A ternary inhibitory system contains two terms in its free energy: the interface energy that favors micro-domain growth and the longer ranging confinement energy that prevents unlimited spreading. In a parameter regime where two constituents are small in size compared to the third constituent and the longer ranging energy does not dominate, there is a double-bubble-like stable stationary point ...

An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form of the boundary conditions, the loop correlators now contain elliptic integrals. This demonstrates the existence of new universality classes for the hermitian...

We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles of random n × n Hermitian matrices Z −1 n,N | det M | 2α e −N Tr V (M) dM with α > −1/2, where the factor | det M | 2α induces critical eigenvalue behavior near the origin. Under the assumption that the limiting mean eigenvalue density associated with V is regul...

Dualizing the “extended bipartite double” construction for distance-regular graphs, we construct a new family of cometric (or Q-polynomial) association schemes with four associate classes based on linked systems of symmetric designs. The analysis of these new schemes naturally leads to structural questions concerning imprimitive cometric association schemes, some of which we answer with others ...

This conjecture has been attributed variously to many mathematicians, but was known to be a consequence of the Strong Embedding Conjecture (Conjecture 2) by W. Tutte, G. Haggard, as well as by G. Szekeres and P. Seymour, amongst others [18], [16]. In what follows, we survey some of what is known about the above conjecture and discuss various related problems and techniques. We discuss the stron...

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.

An even cycle decomposition of a graph is a partition of its edge into even cycles. We first give some results on the existence of even cycle decomposition in general 4-regular graphs, showing that K5 is not the only graph in this class without such a decomposition. Motivated by connections to the cycle double cover conjecture we go on to consider even cycle decompositions of line graphs of 2-c...

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two do...

We use a regression-discontinuity design to study the effects of double blocking sixth-grade students in reading and mathematics on their achievement across three years of middle school. To identify the effect of the intervention, we use sharp cutoffs in the test scores used to assign students to double blocking. We find large, positive, and persistent effects of double blocking in reading, but...

A set A ⊆ ω is cototal if it is enumeration reducible to its complement, A. The skip of A is the uniform upper bound of the complements of all sets enumeration reducible to A. These are closely connected: A has cototal degree if and only if it is enumeration reducible to its skip. We study cototality and related properties, using the skip operator as a tool in our investigation. We give many ex...