describes the trajectory of the fractal models / multifractal F / M by Benoit Mandelbrot. The promise was discovered by the geometry of Mandelbrot covers a broad area of research fields, from meteorology and mathematical physics to the individual and collective behavior in society, besides his contributions to the analysis of the financial crisis in his wonderful essay on The (mis) Behavior of Markets. A fractal view of Risk, Ruin and Reward (2004).Benoit Mandelbrot, Fractals, Financial

Null vectors of the WBC2WBC_2 algebra

Using the fusion principle of Bauer et al. we give explicit expressions for some null vectors in the highest weight representations of the \bc algebra in two different forms. These null vectors are the generalization of the Virasoro ones described by Benoit and Saint-Aubin and analogues of the $W_3$ ones constructed by Bowcock and Watts. We find connection between quantum Toda models and the fusion method.Comment: 8 pages, LaTeX, ITP Budapest 50

Benoit Mandelbrot (1924 - 2011 ) : A Greek among Romans

Posthumous tributes to Benoit Mandelbrot (1924-2010) have highlighted his remarkable influence on the natural sciences, from geometry to meteorology, to theories with non-Euclidean spaces and geospatial models approach. Mandelbrot culminates a series of major thinkers going back to classical Greece: a Greek among RomansMandelbrot, Fractals; Finance, Financial Markets, Epistemology, Thomas Kuhn

Fast vibrational calculation of anharmonic OH-stretch frequencies for two low-energy noradrenaline conformers

We introduce a new reduced-coupling technique to accelerate direct calculations of a selected number of vibrational frequencies in large molecular systems. Our method combines the advantages of the single-to-all correlation-corrected vibrational self-consistent field (STA-CC-VSCF) approach [D. M. Benoit, J. Chem. Phys. 125, 244110 (2006)] with those of the fast-CC-VSCF technique [D. M. Benoit, J. Chem. Phys. 120, 562 (2004)] and allows the ab initio calculation of only the relevant parts of the required potential energy surface (PES). We demonstrate, using a set of five aliphatic alcohol molecules, that the new fast-STA-CC-VSCF method is accurate and leads to very substantial time gains for the computations of the PES. We then use the fast-STA-CC-VSCF method to accelerate the computation of the OH-stretch and NH-stretch frequencies of the two lowest-energy conformers of noradrenaline, namely, AG1a and GG1a. Our new approach enables us to run the calculation 89 times faster than the standard CC-VSCF technique and makes it possible to use a high-level MP2/TZP description of the PES. We demonstrate that the influence of the strong mode-mode couplings is crucial for a realistic description of the particular OH-stretch vibrational signature of each conformer. Finally, of the two possible low-energy conformers, we identify AG1a as the one most likely to have been observed in the experiments of Snoek [Mol. Phys. 101, 1239 (2003)]

Benoit Mandelbrot (1924 - 2010): A Greek among Romans

In this brief note describes the trajectory of the fractal models/multifractal F/M by Benoit Mandelbrot. The promise was discovered by the geometry of Mandelbrot covers a broad area of research fields, from meteorology and mathematical physics to the individual and collective behavior in society, besides his contributions to the analysis of the financial crisis in his wonderful essay on «The (mis) Behavior of Markets. A fractal view of Risk, Ruin and Reward» (2004). Mandelbrot’s arguments have revealed significant anomalies in the prevailing paradigms. Is this a new paradigm in Kuhn’s sense as stated by the same Mandelbrot?Mandelbrot, Fractals, Finance, Financial Markets, Epistemology, Thomas Kuhn.

A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communitiesComment: 40 page

Defence Spending and Economic Growth: Re-examining the Issue of Causality for Pakistan and India

What is the impact of carrying a heavy defence burden on the country’s economic development and growth? Views expressed in the literature1 argue that national defence is a consumption good which reduces economic growth by reducing saving and capital investment. A number of empirical studies have investigated the possible trade-offs between defence spending and other government expenditures like health and education. Empirical evidence concerning the relationship between defence spending and economic growth for developed countries is not inconsistent with the view that defence reduced the resources available for investment and hurts economic growth. See, for example, Benoit (1973). The evidence for developing countries, however, has not been entirely consistent or conclusive.2 Benoit (1978), using data on 44 less developed countries (LDCs) for the period 1950–65, found a strong positive association between defence spending and growth of civilian output per capita. Fredericksen and Looney (1982), using data for the period 1960–78 on a large cross-section, concluded that increased defence spending assists economic growth in resource-rich countries and not in resource-constraint ones. Using a sample of 54 LDCs pertaining to the period 1965–73, Lim (1983) found that defence spending hurts economic growth. Biswas and Ram (1986) in a sample of 58 LDCs for time-periods 1960–70 and 1970–77, using conventional and augmented growth models, concluded that military expenditures neither help nor hurt economic growth to any significant extent.