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Different numerical mappings of the DNA sequences have been studied using a new cluster-scaling method and the well known spectral methods. It is shown, in particular, that the nucleotide sequences in DNA molecules have robust…
Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process…
We present a framework to systematically analyze convolutional neural networks (CNNs) used in classification of cars in autonomous vehicles. Our analysis procedure comprises an image generator that produces synthetic pictures by sampling in…
DNA-based storage offers unprecedented density and durability, but its scalability is fundamentally limited by the efficiency of parallel strand synthesis. Existing methods either allow unconstrained nucleotide additions to individual…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
Autonomous part assembly is a challenging yet crucial task in 3D computer vision and robotics. Analogous to buying an IKEA furniture, given a set of 3D parts that can assemble a single shape, an intelligent agent needs to perceive the 3D…
We use a coarse-grained model of DNA-functionalized particles to understand the role of DNA chain length on their self-assembly. We find that the increasing chain length for a given particle size decreases the propensity to form ordered…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
We introduce AutoGraph, a scalable autoregressive model for attributed graph generation using decoder-only transformers. By flattening graphs into random sequences of tokens through a reversible process, AutoGraph enables modeling graphs as…
Graph Neural Networks (GNNs) have gained traction in the complex domain of drug discovery because of their ability to process graph-structured data such as drug molecule models. This approach has resulted in a myriad of methods and models…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
Graph Theoretic Process Network Synthesis is described as an introduction to biological networks. Genetic, protein and metabolic systems are considered. The theoretical work of Kauffman is discussed and amplified by critical property…
Self-assembly at submicroscopic scales is an important but little understood phenomenon. A prominent example is virus capsid growth, whose underlying behavior can be modeled using simple particles that assemble into polyhedral shells.…
In this paper we propose new solution methods for designing tag sets for use in universal DNA arrays. First, we give integer linear programming formulations for two previous formalizations of the tag set design problem, and show that these…
Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…
A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…
We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA…
A unicellular collection on a surface is a collection of curves whose complement is a single disk. There is a natural surgery operation on unicellular collections, endowing the set of such with a graph structure where the edge relation is…