We all have strong intuitions about a connection between Coordination and the notion of "equivalence" (Hebrew: , תוליקש). This is reflected by the fact that researchers often use terms like ‘parallelism’, ‘similarity’, or ‘symmetry’ when providing structural definitions of coordinated constructions (e.g., Azar 1977; Haspelmath, 2007; Van Valin 1990). Certain questions, such as the following, re...

When learning a directed acyclic graph (DAG) model via observational data, one generally cannot identify the underlying DAG, but can potentially obtain a Markov equivalence class. The size (the number of DAGs) of a Markov equivalence class is crucial to infer causal effects or to learn the exact causal DAG via further interventions. Given a set of Markov equivalence classes, the distribution of...

Contents 1. Introduction 1 2. Decidability results 1 3. Shift and strong shift equivalence for Boolean matrices 3 4. Strong shift equivalence of positive matrices over subrings of R 4 5. Automorphisms of the shift 4 6. The nonzero spectra of nonnegative integral matrices 6 7. The classification problem for shifts of finite type 6 8. Classification of free Z p actions on mixing SFTs 7 9. Topolog...

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2. 1. Introduction. There have recently been several papers demonstrating the global asymptotic equivalence of ce...

We review and extend our recent work on the planar (large N) equivalence between gauge theories with varying degrees of supersymmetry. The main emphasis is on the planar equivalence between N =1 gluodynamics (super-Yang–Mills theory) and a nonsupersymmetric “orientifold field theory”. We outline an “orientifold” large N expansion, analyze its possible phenomenological consequences in one-flavor...

For a cardinal κ and a model M of cardinality κ let No(M) denote the number of non-isomorphic models of cardinality κ which are L∞κ-equivalent to M. In [She82] Shelah established that when κ is a weakly compact cardinal and μ ≤ κ is a nonzero cardinal, there exists a model M of cardinality κ with No(M) = μ. We prove here that if κ is a weakly compact cardinal, the question of the possible value...

We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free actions in terms of algebraic invariants that involve Nielsen equivalence. This is applied to describe the sets of free actions in various cases, including a compl...