## Enrollment Predictions with Machine Learning

Happy to announce that our joint paper, Enrollment Predictions with Machine Learning, co-authored with Hung Dang, Ginger Reyes Reilly and Katharine Soltys, has appeared in Volume 9, number 2, of the Strategic Enrollment Management Quarterly (SEMQ).

In this paper a Machine Learning framework for predicting enrollment is proposed. The framework consists of Amazon Web Services SageMaker together with standard Python tools for Data Analytics, including Pandas, NumPy, MatPlotLib and Scikit-Learn. The tools are deployed with Jupyter Notebooks running on AWS SageMaker. Based on three years of enrollment history, a model is built to compute — individually or in batch mode — probabilities of enrollments for given applicants. These probabilities can then be used during the admission period to target undecided students. The audience for this paper is both SEM practitioners and technical practitioners in the area of data analytics. Through reading this paper, enrollment management professionals will be able to understand what goes into the preparation of Machine Learning model to help with predicting admission rates. Technical experts, on the other hand, will gain a blue-print for what is required from them.

This paper has been made possible in part by the AWS Pilot Program in Machine Learning where California State University Channel Islands was one if the participating institutions.

## Our results in “Edge Covers” picked up by an Astronautics research group at MIT

In May 2018, Ryan McIntyre defended his masters thesis (at CSUCI under my supervision) on  Bounding the size of minimal clique covers. We followed up with a publication of the results in the Journal of Discrete Algorithms (https://doi.org/10.1016/j.jda.2018.03.002) [post], and now, two years later, our results are cited and built upon in an interesting paper Static beam placement and frequency plan algorithms for LEO constellations (https://doi.org/10.1002/sat.1345) written by an Astronautics research group at MIT.

What is interesting about this is the serendipitous manner in which results build on each other: our result consisted in a partial solution to an original problem in combinatorics posed by the itinerant mathematician Paul Ërdos (posed in the mid 1960s), which we then used to partially solve a problem related to string indeterminates (also in this case working on previous results of Joel Helling [post]), which are related to genetics. Now, our work is being used to solve the problem of satellite allocation.

## My book “An Intro to the Analysis of Algorithms”

My book, An Introduction to the Analysis of Algorithms, has been identified by the publisher, World Scientific, as one of the most downloaded ebooks. See my page http://www.msoltys.com/book with all the book details and resources (slides, GitHub repository with implementations of all algorithms, solutions to problems, errata, etc.).

## Our paper with Neerja Mhaskar on logic of stringology appeard in Discrete Applied Math

In this paper, A new formal framework for Stringology is proposed, which consists of a three-sorted logical theory $S$ designed to capture the combinatorial reasoning about finite strings. We propose a language $L_S$ for expressing assertions about strings, and study in detail two sets of formulas $\Sigma_0^B$, a set of formulas decidable in polytime, and $\Sigma_1^B$, a set of formulas with the property that those provable in $S$ yield polytime algorithms.

## Paper with Ryan McIntyre to appear in the Journal of Discrete Algorithms

Happy to announce that Ryan McIntyre’s masters thesis results, An improved upper bound and algorithm for clique covers (prelim), will be published as our joint paper in Journal of Discrete Algorithms.

Our paper is on indeterminate strings, which are important for their applicability in bioinformatics. (They have been considered, for example, in Christodoulakis 2015  and Helling 2017.)

An interesting feature of indeterminate strings is the natural correspondence with undirected graphs. One aspect of this correspondence is the fact that the minimal alphabet size of indeterminates representing any given undirected graph corresponds to the size of the minimal clique cover of this graph. This paper first considers a related problem proposed in Helling 2017: characterize \$latex\Theta_n(m)\$, which is the size of the largest possible minimal clique cover (i.e., an exact upper bound), and hence alphabet size of the corresponding indeterminate, of any graph on $n$ vertices and $m$ edges. We provide improvements to the known upper bound for $\Theta_n(m)$. Helling 2017 also presents an algorithm which finds clique covers in polynomial time. We build on this result with an original heuristic for vertex sorting which significantly improves their algorithm’s results, particularly in dense graphs.

This work was the result of building on Helling 2017 (see this post) and of a year of research undertaken by Ryan McIntyre under my (Michael Soltys) supervision at the California State University Channel Islands.

## Happy that our paper with Ariel Fernandez & Ryszard Janicki will appear in IJCA

Very happy that our paper Computing covers from matchings with permutations, with Ariel Fernández and Ryszard Janicki, is going to appear in the International Journal of Computer Applications.

We present a matrix permutation algorithm for computing a minimal vertex cover from a maximal matching in a bipartite graph. Our algorithm is linear time and linear space, and provides an interesting perspective on a well known problem. Unlike most algorithms, it does not use the concept of alternating paths, and it is formulated entirely in terms of combinatorial operations on a binary matrix. The algorithm relies on permutations of rows and columns of a 0-1 matrix which encodes a bipartite graph together with its maximal matching. This problem has many important applications such as network switches which essentially compute maximal matchings between their incoming and outgoing ports.

## New paper on normalization of inconsistency indicators – to appear in Journal of Approx Reason

Authors: Waldemar W. Koczkodaj, Dominik Strzalka, Jean-Pierr Magnot, Jiri Mazurek, James Peters, Michael Soltys, Jacek Szybowski, Arturo Tozzi, Hojjat Rakhshani

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

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

## Neerja Mhaskar and I have a paper presented at PSC 2015

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: