The curious nonexistence of Gaussian 2-designs

2-designs -- ensembles of quantum pure states whose 2nd moments equal those of the uniform Haar ensemble -- are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space L2(R). This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables, for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have an average state because the averaging integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and continuous quantum mechanics has important implications for optical state and process tomography.Comment: 9 pages, no pretty figures (sorry!

A two-armed bandit based scheme for accelerated decentralized learning

The two-armed bandit problem is a classical optimization problem where a decision maker sequentially pulls one of two arms attached to a gambling machine, with each pull resulting in a random reward. The reward distributions are unknown, and thus, one must balance between exploiting existing knowledge about the arms, and obtaining new information. Bandit problems are particularly fascinating because a large class of real world problems, including routing, QoS control, game playing, and resource allocation, can be solved in a decentralized manner when modeled as a system of interacting gambling machines. Although computationally intractable in many cases, Bayesian methods provide a standard for optimal decision making. This paper proposes a novel scheme for decentralized decision making based on the Goore Game in which each decision maker is inherently Bayesian in nature, yet avoids computational intractability by relying simply on updating the hyper parameters of sibling conjugate priors, and on random sampling from these posteriors. We further report theoretical results on the variance of the random rewards experienced by each individual decision maker. Based on these theoretical results, each decision maker is able to accelerate its own learning by taking advantage of the increasingly more reliable feedback that is obtained as exploration gradually turns into exploitation in bandit problem based learning. Extensive experiments demonstrate that the accelerated learning allows us to combine the benefits of conservative learning, which is high accuracy, with the benefits of hurried learning, which is fast convergence. In this manner, our scheme outperforms recently proposed Goore Game solution schemes, where one has to trade off accuracy with speed. We thus believe that our methodology opens avenues for improved performance in a number of applications of bandit based decentralized decision making

Psychophysiological responses to visceral and somatic pain in functional chest pain identify clinically relevant pain clusters

Background: Despite chronic pain being a feature of functional chest pain (FCP) its experience is variable. The factors responsible for this variability remain unresolved. We aimed to address these knowledge gaps, hypothesizing that the psychophysiological profiles of FCP patients will be distinct from healthy subjects. Methods: 20 Rome III defined FCP patients (nine males, mean age 38.7 years, range 28-59 years) and 20 healthy age-, sex-, and ethnicity-matched controls (nine males, mean 38.2 years, range 24-49) had anxiety, depression, and personality traits measured. Subjects had sympathetic and parasympathetic nervous system parameters measured at baseline and continuously thereafter. Subjects received standardized somatic (nail bed pressure) and visceral (esophageal balloon distension) stimuli to pain tolerance. Venous blood was sampled for cortisol at baseline, post somatic pain and post visceral pain. Key Results: Patients had higher neuroticism, state and trait anxiety, and depression scores but lower extroversion scores vs controls (all p < 0.005). Patients tolerated less somatic (p < 0.0001) and visceral stimulus (p = 0.009) and had a higher cortisol at baseline, and following pain (all p < 0.001). At baseline, patients had a higher sympathetic tone (p = 0.04), whereas in response to pain they increased their parasympathetic tone (p ≤ 0.008). The amalgamating the data, we identified two psychophysiologically distinct 'pain clusters'. Patients were overrepresented in the cluster characterized by high neuroticism, trait anxiety, baseline cortisol, pain hypersensitivity, and parasympathetic response to pain (all p < 0.03). Conclusions & Inferences: In future, such delineations in FCP populations may facilitate individualization of treatment based on psychophysiological profiling

Stochastic volatility and leverage effect

We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows us to fully estimate all parameters involved and it will entail a deeper study on correlated stochastic volatility models with practical applications on option pricing and risk management.Comment: 4 pages, 2 figure

Corporate financing decisions: UK survey evidence

Despite theoretical developments in recent years, our understanding of corporate capital structure remains incomplete. Prior empirical research has been dominated by archival regression studies which are limited in their ability to fully reflect the diversity found in practice. The present paper reports on a comprehensive survey of corporate financing decision-making in UK listed companies. A key finding is that firms are heterogeneous in their capital structure policies. About half of the firms seek to maintain a target debt level, consistent with trade-off theory, but 60 per cent claim to follow a financing hierarchy, consistent with pecking order theory. These two theories are not viewed by respondents as either mutually exclusive or exhaustive. Many of the theoretical determinants of debt levels are widely accepted by respondents, in particular the importance of interest tax shield, financial distress, agency costs and also, at least implicitly, information asymmetry. Results also indicate that cross-country institutional differences have a significant impact on financial decisions

Temporal analyses reveal a pivotal role for sense and antisense enhancer RNAs in coordinate immunoglobulin lambda locus activation.

Transcription enhancers are essential activators of V(D)J recombination that orchestrate non-coding transcription through complementary, unrearranged gene segments. How transcription is coordinately increased at spatially distinct promoters, however, remains poorly understood. Using the murine immunoglobulin lambda (Igλ) locus as model, we find that three enhancer-like elements in the 3' Igλ domain, Eλ3-1, HSCλ1 and HSE-1, show strikingly similar transcription factor binding dynamics and close spatial proximity, suggesting that they form an active enhancer hub. Temporal analyses show coordinate recruitment of complementary V and J gene segments to this hub, with comparable transcription factor binding dynamics to that at enhancers. We find further that E2A, p300, Mediator and Integrator bind to enhancers as early events, whereas YY1 recruitment and eRNA synthesis occur later, corresponding to transcription activation. Remarkably, the interplay between sense and antisense enhancer RNA is central to both active enhancer hub formation and coordinate Igλ transcription: Antisense Eλ3-1 eRNA represses Igλ activation whereas temporal analyses demonstrate that accumulating levels of sense eRNA boost YY1 recruitment to stabilise enhancer hub/promoter interactions and lead to coordinate transcription activation. These studies therefore demonstrate for the first time a critical role for threshold levels of sense versus antisense eRNA in locus activation

Penetration Depth Measurements in MgB_2: Evidence for Unconventional Superconductivity

We have measured the magnetic penetration depth of the recently discovered binary superconductor MgB_2 using muon spin rotation and low field $ac$-susceptibility. From the damping of the muon precession signal we find the penetration depth at zero temperature is about 85nm. The low temperature penetration depth shows a quadratic temperature dependence, indicating the presence of nodes in the superconducting energy gap.Comment: 4 pages 3 figure