Coupled Ito equations of continuous quantum state measurement, and estimation

We discuss a non-linear stochastic master equation that governs the time-evolution of the estimated quantum state. Its differential evolution corresponds to the infinitesimal updates that depend on the time-continuous measurement of the true quantum state. The new stochastic master equation couples to the two standard stochastic differential equations of time-continuous quantum measurement. For the first time, we can prove that the calculated estimate almost always converges to the true state, also at low-efficiency measurements. We show that our single-state theory can be adapted to weak continuous ensemble measurements as well.Comment: 5 pages, RevTeX4. In version v2 some minor revisions and clarifications have been incorporated. Moreover, a new reference has been included. Accepted for publication in Journal of Physics A: Mathematical and Genera

Reflexive Cones

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the properties of their bases. This allows us to prove a characterization of reflexive cones in term of the absence of a subcone isomorphic to the positive cone of \ell_{1}. Moreover, the properties of some specific classes of reflexive cones are investigated. Namely, we consider the reflexive cones such that the intersection with the unit ball is norm compact, those generated by a Schauder basis and the reflexive cones regarded as ordering cones in a Banach spaces. Finally, it is worth to point out that a characterization of reflexive spaces and also of the Schur spaces by the properties of reflexive cones is given.Comment: 23 page

Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

Servicio SURAD, 2011 primer año de funcionamiento

1 copia .pdf del póster original, presentado en tamaño din A0 en las 4as Jornadas de Análisis de la Red de Bibliotecas del CSIC (Madrid. 26-27 abril, 2012). Más información de las Jornadas en: http://jornadas.urici.csic.es/IVjornadas/El servicio SURAD presenta los resultados del 2011, su primer año de actividad. SURAD es el servicio de localización y suministro de documentos científicos para la comunidad investigadora del CSIC, que atiende aquellas solicitudes que no pueden gestionar en primera instancia sus bibliotecas. SURAD se gestiona a través de la Unidad de Recursos de la Información Científica para la Investigación y integrado dentro del Plan 100% Digital del CSIC. Su objetivo es dar un servicio de acceso al documento a la comunidad científica del CSIC que carece de servicio de biblioteca presencial en su centro/instituto y actuar como servicio de último recurso de obtención de documentos para las bibliotecas de la Red, proporcionando los documentos que éstas no puedan obtener.Peer reviewe

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Energy levels in polarization superlattices: a comparison of continuum strain models

A theoretical model for the energy levels in polarization superlattices is presented. The model includes the effect of strain on the local polarization-induced electric fields and the subsequent effect on the energy levels. Two continuum strain models are contrasted. One is the standard strain model derived from Hooke's law that is typically used to calculate energy levels in polarization superlattices and quantum wells. The other is a fully-coupled strain model derived from the thermodynamic equation of state for piezoelectric materials. The latter is more complete and applicable to strongly piezoelectric materials where corrections to the standard model are significant. The underlying theory has been applied to AlGaN/GaN superlattices and quantum wells. It is found that the fully-coupled strain model yields very different electric fields from the standard model. The calculated intersubband transition energies are shifted by approximately 5 -- 19 meV, depending on the structure. Thus from a device standpoint, the effect of applying the fully-coupled model produces a very measurable shift in the peak wavelength. This result has implications for the design of AlGaN/GaN optical switches.Comment: Revtex

A Qualitative Study of an Integrated Maternity, Drugs and Social Care Service for Drug-using Women

Background: The care of drug-using pregnant women is a growing health and social care concern in many countries. A specialist clinic was established offering multidisciplinary care and advice to pregnant drug users in and around Aberdeen (UK) in 1997. The majority of women stabilise and reduce their drug use. By determining the needs and views of the women more appropriate services and prevention strategies may be developed. There has been little research conducted in this area and none in Scotland. Methods: This is a qualitative study that aimed to gain an understanding of the experiences of women drug users, seeking and receiving prenatal care and drug services from a specialist clinic. Twelve women participated in semi-structured one-to-one interviews. Results: The women preferred the multidisciplinary clinic (one-stop shop) to traditional prenatal care centred within General Practice. The relationships of the clients to the range of Clinic professionals and in hospital were explored as well as attitudes to Clinic care. The study participants attributed success in reducing their drug use to the combination of different aspects of care of the multi-agency clinic, especially the high level prenatal support. It is this arrangement of all aspects of care together that seem to produce better outcomes for mother and child than single care elements delivered separately. Some women reported that their pregnancy encouraged them to rapidly detoxify due to the guilt experienced. The most important aspects of the Clinic care were found to be non-judgemental attitude of staff, consistent staff, high level of support, reliable information and multi-agency integrated care. Conclusion: There is an impetus for women drug users to change lifestyle during pregnancy. The study highlighted a need for women to have access to reliable information on the effects of drugs on the baby. Further research is required to determine whether positive outcomes related to clinic attendance in the prenatal period are sustained in the postnatal period. Early referral to a specialist clinic is of benefit to the women, as they reported to receive more appropriate care, especially in relation to their drug use. A greater awareness of needs of the pregnant drug user could help the design of more effective prevention strategies

Magnetic Domains and Stripes in the Spin-Fermion Model for Cuprates

Monte Carlo simulations applied to the Spin-Fermion model for cuprates show the existence of antiferromagnetic spin domains and charge stripes upon doping. The stripes are partially filled, with a filling of approximately 1/2 hole per site, and they separate spin domains with a $\pi$ phase shift among them. The stripes observed run either along the x or y axes and they are separated by a large energy barrier. No special boundary conditions or external fields are needed to stabilize these structures at low temperatures. When magnetic incommensurate peaks are observed at momentum $\pi(1,1-\delta)$ and symmetrical points, charge incommensurate peaks appear at $(0,2 \delta)$ and symmetrical points, as experimentally observed. The strong charge fluctuations responsible for the formation of the stripes also induce a pseudogap in the density of states.Comment: Four pages with four figures embedded in tex