Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation

A parameterization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parameterization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under {\it local} unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parameterization.Comment: significantly rewritten and submitted for publicatio

Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some parameters, set up a metric, which induces a volume element, and perform the integration for the adequate range of the parameters; in most cases our manifolds will be either spheres or (twisted) products of spheres, or quotients of spheres (homogeneous spaces). Our results should be useful in several physical instances, as instanton calculations, propagators in curved spaces, sigma models, geometric scattering in homogeneous manifolds, density matrices for entangled states, etc. Some flag manifolds have also appeared recently as exceptional holonomy manifolds; the volumes of compact Einstein manifolds appear in String theory.Comment: 26 pages, no figures; updated addresses and bibliography. To be published in Rep. Math. Phy

The Frequency of Active and Quiescent Galaxies with Companions: Implications for the Feeding of the Nucleus

We analyze the idea that nuclear activity, either AGN or star formation, can be triggered by interactions, studying the percentage of active, HII and quiescent galaxies with companions. Our sample was selected from the Palomar survey, and avoids selection biases faced by previous studies. The comparison between the local galaxy density distributions showed that in most cases there is no statistically significant difference among galaxies of different activity types. The comparison of the percentage of galaxies with nearby companions showed that there is a higher percentage of LINERs, transition, and absorption line galaxies with companions than Seyferts and HII galaxies. However, we find that when we consider only galaxies of similar morphological types (ellipticals or spirals), there is no difference in the percentage of galaxies with companions among different activity types, indicating that the former result was due to the morphology-density effect. Also, only small differences are found when we consider galaxies with similar Halpha luminosities. The comparison between HII galaxies of different Halpha luminosities shows that there is a significantly higher percentage of galaxies with companions among the higher luminosity HII galaxies, indicating that interactions increase the amount of circumnuclear star formation, in agreement with previous results. The fact that we find that galaxies of different activity types have the same percentage of companions, suggests that interactions between galaxies is not a necessary condition to trigger the nuclear activity in AGNs. We compare our results with previous ones and discuss their implications. (abridged)Comment: 30 pages, including 6 figures and 3 tables. To appear in The Astronomical Journal, November issu

Multicolour Optical Imaging of IR-Warm Seyfert Galaxies. V. Morphologies and Interactions. Challenging the Orientation Model

This paper is the last in a series, investigating the optical properties of a sample of mid-IR Warm Seyfert galaxies and of a control sample of mid-IR cold galaxies. In the present paper we parametrize the morphologies and interaction properties of the host galaxies and combine these with the major conclusions in our previous papers. Our results confirm that nuclear activity is linked to galactic interactions. We suggest an alternative view for the simple orientation-obscuration model postulated for Seyfert types 1 and 2, that takes into account the time evolution of their environmental and morphological properties. Within this view, an evolutionary link between starburst-dominated and AGN-dominated IR emission is also suggested, to account for the observational discriminator (mid-IR excess) between our Warm and Cold samples.Comment: 24 pages, including 6 figures and 3 tables (figure 5 included as independent file), Submitted to Ap

Transvenous removal of pacing and implantable cardiac defibrillating leads using single sheath mechanical dilatation and multiple venous approaches: high success rate and safety in more than 2000 leads

Abstract: The aim of the present study was to describe a 10 years single-centre experience in pacing and defibrillating leads removal using an effective and safe modified mechanical dilatation technique. We developed a single mechanical dilating sheath extraction technique with multiple venous entry site approaches. We performed a venous entry site approach (VEA) in cases of exposed leads and an alternative transvenous femoral approach (TFA) combined with an internal transjugular approach (ITA) in the presence of very tight binding sites causing failure of VEA extraction or in cases of free-floating leads. We attempted to remove 2062 leads [1825 pacing and 237 implantable cardiac defibrillating (ICD) leads; 1989 exposed at the venous entry site and 73 free-floating] in 1193 consecutive patients. The VEA was effective in 1799 leads, the TFA in 28, and the ITA in 205; in the overall population, we completely removed 2032 leads (98.4%), partially removed 18 (0.9%), and failed to remove 12 leads (0.6%). Major complications were observed in eight patients (0.7%), causing three deaths (0.3%). Mechanical single sheath extraction technique with multiple venous entry site approaches is effective, safe, and with a good cost effective profile for pacing and ICD leads removal

Why are naturally ventilated office spaces not popular in New Zealand?

In this paper, we investigated the reason(s) why natural ventilation is not as popular as air-conditioned or mixed-mode ventilation systems in Green-rated office buildings in New Zealand. To achieve this, we had three objectives. Firstly, we reviewed the Green Star criteria for thermal comfort in office buildings to ascertain which ventilation system the NZ Green Star rating tool promotes. Secondly, we ascertained the perception of occupants in office buildings regarding thermal comfort. This was followed by an interview with building experts regarding factors that affect the use of natural ventilation in New Zealand offices. The findings showed that the NZ Green Star thermal comfort criteria encourage the use of mechanical ventilation over natural ventilation which results in designers opting for air conditioning systems in office designs. We observed that occupants of naturally ventilated spaces were least satisfied with the thermal comfort of their offices when compared with occupants of mixed-mode and air-conditioned offices. This study fulfils the need to encourage the use of natural ventilation in office environments by designers and building owners. Further study on other aspects of the indoor environment quality that is related to naturally ventilated systems such as lighting and noise is required in a bid to ascertain its viability in office environments

Tachyon Hair for Two-Dimensional Black Holes

Using a combination of analytical and numerical methods, we obtain a two-dimensional spacetime describing a black hole with tachyon hair. The physical ADM mass of the black hole is finite. The presence of tachyon hair increases the Hawking temperature.Comment: 17 pages, 4 figures (not included), DAMTP-R93-16, IUHET 261 (Sept. 1993

The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: i) when each oscillator is coupled to its own reservoir, and ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function for the off-diagonal peaks of the density matrix, which applies both to a common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation- and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix.Comment: 42 pages, 7 figures, new discussion added, typos adde