Sufficient Conditions for Tuza's Conjecture on Packing and Covering Triangles

Given a simple graph $G=(V,E)$, a subset of $E$ is called a triangle cover if it intersects each triangle of $G$. Let $\nu_t(G)$ and $\tau_t(G)$ denote the maximum number of pairwise edge-disjoint triangles in $G$ and the minimum cardinality of a triangle cover of $G$, respectively. Tuza conjectured in 1981 that $\tau_t(G)/\nu_t(G)\le2$ holds for every graph $G$. In this paper, using a hypergraph approach, we design polynomial-time combinatorial algorithms for finding small triangle covers. These algorithms imply new sufficient conditions for Tuza's conjecture on covering and packing triangles. More precisely, suppose that the set $\mathscr T_G$ of triangles covers all edges in $G$. We show that a triangle cover of $G$ with cardinality at most $2\nu_t(G)$ can be found in polynomial time if one of the following conditions is satisfied: (i) $\nu_t(G)/|\mathscr T_G|\ge\frac13$, (ii) $\nu_t(G)/|E|\ge\frac14$, (iii) $|E|/|\mathscr T_G|\ge2$. Keywords: Triangle cover, Triangle packing, Linear 3-uniform hypergraphs, Combinatorial algorithm

Quantum noise and mixedness of a pumped dissipative non-linear oscillator

Evolutions of quantum noise, characterized by quadrature squeezing parameter and Fano factor, and of mixedness, quantified by quantum von Neumann and linear entropies, of a pumped dissipative non-linear oscillator are studied. The model can describe a signal mode interacting with a thermal reservoir in a parametrically pumped cavity with a Kerr non-linearity. It is discussed that the initial pure states, including coherent states, Fock states, and finite superpositions of coherent states evolve into the same steady mixed state as verified by the quantum relative entropy and the Bures metric. It is shown analytically and verified numerically that the steady state can be well approximated by a nonclassical Gaussian state exhibiting quadrature squeezing and sub-Poissonian statistics for the cold thermal reservoir. A rapid increase is found in the mixedness, especially for the initial Fock states and superpositions of coherent states, during a very short time interval, and then for longer evolution times a decrease in the mixedness to the same, for all the initial states, and relatively low value of the nonclassical Gaussian state.Comment: 10 pages, 12 figure

Frequency and risk factors for incident and redetected Chlamydia trachomatis infection in sexually active, young, multi-ethnic women: a community based cohort study.

OBJECTIVE: To investigate the frequency and risk factors for incident and redetected Chlamydia trachomatis infection in sexually active, young, multi-ethnic women in the community. DESIGN: Cohort study. SETTING: 20 London universities and Further Education colleges. PARTICIPANTS: 954 sexually experienced women, mean age 21.5 years (range 16-27), 26% from ethnic minorities, who were recruited to the Prevention of Pelvic Infection (POPI) chlamydia screening trial between 2004 and 2006, and returned repeat postal self-taken vaginal swabs 11-32 (median 16) months after recruitment. RESULTS: The estimated annual incidence of chlamydia infection among 907 women who tested negative at baseline was 3.4 per 100 person-years (95% CI 2.5 to 4.6 per 100 person-years), but 6.6 per 100 person-years (95% CI 4.5 to 9.3 per 100 person-years) in the 326 teenagers (<20 years). Predictors of incident chlamydia infection were age <20 years (relative risk (RR) 4.0, 95% CI 2.1 to 7.5), and (after adjusting for age) a new sexual partner during 12 months follow-up (RR 4.4, 95% CI 2.0 to 9.9), smoking (RR 2.2 95% CI 1.2 to 3.9), concurrent bacterial vaginosis (RR 2.0 95% CI 1.1 to 3.9) and high risk carcinogenic human papillomavirus (RR 2.2, 95% CI 1.1 to 4.3). Of 47 women positive for chlamydia at baseline, 12 (25.5%, 95% CI 13.9% to 40.3%) had redetected infection at a median of 16 months follow-up. Taking into account follow-up time (65 person-years), the annual redetection rate was 18.5 per 100 person-years (95% CI 9.9 to 30.0 per 100 person-years). CONCLUSIONS: One in four women with chlamydia infection at baseline retested positive, supporting recent recommendations to routinely retest chlamydia positives

Comparison Criteria for Argumentation Semantics

Argumentation reasoning is a way for agents to evaluate a situation. Given a framework made of conflicting arguments, a semantics allows to evaluate the acceptability of the arguments. It may happen that the semantics associated to the framework has to be changed. In order to perform the most suitable change, the current and a potential new semantics have to be compared. Notions of difference measures between semantics have already been proposed, and application cases where they have to be minimized when a change of semantics has to be performed, have been highlighted. This paper develops these notions, it proposes an additional kind of difference measure, and shows application cases where measures may have to be maximized, and combined

Spatial variation in sound frequency components across an urban area derived from mobile surveys

\ua9 2019 The Author(s). Continuous exposure to noise can lead to premature hearing loss, reduced cognitive performance, insomnia, stress, hypertension, cardiovascular diseases and stroke. Road noise affects the health of &gt;125 million people in the European Union and Member States are required to map major noise hotspots. These strategic noise maps are usually derived from traffic counts and propagation models because large- scale measurement of the acoustic environment using conventional methods is infeasible. In this study, the authors surveyed the entire city of Southampton, UK using a mobile survey technique, capturing spatial variations in street- level sound characteristics across multiple frequencies from all sound sources. Over 52,000 calibrated and georeferenced sound clips covering 11 Hz to 22.7 kHz are analysed here to investigate variations in sound frequency composition across urban space and then applied to two issues: the definition of naturalness in the acoustic environment; and perceptions of social inequity in sound exposure. Clusters of acoustic characteristics were identified and mapped using spectral clustering and principal components analysis based on octave bands, ecoacoustic indices and dBA. We found independent patterns in low, mid and high frequencies, and the ecoacoustic indices that related to land use. Ecoacoustic indices partially mapped onto greenspace, identifying naturalness, but not uniquely, probably because urban anthropogenic sounds occur at higher frequencies than in the natural areas where such indices were developed. There was some evidence of inequity in sound exposure according to social deprivation and ethnicity, and results differed according to frequency bands. The consequences of these findings and the benefits of city-wide sound surveys for urban planning are discussed

Surviving sepsis: going beyond the guidelines

The Surviving Sepsis Campaign is a global effort to improve the care of patients with severe sepsis and septic shock. The first Surviving Sepsis Campaign Guidelines were published in 2004 with an updated version published in 2008. These guidelines have been endorsed by many professional organizations throughout the world and come regarded as the standard of care for the management of patients with severe sepsis. Unfortunately, most of the recommendations of these guidelines are not evidence-based. Furthermore, the major components of the 6-hour bundle are based on a single-center study whose validity has been recently under increasing scrutiny. This paper reviews the validity of the Surviving Sepsis Campaign 6-hour bundle and provides a more evidence-based approach to the initial resuscitation of patients with severe sepsis

Actuation of Micro-Optomechanical Systems Via Cavity-Enhanced Optical Dipole Forces

We demonstrate a new type of optomechanical system employing a movable, micron-scale waveguide evanescently-coupled to a high-Q optical microresonator. Micron-scale displacements of the waveguide are observed for milliwatt(mW)-level optical input powers. Measurement of the spatial variation of the force on the waveguide indicates that it arises from a cavity-enhanced optical dipole force due to the stored optical field of the resonator. This force is used to realize an all-optical tunable filter operating with sub-mW control power. A theoretical model of the system shows the maximum achievable force to be independent of the intrinsic Q of the optical resonator and to scale inversely with the cavity mode volume, suggesting that such forces may become even more effective as devices approach the nanoscale.Comment: 4 pages, 5 figures. High resolution version available at (http://copilot.caltech.edu/publications/CEODF_hires.pdf). For associated movie, see (http://copilot.caltech.edu/research/optical_forces/index.htm

Management of the child born small for gestational age through to adulthood: A consensus statement of the international societies of pediatric endocrinology and the Growth Hormone Research Society

Objective: Low birth weight remains a major cause of morbidity and mortality in early infancy and childhood. It is associated with an increased risk of health problems later in life, particularly coronary heart disease and stroke. A meeting was convened to identify the key health issues facing a child born small for gestational age (SGA) and to propose management strategies. Participants: There were 42 participants chosen for their expertise in obstetrics, peri- and neonatal medicine, pediatrics, pediatric and adult endocrinology, epidemiology, and pharmacology. Evidence: Written materials were exchanged, reviewed, revised, and then made available to all. This formed the basis for discussions at the meeting. Where published data were not available or adequate, discussion was based on expert clinical opinions. Consensus Process: Each set of questions was considered by all and then discussed in plenary sessions with consensus and unresolved issues identified. The consensus statement was prepared in plenary sessions and then edited by the group chairs and shared with all participants. Conclusions: The diagnosis of SGA should be based on accurate anthropometry at birth including weight, length, and head circumference. We recommend early surveillance in a growth clinic for those without catch-up. Early neurodevelopment evaluation and interventions are warranted in at-risk children. Endocrine and metabolic disturbances in the SGA child are recognized but infrequent. For the 10% who lack catch-up, GH treatment can increase linear growth. Early intervention with GH for those with severe growth retardation (height SD score, < -2.5; age, 2-4 yr) should be considered at a dose of 35-70 mu g/kg center dot d. Long-term surveillance of treated patients is essential. The associations at a population level between low birth weight, including SGA, and coronary heart disease and stroke in later life are recognized, but there is inadequate evidence to recommend routine health surveillance of all adults born SGA outside of normal clinical practice

Moduli space coordinates and excited state g-functions

We consider the space of boundary conditions of Virasoro minimal models formed from the composition of a collection of flows generated by \phi_{1,3}. These have recently been shown to fall naturally into a sequence, each term having a coordinate on it in terms of a boundary parameter, but no global parameter has been proposed. Here we investigate the idea that the overlaps of particular bulk states with the boundary states give natural coordinates on the moduli space of boundary conditions. We find formulae for these overlaps using the known thermodynamic Bethe Ansatz descriptions of the ground and first excited state on the cylinder and show that they give a global coordinate on the space of boundary conditions, showing it is smooth and compact as expected.Comment: 10 pages, 4 figure

First experimental results of very high accuracy centroiding measurements for the neat astrometric mission

NEAT is an astrometric mission proposed to ESA with the objectives of detecting Earth-like exoplanets in the habitable zone of nearby solar-type stars. NEAT requires the capability to measure stellar centroids at the precision of 5e-6 pixel. Current state-of-the-art methods for centroid estimation have reached a precision of about 2e-5 pixel at two times Nyquist sampling, this was shown at the JPL by the VESTA experiment. A metrology system was used to calibrate intra and inter pixel quantum efficiency variations in order to correct pixelation errors. The European part of the NEAT consortium is building a testbed in vacuum in order to achieve 5e-6 pixel precision for the centroid estimation. The goal is to provide a proof of concept for the precision requirement of the NEAT spacecraft. In this paper we present the metrology and the pseudo stellar sources sub-systems, we present a performance model and an error budget of the experiment and we report the present status of the demonstration. Finally we also present our first results: the experiment had its first light in July 2013 and a first set of data was taken in air. The analysis of this first set of data showed that we can already measure the pixel positions with an accuracy of about 1e-4 pixel.Comment: SPIE conference proceeding