These are expanded notes from four introductory lectures on Ergodic Theory, given at the Minerva summer school Flows on homogeneous spaces at the Technion, Haifa, Israel, in September 2012. 1. Dynamics on a compact metrizable space Given a compact metrizable space X, denote by C(X) the space of continuous functions f : X → C with the uniform norm ‖f‖u = max x∈X |f(x)|. This is a separable Banac...

Mimicking biological neurons by focusing on the excitatory/inhibitory decoding performed by the dendritic trees is a different and attractive alternative to the integrate-and-fire McCullogh-Pitts neuron stylisation. In such alternative analogy, neurons can be seen as a set of RAM nodes addressed by Boolean inputs and producing Boolean outputs. The shortening of the semantic gap between the syna...

Typed Predicate Logicwas developed to o¤er a unifying framework for many of the current logical systems, and especially those that employ some notion of type or sort.

In this chapter we illustrate the use of item response models to analyze data resulting from the measurement of competencies. These item response models deal with data from an instrument such as a test, an inventory, an attitude scale, or a questionnaire – we will call this “test data”. The main purpose of using item response models is the measurement of propensities: specifically, abilities, s...

The versatile MOdeling, Specification and Evaluation Language is the core element of the MOSEL-2 tool. This description languages provides a high-level means for specifying models, performance measures, and the graphical presentation of results. The description languages is implemented in form of an evaluation environment that comprises translators to the modeling languages of several third-par...

The goal of this document is to provide a easier introduction to olympiad inequalities than the standard exposition Olympiad Inequalities, by Thomas Mildorf. I was motivated to write it by feeling guilty for getting free 7’s on problems by simply regurgitating a few tricks I happened to know, while other students were unable to solve the problem. Warning: These are notes, not a full handout. Lo...

The sciences of chaos and complexity include arcane investigations of complicated natural phenomena. Organizational applications of the sciences are no less complicated. Talented persons around the world are struggling to make sense out of the strange and surprising behaviors of complex adaptive systems in nature and in human organizations. This paper presents a brief introduction to some of th...

If a coin is tossed, then there are two possible outcomes: heads and tails. Statements such as ‘the chance that the outcome will be heads is 50%’ are formalized in probability theory, giving a better way to reason about the odds of a certain outcome of an experiment. The possible outcomes of an experiment are called the sample space. For example, the sample space of the coin tossing experiment ...