We study unsaturated poroelasticity, i.e. , coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot’s well-known quasi-static consolidation model. The elliptic-parabolic system partial differential equations is simplified version the general model for multi-phase flow deformable obtained under similar assumptions as usually considere...

There is a long history of stories about events that threaten the end world or life after major catastrophe. The Naxi Annals Creation and Mesopotamian Gilgamesh Epic tell floods all but on Earth. H.G. Well’s 1897 story, War Worlds, Martians invading Earth, who themselves are killed by terrestrial epidemic. 1954 Japanese film, ゴジラ (Godzilla), marine reptile mutated nuclear radiation attacks huma...

We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a mul-tiplicative constant. Furthermore, we g...

This paper presents an application of voting geometry to individual decision making. We demonstrate that a number of decision anomalies can arise as a natural consequence of the aggregation of preferences of different neural systems. We present a proof of existence of a set of voting procedures that can account for the attraction effect, the similarity effect and the compromise effect, and prov...

THIS SUPPLEMENTAL MATERIAL contains the proofs of all the lemmas that do not appear in the printed Appendix to the paper. It also contains the statements of all these lemmas and details of the intervening arguments in the proofs of the propositions. These arguments appeared in the printed Appendix. It also contains a proof of existence for a more general model that implies Proposition 3(ii). Th...