Number Of Distinct Variables Research Articles

Abstract 15274: Social Determinants of Suboptimal Cardiovascular Health Among Pregnant Women in United States

Introduction: Cardiovascular health (CVH) and social determinants of health (SDOH) have a significant impact on maternal morbidity and mortality. We assessed the association and cumulative effects of SDOH on CVH among a nationally representative sample of pregnant women in the United States. Methods: We included cross-sectional data of pregnant women aged 18 to 49 years from the National Health Interview Survey (2013-2017). We ascertained CVH based on the following CV risk factors: hypertension, diabetes mellitus, dyslipidemia, smoking, obesity, and physical activity; classifying participants into optimal (0-1) and suboptimal (≥2) CVH. For each individual, SDOH risk score was calculated that represents the cumulative number of distinct variables (present vs absent) identified on 39 sub-components for 6 domains (economic stability, neighborhood and physical environment, community and social context, food, education, and healthcare system access). SDOH risk score was aggregated and divided into 4 quartiles. Results: Among 1,433 (3.3%, representing 2.2 million) pregnant women in US, one third (33%) of pregnant women (mean age: 33 years, 13% non-Hispanic black) had suboptimal CVH. The prevalence of hypertension, smoking, obesity and physical inactivity across the increasing SDOH quartiles were noted. Overall, 52% pregnant women with unfavorable (4 th quartile) vs 27% with favorable (1 st quartile) SDOH had suboptimal CVH. In multivariable analyses, accounting for demographics and co-morbid conditions, pregnant women with unfavorable SDOH in 4 th quartile had nearly 3-fold higher odds of suboptimal CVH. (Figure). Conclusions: Aggregate SDOH risk score provides significant discrimination of CVH in pregnant women. In pregnant women, suboptimal CVH is common and more than 1 in 2 women with highest risk of SDOH inequities have suboptimal CVH, highlighting the public health urgency for intervention in young high risk women.

PSEUDORECURSIVE VARIETIES OF SEMIGROUPS — II

Constructions that yield pseudorecursiveness in [I] (Int. J. Algebra Comput.6 (1996) 457–510) are extended in this article. Finitely based varieties of semigroups with increasingly strict expansions by additional unary operation symbols or individual constants are shown to have the pseudorecursive property: the equational theory is undecidable, but the subsets obtained by bounding the number of distinct variables are all recursive. The most stringent case considered here is the single unary operation or distinguished element. New techniques of stratified reducibility and interpretation via rewriting rules are employed to show the property inherits along a chain of theories. Pure semigroup varieties that are both finitely based and pseudorecursive will be discussed in a later paper.

On the complexity of alpha conversion

AbstractWe consider three problems concerning alpha conversion of closed terms (combinators).(1) Given a combinator M find the an alpha convert of M with a smallest number of distinct variables.(2) Given two alpha convertible combinators M and N find a shortest alpha conversion of M to N.(3) Given two alpha convertible combinators M and N find an alpha conversion of M to N which uses the smallest number of variables possible along the way.We obtain the following results.(1) There is a polynomial time algorithm for solving problem (1). It is reducible to vertex coloring of chordal graphs.(2) Problem (2) is co-NP complete (in recognition form). The general feedback vertex set problem for digraphs is reducible to problem (2).(3) At most one variable besides those occurring in both M and N is necessary. This appears to be the folklore but the proof is not familiar. A polynomial time algorithm for the alpha conversion of M to N using at most one extra variable is given.There is a tradeoff between solutions to problem (2) and problem (3) which we do not fully understand.

Exact Algorithms for MAX-SAT

The maximum satisfiability problem (MAX-SAT) is stated as follows: Given a boolean formula in CNF, find a truth assignment that satisfies the maximum possible number of its clauses. MAX-SAT is MAX-SNP-complete and received much attention recently. One of the challenges posed by Alber, Gramm and Niedermeier in a recent survey paper asks: Can MAX-SAT be solved in less than 2n “steps”? Here, n is the number of distinct variables in the formula and a step may take polynomial time of the input. We answered this challenge positively by showing that a popular algorithm based on branch-and-bound is bounded by O(2n) in time, where n is the maximum number of occurrences of any variable in the input.When the input formula is in 2-CNF, that is, each clause has at most two literals, MAX-SAT becomes MAX-2-SAT and the decision version of MAX-2-SAT is still NP-complete. The best bound of the known algorithms for MAX-2-SAT is O(m2m/5), where m is the number of clauses. We propose an efficient decision algorithm for MAX-2-SAT whose time complexity is bound by O(n2n). This result is substantially better than the previously known results. Experimental results also show that our algorithm outperforms any algorithm we know on MAX-2-SAT.

SAT-Problems and Reductions with Respect to the Number of Variables

In many algorithms or heuristics for the SAT problem the number of distinct variables occurring in the formula seems to play a central role, e.g. in Davis-Putnam algorithms. For deterministic algorithms, Schiermeyer has proved that 3-SAT is solvable in deterministic time O({vert_bar} {Phi} {vert_bar} c{sup n}), where n is the number of variables of {Phi} and c = 1.579. In contrast, no such algorithm is known (for any c 1 Unique SAT is decidable in deterministic time O({vert_bar} {Phi} {vert_bar} c{sup n}) iff SAT is decidable in deterministic time O({vert_bar} {Phi} {vert_bar} c{sup n}), where n ismore » the number of variables. With slight modifications this holds for k-Unique SAT and k-SAT, too. Finally we present a proof that for each problem in NTIME(n) there is a polynomial reduction to SAT such that the number of variables in f({Phi}) is only O(n) improving Schnorr-Cook`s reduction with O(nlogn) variables.« less

Size complexity in context-free grammars forms

Grammar forms are compared for their efficiency in representing languages, as measured by the sizes (i.e. total number of symbols, number of variable occurrences, number of productions, and number of distinct variables) of interpretation grammars. For every regular set, right- and left-linear forms are essentially equal in efficiency. Any form for the regular sets provides, at most, polynomial improvement over right-linear form. Moreover, any polynomial improvement is attained by some such form, at least on certain languages. Greater improvement for some languages is possible using forms expressing larger classes of languages than the regular sets. However, there are some languages for which no improvement over right-linear form is possible. While a similar set of results holds for forms expressing exactly the linear languages, only linear improvement can occur for forms expressing all the context-free languages.