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High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors (e.g., time and groups). Methods for estimating graphical models…
We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
The 2+1D topological order can be characterized by the mapping-class-group representations for Riemann surfaces of genus-1, genus-2, etc. In this paper, we use those representations to determine the possible gapped boundaries of a 2+1D…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
The challenge of Domain Generalization (DG) in Face Anti-Spoofing (FAS) is the significant interference of domain-specific signals on subtle spoofing clues. Recently, some CLIP-based algorithms have been developed to alleviate this…
We construct rational models for classifying spaces of self-equivalences of bundles over simply connected finite CW-complexes relative to a given simply connected subcomplex. Via work of Berglund-Madsen and Krannich this specializes to…
Computing the cohomology of the tensor product of two vector bundles is central in the study of their moduli spaces and in applications to representation theory, combinatorics and physics. These computations play a fundamental role in the…
A topological constraint on the possible values of the universal quantization parameter is revealed in the case of geometric quantization on (boundary) curves diffeomorphic to $S^1$, analytically extended on a bounded domain in…
The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The…
In computer vision, unsupervised domain adaptation (UDA) is an approach to transferring knowledge from a label-rich source domain to a fully-unlabeled target domain. Conventional UDA approaches have two problems. The first problem is that a…
We obtain full moduli parameters for generic non-planar BPS networks of domain walls in an extended Abelian-Higgs model with $N$ complex scalar fields, and exhaust all exact solutions in the corresponding $\mathbb{C}P^{N -1}$ model. We…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
Here, we develop a framework for the prediction and screening of native defects and functional impurities in a chemical space of Group IV, III-V, and II-VI zinc blende (ZB) semiconductors, powered by crystal Graph-based Neural Networks…
We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…
In this research work, we have demonstrated the application of Mask-RCNN (Regional Convolutional Neural Network), a deep-learning algorithm for computer vision and specifically object detection, to semiconductor defect inspection domain.…
Learning domain-invariant visual representations is important to train a model that can generalize well to unseen target task domains. Recent works demonstrate that text descriptions contain high-level class-discriminative information and…
We introduce an associative algebra $A^{\infty}(V)$ using infinite matrices with entries in a grading-restricted vertex algebra $V$ such that the associated graded space $Gr(W)=\coprod_{n\in \mathbb{N}}Gr_{n}(W)$ of a filtration of a…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…