In this paper we investigate the potential of the analysis of noisy non-stationary time series by quantizing it into streams of discrete symbols and applying finitememory symbolic predictors. The main argument is that careful quantization can reduce the noise in the time series to make model estimation more amenable given limited numbers of samples that can be drawn due to the non-stationarity ...

We use generalized power series to construct algebraically a nonstandard model of the theory of the real eld with exponentiation. This model enables us to show the undeenability of the zeta function and certain non-elementary and improper integrals. We also use this model to answer a question of Hardy by showing that the compositional inverse to the function (log x)(log log x) is not asymptotic...

We derive a simple error estimate for equally spaced, polynomial interpolation of power series that does not require the uniform bounds on derivatives of the Cauchy remainder. The key steps are expressing Newton coefficients in terms of Stirling numbers S(i, j) of the second kind and applying the concavity of lnS(i, j).

Let K be an effective field of characteristic zero. An effective tribe is a subset of K[[z1, z2, ...]] =K ∪K[[z1]] ∪K[[z1, z2]] ∪ ··· which is effectively stable under the Kalgebra operations, restricted division, composition, the implicit function theorem, as well as restricted monomial transformations with arbitrary rational exponents. Given an effective tribe with an effective zero test, we ...

We present regression automata (RA), which are novel type syntactic models for time series forecasting. Building on top of conventional state-merging algorithms for identifying automata, RA use numeric data in addition to symbolic values and make predictions based on this data in a regression fashion. We apply our model to the problem of hourly wind speed and wind power forecasting. Our results...

Cell libraries are collections of logic cores (cells) used to construct larger chip designs; hence, any reduction in their power consumption may have a major impact in the power consumption of larger designs. The power consumption of a cell is often determined by triggering it with all possible input values in all possible orders at each state. In this paper, we first present a technique to mea...

A new class of distributions motivated by systems having both series and parallel structures is introduced. Some mathematical properties the (including moment generating function, moments order statistics) are derived. Estimation addressed maximum likelihood method performance estimators assessed a simulation study. An illustration using three failure data sets shows usefulness class.

Symbolic automata and transducers extend finite automata and transducers by allowing transitions to carry predicates and functions over rich alphabet theories, such as linear arithmetic. Therefore, these models extend their classic counterparts to operate over infinite alphabets, such as the set of rational numbers. Due to their expressiveness, symbolic automata and transducers have been used t...

What are the key cognitive factors that characterize the potential difference between symbolic and nonsymbolic representations of numerical magnitude, and can individual variability in such factors be used to predict differences in more complex mathematical processes? We suggest that the availability of information about relative numerical order is a critical factor that distinguishes symbolic ...

The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series.