In 1925, the German physicist Ernst Ising introduced a simple mathematical model of phase transitions, the abrupt changes of state that occur, for example, when water freezes or a cooling lump of iron becomes magnetic. In the 75 years since, the Ising model has been analyzed, generalized, and computerized—but never, except in special cases, solved. Researchers managed to get exact answers for p...

A complete supersymmetric SO(10) model is constructed, which is the most general consistent with R, discrete, and U(1) flavor symmetries. At the supersymmetric level there are many degenerate vacua, one of which is phenomenologically successful. This vacuum has vevs which align in certain definite directions in SO(10) group space, such as the B − L direction. Although this desired vacuum is not...

We define a mild generalization of classical Fraïssé classes, and in this context, we recover several old (often with novel proofs) and new facts about Ramsey classes and generalized indiscernibles in the sense of [12], [17], and other sources. Of particular novelty are: (1) a new and clearly model-theoretic proof of the equivalence of the Ramsey property and the extreme amenability of the auto...

We consider model checking of timed temporal formulae in durational transition graphs (DTGs), i.e., Kripke structures where transitions have integer durations. Two semantics for DTGs are presented and motivated. We consider timed versions of CTL where subscripts put quantitative constraints on the time it takes before a property is satisfied. We exhibit an important gap between logics where sub...

Team formation, i.e., allocating agents to roles within a team or subteams of a team, and the reorganization of a team upon team member failure or arrival of new tasks are critical aspects of teamwork. They are very important issues in RoboCupRescue where many tasks need to be done jointly. While empirical comparisons (e.g., in a competition setting as in RoboCup) are useful, we need a quantita...

We consider the sabotage modal logic SML which was suggested by van Benthem. SML is the modal logic equipped with a ‘transition-deleting’ modality and hence a modal logic over changing models. It was shown that the problem of uniform model checking for this logic is PSPACE-complete. In this paper we show that, on the other hand, the formula complexity and the program complexity are linear, resp...

The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph a...

In-depth understanding of the generic mechanisms of transitions between distinct patterns of the activity in realistic models of individual neurons presents a fundamental challenge for the theory of applied dynamical systems. The knowledge about likely mechanisms would give valuable insights and predictions for determining basic principles of the functioning of neurons both isolated and network...