Related papers: FORM, Diagrams and Topologies
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…
Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…
With the growing demand for immersive digital applications, the need to understand and reconstruct 3D scenes has significantly increased. In this context, inpainting indoor environments from a single image plays a crucial role in modeling…
We study massless fermions interacting through a particular four fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low energy effective action for the…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
We present a machine learning approach that leverages persistent homology to classify bacterial flagellar motors into two functional states: rotated and stalled. By embedding protein structural data into a topological framework, we extract…
Recent development of deep neural networks (DNNs) for tabular learning has largely benefited from the capability of DNNs for automatic feature interaction. However, the heterogeneity nature of tabular features makes such features relatively…
In this work, we propose HypergraphFormer, a novel and efficient approach to floor plan generation based on learning hypergraph representations with a large language model (LLM). The model is trained via supervised fine-tuning to generate a…
Semantic segmentation of microscopy cell images by deep learning is a significant technique. We considered that the Transformers, which have recently outperformed CNNs in image recognition, could also be improved and developed for cell…
Transformers have achieved great success in effectively processing sequential data such as text. Their architecture consisting of several attention and feedforward blocks can model relations between elements of a sequence in parallel…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
We study higher dimensional models with magnetic fluxes, which can be derived from superstring theory. We study mass spectrum and wavefunctions of massless and massive modes for spinor, scalar and vector fields. We compute the 3-point…
We present a new feature extraction method for complex and large datasets, based on the concept of transport operators on graphs. The proposed approach generalizes and extends the many existing data representation methodologies built upon…
We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical…
We present ShapeFormer, a transformer-based network that produces a distribution of object completions, conditioned on incomplete, and possibly noisy, point clouds. The resultant distribution can then be sampled to generate likely…
The force networks of different granular ensembles are defined and their topological properties studied using the tools of complex networks. In particular, for each set of grains compressed in a square box, it is introduced a force…
Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
An efficient method to calculate tadpole diagrams is proposed. Its capability is demonstrated by analytically evaluating two four-loop tadpole diagrams of current interest in the literature, including their $O(\epsilon)$ terms in…
We review the status of the parallel versions of the computer algebra system FORM. In particular, we provide a brief overview about the historical developments, discuss the strengths of ParFORM and TFORM, and mention typical applications.…