Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces

We provide some new estimates for Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we introduce certain conditions on the weight that imply estimate for the maximal operator on the corresponding weighted space. Also using a well known estimate for the maximal operator by a double maximal operators on different m easures related to the weight we give new estimates for the above Bellman type functions.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1511.0611

Variational characterization of the critical curve for pinning of random polymers

In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges. There are two phases, localized and delocalized, depending on the inverse temperature and on the disorder bias. Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process (Birkner, Greven and den Hollander [6]), we derive variational formulas for the quenched, respectively, annealed critical curve separating the two phases. These variational formulas are used to obtain a necessary and sufficient criterion, stated in terms of relative entropies, for the two critical curves to be different at a given inverse temperature, a property referred to as relevance of the disorder. This criterion in turn is used to show that the regimes of relevant and irrelevant disorder are separated by a unique inverse critical temperature. Subsequently, upper and lower bounds are derived for the inverse critical temperature, from which sufficient conditions under which it is strictly positive, respectively, finite are obtained. The former condition is believed to be necessary as well, a problem that we will address in a forthcoming paper. Random pinning has been studied extensively in the literature. The present paper opens up a window with a variational view. Our variational formulas for the quenched and the annealed critical curve are new and provide valuable insight into the nature of the phase transition. Our results on the inverse critical temperature drawn from these variational formulas are not new, but they offer an alternative approach that is exible enough to be extended to other models of random polymers with disorder. Key words and phrases. Random polymer, random charges, localization vs. delocalization, quenched vs. annealed large deviation principle, quenched vs. annealed critical curve, relevant vs. irrelevant disorder, critical temperature

Introduction: democratisation and punishment

Die experimentelle Aufgabe dieser Arbeit bestand in der Bestimmung der Energieabhängigkeit der Schädigungsrate für die MetalleAluminium, Kupfer und Gold im Energiebereich von 1,o bis 3, 3 Mev. Im Verlauf der Arbeit ergab sich, daß für eine einwandfreie Bestimmung der "idealen 11 Schädigungsrate $\Delta \varphi_{io}$, der Schädigungsrate bei verschwindender Defektkonzentration $\Delta \varphi$ und ohne Auftreten von Störeinflüssen, für die betreffende Probe auch die Abhängigkeit der Schädigungsrate von der Defektkonzentration $\Delta \varphi$ bei einer Energie zu untersuchen ist. Diese Anforderung konnte im Rahmen einer anderen Aufgabenstellung an denselben Proben erledigt werden. Dabei ergab sich, daß die Schädigungsrate von Gold mit zunehmender Defektkonzentration zunächst nichtlinear abfällt und erst ab einer Defektkonzentration $\Delta \varphi = 5 x 10^{-8} \Omega cm$ bei Metallen im allgemeinen beobachteten, nahezu linearen Abfall mit zunehmender Defektkonzentration annimmt. Es wurde festgestellt, daß dieser Effekt von der Bestrahlungstemperatur abhängt. Weitere Untersuchungen bei Bestrahlungstemperaturen T<4,3°K waren jedoch mit der vorhandenen Apparatur nicht durchführbar. Die an Gold bestimmten Schädigungsraten können aufgrund dieses Effektes nicht ausgewertet werden. Außerdem muß angenommen werden, daß aufgrund dieses Effektes alle in der Literatur mitgeteilten Schädigungsraten mit einer merklichen Unsicherheit behaftet sind. Für die minimale Schwellenenergie $E_{d,min}$ wurde etwa 33 eV erhalten. Dieser Wert ist in guter Übereinstimmung mit dem von Bauer und Sosin$^{9)}$ angegebenen Wert von etwa 35 eV. Aus den eigenen Messungen an Aluminium und Kupfer und den Messungen anderer Autoren bei Energien unterhalb 1,o MeV wurde einegeglättete Kurve für die Energieabhängigkeit der Schadigungsrate von der minimalen Schwellenenergie E$_{d,min}$ bis zu der bei dergrößten Elektronenenergie maximal übertragbaren Enerrrie $E^{(N)}_{max}$ erhalten. Diese geglälttete Kurve wurde dann der Berechnung der Verlagerungsfunktion $\varphi _{F}P(E)n(E)$ zuerunde gelegt. Der Verlauf des differentiellen Wirkungsquerschnittes für Energieübertragung bei der Streuung eines Elektrons an einem Gitteratom bedingt, daß Energieübertragungen nahe $E^{(N)}_{max}$ sehr selten vorkommen. Energieübertragungen von der Größe der minimalen Schwellenenergie $E_{d,min}$ dagegen häufig. Das heißt, daß von Energien nahe $E^{(N)}_{max}$ nur ein kleiner Beitrag zu gemessenen Schädigungsraten $\Delta \varphi$ geleistet wird [...

Analysis of a One-Dimensional Continuous Delay-Tolerant Network Model

The packet speed and transmission cost are examined, for a single packet traveling along a simple one-dimensional, continuous-time network, using a combination of wireless transmissions and physical transports. We assume that the network consists of two nodes moving at constant speed on a circle, and changing their direction of travel after independent exponential times. The packet wishes to travel in the clockwise direction as fast and as far as possible. It travels either by being physically transported on a node’s buffer, or by being wirelessly transmitted to the other node when the two are in the same location. We derive exact, explicit expressions for the long-term average packet speed (in the clockwise direction), and also for the average wireless transmission cost. These results can be viewed as initial steps towards the development of analogous exact expressions for the speed and cost, in more realistic, two-dimensional wireless delay-tolerant network models

A simple network of nodes moving on the circle

Two simple Markov processes are examined, one in discrete and one in continuous time, arising from idealized versions of a transmission protocol for mobile, delay-tolerant networks. We consider two independent walkers moving with constant speed on either the discrete or continuous circle, and changing directions at independent geometric (respectively, exponential) times. One of the walkers carries a message that wishes to travel as far and as fast as possible in the clockwise direction. The message stays with its current carrier unless the two walkers meet, the carrier is moving counter-clockwise, and the other walker is moving clockwise. In that case, the message jumps to the other walker. The long-term average clockwise speed of the message is computed. An explicit expression is derived via the solution of an associated boundary value problem in terms of the generator of the underlying Markov process. The average transmission cost is also similarly computed, measured as the long-term number of jumps the message makes per unit time. The tradeoff between speed and cost is examined, as a function of the underlying problem parameters

The maximum of the local time of a diffusion process in a drifted Brownian potential

We consider a one-dimensional diffusion process $X$ in a $(-\kappa/2)$-drifted Brownian potential for $\kappa\neq 0$. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from the behaviour of the maximum local time of the transient random walk in random environment. We also obtain the convergence in law of the maximum local time of $X$ under the annealed law after suitable renormalization when $\kappa \geq 1$. Moreover, we characterize all the upper and lower classes for the hitting times of $X$, in the sense of Paul L\'evy, and provide laws of the iterated logarithm for the diffusion $X$ itself. To this aim, we use annealed technics.Comment: 38 pages, new version, merged with hal-00013040 (arXiv:math/0511053), with some additional result

'Glocal' disorder: causes, conduct and consequences of the 2008 Greek unrest

This article examines the unrest that emanated in Athens and rolled out across Greek cities in December 2008 as a case through which to advance understanding of how local, national and international arenas may together shape localised episodes of disorder. We begin by addressing the proximate and structural causes of the unrest, before turning to explore the multifarious character of protest actions, including novel and derivative forms of contestation deployed by protestors, and public debate about the appropriate apportioning of blame amongst the variety of actors involved. Finally, we look at the diverse outcomes of the unrest and their impact upon extant socio-political tensions. For each stage of the lifecycle of the unrest, we evaluate the relevance of international actors, practices and discourses. Our analysis of the Greek unrest of 2008 suggests, first, that the array of intersections between global, national and local dimensions of unrest are more diverse than has heretofore been recognised by pertinent scholarship; and second, that international or transnational factors may play a significant role in the emergence, conduct and consequences of disorder even in instances where national and local dynamics remain predominant

Copolymer with pinning: variational characterization of the phase diagram

This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges are given by i.i.d. sequences of random variables. The configurations of the polymer are directed paths that can make i.i.d. excursions of finite length above and below the interface. The Hamiltonian has two parts: a monomer-solvent interaction ("copolymer") and a monomer-interface interaction ("pinning"). The quenched and the annealed version of the model each undergo a transition from a localized phase (where the polymer stays close to the interface) to a delocalized phase (where the polymer wanders away from the interface). We exploit the approach developed in [5] and [3] to derive variational formulas for the quenched and the annealed free energy per monomer. These variational formulas are analyzed to obtain detailed information on the critical curves separating the two phases and on the typical behavior of the polymer in each of the two phases. Our main results settle a number of open questions.Comment: 46 pages, 9 figure

From offender to victim-oriented monitoring : a comparative analysis of the emergence of electronic monitoring systems in Argentina and England and Wales

The increasingly psychological terrain of crime and disorder management has had a transformative impact upon the use of electronic monitoring technologies. Surveillance technologies such as electronic monitoring ‑ EM, biometrics, and video surveillance have flourished in commercial environments that market the benefits of asocial technologies in managing disorderly behavior and which, despite often chimerical crime prevention promises, appeal to the ontologically insecure social imagination. The growth of EM in criminal justice has subsequently taken place despite, at best, equivocal evidence that it protects the public and reduces recidivism. Innovative developments in Portugal, Argentina and the United States have re-imagined EM technologies as more personalized devices that can support victims rather than control offenders. These developments represent a re-conceptualization of the use of the technology beyond the neoliberal prism of rational choice theories and offender-oriented thinking that influenced first generation thinking about EM. This paper identifies the socio-political influences that helped conceptualize first generation thinking about EM as, firstly, a community sentence and latterly, as a technique of urban security. The paper reviews attempts to theorize the role and function of EM surveillance technologies within and beyond criminal justice and explores the contribution of victimological perspectives to the use of EM 2.0

Staging women in prisons: Clean Break Theatre Company’s dramaturgy of the cage

The article explores the limitations of the dramaturgies of the cell through a close reading of several key play texts commissioned by the UK’s leading arts in criminal justice organisation working with women, Clean Break. The apparently humanist positioning of women in prison as just like everyone else erases the specificity of women’s backstories. Conversely, by adhering to the constructions of female prisoners as holding binary positions of either ‘monsters’ or ‘victims’ of the system, plays can re-inscribe morally unitary approaches to women’s deviance and resistance. Many plays about women in prison hold a claim for resisting stereotypes and are in opposition to the injustice of criminal justice processes, and yet, in the realist mode, the monster/ victim position seems to be an inescapable binary