Related papers: Computing in the fractal cloud: modular generic so…
We study the moduli space of triples $(C, L_1, L_2)$ consisting of quartic curves $C$ and lines $L_1$ and $L_2$. Specifically, we construct and compactify the moduli space in two ways: via geometric invariant theory (GIT) and by using the…
In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
A way to add an extra dimension is briefly discussed.
Data aggregation in Geographic Information Systems (GIS) is only marginally present in commercial systems nowadays, mostly through ad-hoc solutions. In this paper, we first present a formal model for representing spatial data. This model…
An important first step in computational SAR modeling is to transform the compounds into a representation that can be processed by predictive modeling techniques. This is typically a feature vector where each feature indicates the presence…
We use the combination of argumentative zoning [1] and a legal argumentative scheme to create legal argumentative segments. Based on the argumentative segmentation, we propose a novel task of classifying argumentative segments of legal case…
This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.
This paper proposes a methodology for generating and perturbing detailed derivations of equations at scale, aided by a symbolic engine, to evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems.…
Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific…
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection…
As the cornerstone of modern power systems, the Unit Commitment Problem (UC) is critical for ensuring operational security and economic efficiency in the ongoing global energy transition. However, existing UC studies typically propose…
Identifying affordance regions on 3D objects from semantic cues is essential for robotics and human-machine interaction. However, existing 3D affordance learning methods struggle with generalization and robustness due to limited annotated…
Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We…
We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction,…
In this article, we provide a simple and systematic way to represent general (inhomogeneous) fractals that may look different at different scales and places. By using set-valued compression maps, we express these general fractals as…
In a former paper it has been shown that the elliptic Gau{\ss} sums, whose use has been proposed in the context of counting points on elliptic curves and primality tests, can be computed by using modular functions. In this work we give…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…
A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple…
There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system…