We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is...

In [13], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x1, . . . , x4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x1, x2, x3], where WLP always holds [16]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connected to t...

Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, including the areas of lattice-ordered groups, ideal lattices of rings, linear logic and multi-valued logic. Our exposition aims to cover...

In the last few years, cryptographic multilinear maps have proved their tremendous potential as building blocks for new constructions, in particular the first viable approach to general program obfuscation. After the first candidate construction by Garg, Gentry and Halevi (GGH) based on ideal lattices, a second construction over the integers was described by Coron, Lepoint and Tibouchi (CLT). H...

OBJECTIVES We develop and test a conceptual model of factors influencing women's ideal family size (IFS) in a natural fertility population, the Tsimane of Bolivia. The model posits affects of socioecology, reproductive history, maternal condition, and men's IFS. We test three hypotheses for why women may exceed their IFS despite experiencing socioeconomic development: (H(1) ) limited autonomy; ...

This essay shows that a moral sense or moral sentiments alone cannot identify appropriate morals. To this end, the essay analyzes three defenses of Francis Hutcheson’s, David Hume’s, and Adam Smith’s moral sense theories against the relativism charge that a moral sense or moral sentiments vary across people, societies, cultures, or times. The first defense is the claim that there is a universal...

Politicians and citizens increasingly engage in political conversations on social media outlets such as Twitter. In this paper I show that the structure of the social networks in which they are embedded can be a source of information about their ideological positions. Under the assumption that social networks are homophilic, I develop a Bayesian Spatial Following model that considers ideology a...

We introduce a multidimensional item response theory (IRT) model for binary data based on a proximity response mechanism. Under the model, a respondent at the mode of the item response function (IRF) endorses the item with probability one. The mode of the IRF is the ideal point, or in the multidimensional case, an ideal hyperplane. The model yields closed form expressions for the cell probabili...