The Hamiltonian Formulation of Higher Order Dynamical Systems

Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the present analysis yields in a transparent manner the local structure of the associated phase space and its local sympletic geometry, and is of direct application to {\em constrained\/} higher order Lagrangian systems which are beyond the scope of Ostrogradsky's approach.Comment: 17 pages. Revised: references adde

Phenomenological Aspects of F-theory

Stabilizing a heterotic string vacuum with a large expectation value of the dilaton and simultaneously breaking low-energy supersymmetry is a long-standing problem of string phenomenology. We reconsider these issues in light of the recent developments in F-theory.Comment: 11 pages, phyzzx macro

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor

“Binge drinking? It’s good, it’s harmless fun”:a discourse analysis of accounts of female undergraduate drinking in Scotland

Binge drinking in young people, particularly females and students, is a source of some concern to those engaged in health education. The concept is usually defined in terms of quantities of alcohol consumed within a relatively short space of time. Research suggests that reasons for drinking are varied, and are likely to be influenced by culture and context. This study aimed to explore issues important to female undergraduate students in Scotland. Semi-structured interviews were carried out with 19 participants who were asked to describe what they understand by the term ‘binge drinking’, why they drink and what might trigger excessive consumption. Discourse analysis was used to explore the possible ‘functions’ of what was said, as well as the content. Participants showed sensitivity to how others might interpret their responses. They described binge drinking in terms of its behavioural effects rather than quantities consumed. Crucially, they positioned themselves outside the categories of ‘serious’ or ‘anti-social’ drinkers. These findings have important implications for our understanding of factors influencing drinking behaviour in this group of people, which in turn impacts on the potential design of health-enhancing interventions. The study also demonstrates the usefulness of a discourse analytic approach to accounts of drinking behaviour

Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities

The performance of two recent {\em ab initio} computational thermochemistry schemes, W1 and W2 theory [J.M.L. Martin and G. de Oliveira, J. Chem. Phys. 111, 1843 (1999}], is assessed for an enlarged sample of thermochemical data consisting of the ionization potentials and electron affinities in the G2-1 and G2-2 sets, as well as the heats of formation in the G2-1 and a subset of the G2-2 set. We find W1 theory to be several times more accurate for ionization potentials and electron affinities than commonly used (and less expensive) computational thermochemistry schemes such as G2, G3, and CBS-QB3: W2 theory represents a slight improvement for electron affinities but no significant one for ionization potentials. The use of a two-point $A+B/L^5$ rather than a three-point $A+B/C^L$ extrapolation for the SCF component greatly enhances the numerical stability of the W1 method for systems with slow basis set convergence. Inclusion of first-order spin-orbit coupling is essential for accurate ionization potentials and electron affinities involving degenerate electronic states: inner-shell correlation is somewhat more important for ionization potentials than for electron affinities, while scalar relativistic effects are required for the highest accuracy. The mean deviation from experiment for the G2-1 heats of formation is within the average experimental uncertainty. W1 theory appears to be a valuable tool for obtaining benchmark quality proton affinities.Comment: Journal of Chemical Physics, in press (303115JCP). 2 RevTeX files, first is text and tables, second is E-PAPS tables S-1 through S-5. Additional supplementary material (total energies, basis function exponents) available at http://theochem.weizmann.ac.il/web/papers/w1w2.htm

Poland Divided: Spatial Differences in the June 2003 EU Accession Referendum. Jean Monnet/Robert Schuman Paper Series, Vol. 4 No. 1, January 2004

(From the introduction). Thus, our purpose here is to describe and analyze geographical patterns within Poland of approval, disapproval, and abstention from this crucial vote on joining the EU, and to link those outcomes to the social and economic situation obtaining in the regions. From these associations we can shed additional light on how Poland divided on this pivotal issue and posit some challenges for both Polish and EU policy makers in the years ahead. To guide us we refer to several studies of the emergence of electoral politics in former- Soviet states (notably Russia and Ukraine) and in Central and Eastern Europe that have pointed to the salience of geographical differences in voting outcomes and voter turnout in the postcommunist period. (7) Complementing research based on individual level, or survey, data, these geographic studies using aggregate data relate variations in the social, economic, and demographic traits of regions to party, candidate, and issue preferences across these same units. For example, it has been almost universally the case in the post-communist countries that rural, older, agricultural populations have voted mainly for parties of the left and against reform, while urban, better-educated, white collar areas have, for the most part, favored parties and candidates that have advocated reform and privatization. These outcomes match very closely the kinds of divisions within societies that we find in surveys. Clearly, however, we must recognize the limitations of aggregate data analysis, especially the need to avoid imputing individual action from collective figures. Surveys, of course, have advantages over one-time aggregate data, including their ability to probe attitudes and to conduct sampling over time. However, polling results have their own limitations especially that they tend to be a–spatial (and therefore cannot usually be used to illuminate important regional issues), and that respondents are not always truthful, particularly on sensitive subjects. But taken together, survey and aggregate data provide us with a higher degree of confidence in the analysis of the correlates of voting behavior. Following the methodology used in these other geographic studies of post-communist states, here we will test several propositions relating to the affinity for EU membership within different segments of Poland’s electorate. We will do this by cross-tabulating results of the June accession referendum with key social and economic variables among the 373 powiaty of Poland. According to the administrative reform of 1999, Poland is divided into 16 provinces (województwa, or voivodships), which are in turn divided into sub-regions (podregiony) and further into the powiaty. (8) The powiat scale of analysis is ideal for our purposes; powiaty are “county” level units or individual cities “with powiat status” (what we will call here “urban powiaty”) that provide an excellent degree of spatial resolution and, most importantly, for which the Polish government provides superb, detailed socioeconomic data and electoral results. (9) Powiaty typically range from 50,000 to 150,000 inhabitants and between 500-2,000 km2. Urban powiaty range from relatively small to medium-sized urban centers with populations around 100,000 people to the largest cities such as Poznań (572,000), Wrocław (624,000), Kraków (741,000) and Łódz (786,526). The Warsaw conurbation comprises the powiat of Warsaw (1.610 million). (10) As will be seen, there is a remarkable diversity within Poland—not unexpectedly in such a large and heterogeneous country—with regard both to social and economic conditions and to the demonstrated preferences of voters, with the two being related

Bell Inequalities for Position Measurements

Bell inequalities for position measurements are derived using the bits of the binary expansion of position-measurement results. Violations of these inequalities are obtained from the output state of the Non-degenerate Optical Parametric Amplifier.Comment: revtex4, 2 figure

Sample path properties of stochastic processes represented as multiple stable integrals

Originally published as a technical report no. 871, October 1989 for Cornell University Operations Research and Industrial Engineering. Available online: http://hdl.handle.net/1813/8754This paper studies the sample path properties of stochastic processes represented by multiple symmetric α-stable integrals. It relates the “smoothness” of the sample paths to the “smoothness” of the (non-random) integrand. It also contains results about the behavior of the distribution of suprema and zero-one laws

Characteristic matrices for linear periodic delay differential equations

Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way can have a discrete set of poles in the complex plane, which may possibly obstruct their use when determining the stability of the linear system. Then we modify and generalize the original construction such that the poles get pushed into a small neighborhood of the origin of the complex plane.Comment: 17 pages, 1 figur