Penalty Logic is a natural and commonsense Knowledge Representation technique to deal with potentially inconsistent beliefs. Penalty Logic allows some kind of compensation between different pieces of information. But one of the main and less studied flaws of Penalty Logic is the influence of the choice of weights on inference: the same pieces of information can provide extremely different resul...

The Stochastic Context Tree (SCOT) is a useful tool for studying infinite random sequences generated by an m-Markov Chain (m-MC). It captures the phenomenon that the probability distribution of the next state sometimes depends on less than m of the preceding states. This allows compressing the information needed to describe an m-MC. The SCOT construction has been earlier used under various name...

Statistical analysis usually treats all observations as equally important. In some circumstances, however, it is appropriate to vary the weight given to different observations. Well known examples are in meta-analysis, where the inverse variance (precision) weight given to each contributing study varies, and in the analysis of clustered data. Differential weighting is also used when different p...

Our system used an empirical method for estimating term weights directly from relevance judgements, avoiding various standard but potentially troublesome assumptions. It is common to assume, for example, that weights vary with term frequency ( ) and inverse document frequency ( ) in a particular way, e.g., , but the fact that there are so many variants of this formula in the literature suggests...

Sara Solla explores what it means for groups of neurons to most efficiently represent information in the sensory world.

Introduction Feldkamp-Davis-Kress (FDK) reconstructions of CT scans [1] require an appropriate pre-weighting of the CT rawdata to account for the redundancies of the measured x-rays. Currently, there exist several weighting schemes for dedicated scan trajectories, e.g. the well-known Parker weighting for circular short scans [2], the shifted-detector weighting [3], the partial scan shifted dete...

Non-linear probability weighting is an integral part of descriptive theories of choice under risk such as prospect theory. But why do these objective errors in information processing exist? Should we try to help individuals overcome their mistake of overweighting small and underweighting large probabilities? In this paper, we argue that probability weighting can be seen as a compensation for pr...

A modification of the edge stabilization technique is proposed to improve the behavior of the method when solving conservation equations with nonsmooth data or nonsmooth solutions. The key ingredient is tempering the edge stabilization in regions of large gradients through appropriate weights. The new method is shown to preserve the convergence properties of the original method on smooth soluti...

This paper provides preference foundations for parametric weighting functions under rank-dependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by allowing probabilistic risk attitudes to vary withi...