We consider ill-posed problems of the form (1) g(t) = jQKit, s)fis)ds, 0 < t « 1, where g and K are given, and we must compute /. The Tikhonov regularizaron procedure replaces (1) by a one-parameter family of minimization problems— 2 Minimize i\\Kf g\\ + aft(/))—where ft is a smoothing norm chosen by the user. We demonstrate by example that the choice of ft is not simply a matter of convenience...

We show that the quantum query complexity of evaluating nand-tree instances with average choice complexity at most W is O(W ), where average choice complexity is a measure of the difficulty of winning the associated two-player game. This generalizes a superpolynomial speedup over classical query complexity due to Zhan et al. We further show that the player with a winning strategy for the two-pl...

High throughput assays tend to be expensive per subject. Often studies are limited not so much by the number of subjects available as by assay costs, making assay choice a critical issue. We have developed a framework for assay choice that maximises the number of true disease causing mechanisms 'seen', given limited resources. Although straightforward, some of the ramifications of our methodolo...

Chimpanzees are proficient tool users and have been shown to use properties of weight and length to select effective tools. Researchers have, however, neglected to investigate whether chimpanzees utilize other tool properties. This study investigated whether chimpanzees use other properties to choose effective tools, how feedback influences their ability to select effective tools, and whether o...

A common approach to complex systems such as colloidal suspensions or polymer solutions describes the mesoscopic behavior using effective interactions. These potentials act between the macromolecular entities and can be derived by integrating out the microscopic degrees of freedom. The remaining macroparticle coordinates need to be chosen a priori. Two obvious choices are (i) the centers of mas...

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or compu...

    This study investigated the effects of different learning levels, including Remember an Instance (RI), Remember a Generality (RG), and Use a Generality (UG) in multiple-choice and essay tests on immediate and delayed retention. Three-hundred pre-intermediate students participated in the study. Reading passages with multiple-choice and essay questions in different levels of learning were giv...