The problem of determining which abelian groups admit a full-rank normalized factorization is settled for the orders 64 = 26, 81 = 34, and 128 = 27. By a computer-aided approach, it is shown that such groups of these orders are exactly those of type (22, 22, 22), (22, 22, 2, 2), (23, 22, 22), (23, 22, 2, 2), (22, 22, 22, 2), and (22, 22, 2, 2, 2). Mathematics Subject Classification (2000): Prim...

The full-information secretary problem in which the objective is to minimize the expected rank is seen to have a value smaller than 7/3 for all n (the number of options). This can be achieved by a simple memoryless threshold rule. The asymptotically optimal value for the class of such rules is about 2.3266. For a large finite number of options, the optimal stopping rule depends on the whole seq...

In this paper, we propose a construction of fullrank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of fullrank binary 1-perfect codes (1994). Properties of i-components of q-ary Hamming codes are investigated and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1...

An algebraic branching program (ABP) A can be modelled as a product expression X1 · X2 · · · · · Xd, where X1 and Xd are 1× w and w× 1 matrices respectively, and every other Xk is a w×w matrix; the entries of these matrices are linear forms in m variables over a field F (which we assume to be either Q or a field of characteristic poly(m)). The polynomial computed by A is the entry of the 1× 1 m...

It was proven in [8] that the PhaseLift algorithm recovers signals x ∈ Cn exactly from m = O(n log n) measurements {|〈x, zi〉|2}i=1 with high probability when the measurement vectors zi ∈ C n are iid gaussian and that this procedure is provably stable with respect to measurement noise under the same assumptions. To be precise, this means that in the noiseless case, for a fixed x ∈ Cn and definin...