The model of arithmetic branching programs is an algebraic model of computation generalizing the model of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs, a model introduced by Pudll ak and Sgall 20]. Using this equivalence we prove that dependency programs are closed under conjunctio...

We describe a deterministic algorithm that, for constant k, given a k-DNF or kCNF formula φ and a parameter ε, runs in time linear in the size of φ and polynomial in 1/ε and returns an estimate of the fraction of satisfying assignments for φ up to an additive error ε. For k-DNF, a multiplicative approximation is also achievable in time polynomial in 1/ε and linear in the size of φ. Previous alg...

We consider the model of arithmetic branching programs, which is a generalization of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs, a model introduced by Pudl ak and Sgall [14]. Using this equivalence we prove that dependency programs are closed under conjunction, answering an open ...

The system AProVE (Automated Program Verification Environment) offers a variety of techniques for automated (innermost) termination proofs of (possibly conditional) TRSs, logic programs, and first-order functional programs. Besides efficient implementations of classical simplification orders (Sect. 2), it offers the dependency pair technique [2,11] which allows the application of classical orde...

In [13], a new size-change principle was proposed to verify termination of functional programs automatically. We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs). Moreover, we compare this approach with existing techniques for termination analysis of TRSs (such as recursive path orderings or dependency pairs). It turns out th...

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values betwee...

Background: A large proportion of patients presenting with lumbar disc disease are opium addicts in our region. It was, therefore, hypothesized that morphine might affect the intervertebral disc. We investigated the histological findings of morphine dependency on intervertebral discs in rat. Methods: Forty NMRI adult male rats (230-250 g) placed on ordinary diet and received aqueous solution of...

Biodiversity and structure of the benthic macrofauna communities were studied in the southeast the Caspian Sea (Golestan Province – Iran) during one year from October 2014 to September 2015. Seasonal samplings were done at 6 stations in 3 transects. Depth, temperature, salinity, pH, E.C., total organic matter and grain size were measured. More than 4,037 individuals belonging to five orders, Po...

There is divergence of opinion regarding the consequences of population growth for economic development. Some view rapid population growth as a real problem while others assert that it is not a matter of grave concern. Crossnational evidence on the relationship between population growth and economic growth is inconsistent because the underlying parameters and assumptions vary across countries. ...