We study the query complexity of WEAK PARITY: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2+ε fraction of input strings, but must do so with high probability on those inputs where one does succeed. It is well-known that n randomized queries and n/2 quantum queries are needed to compute parity on all inputs. But surprisingly, we give a rando...

We study the complexity of computing the Fréchet distance (also called dog-leash distance) between two polygonal curves with a total number of n vertices. For two polygonal curves in the plane we prove an Ω(n log n) lower bound for the decision problem in the algebraic computation tree model allowing arithmetic operations and tests. Up to now only a O(n) upper bound for the decision problem was...

In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an expl...

BACKGROUND Measurements of respiratory muscle strength are widely used for assessment in children; however, clearly defined predictive equations for the Brazilian pediatric population have yet to be established. OBJECTIVE To determine the prediction equations for maximal respiratory pressures in healthy children. METHOD Cross-sectional observational study with normal-weight students aged 7-...

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...