This paper suggests a method for multiclass learning with many classes by simultaneously learning shared characteristics common to the classes, and predictors for the classes in terms of these characteristics. We cast this as a convex optimization problem, using trace-norm regularization and study gradient-based optimization both for the linear case and the kernelized setting.

Abstract. Consider an asynchronous system where each process begins with an arbitrary real value. Given some fixed > 0, an approximate agreement algorithm must have all non-faulty processes decide on values that are at most from each other and are in the range of the initial values of the non-faulty processes.Previous constructions solved asynchronous approximate agreement only when there were at least 5t + 1 processes, t of which may be Byzantine. In this paper we close an open problem raised by Dolev et al. in 1983. We present a deterministic optimal resilience approximate agreement algorithm that can tolerate any t Byzantine faults while requiring only 3t + 1 processes.The algorithm's rate of convergence and total message complexity are efficiently bounded as a function of the range of the initial values of the non-faulty processes. All previous asynchronous algorithms that are resilient to Byzantine failures may require arbitrarily many messages to be sent.

We studied the effect of skinfold thickness on the correlation between serum total bilirubin level and transcutaneous bilirubin (TcB) readings. Skinfold thickness measurements were taken at 1–4 h of age. Serum total bilirubin levels and TcB readings were obtained at 1–4 (first) and 44–56 h of age (discharge). No correlation was found between first reading and skinfold thickness (rho = ––0.196), whereas correlations with first serum bilirubin level and blood hematocrit were 0.397 and ––0.373, respectively. The correlation between discharge serum total bilirubin level and TcB reading was affected by skinfold thickness, and not improved with the use of first reading as a reference for discharge reading.

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