Borel Isomorphism of SPR Markov Shifts

We show that strongly positively recurrent Markov shifts (in particular shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points

Good potentials for almost isomorphism of countable state Markov shifts

Almost isomorphism is an equivalence relation on countable state Markov shifts which provides a strong version of Borel conjugacy; still, for mixing SPR shifts, entropy is a complete invariant of almost isomorphism. In this paper, we establish a class of potentials on countable state Markov shifts whose thermodynamic formalism is respected by almost isomorphism

Almost isomorphism for countable state Markov shifts

Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important class of strongly positive recurrent Markov shifts. This gives a complete classification up to entropy conjugacy of the natural extensions of smooth entropy expanding maps, including all smooth interval maps with non-zero topological entropy

Flow Equivalence of G-SFTs

In this paper, a G-shift of finite type (G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G. For a special case of two irreducible components with G$=\mathbb Z_2$, we compute explicit complete invariants. We relate our matrix structures to the Adler-Kitchens-Marcus group actions approach. We give examples of G-SFT applications, including a new connection to involutions of cellular automata.Comment: The paper has been augmented considerably and the second version is now 81 pages long. This version has been accepted for publication in Transactions of the American Mathematical Societ

Promising Practices: Advanced Referral System - Illinois Division of Rehabilitation Services, BPA&O Project Human Services Center

Changes in disability policy at the state and federal level have presented many new opportunities for meaningful systems change and services delivery for people with disabilities. Since 2000, the Social Security Administration, the U.S. Department of Labor, the Centers for Medicare & Medicaid Services and the Rehabilitation Services Administration have issued many grants to state agencies, community-based service providers and advocates to address barriers to employment for people with disabilities. Many of these grants have competitive employment as the goal, yet very few of these grants have built in support for benefits planning and assistance – a function that many believe is critical to achieving competitive employment. In this Promising Practices, the Illinois Division of Rehabilitation Services BPA&O Project (DRS BPA&O Project) and the Human Services Center (HSC), a community-based mental health center and the recipient of a DOL Customized Employment Grant, created a model partnership to ensure that the 600 consumers with severe mental illness served by HSC under their grant would gain access to benefits planning services. They call their model partnership an “Advanced Referral System.