We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initial quadrilateral or an initial hexahedral scaffold conforming to individual particles. The scaffolds are subsequently refined via applications of recursive subdivision (splitting and averaging rules). Our choice of averaging rules yield a particle conforming quadrilateral/hexahedral mesh, of good quality, along with being smooth and differentiable in the limit. Extensions of the basic scheme to dynamic re-meshing in the case of addition, deletion, and moving particles are also discussed. Motivating applications of the use of these static and dynamic meshes for particle systems include the mechanics of epoxy/glass composite materials, bio-molecular force field calculations, and gas hydrodynamics simulations in cosmology.

It is widely known among photographers that photographing a room with a wide-angle lens exaggerates the size of the room; nevertheless, such images are commonly found on hotel-reservation web sites. The present paper points out that the size exaggeration is a kind of optical illusion caused by an inappropriate viewpoint from which the image is seen, and presents a method we developed for removing the illusion and thus recovering the true appearance of the room. This method requires only a single image together with the lens center at which the image is taken. From this information, we can generate images that would be obtained if we stand at the same point as the camera and pan around the original scene, changing the view direction. The validity of the method is shown by examples. Possible applications to size-exaggerated images posted on web sites are also discussed.

A deterministic model is designed and used to analyze the transmission dynamics and the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antiviral both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally asymptotically stable under a condition involving the threshold quantity-reproduction number . The disease persists uniformly if and the model has a unique endemic equilibrium under certain condition. The model undergoes backward bifurcation if the antiviral drugs are completely efficient. Uncertainty and sensitivity analysis is presented to identify and study the impact of critical model parameters on the reproduction number. A time dependent optimal treatment strategy is designed using Pontryagin's maximum principle to minimize the treatment cost and the infected population. Finally the reproduction number is estimated for the influenza outbreak and model provides a reasonable fit to the observed swine (H1N1) pandemic data in Manitoba, Canada, in 2009.

Lattice enumeration is a widely used framework for investigating the computational properties of lattices. Its tree-based algorithm (Kannan in: STOC. ACM, New York, pp 193-206, 1983; Fincke and Pohst in J Math Comput 44(170):463-471, 1985) to find vectors which meet specific conditions is a fundamental subroutine in various applications. However, its time complexity is typically super-exponential in the lattice rank, which motivated Schnorr et al. in the 1990s to find a trade-off between the time complexity and the success probability of finding a solution. This effort was revisited by Gama et al. (EUROCRYPT 2010. Lecture notes in computer science. Springer, vol 6110, pp 257-278, 2010) and led to the extreme pruning strategy, which offers exponential speedups. They proposed an efficient algorithm to output a pruning strategy and a predicted cost for any given success probability. In this paper, we present a practical situation in which the actual cost of pruned enumeration is significantly larger than the predicted cost, which precisely happens when the Gaussian heuristic fails: the number of lattice points in some cylinder intersection is much bigger than the ratio between the intersection volume and the lattice co-volume. This phenomenon occurs when pruning parameters are set for a very small success probability. The likely source of this occurrence is the confinement of the searching region to a subspace. To address this, we propose a modification to the cost prediction and an update to the discussion of the cost lower bound (Aono et al. in Advances in Cryptology-CRYPTO 2018. Springer, Cham, pp 608-637, 2018). The revised lower bounds are approximately 20-30 times larger than the previous ones in cryptographically used settings.