Related papers: Study of weaving frames in Krein spaces

This piece of work presents a meaningful example for the advantages of using bitwise operations for creating effective algorithms in programming. A task connected with mathematical modeling in weaving industry is examined and computed.

In this work, we introduce the notion of a two-Krein space and show that, starting from any classical Krein space, it is possible to construct spaces endowed with an indefinite two-inner product (admitting both positive and negative…

We consider a dynamic inverse problem for a dynamical system which describes the propagation of waves in a Krein string. The problem is reduced to an integral equation and an important special case is considered when the string density is…

We characterize Riesz frames and frames with the subframe property and use this to answer most of the questions from the literature concerning these properties and their relationships to the projection methods etc.

This paper reviews machine learning applications and approaches to detection, classification and control of intelligent materials and structures with embedded distributed computation elements. The purpose of this survey is to identify…

Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and few results in Bognar's paper are generalized.

The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

Interweaving relations are introduced and studied here in a general Markovian setting as a strengthening of usual intertwining relations between semigroups, obtained by adding a randomized delay feature. They provide a new classification…

Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi…

Explainability of deep neural networks is one of the most challenging and interesting problems in the field. In this study, we investigate the topic focusing on the interpretability of deep learning-based registration methods. In…

Data erasure can often occur in communication. Guarding against erasures involves redundancy in data representation. Mathematically this may be achieved by redundancy through the use of frames. One way to measure the robustness of a frame…

A broad class of problems at the core of computational imaging, sensing, and low-level computer vision reduces to the inverse problem of extracting latent images that follow a prior distribution, from measurements taken under a known…

The present paper provides a comprehensive study of de-noising properties of frames and, in particular, tight frames, which constitute one of the most popular tools in contemporary signal processing. The objective of the paper is to bridge…

In architecture and computer-aided design, wireframes (i.e., line-based models) are widely used as basic 3D models for design evaluation and fast design iterations. However, unlike a full design file, a wireframe model lacks critical…

Diffusion models have enabled high-quality, conditional image editing capabilities. We propose to expand their arsenal, and demonstrate that off-the-shelf diffusion models can be used for a wide range of cross-domain compositing tasks.…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…

We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new versions of de Branges' Ordering Theorem for nearly…