Let G = (V,E) be a graph and r : V → Z+. An r-detachment of G is a graph H obtained by ‘splitting’ each vertex v ∈ V into r(v) vertices, called the pieces of v in H. Every edge uv ∈ E corresponds to an edge of H connecting some piece of u to some piece of v. An r-degree specification for G is a function f on V , such that, for each vertex v ∈ V , f(v) is a partition of d(v) into r(v) positive i...

J. Benhabib and R. E. A. Farmer (1994, J. Econ. Theory 63, 19 41) showed that a single sector growth model in the presence of increasing returns-to-scale may display an indeterminate equilibrium if the demand and supply curves cross with the ``wrong slopes.'' We generalize their result to a model with preferences that are nonseparable in consumption and leisure. We provide a simple analog of th...

Regularization has played a key role in deriving sensible estimators in high dimensional statistical inference. A substantial amount of recent works has argued for nonconvex regularizers in favor of their superior theoretical properties and excellent practical performances. In a different but analogous vein, nonconvex loss functions are promoted because of their robustness against “outliers”. H...

We give two pathological phenomena for non-separable AF-algebras which do not occur for separable AF-algebras. One is that non-separable AFalgebras are not determined by their Bratteli diagrams, and the other is that there exists a non-separable AF-algebra which is prime but not primitive.

Tutte founded the theory of enumeration of planar maps in a series of papers in the 1960s. Rooted non-separable planar maps have connections, for example, to pattern-avoiding permutations, and they are in one-to-one correspondence with the β(1, 0)-trees introduced by Cori, Jacquard and Schaeffer in 1997. In this paper we enumerate 2-face-free rooted non-separable planar maps and obtain restrict...