Nadir Murru

A Bayesian approach for initialization of weights in backpropagation neural net with application to character recognition

Convergence rate of training algorithms for neural networks is heavily affected by initialization of weights. In this paper, an original algorithm for initialization of weights in backpropagation neural net is presented with application to character recognition. The initialization method is mainly based on a customization of the Kalman filter, translating it into Bayesian statistics terms. A metrological approach is used in this context considering weights as measurements modeled by mutually dependent normal random variables. The algorithm performance is demonstrated by reporting and discussing results of simulation trials. Results are compared with random weights initialization and other methods. The proposed method shows an improved convergence rate for the backpropagation training algorithm.

On the periodic writing of cubic irrationals and a generalization of Rédei functions

In this paper, we provide a periodic representation (by means of periodic rational or integer sequences) for any cubic irrationality. In particular, for a root α of a cubic polynomial with rational coefficients, we study the Cerruti polynomials , and , which are defined via Using these polynomials, we show how any cubic irrational can be written periodically as a ternary continued fraction. A periodic multidimensional continued fraction (with pre-period of length 2 and period of length 3) is proved convergent to a given cubic irrationality, by using the algebraic properties of cubic irrationalities and linear recurrent sequences.

Full length article: Periodic representations and rational approximations of square roots

In this paper the properties of Redei rational functions are used to derive rational approximations for square roots and both Newton and Pade approximations are given as particular cases. As a consequence, such approximations can be derived directly by power matrices. Moreover, Redei rational functions are introduced as convergents of particular periodic continued fractions and are applied for approximating square roots in the field of p-adic numbers and to study periodic representations. Using the results over the real numbers, we show how to construct periodic continued fractions and approximations of square roots which are simultaneously valid in the real and in the p-adic field.

An Automatized Method Based on LaTeX for the Realization of Accessible PDF Documents Containing Formulae

Assistive technologies for visually impaired people (screen readers and braille displays) perform satisfactorily with regard to digital documents containing alphabet characters, but they still have a long way to go as far as formulae and graphs are concerned. In general, the most spread digital documents are in PDF format. However, in the case of mathematical contents, they are not accessible at all, since formulae are usually unreadable by screen readers. Currently, a standard and fast method for inserting accessible formulae into a PDF document is still lacking despite it is a very important issue for spreading accessible digital scientific documents. In this paper, we propose a method for automatically generating a PDF document with mathematical contents accessible by assistive technologies for visually impaired people. Specifically, we have developed a LaTeX package that produces a final PDF document where the formulae are totally accessible by screen readers and braille displays.

On the accessibility of Moodle 2 by visually impaired users, with a focus on mathematical content

In this paper we study the accessibility by visually impaired people of the learning management system (LMS) Moodle 2. The study is conducted by testing four different visually impaired subjects, with different degrees of disability and performing different tasks connected to different roles in the LMS. A peculiar focus is given to the accessibility of content involving mathematics. At the end of the paper, some recommendations to improve the accessibility of Moodle 2 are given.

On the operations of sequences in rings and binomial type sequences

Given a commutative ring with identity R, many different and interesting operations can be defined over the set

An isomorphism between the convolution product and the componentwise sum connected to the D’Arcais numbers and the Ramanujan tau function

H_R

Groups and monoids of Pythagorean triples connected to conics

HR of sequences of elements in R. These operations can also give