Authors: Waldemar W. Koczkodaj, Dominik Strzalka, Jean-Pierr Magnot, Jiri Mazurek, James Peters, Michael Soltys, Jacek Szybowski, Arturo Tozzi, Hojjat Rakhshani
Title: On normalization of inconsistency indicators in pairwise comparisons
Abstract: In this study, we provide mathematical and practice-driven justification for using [0, 1] normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.
Accepted for publication in the International Journal of Approximate Reasoning, April 2017.
A new paper: On normalization of inconsistency indicators in pairwise comparisons, by W.W. Koczkodaj, J.-P. Magnot, J. Mazurek, J.F. Peters, H. Rakhshani, M. Soltys, D. Strzałka, J. Szybowski and A. Tozzi.
Abstract: In this study, we provide mathematical and practice-driven justification for using [0,1] normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.
The paper can be found here: https://arxiv.org/abs/1702.07205v2
We (Neerja Mhaskar and Michael Soltys) had our paper presented at the Prague Stringology Conference; the paper introduces a new formal framework for Stringology, which consists of a three-sorted logical theory S designed to capture the combinatorial reasoning about finite words:
And these are the slides:
In a new paper, Square-free strings over alphabet lists, my PhD student Neerja Mhaskar and I, solve an open problem that was posed in A new approach to non repetitive sequences, by Jaroslaw Grytczuk, Jakub Kozik, and Pitor Micek, in arXiv:1103.3809, December 2010.
The problem can be stated as follows: Given an alphabet list $L=L_1,\ldots,L_n$, where $|L_i|=3$ and $0 \leq i \leq n$, can we always find a square-free string, $W=W_1W_2 \ldots W_n$, where $W_i\in L_i$? We show that this is indeed the case. We do so using an “offending suffix” characterization of forced repetitions, and a counting, non-constructive, technique. We discuss future directions related to finding a constructive solution, namely a polytime algorithm for generating square-free words over such lists.
Our paper will be presented and published in the 26th International Workshop on Combinatorial Algorithms (IWOCA), Verona, Italy, October 2015.
I wrote a paper about finite games which I presented at Computability in Europe in Athens, 2009. Now it turns out, that the Vienna school of Economics, Wirtschaftsuniversität Wien, has been citing it repeatedly in the last few months, in particular Aurélien Fichet de Clairfontaine. It is very satisfying to see research being picked up by other areas!
Title: Non-repetitive strings over alphabet lists
Authors: Neerja Mhaskar and Michael Soltys
Abstract: A word is non-repetitive if it does not contain a subword of the form vv. Given a list of alphabets L = L1, L2, . . . , Ln, we investigate the question of generating non-repetitive words w = w1w2 . . . wn, such that the symbol wi is a letter in the alphabet Li. This problem has been studied by several authors (e.g., [GKM10], [Sha09]), and it is a natural extension of the original problem posed and solved by A. Thue. While we do not solve the problem in its full generality, we show that such strings exist over many classes of lists. We also suggest techniques for tackling the problem, ranging from online algorithms, to combinatorics over 0-1 matrices, and to proof complexity. Finally, we show some properties of the extension of the problem to abelian squares.