We find the minimal weighted energy ∫ Ω a(x)∣Du∣ of maps u ∶ Ω ⊂ Rm+n → S with prescribed singularities, where a(⋅) is a continuous positive weight. Our result extends previous ones of H. Brezis, J-M. Coron and E.H. Lieb (1986), G. Alberti, S. Baldo and G. Orlandi (2003), and V. Millot (2005).

The short-scan case in fan-beam computed tomography requires the introduction of a weighting function to handle redundant data. Parker introduced such a weighting function for a scan over pi plus the opening angle of the fan. In this article we derive a general class of weighting functions for arbitrary scan angles between pi plus fan angle and 2pi (over-scan). These weighting functions lead to...

Using the same interactive IR component as for TREC 2006, this submission probed the ability of a user without requisite domain knowledge to interactively set appropriate weights. The weighted keyword proximity method employed allowed a computer science undergraduate to achieve rankings above the median for all measures without the use of external knowledge sources or term expansion techniques ...

Tables of the relation between height and weight are now common in many countries, and if reasonably used are certainly helpful. It is not that a youth, a man, or woman, of a certain height must closely conform to the weight tabulated, a margin of 15 or 20 per cent, on either side is allowable. Such a table is undoubtedly useful in comparing the recruits or the prisoners it may be of one year (...

We consider the stochastic optimization problem where a convex function is minimized observing recursively the gradients. We introduce SAEW, a new procedure that accelerates exponential weights procedures with the slow rate 1/ √ T to procedures achieving the fast rate 1/T . Under the strong convexity of the risk, we achieve the optimal rate of convergence for approximating sparse parameters in ...

Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights, which is very beneficial for both theoretical considerations and practical computations with many members. We present quantitative approximation results with p...

Based of the strong idempotency of aggregation operators, quantitative weights are incorporated into the fusion process. Our general method is compared with some previous specific cases. Several examples are included.

Professors Greenwald and Oyakawa 2017-04-19 In these notes, we improve on the basic expert advice algorithms previously introduced. The basis for this technique is that we give each expert a weight, which influences how much sway she has in the algorithm’s decision. An expert who is wrong will frequently have her weight reduced and will therefore have less of an impact on the algorithm’s decisi...