Linial, Mansour and Nisan [7] proved that a function computed by a small-depth circuit of limited size has most of its Fourier support on small sets. We improve their bounds. When the bottom fanin is bounded we use essentially their argument, but to reduce the general case to this case without a loss in the asymptotic bounds requires a new argument. Warning: Essentially this paper is accepted f...

Diana Mansour, in her commentary1 in the July 2011 issue of this Journal, pointed out the inadequacy of the wording of the emergency contraception advice in the Medicines and Healthcare products Regulatory Authority’s Combined Oral Contraceptives (The Pill): When to Start Taking The Pill, and Missed Pill Advice.2 We also need to remember the women who have forgotten one pill in the week before ...

Branching programs are a generalization of decision trees. From the viewpoint of boosting theory the former appear to be exponentially more eecient. However, earlier experience demonstrates that such results do not necessarily translate to practical success. In this paper we develop a practical version of Mansour and McAllester's 13] algorithm for branching program boosting. We test the algorit...

In the past ten years, boosting has become a major field of machine learning and classification. This paper brings contributions to its theory and algorithms. We first unify a well-known top-down decision tree induction algorithm due to [Kearns and Mansour, 1999], and discrete AdaBoost [Freund and Schapire, 1997], as two versions of a same higher-level boosting algorithm. It may be used as the ...

Let N be the set of all positive integers and let A be any ordered subset of N. Recently, Heubach and Mansour enumerated the number of compositions of nwithm parts inA that contain the subword τ exactly r times, where τ ∈ {111, 112, 221, 123}. Our aims are (1) to generalize the above results, i.e., to enumerate the number of compositions of n with m parts in A that contain an `-letter subword, ...

The promotion of an operational network between hospitals and medical schools in Iraq and in Western countries is a primary humanitarian objective of international collaboration. As a consequence of a collaborative project between the Al Mansour Hospital for Pediatrics in Baghdad and the Pediatric Unit of Hematology of "La Sapienza" University, in Rome, in October 2003 a specific all-trans-reti...

In this paper, we consider two sets of pattern-avoiding ascent sequences: those avoiding both 201 and 210 and those avoiding 0021. In each case we show that the number of such ascent sequences is given by the binomial convolution of the Catalan numbers. The result for {201, 210}-avoiders completes a family of results given by Baxter and the current author in a previous paper. The result for 002...