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We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of e/(e-1), and provide a 4e/(e-1)-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm. 

Abstract A 6.5-month, convection-permitting simulation is conducted over Argentina covering the Remote Sensing of Electrification, Lightning, And Mesoscale/Microscale Processes with Adaptive Ground Observations and Clouds, Aerosols, and Complex Terrain Interactions (RELAMPAGO-CACTI) field campaign and is compared with observations to evaluate mesoscale convective system (MCS) growth prediction. Observed and simulated MCSs are consistently identified, tracked, and separated into growth, mature, and decay stages using top-of-the-atmosphere infrared brightness temperature and surface rainfall. Simulated MCS number, lifetime, seasonal and diurnal cycles, and various cloud-shield characteristics including growth rate are similar to those observed. However, the simulation produces smaller rainfall areas, greater proportions of heavy rainfall, and faster system propagations. Rainfall area is significantly underestimated for long-lived MCSs but not for shorter-lived MCSs, and rain rates are always overestimated. These differences result from a combination of model and satellite retrieval biases, in which simulated MCS rain rates are shifted from light to heavy, while satellite-retrieved rainfall is too frequent relative to rain gauge estimates. However, the simulation reproduces satellite-retrieved MCS cloud-shield evolution well, supporting its usage to examine environmental controls on MCS growth. MCS initiation locations are associated with removal of convective inhibition more than maximized low-level moisture convergence or instability. Rapid growth is associated with a stronger upper-level jet (ULJ) and a deeper northwestern Argentinean low that causes a stronger northerly low-level jet (LLJ), increasing heat and moisture fluxes, low-level vertical wind shear, baroclinicity, and instability. Sustained growth corresponds to similar LLJ, baroclinicity, and instability conditions but is less sensitive to the ULJ, large-scale vertical motion, or low-level shear. Growth sustenance controls MCS maximum extent more than growth rate. 

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.