Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. Tail probability bounds are also derived. For random variables B_t>0 and A_t, let Y_t(\lambda)=\exp{\lambda A_t-\lambda ^2B_t^2/2}. We develop inequalities for the moments of A_t/B_{t} or sup_{t\geq 0}A_t/{B_t(\log \log B_{t})^{1/2}} and variants thereof, when EY_t(\lambda )\leq 1 or when Y_t(\lambda) is a supermartingale, for all \lambda belonging to some interval. Our results are valid for a wide class of random processes including continuous martingales with A_t=M_t and B_t=\sqrt _t, and sums of conditionally symmetric variables d_i with A_t=\sum_{i=1}^td_i and B_t=\sqrt\sum_{i=1}^td_i^2. A sharp maximal inequality for conditionally symmetric random variables and for continuous local martingales with values in R^m, m\ge 1, is also established. Another development in this paper is a bounded law of the iterated logarithm for general adapted sequences that are centered at certain truncated conditional expectations and self-normalized by the square root of the sum of squares. The key ingredient in this development is a new exponential supermartingale involving \sum_{i=1}^td_i and \sum_{i=1}^td_i^2.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000039

Prototype of a bistable polariton field-effect transistor switch

This work has been supported by the State of Bavaria.Microcavity exciton polaritons are promising candidates to build a new generation of highly nonlinear and integrated optoelectronic devices. Such devices range from novel coherent light emitters to reconfigurable potential landscapes for electrooptical polariton-lattice based quantum simulators as well as building blocks of optical logic architectures. Especially for the latter, the strongly interacting nature of the light-matter hybrid particles has been used to facilitate fast and efficient switching of light by light, something which is very hard to achieve with weakly interacting photons. We demonstrate here that polariton transistor switches can be fully integrated in electro-optical schemes by implementing a one-dimensional polariton channel which is operated by an electrical gate rather than by a control laser beam. The operation of the device, which is the polariton equivalent to a field-effect transistor, relies on combining electro-optical potential landscape engineering with local exciton ionization to control the scattering dynamics underneath the gate. We furthermore demonstrate that our device has a region of negative differential resistance and features a completely new way to create bistable behavior.Publisher PDFPeer reviewe

Biogeochemical modelling of dissolved oxygen in a changing ocean

Secular decreases in dissolved oxygen concentration have been observed within the tropical oxygen minimum zones (OMZs) and at mid- to high latitudes over the last approximately 50 years. Earth system model projections indicate that a reduction in the oxygen inventory of the global ocean, termed ocean deoxygenation, is a likely consequence of on-going anthropogenic warming. Current models are, however, unable to consistently reproduce the observed trends and variability of recent decades, particularly within the established tropical OMZs. Here, we conduct a series of targeted hindcast model simulations using a state-of-the-art global ocean biogeochemistry model in order to explore and review biases in model distributions of oceanic oxygen. We show that the largest magnitude of uncertainty is entrained into ocean oxygen response patterns due to model parametrization of pCO2-sensitive C : N ratios in carbon fixation and imposed atmospheric forcing data. Inclusion of a pCO2-sensitive C : N ratio drives historical oxygen depletion within the ocean interior due to increased organic carbon export and subsequent remineralization. Atmospheric forcing is shown to influence simulated interannual variability in ocean oxygen, particularly due to differences in imposed variability of wind stress and heat fluxes

Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field

We present a discussion of the linear thermoelectric response of an interacting electron gas in a quantizing magnetic field. Boundary currents can carry a significant fraction of the net current passing through the system. We derive general expressions for the bulk and boundary components of the number and energy currents. We show that the local current density may be described in terms of ``transport'' and ``internal magnetization'' contributions. The latter carry no net current and are not observable in standard transport experiments. We show that although Onsager relations cannot be applied to the local current, they are valid for the transport currents and hence for the currents observed in standard transport experiments. We relate three of the four thermoelectric response coefficients of a disorder-free interacting two-dimensional electron gas to equilibrium thermodynamic quantities. In particular, we show that the diffusion thermopower is proportional to the entropy per particle, and we compare this result with recent experimental observations.Comment: 18 pages, 2 postscript figures included. Revtex with epsf.tex and multicol.sty. In the revised version, the comparison with experimental observations at $\nu=1/2, 3/2$ is extended to include the possibility of corrections due to weak impurity scattering. The conclusions that we reach regarding the applicability of the composite fermion model at these filling fractions are not affecte

Towards a Phenomenology of Grief : insights from Merleau-Ponty

This paper shows how phenomenological research can enhance our understanding of what it is to experience grief. I focus specifically on themes in the work of Maurice Merleau-Ponty, in order to develop an account that emphasizes two importantly different ways of experiencing indeterminacy. This casts light on features of grief that are disorienting and difficult to describe, while also making explicit an aspect of experience upon which the possibility of phenomenological inquiry itself depends

Hormonal Signal Amplification Mediates Environmental Conditions during Development and Controls an Irreversible Commitment to Adulthood

Many animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it can adopt one of two developmental fates (adulthood or diapause) depending on environmental conditions. The steroid hormone dafachronic acid (DA) directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We used a combination of physiological and molecular biology techniques to demonstrate that commitment to reproductive adult development occurs when DA levels, produced in the neuroendocrine XXX cells, exceed a threshold. Furthermore, imaging and cell ablation experiments demonstrate that the XXX cells act as a source of DA, which, upon commitment to adult development, is amplified and propagated in the epidermis in a DAF-12 dependent manner. This positive feedback loop increases DA levels and drives adult programs in the gonad and epidermis, thus conferring the irreversibility of the decision. We show that the positive feedback loop canalizes development by ensuring that sufficient amounts of DA are dispersed throughout the body and serves as a robust fate-locking mechanism to enforce an organism-wide binary decision, despite noisy and complex environmental cues. These mechanisms are not only relevant to C. elegans but may be extended to other hormonal-based decision-making mechanisms in insects and mammals

The Clean Power Plan: Issues to Watch

Although the Clean Air Act is an imperfect tool for addressing the nation’s greenhouse gas emissions, it is the only available federal mechanism for directly addressing power plant carbon emissions. The Obama Administration’s Clean Power Plan, published in final form in August 2015, tackles the challenge. This paper from the Center for Progressive Reform (CPR) compiles 13 separately authored essays from 11 CPR Member Scholars, each addressing a different topic related to the Clean Power Plan, and each representing the expertise and views of its individual author(s). Published in July 2015, just before the release of the final rule, the essays tee up key questions about the rule’s legality, implications for the energy sector, and a series of discrete implementation questions, including the role of cap-and-trade (and offsets), the nature and distribution of state targets, and implications for environmental justice

The Clean Power Plan: Issues to Watch

Although the Clean Air Act is an imperfect tool for addressing the nation’s greenhouse gas emissions, it is the only available federal mechanism for directly addressing power plant carbon emissions. The Obama Administration’s Clean Power Plan, published in final form in August 2015, tackles the challenge. This paper from the Center for Progressive Reform (CPR) compiles 13 separately authored essays from 11 CPR Member Scholars, each addressing a different topic related to the Clean Power Plan, and each representing the expertise and views of its individual author(s). Published in July 2015, just before the release of the final rule, the essays tee up key questions about the rule’s legality, implications for the energy sector, and a series of discrete implementation questions, including the role of cap-and-trade (and offsets), the nature and distribution of state targets, and implications for environmental justice

A Response to the IPCC Fifth Assessment

The Intergovernmental Panel on Climate Change\u27s (IPCC) Fifth Assessment Report presented significant data and findings about climate change. But the IPCC\u27s working groups\u27 summaries for policymakers avoid making normative statements about the IPCC\u27s findings. The authors, members of the Environmental Law Collaborative, bridge this gap by identifying the normative claims that stem from the working groups\u27 summaries to spark deeper discussion and help shape the IPCC\u27s sixth assessment