Related papers: Complex Equiangular Tight Frames and Erasures
Fine-grained entity typing (FET) aims to deduce specific semantic types of the entity mentions in text. Modern methods for FET mainly focus on learning what a certain type looks like. And few works directly model the type differences, that…
Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to…
The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.
This paper focuses on the study of recognizing discontiguous entities. Motivated by a previous work, we propose to use a novel hypergraph representation to jointly encode discontiguous entities of unbounded length, which can overlap with…
SAR image classification naturally has to deal with huge noise and a high dynamic range particularly requiring robust classification models. Additionally, the deployment of these models on edge devices, such as drones and military aircraft,…
A complex projective tower or simply a $\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\mathbb CP$-towers up to diffeomorphism, and as a consequence, we…
Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast,…
All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme…
This paper is devoted to discussing the weighted linear tensor product problems in the worst case setting. We consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We investigate exponential $(s,…
Though high redundancy rate of a tight frame can improve performance in applications, as the dimension increases, it also makes the computational cost skyrocket and the storage of frame coefficients increase exponentially. This seriously…
This paper concerns the overcompleteness of coherent frames for unimodular amenable groups. It is shown that for coherent frames associated with a localized vector a set of positive Beurling density can be removed yet still leave a frame.…
This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive framework for the MRC, emphasizing its importance in ensuring…
Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…
The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real $n$-dimensional manifolds into $\mathbb{C}^n$. The generic topological structure of…
Extreme Learning Machines (ELM) provide a fast alternative to traditional gradient-based learning in neural networks, offering rapid training and robust generalization capabilities. Its theoretical basis shows its universal approximation…
We compute the tensor triangular spectrum of perfect complexes of filtered modules over a commutative ring, and deduce a classification of the thick tensor ideals. We give two proofs: one by reducing to perfect complexes of graded modules…
We analyse the complexity of the satisfiability problem, or similarly feasibility problem, (trSAT) for transformer encoders (TE), which naturally occurs in formal verification or interpretation, collectively referred to as formal reasoning.…
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…