37,512 research outputs found
The Problem of an Insured Delaying Notice to an Insurer of a Claim Against the Insurer: A Problem with Presumed Prejudice
A Lower Bound of Conditional Branches for Boolean Satisfiability on Post Machines
We establish a lower bound of conditional branches for deciding the
satisfiability of the conjunction of any two Boolean formulas from a set called
a full representation of Boolean functions of variables - a set containing
a Boolean formula to represent each Boolean function of variables. The
contradiction proof first assumes that there exists a Post machine (Post's
Formulation 1) that correctly decides the satisfiability of the conjunction of
any two Boolean formulas from such a set by following an execution path that
includes fewer than conditional branches. By using multiple runs of this
Post machine, with one run for each Boolean function of variables, the
proof derives a contradiction by showing that this Post machine is unable to
correctly decide the satisfiability of the conjunction of at least one pair of
Boolean formulas from a full representation of -variable Boolean functions
if the machine executes fewer than conditional branches. This lower bound
of conditional branches holds for any full representation of Boolean
functions of variables, even if a full representation consists solely of
minimized Boolean formulas derived by a Boolean minimization method. We discuss
why the lower bound fails to hold for satisfiability of certain restricted
formulas, such as 2CNF satisfiability, XOR-SAT, and HORN-SAT. We also relate
the lower bound to 3CNF satisfiability. The lower bound does not depend on
sequentiality of access to the boxes in the symbol space and will hold even if
a machine is capable of non-sequential access.Comment: This article draws heavily from arXiv:1406.597
Model Verification and the Likelihood Principle
The likelihood principle (LP) is typically understood as a constraint on any measure of evidence arising from a statistical experiment. It is not sufficiently often noted, however, that the LP assumes that the probability model giving rise to a particular concrete data set must be statistically adequate—it must “fit” the data sufficiently. In practice, though, scientists must make modeling assumptions whose adequacy can nevertheless then be verified using statistical tests. My present concern is to consider whether the LP applies to these techniques of model verification. If one does view model verification as part of the inferential procedures that the LP intends to constrain, then there are certain crucial tests of model verification that no known method satisfying the LP can perform. But if one does not, the degree to which these assumptions have been verified is bracketed from the evidential evaluation under the LP. Although I conclude from this that the LP cannot be a universal constraint on any measure of evidence, proponents of the LP may hold out for a restricted version thereof, either as a kind of “ideal” or as defining one among many different forms of evidence
Cavitation Inception in Spool Valves
Cavitation has been investigated in directional control valves in order to identify damage mechanisms characteristic of components of aircraft hydraulic systems. Tests have been conducted in a representative metal spool valve and in a model three times larger. Data taken under noncavitating conditions with both valves showed that the position of the high-velocity annular jet shifts orientation, depending upon valve opening and Reynolds number. By means of high-frequency response pressure transducers strategically placed in the valve chamber cavitation could be sensed by the correlation of noise with a cavitation index. The onset of cavitation can be detected by comparing energy spectra for a fixed valve opening and a constant discharge. Another sensitive indicator of cavitation inception is the ratio of cavitating to noncavitating spectral densities. The incipient cavitation number as defined in this investigation is correlated with the Reynolds number for both valves
- …