Related papers: GridPyM: a Python module to handle grid diagrams

Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…

We present an open-source simulation framework for optically detected magnetic resonance, developed in Python. The framework allows users to construct, manipulate, and evolve multipartite quantum systems that consist of spins and electronic…

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…

We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a presentation of a module to an $R$-diagram. The latter is the…

Given a large social or computer network, how can we visualize it, find patterns, outliers, communities? Although several graph visualization tools exist, they cannot handle large graphs with hundred thousand nodes and possibly million…

Many interesting datasets ubiquitous in machine learning and deep learning can be described via graphs. As the scale and complexity of graph-structured datasets increase, such as in expansive social networks, protein folding, chemical…

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…

Knitting, an ancient fiber art, creates a structured fabric consisting of loops or stitches. Publishing hand knitting patterns involves lengthy testing periods and numerous knitters. Modeling knitting patterns with graphs can help expedite…

Software that processes real-world data or that models a physical system must have some way of managing units. While simple approaches like the understood convention that all data are in a unit system (such as the MKS SI unit system) do…

Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot…

Complex models, such as neural networks (NNs), are comprised of many interrelated components. In order to represent these models, eliciting and characterising the relations between components is essential. Perhaps because of this, diagrams,…

An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…

We defined a grid homology theory for spatial graphs. We showed that the skein exact sequence of singular knots can be extended to our grid homology for spatial graphs.

Since their Nobel Prize winning discovery in 2005, grid cells have been studied extensively by neuroscientists. Their multi-scale periodic firing rates tiling the environment as the animal moves around has been shown as critical for path…

An open source symbolic tool for vector fields analysis 'SymFields' is developed in Python. The SymFields module is constructed upon Python symbolic module sympy, which could only conduct scaler field analysis. With SymFields module, you…

Array programming provides a powerful, compact, expressive syntax for accessing, manipulating, and operating on data in vectors, matrices, and higher-dimensional arrays. NumPy is the primary array programming library for the Python…

In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of…

We present python libraries for Feynman graphs manipulation. The key feature of these libraries is usage of generalization of graph representation offered by B. G. Nickel et al. In this approach graph is represented in some unique…

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…