Related papers: Assembly in Directed Hypergraphs
Self-assembly of dilute sequence-defined macromolecules is a complex phenomenon in which the local arrangement of chemical moieties can lead to the formation of long-range structure. The dependence of this structure on the sequence…
Graph pattern matching, one of the fundamental graph mining problems, aims to extract structural patterns of interest from an input graph. The state-of-the-art graph matching algorithms and systems are mainly designed for undirected graphs.…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…
This paper investigates given an assembly graph, find the possible micronuclear sequences in terms of MDSs and IESs; which represent Hamiltonian polygonal paths. We will consider the orientations of the assembly graph and Hamiltonian…
For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all…
We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the…
Genome assembly is a fundamental problem in Bioinformatics, requiring to reconstruct a source genome from an assembly graph built from a set of reads (short strings sequenced from the genome). A notion of genome assembly solution is that of…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
This study proposed a model to give a full-scale simulation for the dynamics of the collaborations in the dblp dataset. It is a distributed model with the capability of simulating large hypergraphs, namely systems with heterogeneously…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Retrosynthetic planning, which aims to find a reaction pathway to synthesize a target molecule, plays an important role in chemistry and drug discovery. This task is usually modeled as a search problem. Recently, data-driven methods have…
We present an innovative approach to the synthesis of linear arrays having the least possible number of elements while radiating shaped beams lying in completely arbitrary power masks. The approach, based on theory and procedures lend from…
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph ${\tt G}$ is the simplicial complex whose faces are the multipaths of ${\tt G}$. We compute the Euler characteristic, and associated…
Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…