On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives

We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources or services from a set of agents. Ideally, the auctioneer would like to select a subset of the resources so as to maximize his valuation function, without exceeding a given budget. As the resources are owned by strategic agents however, our overall goal is to design mechanisms that are truthful, budget-feasible, and obtain a good approximation to the optimal value. Budget-feasibility creates additional challenges, making several approaches inapplicable in this setting. Previous results on budget-feasible mechanisms have considered mostly monotone valuation functions. In this work, we mainly focus on symmetric submodular valuations, a prominent class of non-monotone submodular functions that includes cut functions. We begin first with a purely algorithmic result, obtaining a $\frac{2e}{e-1}$-approximation for maximizing symmetric submodular functions under a budget constraint. We view this as a standalone result of independent interest, as it is the best known factor achieved by a deterministic algorithm. We then proceed to propose truthful, budget feasible mechanisms (both deterministic and randomized), paying particular attention on the Budgeted Max Cut problem. Our results significantly improve the known approximation ratios for these objectives, while establishing polynomial running time for cases where only exponential mechanisms were known. At the heart of our approach lies an appropriate combination of local search algorithms with results for monotone submodular valuations, applied to the derived local optima.Comment: A conference version appears in WINE 201

A Bayesian approach to quantifying the effects of mass poultry vaccination upon the spatial and temporal dynamics of H5N1 in Northern Vietnam.

Published versio

A hierarchical Bayesian model for understanding the spatiotemporal dynamics of the intestinal epithelium

Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions-uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales

Spatial risk profiling of Plasmodium falciparum parasitaemia in a high endemicity area in Côte d'Ivoire

Background. The objective of this study was to identify demographic, environmental and socioeconomic risk factors and spatial patterns of Plasmodium falciparum parasitaemia in a high endemicity area of Africa, and to specify how this information can facilitate improved malaria control at the district level. Methods. A questionnaire was administered to about 4,000 schoolchildren in 55 schools in western Ĉte d'Ivoire to determine children's socioeconomic status and their habit of sleeping under bed nets. Environmental data were obtained from satellite images, digitized ground maps and a second questionnaire addressed to school directors. Finger prick blood samples were collected and P. falciparum parasitaemia determined under a microscope using standardized, quality-controlled methods. Bayesian variogram models were utilized for spatial risk modelling and mapping of P. falciparum parasitaemia at non-sampled locations, assuming stationary and non-stationary underlying spatial dependence. Results. Two-thirds of the schoolchildren were infected with P. falciparum and the mean parasitaemia among infected children was 959 parasites/μl of blood. Age, socioeconomic status, not sleeping under a bed net, coverage rate with bed nets and environmental factors (e.g., normalized difference vegetation index, rainfall, land surface temperature and living in close proximity to standing water) were significantly associated with the risk of P. falciparum parasitaemia. After accounting for spatial correlation, age, bed net coverage, rainfall during the main malaria transmission season and distance to rivers remained significant covariates. Conclusion. It is argued that a massive increase in bed net coverage, particularly in villages in close proximity to rivers, in concert with other control measures, is necessary to bring malaria endemicity down to intermediate or low levels

Biophysical Factors Affecting the Distribution of Demersal Fish around the Head of a Submarine Canyon Off the Bonney Coast, South Australia

We sampled the demersal fish community of the Bonney Canyon, South Australia at depths (100–1,500 m) and locations that are poorly known. Seventy-eight species of demersal fish were obtained from 12 depth-stratified trawls along, and to either side, of the central canyon axis. Distributional patterns in species richness and biomass were highly correlated. Three fish assemblage groupings, characterised by small suites of species with narrow depth distributions, were identified on the shelf, upper slope and mid slope. The assemblage groupings were largely explained by depth (ρw = 0.78). Compared to the depth gradient, canyon-related effects are weak or occur at spatial or temporal scales not sampled in this study. A conceptual physical model displayed features consistent with the depth zonational patterns in fish, and also indicated that canyon upwelling can occur. The depth zonation of the fish assemblage was associated with the depth distribution of water masses in the area. Notably, the mid-slope community (1,000 m) coincided with a layer of Antarctic Intermediate Water, the upper slope community (500 m) resided within the core of the Flinders Current, and the shelf community was located in a well-mixed layer of surface water (<450 m depth)

A Bayesian hierarchical approach for spatial analysis of climate model bias in multi-model ensembles

Coupled atmosphere–ocean general circulation models are key tools to investigate climate dynamics and the climatic response to external forcings, to predict climate evolution and to generate future climate projections. Current general circulation models are, however, undisputedly affected by substantial systematic errors in their outputs compared to observations. The assessment of these so-called biases, both individually and collectively, is crucial for the models’ evaluation prior to their predictive use. We present a Bayesian hierarchical model for a unified assessment of spatially referenced climate model biases in a multi-model framework. A key feature of our approach is that the model quantifies an overall common bias that is obtained by synthesizing bias across the different climate models in the ensemble, further determining the contribution of each model to the overall bias. Moreover, we determine model-specific individual bias components by characterizing them as non-stationary spatial fields. The approach is illustrated based on the case of near-surface air temperature bias in the tropical Atlantic and bordering regions from a multi-model ensemble of historical simulations from the fifth phase of the Coupled Model Intercomparison Project. The results demonstrate the improved quantification of the bias and interpretative advantages allowed by the posterior distributions derived from the proposed Bayesian hierarchical framework, whose generality favors its broader application within climate model assessment