The model theory of fields with operators has proven to be very useful in applications of model theory to problems outside logic. Differentially closed fields and separably closed fields were instrumental in Hrushovski’s proof of the conjecture of Mordell-Lang ([39]), and in work of Hrushovski and Pillay on counting the number of transcendental points on certain varieties ([44]). Let me also me...

To reveal the fundamental skills involved in slacklining, this study examined a hypothesis regarding single-leg standing on a slackline. In the field of practice, instructors teach learners how to maintain balance on a swinging flat belt (slackline), such as by moving their hands in parallel. We hypothesized that bimanual coordination in the horizontal direction might contribute to dynamic bala...

The problem of global asymptotic stability of a time-variant mth-order difference equation is addressed. Stable regions in the parameter space will be derived for two cases: the case of a time-invariant parameter region, and the case of a time-variant parameter region. These results find applications in the area of adaptive digital filters.

This paper deals with two concepts of polynomial dichotomy for linear difference equations which are defined in a Banach space and whose norms can increase not faster than exponentially. Some illustrating examples clarify the relations between these concepts. Our approach is based on the extension of techniques for exponential dichotomy to the case of polynomial dichotomy. The obtained results ...

We report our results on non-periodic experimental time series of pressure in a spark ignition engine. The experiments were performed for a low rotational velocity of a crankshaft and a relatively large spark advance angle. We show that the combustion process has many chaotic features. Surprisingly, the reconstructed attractor has a characteristic butterfly shape similar to a chaotic attractor ...

While conversing face-to-face, romantic partners are thought to form a coupled and co-regulatory system, unintentionally shaping each other’s emotional states on a moment-by-moment basis. What has been less explored, however, are the ways in which this coupling is modulated by high-level interpersonal factors, such as discussing topics that are stressful for one or both partners. We provide an ...

In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...

The probability densities of the mean recurrence time, which is the average time needed for a system to recur to a previously visited neighborhood, are investigated in various dynamical regimes and are found to be in agreement with those of the finite-time Lyapunov exponents. The important advantages of the former ones are that they are easy to estimate and that comparable short time series are...

The combination of a nonlinear time series analysis technique, Recurrence Quantification Analysis (RQA) based on Recurrence Plots (RPs), and traditional statistical analysis for neuronal electrophysiology is proposed in this paper as an innovative paradigm for studying the variation of spontaneous electrophysiological activity of in vitro Neuronal Networks (NNs) coupled to Multielectrode Array ...

We present an automatic method for computing tight upper bounds on the iteration number of special classes of program loops. These upper bounds are further used in the WCET analysis of programs. To do so, we refine program flows using SMT reasoning and rewrite multi-path loops into single-path ones. Single-path loops are further translated into a set of recurrence relations over program variabl...