Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of (...) Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)

Das mythologische Handbuch Die uns uberlieferte Endfassung von Apollodors Sagensammlung stammt vermutlich aus dem 1. Jahrhundert n. Chr. Die Wurzeln dieses mythologischen Handbuchs reichen aber, wie Paul Drager nachweist, wesentlich weiter zuruck. Wir finden hier - unbeeinflusst von Pindar, Apollonios Rhodios oder den grossen Tragodiendichtern - die Urfassung der antiken Gotter- und Heldensagen: von Uranos und Gaia bis zur Heimkehr des Odysseus nach Ithaka.".

Die neue herausragende Übertragung. Cicero verfasste "De officiis" in den Monaten nach der Ermordung Caesars als Vermächtnis an seinen Sohn. Von allen Werken Ciceros hat es am stärksten auf die Nachwelt gewirkt. Es wurde am häufigsten übersetzt und kommentiert. Voltaire und Friedrich der Große hielten "De officiis" für das beste Buch zum Thema moralisches Verhalten.

Theories of linguistic meaning have been a major influence in twentieth century philosophy. This is due, in part, to the assumption that meaning is the crucial and interesting thing about language. To know the meaning of an expression is to understand it, and since understanding is central to philosophy in many different ways, it should be no surprise that the notion of meaning has often taken center stage. The aim of this paper is to briefly explore some influential views concerning (...) linguistic meaning. The final objective will be to demonstrate some alternatives which are open to theory with respect to this notion,for there are those who have wanted to ban talk of meaning from serious scientific discourse. The point is that many of the disadvantages of traditional notions of meaning are avoidable¾in particular, they are avoidable along a path which starts from Frege and moves on via Tarski and Davidson. (shrink)

In this early paper I set out an argument in favor of the standard semantics of first-order logic, to the effect that (Vx)(Ey)x=y. Though my arguments from the paper have since been revised in details, The conclusion of the paper seems still viable and acceptable.