The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions— -approximations and -nets—that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration. An example prob...

We present improved distributed algorithms for variants of the triangle finding problem in model. show that detection, counting, and enumeration can be solved $\tilde{O}(n^{1/3})$?> rounds using expander decompositions . This matches lower bound $\tilde{\Omega }(n^{1/3})$?> by Izumi Le Gall [PODC’17] Pandurangan, Robinson, Scquizzato [SPAA’18], which holds even {CONG...

A population of cells that express mast cell markers, including the membrane protein p161, but that lack expression of the high affinity IgE receptor, Fc epsilon RI, can be routinely grown from bone marrow. Ionomycin, but not IgE immune complexes, causes these cells to release serotonin and to express IL-3 and IL-13 mRNA, consistent with their being FC epsilon RI-deficient mast cells. These p16...

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is ac...

Protein kinase C (PKC) plays a prominent role in immune signaling, and the paradigms for isoform selective signaling are beginning to be elucidated. Real-time microscopy was combined with molecular and biochemical approaches to demonstrate a role for PKC- epsilon in Fc gamma receptor (Fc gammaR)-dependent phagocytosis. RAW 264.7 macrophages were transfected with GFP-conjugated PKC isoforms, and...

We consider the following perturbed critical Dirichlet problem involving Hardy-Schr\"odinger operator on a smooth bounded domain $\Omega \subset \mathbb{R}^N$, $N\geq 3$, with $0 \in \Omega$: $$ \left\{ \begin{array}{ll}-\Delta u-\gamma \frac{u}{|x|^2}-\epsilon u=|u|^{\frac{4}{N-2}}u &\hbox{in }\Omega u=0 & \hbox{on }\partial \Omega, \end{array}\right. when $\epsilon>0$ is small and $\gamma< {(...

Using computational fluid dynamics (CFD) techniques to model buoyancy-driven airflows has always proved challenging. This work investigates CFD modelling of buoyancy-driven natural ventilation flows in a single-storey space connected to an atrium. The atrium is taller than the ventilated space and when warmed by internal heat gains producing a column of warm air in the atrium and connect space ...