We present a reduction framework from ordinal regression to binary classification based on extended examples. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranking rule from the binary classifier. A weighted 0/1 loss of the binary c...

2 Binary search trees 2 2.1 Definition of a binary search tree . . . . . . . . . . . . . . . . . . 2 2.2 Profile. Discrete martingale . . . . . . . . . . . . . . . . . . . . . 3 2.3 Embedding in continuous time. Yule tree . . . . . . . . . . . . . . 4 2.4 Martingale connection Yule tree binary search tree . . . . . . . . 5 2.5 Asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

In general, most search engines display a certain number of search results on a search results page at one time, separating the entire search results into multiple search results pages. Therefore, lower ranked results (e.g., 11thranked result) may be displayed on the top area of the next (second) page and might be more likely to be browsed by users, rather than results displayed on the bottom o...

Soft constraint minimization problems (SCMPs) contain hard constraints that cannot be violated and soft constraints that may be violated but carry penalties if not satisfied. In this paper, we first extend local search, WalkSAT in particular, to SCMPs and study the existing SAT encoding schemes for SCMPs. We propose a general encoding method called k-encoding. We then investigate the effects of...

Proper estimation of droplet growth rate plays a crucial role on appropriate prediction of supersonic separators performance for separation of fine droplets from a gas stream. Up to now, all available researches employ empirical or semi-empirical correlations to define the relationship between droplet growth rate (dr/dt) and other operating variables such as temperatures (T and TL), Pressure (P...