GOLDSTONE THEOREM AND JAHN-TELLER EFFECT

The Goldstone theorem requires that a many-body system with broken symmetry has an excitation branch, whose frequency tends to zero in the limit of infinite wavelength. We treat a system where the broken symmetry comes from the terms which give rise to the Jahn-Teller effect. Both the excitation branches we discuss in detail have finite frequencies at infinite wavelength when there is no Jahn-Teller term; the introduction of this term forces one branch to have zero frequency at infinite wavelength, in agreement with the Goldstone theorem The main point of this paper is this striking illustration of Goldstone's conjecture. Some of the simpler features of the excitation branches are discussed, they do not appear to have been treated in detail in the literature. Systems of ions in twofold degenerate E ground states may exhibit such excitations, which will have a characteristic velocity considerably less than that of sound

On the dynamics of lending and deposit interest rates in emerging markets: A non-linear approach

This paper studies the dynamics of lending and deposit rates in two emerging markets in Latin America: Colombia and Mexico. The dynamics of lending (deposit) interest rates are driven by the exogenous interbank interest rate and deviations from the long-run lending-interbank (deposit-interbank) interest rate relationship. Allowing for different interest rate behavior during periods characterized by large and small values of the spread, the non-linear specification proves superior to the linear one

Sex differences in the relationship between sensation seeking, trait emotional intelligence and delinquent behaviour

Levels of sensation seeking peak in adolescence and there is a well-documented association with delinquency and other risk taking behaviours. The present study investigated the potential moderating effect of trait Emotional Intelligence (EI) on this relationship. Trait EI encompasses high levels of empathy and emotion regulation and is associated with positive outcomes and wellbeing. 96 young adults (48 female; overall Mage = 19.76) completed measures of sensation seeking, trait EI and self-reported delinquent behaviours since age 12. Results indicated that sensation seeking and frequency of delinquent behaviours were positively associated, but this effect was moderated by trait EI for male participants - those with lower trait EI showed a greater increase in delinquency in line with a rise in sensation seeking. No moderation effect was observed for females, and females with higher levels of trait EI reported more delinquent behaviours. The results are discussed in terms of the protective role of trait EI in supporting self-regulation and whether, for some females, high levels of EI might predispose to antisocial relational behaviours

The Cone Dysfunction Syndromes

The cone dysfunction syndromes are a heterogeneous group of inherited, predominantly stationary retinal disorders characterised by reduced central vision, and varying degrees of colour vision abnormalities, nystagmus and photophobia. This review details the following conditions: complete and incomplete achromatopsia, blue-cone monochromatism, oligocone trichromacy, bradyopsia, and Bornholm eye disease. We describe the clinical, psychophysical, electrophysiological and imaging findings that are characteristic to each condition, in order to aid their accurate diagnosis, as well as highlight some classically held notions about these diseases that have come to be challenged over recent years. The latest data regarding the genetic aetiology and pathological changes observed in the cone dysfunction syndromes are discussed, and, where relevant, translational avenues of research, including completed and anticipated interventional clinical trials, for some of the diseases described herein will be presented. Finally, we briefly review the current management of these disorders

Transition Property for α\alpha-Power Free Languages with α≥2\alpha\geq 2 and k≥3k\geq 3 Letters

In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $\alpha$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $\alpha$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denote the $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$ is a rational number or a rational "number with $+$". If $\alpha$ is a "number with $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" a number then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We show that: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and $v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a (transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show a construction of the word $w$

Periodicity and frequency coding in human auditory cortex

Understanding the neural coding of pitch and frequency is fundamental to the understanding of speech comprehension, music perception and the segregation of concurrent sound sources. Neuroimaging has made important contributions to defining the pattern of frequency sensitivity in humans. However, the precise way in which pitch sensitivity relates to these frequency-dependent regions remains unclear. Single-frequency tones also cannot be used to test this hypothesis as their pitch always equals their frequency. Here, temporal pitch (periodicity) and frequency coding were dissociated using stimuli that were bandpassed in different frequency spectra (centre frequencies 800 and 4500 Hz), yet were matched in their pitch characteristics. Cortical responses to both pitch-evoking stimuli typically occurred within a region that was also responsive to low frequencies. Its location extended across both primary and nonprimary auditory cortex. An additional control experiment demonstrated that this pitch-related effect was not simply caused by the generation of combination tones. Our findings support recent neurophysiological evidence for a cortical representation of pitch at the lateral border of the primary auditory cortex, while revealing new evidence that additional auditory fields are also likely to play a role in pitch coding

THE SPECTROSCOPY OF CRYSTAL DEFECTS - A COMPENDIUM OF DEFECT NOMENCLATURE

The authors bring together tables of current defect nomenclature and a summary of the rules actually practised (rather than idealised schemes) in choosing such labels for signals obtained with a range of spectroscopies. As well as providing a source of reference for the user lost in a maze of labels, the compilation also indicates parallels between similar defect species in very different systems (e.g. ice and quartz), even though the relationships may be far from obvious from the labels. The systems considered are all non-metals, namely ionic crystals (including oxides), silica, semiconductors (e.g. III-V and tetrahedrally coordinated II-VI), valence crystals (e.g. diamond, c-Si, a-Si) and other special hosts like ice and conducting polymers

Implicit Bias Reflects the Personal and the Social

This issue’s target article by Payne, Vuletich, and Lundberg (PV&L) does exactly what one should, presenting an argument that is thought-provoking and that challenges current orthodoxy. It also addresses an issue that has increasingly confounded attitudes researchers in recent years. The construct of “implicit bias” was initially conceptualized as a latent construct that exists within persons, relatively resistant to situational influences. A plethora of theoretical models converge on the notion that implicit biases, including intergroup biases, are representations that are stored in memory (e.g., Devine,1989; Fazio, Jackson, Dunton, & Williams, 1995; Gawronski & Bodenhausen, 2006; Greenwald et al., 2002; Wilson, Lindsay, & Schooler, 2000). Although some perspectives emphasize the role of culture in contributing to implicit measures of bias, even these perspectives rely on the learning and storage of mental representations (Olson & Fazio, 2004)

Data-efficient learning of feedback policies from image pixels using deep dynamical models

Data-efficient reinforcement learning (RL) in continuous state-action spaces using very high-dimensional observations remains a key challenge in developing fully autonomous systems. We consider a particularly important instance of this challenge, the pixels-to-torques problem, where an RL agent learns a closed-loop control policy ( torques ) from pixel information only. We introduce a data-efficient, model-based reinforcement learning algorithm that learns such a closed-loop policy directly from pixel information. The key ingredient is a deep dynamical model for learning a low-dimensional feature embedding of images jointly with a predictive model in this low-dimensional feature space. Joint learning is crucial for long-term predictions, which lie at the core of the adaptive nonlinear model predictive control strategy that we use for closed-loop control. Compared to state-of-the-art RL methods for continuous states and actions, our approach learns quickly, scales to high-dimensional state spaces, is lightweight and an important step toward fully autonomous end-to-end learning from pixels to torques