Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today. Interval methods are useful whenever we have to deal with uncertainties, which can be rigorously bounded. Fuzzy sets, rough sets and probability calculus can perf...

For the familiar Fibonacci sequence (defined by f1 = f2 = 1, and fn = fn−1 + fn−2 for n > 2), fn increases exponentially with n at a rate given by the golden ratio (1 + √ 5)/2 = 1.61803398 . . . . But for a simple modification with both additions and subtractions — the random Fibonacci sequences defined by t1 = t2 = 1, and for n > 2, tn = ±tn−1 ± tn−2, where each ± sign is independent and eithe...

In this paper we address the problem of topic classification of speech data. Our concern in this paper is the situation in which there is no speech or phoneme recognizer available for the domain of the speech data. In this situation the only inputs for training the system are audio speech files labeled according to the topics of interest. The process that we follow in developing the topic class...

In recent years, small and medium-sized enterprises (SMEs) have increasingly adopted Social Media technologies with the purpose of fostering the bidirectional communication with customers or to facilitate the collaboration between employees amongst each other. Thereby, customer posts in a company’s Social Media channels capture consumers’ current attitude towards product and service offerings o...

Interval arithmetic was original developed to estimate rounding errors on floating-point computations but it is used in a wide variety of applications from constraint solvers and global optimizers to power and timing analysis of software processes. The objective of interval analysis is to determine the output ranges (or interval) of a computation set. The main problem of classical interval anal...

1. Review of published ecological studies using path analysis suggests that path analysis is often misused and collinearity is a moderate to severe problem in a majority of the analyses. 2. Multiple regression is shown to be related to path analysis, and thus collinearity, which is a well-known problem in regression analysis, can also be a problem in path analysis. Collinearity occurs when inde...

Finite precision computations may affect the stability of algorithms and the accuracy of computed solutions. In this paper we first obtain a relation for computing the number of common significant digits between the exact solution and a computed solution of a one-dimensional initial-value problem obtained by using a single-step or multi-step method. In fact, by using the approximate solutions o...

Local isotropy, or the statistical isotropy of small scales, is one of the basic assumptions underlying Kolmogorov’s theory of universality of small-scale turbulent motion. The literature is replete with studies purporting to examine its validity and limitations. While, until the midseventies or so, local isotropy was accepted as a plausible approximation at high enough Reynolds numbers, variou...

Finite diierence methods, like the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial diierential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in computer approximations, are strongly ampliied i...

We propose an algorithm for solving two polynomial equations in two variables. Our algorithm is based on the Macaulay resultant approach, combined with new techniques including randomization to make the algorithm accurate in the presence of roundoff error. The ultimate computation is the solution of a generalized eigenvalue problem via the QZ method. We analyze the error due to roundoff of the ...