Related papers: Roofs and Convexity
We discuss the geometric aspects of a recently described unfolding procedure and show the form of objects relevant in the field of Quantum Information Geometry in the unfolding space. In particular, we show the form of the quantum monotone…
In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied…
We present a novel technical method for analyzing the hidden convex structure embedded in the joint range of a quadratic mapping defined on a Hilbert space. Our approach stands out by relying exclusively on elementary mathematical…
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by…
As observed by Auderset et al. (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter. In…
Based on the AdS/CFT correspondence, we study how to reconstruct bulk spacetime metrics by various quantum information measures on the boundary field theories, which include entanglement entropy, mutual information, entanglement of…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
This is a brief overview of some applications of the ideas of abstract convexity to the upper semilattices of gauges in finite dimensions.
In addition to being a workhorse for modern quantum technologies, entanglement plays a key role in fundamental tests of quantum mechanics. The entanglement of photons in multiple levels, or dimensions, explores the limits of how large an…
Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to…
For a quantale $\mathsf{V}$ we introduce $\mathsf{V}$-approach spaces via $\mathsf{V}$-valued point-set-distance functions and, when $\mathsf{V}$ is completely distributive, characterize them in terms of both, so-called closure towers and…
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…
Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…
Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…