Related papers: Computing Defects Associated to Bounded Domain Wal…
In this paper we generalize the classical Groebner basis technique to prove the existence and present a method of computation of a dimension polynomial in two variables associated with a finitely generated D-module, that is, a finitely…
Learning universal graph representations across heterogeneous domains is difficult because graph datasets differ in topology, node-attribute semantics, feature dimensions, and even attribute availability. We propose GraphVec, a…
We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength. We derive the defect gluing condition for the sigma-model fields and their derivatives, and use it to…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
We solve the problem of determining basic topological properties of flat samples by performing measurements on their outer edge. The global maximum of four probe resistances shows a characteristic behaviour, which is dependent on the genus…
We study surface defects in three-dimensional topological quantum field theories which separate different theories of Reshetikhin-Turaev type. Based on the new notion of a Frobenius algebra over two commutative Frobenius algebras, we…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key…
We study the problem of computing the conformal modulus of rings and quadrilaterals with strong singularities and cusps on their boundary. We reduce this problem to the numerical solution of the associated Dirichlet and Dirichlet-Neumann…
Discrete symmetry-breaking phase transitions in the early universe may have caused the formation of networks of sheet-like topological defects, usually referred to as domain walls, which separate regions that have settled into different…
The best merge problem in industrial data science generates instances where disparate data sources place incompatible relational structures on the same set $V$ of objects. Graph vertex labelling data may include (1) missing or erroneous…
We devise and analyze hybrid polyhedral methods of arbitrary order for the approximation of div-curl systems on three-dimensional domains featuring non-trivial topology. The div-curl systems we are interested in stem from magnetostatics,…
We consider a classical field configuration, corresponding to intersection of two domain walls in a supersymmetric model, where the field profile for two parallel walls at a finite separation is known explicitly. An approximation to the…
We discuss classical and quantum aspects of the dynamics of a family of domain walls arising in a generalized Wess-Zumino model. These domain walls can be embedded in ${\cal N}=1$ supergravity as exact solutions and are composed of two…
In this paper, we propose a new deep learning network "GENet", it combines the multi-layer network architec- ture and graph embedding framework. Firstly, we use simplest unsupervised learning PCA/LDA as first layer to generate the low-…
Deep models suffer from limited generalization capability to unseen domains, which has severely hindered their clinical applicability. Specifically for the retinal vessel segmentation task, although the model is supposed to learn the…
AlphaFold can be used for both single-chain and multi-chain protein structure prediction, while the latter becomes extremely challenging as the number of chains increases. In this work, by taking each chain as a node and assembly actions as…
A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the…
This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…
Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of defects or domain walls. This perspective allows for a rich generalisation of the orbifolding procedure, which we study in detail for the case of…
Over a field of characteristic $0$ we give a concrete, computation--ready description of Jordan algebra structures and their low--order deformation theory. The Jordan identity is quartic in the elements and cubic in the multiplication, and…