I earned my Master’s degree in mathematics from Sharif University of Technology, Tehran, Iran and my PhD in mathematics from Rutgers University, New Brunswick, New Jersey. I have taught and done research at Center for Quantum Geometry, Denmark, Uppsala University, Sweden and the Biocomplexity Institute at the University of Virginia. I am currently a professor of mathematics and computer science at Shiraz University, Shiraz, Iran. My interests include complex networks, technological analysis, natural language processing and RNA bioinformatics. I am also an AI enthusiast.
My teaching material can be found here.
My research interests are described below. My Google Scholar page is here. For copyright reasons I cannot post PDF files of my publications here but I can send you a copy if you send me a line.
Technological Analysis and Forecasting
Technological Analysis and Forecasting pertains to analyzing the progress of different technological domains, the relationship between technologies (such as technological convergence) and predicting future technological trends such as the improvement rates of different technologies. This is usually achieved using patent data. Professor Christopher Magee of MIT has done a lot of groundbreaking research in technological analysis. I am lucky to have written a paper on estimating the improvement rates of AI subdomains with him.
This story goes back to 2015 when Benson and Magee discovered a strong correlation between a technology’s improvement rates and the average centrality of its patents. Centrality is a notion from complex network theory which quantifies how central a node is in the network. Patents form a network (called the Patent Citation Network) in which links are given by citations from a patent to another one. Such a citation means that an invention makes use of an earlier invention. The result of Benson and Magee simply means that the more central are the inventions belonging to a technological domain, in the global flow of technology, the faster it improves. Later, Triulzi, Alstott and Magee improved this result and obtained a way of estimating a technology’s improvement rate based on the centrality of its patents, using regression analysis. In our work we applied this method to subdomains of Artificial Intelligence. Using a mixture of keywords and patent subject classification, we found about 20000 patents. (Finding AI patents is not easy and different researchers and organizations have devised different methods for this task.)
Our results were quite interesting in that they uncovered a few hidden gems of AI and warned against equating AI with deep learning. Rule-based-Machine Learning (RBML) is little-known but powerful ML method which uses genetic algorithms to obtain local rules which relate the dependent variable to the features in your dataset. It is very explainable and can handle complex relations in data. It is used for supervised, unsupervised, as well as reinforcement learning. Our analysis estimated the highest improvement rate among technical AI subdomains for RBML! On the contrary, our results showed quite an average improvement rate for Deep Learning. The explanations for this are detailed in the paper and also in a Linkedin article, and have to do with the complexity of Deep Learning and the amount of computational power it needs. Roughly speaking, much of the progress of Deep Learning-based methods in recent years is due to the increase in computational power and the incorporation of parallel computing which has been enabled by the transformer neural networks. However the needed computational power has been increasing much faster than the actual increase in computational power, as the following plot from OpenAI demonstrates. See also this report by Center for Security and Emerging Technology.
Another point is that Deep Learning does not have an edge over the “shallow” machine learning methods for all types of data. For example, a study by Ravid Shwartz-Ziv, Amitai Armon shows that XGBoost beats all Deep Learning-based methods for tabular data.
Natural Language Processing (NLP)
NLP is a branch of AI which tries to make it possible to process human language by computers. Problems in NLP include text generation, dialogue (between man and machine), machine translation, natural language understanding (by machine), text classification, speech to text and text to speech conversion, etc. ChatGPT is probably the most well-known product of NLP. As with other types of data, text has to be converted to vectors of numbers before it can be processed by AI algorithms. This is the problem of text representation. One of the classic and famous attempts at text representation was word2vec, which assigns a vector in Euclidean space (of hundreds of dimensions) to each word, in such a way that words that occur close to each other in a corpus of text (and thus, presumably have close meanings), have similar vectors. This approach has been very successful in helping machines understand semantic relatedness of different words, and has paved the way for more advanced text representation methods such as BERT. However one problem with this approach is that the basis of the Euclidean space used for embedding words and sentences, does not have any inherent meaning.
It is for this reason that I am interested in some of the “shallow” methods of text representation such as topic modeling. In topic modeling we start with a corpus of documents and try to find a set of topics such that each of the documents in the corpus can be decomposed as a
Machine Learning
I have taught several courses on Machine Learning for the students of mathematics, computer science and statistics. I’m also in the process of turning the notes for the courses into a book. I have written a chapter of a book on Industry 4.0 which introduces various AI methods and their applications in industry. It was published by Wiley and is available here.
Topological Data Analysis (TDA)
TDA is a relatively new branch of applied mathematics and machine learning which aims at obtaining information from the shape of data. Starting with a dataset of points in the Euclidean space, and choosing a threshold we form the proximity graph of the data which is obtained by connecting pairs of data points whose distance is less than the threshold.
In a work with Samarth Swarup, we extended TDA to data which consist of paths instead of points. Such paths can be e.g. time series, spatial paths of passengers or itinerant animals or the motion path of an agent on a network in an agent-based simulation.
Samarth Swarup, Reza Rezazadegan, Generating an Agent Taxonomy using Topological Data Analysis
RNA Bioinformatics
RNA molecules are some of the most important molecules in biology. They are involved in the expression of genes into proteins and many viruses are based on RNA. The function of an RNA molecule is determined by its tertiary (spatial) structure, which is approximated by its secondary structure. RNA bioinformatics studies problems such as predicting the secondary or tertiary RNA structure from RNA sequence, inverse folding (finding RNA sequences which fold to a given structure) and studying RNA evolution.