Papers by Donatella Merlini
Springer monographs in mathematics, 2022
Springer monographs in mathematics, 2022
Discrete Mathematics, May 1, 2007
We study the relation between binary words excluding a pattern and proper Riordan arrays. In part... more We study the relation between binary words excluding a pattern and proper Riordan arrays. In particular, we prove necessary and sufficient conditions under which the number of words counted with respect to the number of zeroes and ones bits are related to proper Riordan arrays. We also give formulas for computing the generating functions (d(x), h(x)) defining the Riordan array.
Springer monographs in mathematics, 2022
Springer monographs in mathematics, 2022
Springer Monographs in Mathematics
Springer Monographs in Mathematics
Springer Monographs in Mathematics
This series publishes advanced monographs giving well-written presentations of the "state-of-the-... more This series publishes advanced monographs giving well-written presentations of the "state-of-the-art" in fields of mathematical research that have acquired the maturity needed for such a treatment. They are sufficiently self-contained to be accessible to more than just the intimate specialists of the subject, and sufficiently comprehensive to remain valuable references for many years. Besides the current state of knowledge in its field, an SMM volume should ideally describe its relevance to and interaction with neighbouring fields of mathematics, and give pointers to future directions of research.
Proceedings of the 8th International Conference on Computer Supported Education, 2016
In a data mining project evolved on a relational database often a significant effort needs to be ... more In a data mining project evolved on a relational database often a significant effort needs to be done to construct the data set for the analysis. In fact, usually the database contains a series of normalized tables that need to be joined, aggregated and processed in an appropriate way to build the data set. This process generates various SQL queries that are written independently of each other, in a disordered manner. In this way, the database grows with tables and views which are not present at the conceptual level and this can yield problems for the development of the database. In this paper we consider a typical database containing data about students, courses and exams and illustrate some SQL transformations to build a data set to perform a sequential pattern analysis eventually combined with clustering and classification. In particular, we introduce in the student database some interesting patterns representing relationship between the exams given by students in various periods and the career of each student. This is achieved by introducing a particular encoding of a the career of a student. The resulting table can be analyzed with clustering and classification algorithms. We present a case study following this organization.
Linear Algebra and its Applications, 2016
Using the inverse limit tool, we obtain the Riordan group in its infinite and bi-infinite represe... more Using the inverse limit tool, we obtain the Riordan group in its infinite and bi-infinite representations from groups of finite Riordan matrices. We define two different reflections for bi-infinite Riordan matrices. Employing these definitions, we give answers to the problems D ⊥ = D and D ♦ = D in the Riordan group. So, we describe the self-complementary and self-dual Riordan matrices.
Maple Transactions
Teaching analysis of algorithms to students in Computer Science degrees, using the approach popul... more Teaching analysis of algorithms to students in Computer Science degrees, using the approach popularized by Knuth in his series of books ``The Art of Computer Programming" and later by Sedgewick and Flajolet in the book ``An Introduction to the Analysis of Algorithms", is not a simple task since, in general, these students are more interested in the implementation of an algorithm than in the corresponding theoretical aspects. This approach concentrates on precisely characterizing the performance of algorithms by determining their best, worst and average case performance using a methodology based on symbolic tools such as recurrence relations and generating functions.The most difficult aspect is to understand the average case since this corresponds to studying the algorithm as its possible inputs vary: this represents the most important goal since generally students have no difficulty in understanding the best and worst cases, corresponding to particular input configurations...
Discrete Mathematics & Theoretical Computer Science, 2003
Discrete Mathematics & Theoretical Computer Science, 2005
Data, 2022
In this paper we consider courses of a Computer Science degree in an Italian university from the ... more In this paper we consider courses of a Computer Science degree in an Italian university from the year 2011 up to 2020. For each course, we know the number of exams taken by students during a given calendar year and the corresponding average grade; we also know the average normalized value of the result obtained in the entrance test and the distribution of students according to the gender. By using classification and clustering techniques, we analyze different data sets obtained by pre-processing the original data with information about students and their exams, and highlight which courses show a significant deviation from the typical progression of the courses of the same teaching year, as time changes. Finally, we give heat maps showing the order in which exams were taken by graduated students. The paper shows a reproducible methodology that can be applied to any degree course with a similar organization, to identify courses that present critical issues over time. A strength of the...
Communications in Computer and Information Science, 2018
Advanced clustering techniques are used on educational data concerning various cohorts of univers... more Advanced clustering techniques are used on educational data concerning various cohorts of university students. First, K-means analysis is used to classify students according to the results of the self assessment test and the first year performance. Then, the analysis concentrates on the subset of the data involving the cohorts of students for which the behavior during the first, second and third year of University is known. The results of the second and third year are analyzed and the students are re-assigned to the clusters obtained during the analysis of the first year. In this way, for each student we are able to obtain the sequence of traversed clusters during three years, based on the results achieved during the first. For the data set under analysis, this analysis highlights three groups of students strongly affected by the results of the first year: high achieving students who start high and maintain their performance over the time, medium-high achieving students throughout the entire course of study and, low achieving students unable to improve their performance who often abandon their studies. This kind of study can be used by the involved laurea degree to detect critical issues and undertake improvement strategies.
We consider some Riordan arrays related to binary words avoiding a pattern p, which can be easily... more We consider some Riordan arrays related to binary words avoiding a pattern p, which can be easily studied by means of an A-matrix rather than their A-sequence. Both concepts allow us to define every element as a linear combination of other elements in the array; the A-sequence is unique and corresponds to a linear dependence from the previous row. The A-matrix is not unique and corresponds to a linear dependence from several previous rows. However, for the problems considered in the present paper, we show that the A-matrix approach is more convenient. We provide explicit algebraic generating functions for these Riordan arrays and obtain many statistics on the corresponding languages. We thus obtain a deeper insight of the languages L[p] of binary words avoiding p having a number of zeroes less or equal to the number of ones. 1
We give an alternative proof of an identity that appeared recently in Integers. By using the conc... more We give an alternative proof of an identity that appeared recently in Integers. By using the concept of Riordan arrays we obtain a short, elementary proof.
Proceedings of the 6th International Conference on Computer Supported Education, 2014
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Papers by Donatella Merlini