We present an efficient algorithm for scoring clones given an ordering of probes under a schema proposed by Alizadeh et al. (1994) in the context of physical mapping with unique probes. The algorithm runs in time linear in the number of blocks of ones in the underlying sparse incidence matrix. A sparse and efficient algorithm for this task is important as it appears to be a central task in most...

A hypergraph G with n vertices and m hyperedges with d endpoints each is (k, l)-sparse if for all sub-hypergraphs G on n vertices and m edges, m ≤ kn − l. For integers k and l satisfying 0 ≤ l ≤ dk − 1, this is known to be a linearly representable matroidal family. Motivated by problems in rigidity theory, we give a new linear representation theorem for the (k, l)-sparse hypergraphs that is nat...

Many model-tracing intelligent tutoring systems give, upon demand, a series of hints until they reach the bottom-out hint that tells them exactly what to do (exact answer of the question). Since students don’t know the number of hints available for a given question, some students might be surprised to, all of a sudden, be told the final answer; letting them know when the bottom out hint is gett...

We determine the p-rank of the incidence matrix of hyperplanes of PG(n, pe) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in O10(2e), O10(3e), O9(5e), O12(5e) and O12(7e). We also give slightly weaker bounds for more general finite classical polar spaces. Another applic...

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Difference sets have been extensively studied in groups, principally in Abelian groups. Here we extend the notion of a difference set to loops. This entails considering the class of principal block partial designs (PBPDs) and (v, k, A) designs. By means of a certain permutation matrix decomposition of the incidence matrices of a system and...

Chest X-rays of 1057 potential Gurkha recruits from East Nepal and 964 from West Nepal were examined. Seventy-four X-rays from Eastern Nepalis showed changes suggestive of past or present tuberculosis (including 18 with calcified primary complexes) but only 34 (five with calcified primary complexes) from Western Nepalis suggesting that there is a higher tuberculosis infection rate in men from E...