According to the second law of thermodynamics, for every transformation performed on a system which is in contact with an environment of fixed temperature, the average extracted work is bounded by the decrease of the free energy of the system. However, in a single realization of a generic process, the extracted work is subject to statistical fluctuations which may allow for probabilistic violat...

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. The vast majority of the literature on the subject deals with affine normalization. We argue that more general normalizations are natural from a mathematical and physical point of view and work them out. The problem is approa...

We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving transformations T1, T2, . . . , Td : Z y (X,Σ, μ) ([5]), and so, via the Furstenberg correspondence principle introduced in [4], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the detailed analysis of certain towers of factors of a probability-preserving...

We deene point attractors and set attractors for random dynamical systems via convergence in probability forward in time. This deenition of a set attractor is weaker than the usual one via almost sure pullback convergence. We derive basic properties of our weak random attractors such as uniqueness, support of invariant measures and invari-ance under (random) coordinate transformations. The noti...

Twenty-eight Grade 4 – 6 students participated in 1 hr. clinical interviews in a design-based study that investigated: (a) probability-related intuitions; (b) the affordances of a set of innovative mixed-media learning tools for articulating these intuitions; and (c) the utility of the learning-axes-and-bridging-tools framework supporting diagnosis, design, and data-analysis. Students intuited ...

− At the application level, it is important to be able to define around the measurement result an interval which will contain an important part of the distribution of the measured values, that is, a confidence interval. This practice acknowledged by the ISO Guide is a major shift from the probabilistic representation as a confidence interval represents a set of possible values for a parameter a...

We investigate the tree-series-to-tree-series (ts-ts) transformation computed by tree series transducers. Unless the used semiring is complete, this transformation is, in general, not well-defined. In practice, many used semirings are not complete (like the probability semiring). We establish a syntactical condition that guarantees well-definedness of the ts-ts transformation in arbitrary commu...

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. ...

The principle of categorial matching that has been invoked to mandate that transformations of theories by contraction removing some proposition h from a belief state K should include a specification of the entrenchment of the new belief state K − h as well as the entrenchment of the initial state K masks a substantial assumption that ought to be subject to critical scrutiny and which personally...

Previous research on diffusion networks has focused predominately on the final step in diffusion, adoption, rather than the primary phase of information acquisition. To explain the information spread, I propose a theory of information transfer based on the characteristics of the dyad and the characteristics of the sender. To understand information transfer, I examine the transmission of project...