Effective Polynomial Ballisticity Condition for Random Walk in Random Environment

The conditions $(T)_\gamma,$ $\gamma \in (0,1),$ which have been introduced by Sznitman in 2002, have had a significant impact on research in random walk in random environment. Among others, these conditions entail a ballistic behaviour as well as an invariance principle. They require the stretched exponential decay of certain slab exit probabilities for the random walk under the averaged measure and are asymptotic in nature. The main goal of this paper is to show that in all relevant dimensions (i.e., $d \ge 2$), in order to establish the conditions $(T)_\gamma$, it is actually enough to check a corresponding condition $(\mathcal{P})$ of polynomial type. In addition to only requiring an a priori weaker decay of the corresponding slab exit probabilities than $(T)_\gamma,$ another advantage of the condition $(\mathcal{P})$ is that it is effective in the sense that it can be checked on finite boxes. In particular, this extends the conjectured equivalence of the conditions $(T)_\gamma,$ $\gamma \in (0,1),$ to all relevant dimensions.Comment: 21 pages, 2 figures; followed referee's and readers' comments, corrected minor errors; to appear in Comm. Pure Appl. Mat

Price Strategy Implementation

Consider a situation in which a company sells several different items to a set of customers. However, the company is not satisfied with the current pricing strategy and wishes to implement new prices for the items. Implementing these new prices in one single step mightnot be desirable, for example, because of the change in contract prices for the customers. Therefore, the company changes the prices gradually, such that the prices charged to a subset of the customers, the target market, do not differ too much from one period to the next. We propose a polynomial time algorithm to implement the new prices in the minimum number of time periods needed, given that the prices charged to the customers in the target market increase by at most a factor 1 + δ, for predetermined δ > 0. Furthermore, we address the problem to maximize the revenue when also a maximum number of time periods is predetermined. For this problem, we describe a dynamic program if the numberof possible prices is limited, and a local search algorithm if all prices are allowed. Also, we present the integer program that models this problem. Finally, we apply the obtained algorithms in a practical study.operations research and management science;

On Gromov-Hausdorff stability in a boundary rigidity problem

Let $M$ be a compact Riemannian manifold with boundary. We show that $M$ is Gromov-Hausdorff close to a convex Euclidean region $D$ of the same dimension if the boundary distance function of $M$ is $C^1$-close to that of $D$. More generally, we prove the same result under the assumptions that the boundary distance function of $M$ is $C^0$-close to that of $D$, the volumes of $M$ and $D$ are almost equal, and volumes of metric balls in $M$ have a certain lower bound in terms of radius.Comment: 16 pages, v3: added a preliminaries sectio

Discovering Unexpected Patterns in Temporal Data Using Temporal Logic

There has been much attention given recently to the task of finding interesting patterns in temporal databases. Since there are so many different approaches to the problem of discovering temporal patterns, we first present a characterization of different discovery tasks and then focus on one task of discovering interesting patterns of events in temporal sequences. Given an (infinite) temporal database or a sequence of events one can, in general, discover an infinite number of temporal patterns in this data. Therefore, it is important to specify some measure of interestingness for discovered patterns and then select only the patterns interesting according to this measure. We present a probabilistic measure of interestingness based on unexpectedness, whereby a pattern P is deemed interesting if the ratio of the actual number of occurrences of P exceeds the expected number of occurrences of P by some user defined threshold. We then make use of a subset of the propositional, linear temporal logic and present an efficient algorithm that discovers unexpected patterns in temporal data. Finally, we apply this algorithm to synthetic data, UNIX operating system calls, and Web logfiles and present the results of these experiments.Information Systems Working Papers Serie

Asynchronous sessions with implicit functions and messages

Session types are a well-established approach to ensuring protocol conformance and the absence of communication errors such as deadlocks in message passing systems. Haskell introduced implicit parameters, Scala popularised this feature and recently gave implicit types first-class status, yielding an expressive tool for handling context dependencies in a type-safe yet terse way. We ask: can type-safe implicit functions be generalised from Scala’s sequential setting to message passing computation? We answer this question in the affirmative by presenting the first concurrent functional language with implicit message passing. The key idea is to generalise the concept of an implicit function to an implicit message, its concurrent analogue. Our language extends Gay and Vasconcelos’s calculus of linear types for asynchronous sessions (LAST) with implicit functions and messages. We prove the resulting system sound by translation into LAST

Erkundungen im Spannungsfeld von Pädagogik, Spielspass und technischer Machbarkeit. Gedanken zur Konzeption und Entwicklung spielbasierter digitaler Lernumgebung

Computerspiele sind heute aus der digitalen Medienwelt nicht mehr wegzudenken. Ihre rasante technische Entwicklung sowie ihre hohe Akzeptanz in der Jugendkultur werfen Fragen nach pädagogischer Verwertbarkeit dieses Mediums auf. Auf diesem Gebiet besteht Forschungsbedarf: Für den Einsatz aktueller Spielkonzepte als Lehrmittel existieren keine fundierten Theorien oder Konzepte. Der schöpferische Umgang mit Spielen durch Anwender («Emergent Gameplay») bietet hier durch sein hohes Motivationspotential einen vielversprechenden Ansatz. Die oft wenig beachtete Rolle der digitalen Spielen zugrunde liegenden Softwaretechnik sollte stärkere Berücksichtigung finden: Es existiert einerseits ein für die Akzeptanz beim Anwender notwendiges Minimum, andererseits ist der Einsatz des aktuellen technischen «state of the art» für die Umsetzung pädagogischer und didaktischer Ambitionen durch seine enormen Anforderungen wenig zielführend. Im Ergebnis sind Idee und Spielspass das Mass auch für Anwendungen des Game Based Learn­ing