A note on rectangular partially massless fields

We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.Comment: 31 pages, 4 figures; v2: typos corrected and references adde

MELT - a Translated Domain Specific Language Embedded in the GCC Compiler

The GCC free compiler is a very large software, compiling source in several languages for many targets on various systems. It can be extended by plugins, which may take advantage of its power to provide extra specific functionality (warnings, optimizations, source refactoring or navigation) by processing various GCC internal representations (Gimple, Tree, ...). Writing plugins in C is a complex and time-consuming task, but customizing GCC by using an existing scripting language inside is impractical. We describe MELT, a specific Lisp-like DSL which fits well into existing GCC technology and offers high-level features (functional, object or reflexive programming, pattern matching). MELT is translated to C fitted for GCC internals and provides various features to facilitate this. This work shows that even huge, legacy, software can be a posteriori extended by specifically tailored and translated high-level DSLs.Comment: In Proceedings DSL 2011, arXiv:1109.032

From a kinetic equation to a diffusion under an anomalous scaling

A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, and Y(t) is an additive functional of K(t). We prove that under an anomalous rescaling Y converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately rescaled solution of the Boltzmann equation converges to a diffusion equation

Mayakovsky’s Bedbug: Revolution, Time and Utopia

The article was submitted on 25.04.2017.In Russia, the very idea of a Communist revolution – from 1905 onwards – meant both hope and dread. This attitude is quite clearly shown in a very significant part of the Russian literary process, from 1908 to the beginning of the Stalin era. An obvious thread, in fact, connects Aleksandr Bogdanov (Red Star, 1908), Evgeny Zamyatin (We, 1921) and Vladimir Mayakovsky (The Bedbug, 1929): the growing awareness that the Communist revolution, as Lenin had conceived it, was little more than a model and that a model could not describe – much less forecast – a complex reality (a complex system) like a social and political one. As a result of this awareness, hope and a dark prophecy (Bogdanov) slowly turn into despair (Mayakovsky). The model is subsumed by Vladimir Mayakovsky’s dystopian satire of The Bedbug and The Bathhouse which propose a new paradigm of dystopia: a bottleneck in the flow of the information produced by blind adherence to a preconceived project that prevents the discovery and the implementation of la volonté générale in so complex a system as human society.Для периода господства революционных идей в России начала XX в. были характерны противоречивые настроения надежды и страха. Это ярко проявлялось и во многих произведениях русской литературы, начиная с 1908 г. и вплоть до сталинской эпохи. Такие представления были связующей нитью для творчества Александра Богданова (Красная Звезда, 1908), Евгения Замятина (Мы, 1921) и Владимира Маяковского (Клоп, 1929): по их изменениям можно проследить то, как в сознании людей росло убеждение, что коммунистическая революция – всего лишь абстрактная модель. А модель не может описать и, тем более, предсказать сложную реальность, включающую в себя социальную и политическую системы. Из осознания этого факта, по мнению автора, и происходит мрачное пророчество А. Богданова (соединенное с надеждой), которое затем перерастает в отчаяние у В. Маяковского. Эта модель представлена в сатире Маяковского – в «Клопе» и «Бане», в которых возникает новая парадигма антиутопии: информационная ограниченность, вызванная слепым следованием заранее заданному замыслу, препятствует открытию и внедрению volonté générale (всеобщей воли как результата ограничения людьми своих прав) в такой сложной системе как человеческое общество

Mackie\u27s Arguement for the Infinite Man

Theists and non-theists alike have toiled with the characteristics of the Judeo-Christian God and how they may or may not be contradictory with the existence of evil. Some philosophers, such as J. L. Mackie, have decided that God and evil cannot coexist, mainly because the existence of evil means that any God is unable to keep evil and suffering away from His beloved creation, and such a limited God is no God at all. But Mackie’s argument rests on flawed foundation. Mankind is necessarily finite because even the infinite God cannot do the logically impossible and create the infinite—nothing infinite can be created. Mackie argues that mankind, in its unavoidably limited state, should function with limitless abilities to always choose good over evil. This “solution” requires that finite man can function with infinite capabilities, which is metaphysically impossible. The fact that mankind can potentially always choose the good choice does not mean that he can actualize this desire for good, for this would require an infinite capacity to both know and do good

Gender Differences in K-12 Education: What Indicators Are Important?

Although gender differences have been identified in scholarly research, there is little state reporting of indicators by gender. The purpose of this paper is to identify the gender gaps in K-12 education that have been reported in the literature, to discuss how and when these gaps manifest themselves, and to recommend which of the educational performance indicators should be reported by gender in Georgia. Ultimately, the purpose of reporting indicators by gender is to aid in the efforts to close gender gaps in education.A review of the literature reveals that gender gaps exist at both empirical and experiential levels. Empirically, gaps exist in math, science, and reading proficiency scores, as well as in course enrollment in higher level math and science and graduation rates. Experientially, gaps exist in self esteem levels, personal perceptions of ability, teacher interaction with students, as well as in the advice and opportunities that are afforded students. While studies show that girls and boys start kindergarten on a generally equal footing, by grade twelve girls are generally in a lower academic position than their male counterparts, particularly in the areas of math and science. Research shows that the most critical age for the development of gender gaps is early adolescence, particularly grade seven in which girls= educational performance in math and science begins to plummet.Based on the research and data reported in this paper, the following indicators are recommended to be reported by gender. They are separated into indicators that are currently available by gender, and indicators that are recommended to be reported by gender in the future

Donsker-Varadhan asymptotics for degenerate jump Markov processes

We consider a class of continuous time Markov chains on a compact metric space that admit an invariant measure strictly positive on open sets together with absorbing states. We prove the joint large deviation principle for the empirical measure and flow. Due to the lack of uniform ergodicity, the zero level set of the rate function is not a singleton. As corollaries, we obtain the Donsker-Varadhan rate function for the empirical measure and a variational expression of the rate function for the empirical flow

Design, Synthesis, and Screening of Non-Estrogenic Bisphenol A Mimics

Undergraduate Basi

Structure constants of shs[λ][\lambda]: the deformed-oscillator point of view

We derive and spell out the structure constants of the $\mathbb{Z}_2$-graded algebra $\mathfrak{shs}[\lambda]\,$ by using deformed-oscillators techniques in $Aq(2;\nu)\,$, the universal enveloping algebra of the Wigner-deformed Heisenberg algebra in 2 dimensions. The use of Weyl ordering of the deformed oscillators is made throughout the paper, via the symbols of the operators and the corresponding associative, non-commutative star product. The deformed oscillator construction was used by Vasiliev in order to construct the higher spin algebras in three spacetime dimensions. We derive an expression for the structure constants of $\mathfrak{shs}[\lambda]\,$ and show that they must obey a recurrence relation as a consequence of the associativity of the star product. We solve this condition and show that the $\mathfrak{hs}[\lambda]\,$ structure constants are given by those postulated by Pope, Romans and Shen for the Lone Star product.Comment: 22 pages, no figures. Contribution to the proceedings of the workshop "About various kinds of interactions", 4-5 June 2015 at UMONS, in honour of Philippe Spindel; v2: references and comments on Moyal product added; v3: Expanded version of the proceedings, covering the fermionic sector of $Aq(2;\nu)$. 1+27 pages, no figure