Single-Photon Observables and Preparation Uncertainty Relations

We propose a procedure for defining all single-photon observables in terms of Positive-Operator Valued Measures (POVMs), in particular spin and position. We identify the suppression of $0$-helicity photon states as a projection from an extended Hilbert space onto the photon Hilbert space. We show that all single-photon observables are in general described by POVMs, obtained by applying this projection to opportune Projection-Valued Measures (PVMs), defined on the extended Hilbert space. The POVMs associated to momentum and helicity reduce to PVMs, unlike those associated to position and spin, this fact reflecting the intrinsic unsharpness of these observables. We finally extensively study the preparation uncertainty relations for position and momentum and the probability distribution of spin, exploring single photon Gaussian states for several choices of spin and polarization.Comment: 25 pages (7 Figures); revised and extended version; in submissio

The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Market-based Instruments for Environmental Policymaking in Latin America and the Caribbean: Lessons from Eleven Countries

This report is a summary of country studies in Latin America and the Caribbean, addressing the use of market-based instruments (MBIs) and command-and-control (CAC) measures for environmental management in the region. Even though MBIs can significantly add efficiency to existing CAC mechanisms, the scope of MBIs should match the countries institutional capacity to implement them. Gradual and flexible reforms are likely to succeed within the current regional context of continued institutional changes. A key function of MBIs is usually revenue collection, though it does not necessarily lead to successful environmental management. The study suggests that revenues should be channeled to local authorities for an effective MBI's implementation. The report also critiques the regular practice of international donor agencies in recommending the solutions suitable for developed countries, without considering the institutional conditions in developing countries. Further, the study explores both the successes and difficulties experienced in the region regarding regulations, macro-policies, and MBIs; the institutional frameworks of the countries under review; and, the issues considered in the design of MBIs, in order to promote a beneficial dialogue among them

A Higher-order Maximum Principle for Impulsive Optimal Control Problems

We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to $u$. This lack of coercivity gives the problem an {\it impulsive} character, meaning that minimizing sequences of trajectories happen to converge towards discontinuous paths. As is known, a distributional approach does not make sense in such a nonlinear setting, where, instead, a suitable embedding in the graph-space is needed. We provide higher order necessary optimality conditions for properly defined impulsive minima, in the form of equalities and inequalities involving iterated Lie brackets of the dynamical vector fields. These conditions are derived under very weak regularity assumptions and without any constant rank conditions

Necessary conditions involving Lie brackets for impulsive optimal control problems

We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are unbounded and the absence of coercivity assumptions makes big speeds quite likely, minimizing sequences happen to converge toward "impulsive", namely discontinuous, trajectories. As is known, a distributional approach does not make sense in such a nonlinear setting, where instead a suitable embedding in the graph space is needed. We will illustrate how the chance of using impulse perturbations makes it possible to derive a Higher Order Maximum Principle which includes both the usual needle variations (in space-time) and conditions involving iterated Lie brackets. An example, where a third order necessary condition rules out the optimality of a given extremal, concludes the paper.Comment: Conference pape

Collaborative semantic web browsing with Magpie

Web browsing is often a collaborative activity. Users involved in a joint information gathering exercise will wish to share knowledge about the web pages visited and the contents found. Magpie is a suite of tools supporting the interpretation of web pages and semantically enriched web browsing. By automatically associating an ontology-based semantic layer to web resources, Magpie allows relevant services to be invoked as well as remotely triggered within a standard web browser. In this paper we describe how Magpie trigger services can provide semantic support to collaborative browsing activities

Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344

Fast variability as a tracer of accretion regimes in black hole transients

We present the rms-intensity diagram for black hole transients. Using observations taken with the Rossi X-ray timing explorer we study the relation between the root mean square (rms) amplitude of the variability and the net count-rate during the 2002, 2004 and 2007 outbursts of the black hole X-ray binary GX 339-4. We find that the rms-flux relation previously observed during the hard state in X-ray binaries does not hold for the other states, when different relations apply. These relations can be used as a good tracer of the different accretion regimes. We identify the hard, soft and intermediate states in the rms-intensity diagram. Transitions between the different states are seen to produce marked changes in the rms-flux relation. We find that one single component is required to explain the ~ 40 per cent variability observed at low count rates, whereas no or very low variability is associated to the accretion-disc thermal component.Comment: Accepted for publication in MNRAS. 6 pages, 4 figure

Transport properties of armchair graphene nanoribbon junctions between graphene electrodes

The transmission properties of armchair graphene nanoribbon junctions between graphene electrodes are investigated by means of first-principles quantum transport calculations. First the dependence of the transmission function on the size of the nanoribbon has been studied. Two regimes are highlighted: for small applied bias transport takes place via tunneling and the length of the ribbon is the key parameter that determines the junction conductance; at higher applied bias resonant transport through HOMO and LUMO starts to play a more determinant role, and the transport properties depend on the details of the geometry (width and length) of the carbon nanoribbon. In the case of the thinnest ribbon it has been verified that a tilted geometry of the central phenyl ring is the most stable configuration. As a consequence of this rotation the conductance decreases due to the misalignment of the $pi$ orbitals between the phenyl ring and the remaining part of the junction. All the computed transmission functions have shown a negligible dependence on different saturations and reconstructions of the edges of the graphene leads, suggesting a general validity of the reported results