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In order to extract hidden joint information from two possibly uncorrelated time-series, we explored the measures of network science. Alongside common methods in time-series analysis of the economic markets, mapping the joint structure of…
Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay;…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
This paper addresses the problem of generating recommendations for completing the outfit given that a user is interested in a particular apparel item. The proposed method is based on a siamese network used for feature extraction followed by…
A matching M is a dominating induced matching of a graph, if every edge of the graph is either in $M$ or has a common end-vertex with exactly one edge in $M$. The concept of complete dominating induced matching is introduced as graphs where…
Word embeddings generated by neural network methods such as word2vec (W2V) are well known to exhibit seemingly linear behaviour, e.g. the embeddings of analogy "woman is to queen as man is to king" approximately describe a parallelogram.…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn, can affect the outcomes of…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Checkerboard framings are an extension of checkerboard colorings for virtual links. According to checkerboard framings, in 2017, Dye obtained an independent invariant of virtual links: the cut point number. Checkerboard framings and cut…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
Analysis of complex networks, particularly material networks such as the carbon skeleton of hydrocarbons generated in hydrocarbon pyrolysis in carbon-rich systems, is essential for effectively describing, modeling, and predicting their…
Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other…