Aggregation of Votes with Multiple Positions on Each Issue

We consider the problem of aggregating votes cast by a society on a fixed set of issues, where each member of the society may vote for one of several positions on each issue, but the combination of votes on the various issues is restricted to a set of feasible voting patterns. We require the aggregation to be supportive, i.e. for every issue $j$ the corresponding component $f_j$ of every aggregator on every issue should satisfy $f_j(x_1, ,\ldots, x_n) \in \{x_1, ,\ldots, x_n\}$. We prove that, in such a set-up, non-dictatorial aggregation of votes in a society of some size is possible if and only if either non-dictatorial aggregation is possible in a society of only two members or a ternary aggregator exists that either on every issue $j$ is a majority operation, i.e. the corresponding component satisfies $f_j(x,x,y) = f_j(x,y,x) = f_j(y,x,x) =x, \forall x,y$, or on every issue is a minority operation, i.e. the corresponding component satisfies $f_j(x,x,y) = f_j(x,y,x) = f_j(y,x,x) =y, \forall x,y.$ We then introduce a notion of uniformly non-dictatorial aggregator, which is defined to be an aggregator that on every issue, and when restricted to an arbitrary two-element subset of the votes for that issue, differs from all projection functions. We first give a characterization of sets of feasible voting patterns that admit a uniformly non-dictatorial aggregator. Then making use of Bulatov's dichotomy theorem for conservative constraint satisfaction problems, we connect social choice theory with combinatorial complexity by proving that if a set of feasible voting patterns $X$ has a uniformly non-dictatorial aggregator of some arity then the multi-sorted conservative constraint satisfaction problem on $X$, in the sense introduced by Bulatov and Jeavons, with each issue representing a sort, is tractable; otherwise it is NP-complete

Biomechanical comparison of graft structures in anterior cruciate ligament reconstruction

PURPOSE: Double-bundle (DB) anterior cruciate ligament (ACL) reconstruction may offer kinematic restoration superior to anatomic single bundle (SB), but it remains technically challenging. The femoral attachment site has the most effect on ACL graft isometry, so a simplified three-socket (3S) construct which still uses two sockets to cover the femoral ACL attachment is attractive. It was hypothesised that ACL reconstruction using three- and four-socket techniques would more closely restore native knee kinematics compared to anatomic two-socket (SB) surgery. METHODS: Nine cadaveric knees were used to evaluate the kinematics of ACL-intact, ACL-deficient, anatomic SB, three-socket, and DB arthroscopic ACL reconstructions. Suspensory fixation was used, and grafts were tensioned to match the anterior draw of the intact knee at 20°. A six-degree-of-freedom robotic system measured knee laxity under 90 N anterior tibial force and rotational laxity under 5 N-m torque. Combined moments were applied to simulate the pivot-shift subluxation: 4 N-m internal rotation and 8 N-m valgus. RESULTS: Significant differences between reconstructions were not found during anterior tibial loading, apart from SB being more lax than DB at 60° flexion. All reconstructions produced comparable laxity to the intact state, apart from SB at 60°. Significant differences between reconstructions were not found at any flexion angle during tibial internal/external applied torques. Under combined loading, DB produced significantly less laxity than SB constructs apart from anterior tibial translation at 0° and internal rotation at 45°. 3S and DB were comparable to the native knee throughout. CONCLUSION: Although 3S restored laxities to a similar extent to DB, significant superiority over SB surgery was not observed. Although statistically significant differences were found between SB and DB surgery during anterior tibial and simulated pivot-shift loading, both remained similar to the native knee. The clinical relevance is that this study did not support an ACL graft construct more complex than an anatomic single bundle

Mixing and internal dynamics of droplets impacting and coalescing on a solid surface.

The coalescence and mixing of a sessile and an impacting liquid droplet on a solid surface are studied experimentally and numerically in terms of lateral separation and droplet speed. Two droplet generators are used to produce differently colored droplets. Two high-speed imaging systems are used to investigate the impact and coalescence of the droplets in color from a side view with a simultaneous gray-scale view from below. Millimeter-sized droplets were used with dynamical conditions, based on the Reynolds and Weber numbers, relevant to microfluidics and commercial inkjet printing. Experimental measurements of advancing and receding static contact angles are used to calibrate a contact angle hysteresis model within a lattice Boltzmann framework, which is shown to capture the observed dynamics qualitatively and the final droplet configuration quantitatively. Our results show that no detectable mixing occurs during impact and coalescence of similar-sized droplets, but when the sessile droplet is sufficiently larger than the impacting droplet vortex ring generation can be observed. Finally we show how a gradient of wettability on the substrate can potentially enhance mixing.This work was supported by the Engineering and Physical Sciences Research Council (Grant No. EP/H018913/, Innovation in industrial inkjet technology) and the KACST-Cambridge Research Centre.This is the accepted version of the original article published in Physical Review E and available online here: http://link.aps.org/doi/10.1103/PhysRevE.88.023023

Cavity formation on the surface of a body entering water with deceleration

The two-dimensional water entry of a rigid symmetric body with account for cavity formation on the body surface is studied. Initially the liquid is at rest and occupies the lower half plane. The rigid symmetric body touches the liquid free surface at a single point and then starts suddenly to penetrate the liquid vertically with a time-varying speed. We study the effect of the body deceleration on the pressure distribution in the flow region. It is shown that, in addition to the high pressures expected from the theory of impact, the pressure on the body surface can later decrease to sub-atmospheric levels. The creation of a cavity due to such low pressures is considered. The cavity starts at the lowest point of the body and spreads along the body surface forming a thin space between a new free surface and the body. Within the linearised hydrodynamic problem, the positions of the two turnover points at the periphery of the wetted area are determined by Wagner’s condition. The ends of the cavity’s free surface are modelled by the Brillouin–Villat condition. The pressure in the cavity is assumed to be a prescribed constant, which is a parameter of the model. The hydrodynamic problem is reduced to a system of integral and differential equations with respect to several functions of time. Results are presented for constant deceleration of two body shapes: a parabola and a wedge. The general formulation made also embraces conditions where the body is free to decelerate under the total fluid force. Contrasts are drawn between results from the present model and a simpler model in which the cavity formation is suppressed. It is shown that the expansion of the cavity can be significantly slower than the expansion of the corresponding zone of sub-atmospheric pressure in the simpler model. For forced motion and cavity pressure close to atmospheric, the cavity grows until almost complete detachment of the fluid from the body. In the problem of free motion of the body, cavitation with vapour pressure in the cavity is achievable only for extremely large impact velocities

Searching for O2_2 in the SMC:Constraints on Oxygen Chemistry at Low Metallicities

We present a 39 h integration with the Odin satellite on the ground-state 118.75 GHz line of O2 towards the region of strongest molecular emission in the Small Magellanic Cloud. Our 3sigma upper limit to the O2 integrated intensity of <0.049 K km/s in a 9'(160 pc) diameter beam corresponds to an upper limit on the O2/H2 abundance ratio of <1.3E-6. Although a factor of 20 above the best limit on the O2 abundance obtained for a Galactic source, our result has interesting implications for understanding oxygen chemistry at sub-solar metal abundances. We compare our abundance limit to a variety of astrochemical models and find that, at low metallicities, the low O2 abundance is most likely produced by the effects of photo-dissociation on molecular cloud structure. Freeze-out of molecules onto dust grains may also be consistent with the observed abundance limit, although such models have not yet been run at sub-solar initial metallicities.Comment: 4 pages, accepted to A&A Letter

Interplay of quantum and classical fluctuations near quantum critical points

For a system near a quantum critical point (QCP), above its lower critical dimension $d_L$, there is in general a critical line of second order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, $d_{eff}=d+z$ ($d$ is the Euclidean dimension of the system and $z$ the dynamic quantum critical exponent) is above its upper critical dimension $d_C$, there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation $\psi=\nu z$ between the shift exponent $\psi$ of the critical line and the crossover exponent $\nu z$, for $d+z>d_C$ by a \textit{dangerous irrelevant interaction}. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.Comment: 10 pages, 6 figures, to be published in Brazilian Journal of Physic

Who bullies whom at a garden feeder? Interspecific agonistic interactions of small passerines during a cold winter

Interspecific agonistic interactions are important selective factors for maintaining ecological niches of different species, but their outcome is difficult to predict a priori. Here, we examined the direction and intensity of interspecific interactions in an assemblage of small passerines at a garden feeder, focussing on three finch species of various body sizes. We found that large and mediumsized birds usually initiated and won agonistic interactions with smaller species. Also, the frequency of fights increased with decreasing differences in body size between the participants. Finally, the probability of engaging in a fight increased with the number of birds at the feeder

The helicase HAGE prevents interferon-a-induced PML expression in ABCB5+ malignant melanoma-initiating cells by promoting the expression of SOCS1

The tumour suppressor PML (promyelocytic leukaemia protein) regulates several cellular pathways involving cell growth, apoptosis, differentiation and senescence. PML also has an important role in the regulation of stem cell proliferation and differentiation. Here, we show the involvement of the helicase HAGE in the transcriptional repression of PML expression in ABCB5 + malignant melanoma-initiating cells (ABCB5 + MMICs), a population of cancer stem cells which are responsible for melanoma growth, progression and resistance to drug-based therapy. HAGE prevents PML gene expression by inhibiting the activation of the JAK-STAT (janus kinase-signal transducers and activators of transcription) pathway in a mechanism which implicates the suppressor of cytokine signalling 1 (SOCS1). Knockdown of HAGE led to a significant decrease in SOCS1 protein expression, activation of the JAK-STAT signalling cascade and a consequent increase of PML expression. To confirm that the reduction in SOCS1 expression was dependent on the HAGE helicase activity, we showed that SOCS1, effectively silenced by small interfering RNA, could be rescued by re-introduction of HAGE into cells lacking HAGE. Furthermore, we provide a mechanism by which HAGE promotes SOCS1 mRNA unwinding and protein expression in vitro

Virtual patients design and its effect on clinical reasoning and student experience : a protocol for a randomised factorial multi-centre study

Background Virtual Patients (VPs) are web-based representations of realistic clinical cases. They are proposed as being an optimal method for teaching clinical reasoning skills. International standards exist which define precisely what constitutes a VP. There are multiple design possibilities for VPs, however there is little formal evidence to support individual design features. The purpose of this trial is to explore the effect of two different potentially important design features on clinical reasoning skills and the student experience. These are the branching case pathways (present or absent) and structured clinical reasoning feedback (present or absent). Methods/Design This is a multi-centre randomised 2x2 factorial design study evaluating two independent variables of VP design, branching (present or absent), and structured clinical reasoning feedback (present or absent).The study will be carried out in medical student volunteers in one year group from three university medical schools in the United Kingdom, Warwick, Keele and Birmingham. There are four core musculoskeletal topics. Each case can be designed in four different ways, equating to 16 VPs required for the research. Students will be randomised to four groups, completing the four VP topics in the same order, but with each group exposed to a different VP design sequentially. All students will be exposed to the four designs. Primary outcomes are performance for each case design in a standardized fifteen item clinical reasoning assessment, integrated into each VP, which is identical for each topic. Additionally a 15-item self-reported evaluation is completed for each VP, based on a widely used EViP tool. Student patterns of use of the VPs will be recorded. In one centre, formative clinical and examination performance will be recorded, along with a self reported pre and post-intervention reasoning score, the DTI. Our power calculations indicate a sample size of 112 is required for both primary outcomes

Large emissions from floodplain trees close the Amazon methane budget

Wetlands are the largest global source of atmospheric methane (CH4), a potent greenhouse gas. However, methane emission inventories from the Amazon floodplain, the largest natural geographic source of CH4 in the tropics, consistently underestimate the atmospheric burden of CH4 determined via remote sensing and inversion modelling, pointing to a major gap in our understanding of the contribution of these ecosystems to CH4 emissions. Here we report CH4 fluxes from the stems of 2,357 individual Amazonian floodplain trees from 13 locations across the central Amazon basin. We find that escape of soil gas through wetland trees is the dominant source of regional CH4 emissions. Methane fluxes from Amazon tree stems were up to 200 times larger than emissions reported for temperate wet forests6 and tropical peat swamp forests, representing the largest non-ebullitive wetland fluxes observed. Emissions from trees had an average stable carbon isotope value (δ13C) of −66.2 ± 6.4 per mil, consistent with a soil biogenic origin. We estimate that floodplain trees emit 15.1 ± 1.8 to 21.2 ± 2.5 teragrams of CH4 a year, in addition to the 20.5 ± 5.3 teragrams a year emitted regionally from other sources. Furthermore, we provide a ‘top-down’ regional estimate of CH4 emissions of 42.7 ± 5.6 teragrams of CH4 a year for the Amazon basin, based on regular vertical lower-troposphere CH4 profiles covering the period 2010–2013. We find close agreement between our ‘top-down’ and combined ‘bottom-up’ estimates, indicating that large CH4 emissions from trees adapted to permanent or seasonal inundation can account for the emission source that is required to close the Amazon CH4 budget. Our findings demonstrate the importance of tree stem surfaces in mediating approximately half of all wetland CH4 emissions in the Amazon floodplain, a region that represents up to one-third of the global wetland CH4 source when trees are combined with other emission sources