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This document aims to familiarize readers with temporal graph learning (TGL) through a concept-first approach. We have systematically presented vital concepts essential for understanding the workings of a TGL framework. In addition to…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…
Let $\Gamma$ be a metric graph having a linear system $g^r_{2r}$ for some $2 \leq r \leq g-2$ then $\Gamma$ has a linear system $g^1_2$. This is similar to the well-known Clifford's Theorem from the theory of linear systems on smooth…
Numerous social, medical, engineering and biological challenges can be framed as graph-based learning tasks. Here, we propose a new feature based approach to network classification. We show how dynamics on a network can be useful to reveal…
We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout…
We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…
A proof of Petri's general conjecture on the unobstructedness of linear systems on a general curve is proposed, using only the local properties of the deformation space of the pair (curve, line bundle).
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
We study a family of pattern-detection problems in vertex-colored temporal graphs. In particular, given a vertex-colored temporal graph and a multiset of colors as a query, we search for temporal paths in the graph that contain the colors…
We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc…
We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time…
We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
Many time series are generated by a set of entities that interact with one another over time. This paper introduces a broad, flexible framework to learn from multiple inter-dependent time series generated by such entities. Our framework…
A (possibly denerate) drawing of a graph $G$ in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph…
Graph embeddings learn the structure of networks and represent it in low-dimensional vector spaces. Community structure is one of the features that are recognized and reproduced by embeddings. We show that an iterative procedure, in which a…
We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. Burdzy and Pal in their paper proposed a continuous version of graphical models --…