Related papers: FORM, Diagrams and Topologies
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Control theory uses `signal-flow diagrams' to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. These diagrams can be seen as string diagrams for…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
Granular materials exhibit intricate force networks, often concentrated in chains rather than being uniformly distributed. These meso-scale structures are complex to characterize, owing to their heterogeneous and anisotropic nature. We…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast…
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created…
Graph is a well known data structure to represent the associated relationships in a variety of applications, e.g., data science and machine learning. Despite a wealth of existing efforts on developing graph processing systems for improving…
Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node…
In this paper we discuss different recursion relations (BCFW and all-line shift) for the form factors of the operators from the $\mathcal{N}=4$ SYM stress-tensor current supermultiplet $T^{AB}$ in momentum twistor space. We show that…
Modeling long texts has been an essential technique in the field of natural language processing (NLP). With the ever-growing number of long documents, it is important to develop effective modeling methods that can process and analyze such…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in…
The form-factor bootstrap approach is applied to the perturbed minimal models $M_{2,2n+3}$ in the direction of the primary field $\phi_{1,3}$. These theories are integrable and contain $n$ massive scalar particles, whose $S$--matrix is…
In order to reduce the computational complexity of large language models, great efforts have been made to to improve the efficiency of transformer models such as linear attention and flash-attention. However, the model size and…
We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the "in-in" formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the…
In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent…
Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…