In this paper, we analyze Boolean formulas in conjunctive normal form (CNF) from the perspective of read-once resolution (ROR) refutation schemes. A read-once (resolution) refutation is one in which each clause is used at most once. Derived clauses can be used as many times as they are deduced. However, clauses in the original formula can only be used as part of one derivation. It is well known that ROR is not complete; that is, there exist unsatisfiable formulas for which no ROR exists. Likewise, the problem of checking if a 3CNF formula has a read-once refutation is NP-complete. This paper is concerned with a variant of satisfiability called not-all-equal satisfiability (NAE-satisfiability). A CNF formula is NAE-satisfiable if it has a satisfying assignment in which at least one literal in each clause is set to false. It is well known that the problem of checking NAE-satisfiability is NP-complete. Clearly, the class of CNF formulas which are NAE-satisfiable is a proper subset of satisfiable CNF formulas. It follows that traditional resolution cannot always find a proof of NAE-unsatisfiability. Thus, traditional resolution is not a sound procedure for checking NAE-satisfiability. In this paper, we introduce a variant of resolution called NAE-resolution which is a sound and complete procedure for checking NAE-satisfiability in CNF formulas. The focus of this paper is on a variant of NAE-resolution called read-once NAE-resolution in which each clause (input or derived) can be part of at most one NAE-resolution step. Our principal result is that read-once NAE-resolution is a sound and complete procedure for 2CNF formulas. Furthermore, we provide an algorithm to determine the smallest such NAE-resolution in polynomial time. This is in stark contrast to the corresponding problem concerning 2CNF formulas and ROR refutations. We also show that the problem of checking whether a 3CNF formula has a read-once NAE-resolution is NP-complete.

OBJECTIVES/SPECIFIC AIMS: To examine rural-urban disparities in prevalence of diagnosed diabetes in veterans receiving care at the VA and to determine the extent to which demographic factors and obesity levels contribute to identified disparities. METHODS/STUDY POPULATION: A retrospective serial cross-sectional analysis was employed. A stratified weighted random sample of veterans who received care at a VA facility was selected each year for 2007 through 2012. Rural Urban Commuting Area (RUCA) codes were based on resident zip code. Diabetes was defined by two or more primary or secondary ICD-9 codes for diabetes (250.xx) within a 12 month period. Data were analyzed using complex survey-specific procedures. RESULTS/ANTICIPATED RESULTS: Diabetes prevalence 2007-2012 was lowest in urban (20.5%-21.0%), followed by highly rural (21.1%-22.1%) and rural (22.3%-23.0%) areas with the prevalence being significantly higher on the insular islands (31.0%-32.4%). In 2012, 41% of urban, 43% of rural and highly rural and 30% of insular island veterans were obese. Relative to urban areas, the odds ratio for prevalent diabetes was 1.10 (95% CI: 1.08, 1.12) for rural veterans, 1.19 (95% CI: 1.16, 1.23) for insular island veterans, and 1.00 (95% CI: 0.98, 1.02) for highly rural veterans. DISCUSSION/SIGNIFICANCE OF IMPACT: Prevalence of diagnosed diabetes is high in veterans residing in rural, highly rural and urban areas, but markedly higher on the insular islands. Understanding the burden of disease and factors driving disparities provides information required to develop targeted interventions.