The Core of the Participatory Budgeting Problem

In participatory budgeting, communities collectively decide on the allocation of public tax dollars for local public projects. In this work, we consider the question of fairly aggregating the preferences of community members to determine an allocation of funds to projects. This problem is different from standard fair resource allocation because of public goods: The allocated goods benefit all users simultaneously. Fairness is crucial in participatory decision making, since generating equitable outcomes is an important goal of these processes. We argue that the classic game theoretic notion of core captures fairness in the setting. To compute the core, we first develop a novel characterization of a public goods market equilibrium called the Lindahl equilibrium, which is always a core solution. We then provide the first (to our knowledge) polynomial time algorithm for computing such an equilibrium for a broad set of utility functions; our algorithm also generalizes (in a non-trivial way) the well-known concept of proportional fairness. We use our theoretical insights to perform experiments on real participatory budgeting voting data. We empirically show that the core can be efficiently computed for utility functions that naturally model our practical setting, and examine the relation of the core with the familiar welfare objective. Finally, we address concerns of incentives and mechanism design by developing a randomized approximately dominant-strategy truthful mechanism building on the exponential mechanism from differential privacy

On the type Ia supernovae 2007on and 2011iv: Evidence for Chandrasekhar-mass explosions at the faint end of the luminosity-width relationship

Radiative transfer models of two transitional type Ia supernovae (SNe Ia) have been produced using the abundance stratification technique. These two objects - designated SN 2007on and SN 2011iv - both exploded in the same galaxy, NGC1404, which allows for a direct comparison. SN 2007on synthesized 0.25M⊙of56Ni and was less luminous than SN 2011iv, which produced 0.31M⊙of56Ni. SN2007on had a lower central density (ρc) and higher explosion energy (Ekin~1.3 ± 0.3 × 1051erg) than SN 2011iv, and it produced less nuclear statistical equilibrium (NSE) elements (0.06M⊙). Whereas, SN2011iv had a larger ρc, which increased the electron capture rate in the lowest velocity regions, and produced 0.35M⊙of stable NSE elements. SN 2011iv had an explosion energy of ~Ekin~0.9 ± 0.2 × 1051erg. Both objects had an ejecta mass consistent with the Chandrasekhar mass (Ch-mass), and their observational properties are well described by predictions from delayed-detonation explosion models. Within this framework, comparison to the sub-luminous SN 1986G indicates SN 2011iv and SN 1986G have different transition densities (ρtr) but similar ρc. Whereas SN 1986G and SN 2007on had a similar ρtrbut different ρc. Finally, we examine the colour-stretch parameter sBVversus Lmaxrelation and determine that the bulk of SNe Ia (including the sub-luminous ones) are consistent with Ch-mass delayed-detonation explosions, where the main parameter driving the diversity is ρtr. We also find ρcto be driving the second-order scatter observed at the faint end of the luminosity-width relationship. © 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society

Strong Ultraviolet Pulse From a Newborn Type Ia Supernova

Type Ia supernovae are destructive explosions of carbon oxygen white dwarfs. Although they are used empirically to measure cosmological distances, the nature of their progenitors remains mysterious, One of the leading progenitor models, called the single degenerate channel, hypothesizes that a white dwarf accretes matter from a companion star and the resulting increase in its central pressure and temperature ignites thermonuclear explosion. Here we report observations of strong but declining ultraviolet emission from a Type Ia supernova within four days of its explosion. This emission is consistent with theoretical expectations of collision between material ejected by the supernova and a companion star, and therefore provides evidence that some Type Ia supernovae arise from the single degenerate channel.Comment: Accepted for publication on the 21 May 2015 issue of Natur

Supernova 2007bi as a pair-instability explosion

Stars with initial masses 10 M_{solar} < M_{initial} < 100 M_{solar} fuse progressively heavier elements in their centres, up to inert iron. The core then gravitationally collapses to a neutron star or a black hole, leading to an explosion -- an iron-core-collapse supernova (SN). In contrast, extremely massive stars (M_{initial} > 140 M_{solar}), if such exist, have oxygen cores which exceed M_{core} = 50 M_{solar}. There, high temperatures are reached at relatively low densities. Conversion of energetic, pressure-supporting photons into electron-positron pairs occurs prior to oxygen ignition, and leads to a violent contraction that triggers a catastrophic nuclear explosion. Tremendous energies (>~ 10^{52} erg) are released, completely unbinding the star in a pair-instability SN (PISN), with no compact remnant. Transitional objects with 100 M_{solar} < M_{initial} < 140 M_{solar}, which end up as iron-core-collapse supernovae following violent mass ejections, perhaps due to short instances of the pair instability, may have been identified. However, genuine PISNe, perhaps common in the early Universe, have not been observed to date. Here, we present our discovery of SN 2007bi, a luminous, slowly evolving supernova located within a dwarf galaxy (~1% the size of the Milky Way). We measure the exploding core mass to be likely ~100 M_{solar}, in which case theory unambiguously predicts a PISN outcome. We show that >3 M_{solar} of radioactive 56Ni were synthesized, and that our observations are well fit by PISN models. A PISN explosion in the local Universe indicates that nearby dwarf galaxies probably host extremely massive stars, above the apparent Galactic limit, perhaps resulting from star formation processes similar to those that created the first stars in the Universe.Comment: Accepted version of the paper appearing in Nature, 462, 624 (2009), including all supplementary informatio

Student responses to the introduction of case-based learning and practical activities into a theoretical obstetrics and gynaecology teaching programme

BACKGROUND: The fourth-year Obstetrics and Gynaecology course at our institution had previously been taught using theory classes alone. A new teaching model was introduced to provide a better link with professional practice. We wished to evaluate the impact of the introduction of case discussions and other practical activities upon students' perceptions of the learning process. METHODS: Small-group discussions of cases and practical activities were introduced for the teaching of a fourth-year class in 2003 (Group II; 113 students). Comparisons were made with the fourth-year class of 2002 (Group I; 108 students), from before the new programme was introduced. Students were asked to rate their satisfaction with various elements of the teaching programme. Statistical differences in their ratings were analysed using the chi-square and Bonferroni tests. RESULTS: Group II gave higher ratings to the clarity of theory classes and lecturers' teaching abilities (p < 0.05) and lecturers' punctuality (p < 0.001) than did Group I. Group II had greater belief that the knowledge assessment tests were useful (p < 0.001) and that their understanding of the subject was good (p < 0.001) than did Group I. Group II gave a higher overall rating to the course (p < 0.05) than did Group I. However, there was no difference in the groups' assessments of the use made of the timetabled hours available for the subject or lecturers' concern for students' learning. CONCLUSIONS: Students were very receptive to the new teaching model

Potential role of differential medication use in explaining excess risk of cardiovascular events and death associated with chronic kidney disease: A cohort study

<p>Abstract</p> <p>Background</p> <p>Patients with chronic kidney disease (CKD) are less likely to receive cardiovascular medications. It is unclear whether differential cardiovascular drug use explains, in part, the excess risk of cardiovascular events and death in patients with CKD and coronary heart disease (CHD).</p> <p>Methods</p> <p>The ADVANCE Study enrolled patients with new onset CHD (2001-2003) who did (N = 159) or did not have (N = 1088) CKD at entry. The MDRD equation was used to estimate glomerular filtration rate (eGFR) using calibrated serum creatinine measurements. Patient characteristics, medication use, cardiovascular events and death were ascertained from self-report and health plan electronic databases through December 2008.</p> <p>Results</p> <p>Post-CHD event ACE inhibitor use was lower (medication possession ratio 0.50 vs. 0.58, P = 0.03) and calcium channel blocker use higher (0.47 vs. 0.38, P = 0.06) in CKD vs. non-CKD patients, respectively. Incidence of cardiovascular events and death was higher in CKD vs. non-CKD patients (13.9 vs. 11.5 per 100 person-years, P < 0.001, respectively). After adjustment for patient characteristics, the rate of cardiovascular events and death was increased for eGFR 45-59 ml/min/1.73 m²(hazard ratio [HR] 1.47, 95% CI: 1.10 to 2.02) and eGFR < 45 ml/min/1.73 m²(HR 1.58, 95% CI: 1.00 to 2.50). After further adjustment for statins, β-blocker, calcium channel blocker, ACE inhibitor/ARB use, the association was no longer significant for eGFR 45-59 ml/min/1.73 m²(HR 0.82, 95% CI: 0.25 to 2.66) or for eGFR < 45 ml/min/1.73 m²(HR 1.19, 95% CI: 0.25 to 5.58).</p> <p>Conclusions</p> <p>In adults with CHD, differential use of cardiovascular medications may contribute to the higher risk of cardiovascular events and death in patients with CKD.</p

Observational and Physical Classification of Supernovae

This chapter describes the current classification scheme of supernovae (SNe). This scheme has evolved over many decades and now includes numerous SN Types and sub-types. Many of these are universally recognized, while there are controversies regarding the definitions, membership and even the names of some sub-classes; we will try to review here the commonly-used nomenclature, noting the main variants when possible. SN Types are defined according to observational properties; mostly visible-light spectra near maximum light, as well as according to their photometric properties. However, a long-term goal of SN classification is to associate observationally-defined classes with specific physical explosive phenomena. We show here that this aspiration is now finally coming to fruition, and we establish the SN classification scheme upon direct observational evidence connecting SN groups with specific progenitor stars. Observationally, the broad class of Type II SNe contains objects showing strong spectroscopic signatures of hydrogen, while objects lacking such signatures are of Type I, which is further divided to numerous subclasses. Recently a class of super-luminous SNe (SLSNe, typically 10 times more luminous than standard events) has been identified, and it is discussed. We end this chapter by briefly describing a proposed alternative classification scheme that is inspired by the stellar classification system. This system presents our emerging physical understanding of SN explosions, while clearly separating robust observational properties from physical inferences that can be debated. This new system is quantitative, and naturally deals with events distributed along a continuum, rather than being strictly divided into discrete classes. Thus, it may be more suitable to the coming era where SN numbers will quickly expand from a few thousands to millions of events.Comment: Extended final draft of a chapter in the "SN Handbook". Comments most welcom

An optical supernova associated with the X-ray flash XRF 060218

Long-duration gamma-ray bursts (GRBs) are associated with type Ic supernovae that are more luminous than average and that eject material at very high velocities. Less-luminous supernovae were not hitherto known to be associated with GRBs, and therefore GRB-supernovae were thought to be rare events. Whether X-ray flashes - analogues of GRBs, but with lower luminosities and fewer gamma-rays - can also be associated with supernovae, and whether they are intrinsically 'weak' events or typical GRBs viewed off the axis of the burst, is unclear. Here we report the optical discovery and follow-up observations of the type Ic supernova SN 2006aj associated with X-ray flash XRF 060218. Supernova 2006aj is intrinsically less luminous than the GRB-supernovae, but more luminous than many supernovae not accompanied by a GRB. The ejecta velocities derived from our spectra are intermediate between these two groups, which is consistent with the weakness of both the GRB output and the supernova radio flux. Our data, combined with radio and X-ray observations, suggest that XRF 060218 is an intrinsically weak and soft event, rather than a classical GRB observed off-axis. This extends the GRB-supernova connection to X-ray flashes and fainter supernovae, implying a common origin. Events such as XRF 060218 are probably more numerous than GRB-supernovae.Comment: Final published versio

A non-spherical core in the explosion of supernova SN 2004dj

An important and perhaps critical clue to the mechanism driving the explosion of massive stars as supernovae is provided by the accumulating evidence for asymmetry in the explosion. Indirect evidence comes from high pulsar velocities, associations of supernovae with long-soft gamma-ray bursts, and asymmetries in late-time emission-line profiles. Spectropolarimetry provides a direct probe of young supernova geometry, with higher polarization generally indicating a greater departure from spherical symmetry. Large polarizations have been measured for 'stripped-envelope' (that is, type Ic) supernovae, which confirms their non-spherical morphology; but the explosions of massive stars with intact hydrogen envelopes (type II-P supernovae) have shown only weak polarizations at the early times observed. Here we report multi-epoch spectropolarimetry of a classic type II-P supernova that reveals the abrupt appearance of significant polarization when the inner core is first exposed in the thinning ejecta (~90 days after explosion). We infer a departure from spherical symmetry of at least 30 per cent for the inner ejecta. Combined with earlier results, this suggests that a strongly non-spherical explosion may be a generic feature of core-collapse supernovae of all types, where the asphericity in type II-P supernovae is cloaked at early times by the massive, opaque, hydrogen envelope.Comment: Accepted for publication by Nature (results embargoed until 23 March 2006); 14 pages, 2 figure