Related papers: A general framework for island systems
Islands are combinatorial objects that can be intuitively defined on a board consisting of a finite number of cells. Based on the neighbor relation of the cells, it is a fundamental property that two islands are either containing or…
It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of…
A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…
We study the implementation of the island prescription in fuzzball-inspired models of black holes. As a simplified setup, we model a fuzzball by replacing the event horizon with a reflecting boundary (stretched horizon). In the framework of…
Entanglement islands have played a key role in the recent derivation of the Page curve and other progress on the black hole information problem. Arising from the inclusion of connected wormhole saddles in a gravitational replica trick,…
The domain of cluster analysis is a meeting point for a very rich multidisciplinary encounter, with cluster-analytic methods being studied and developed in discrete mathematics, numerical analysis, statistics, data analysis, data science,…
In this paper we propose a mechanism to generate entanglement islands in quantum systems from a purely quantum information perspective. More explicitly we show that, if we impose certain constraints on a quantum system by projecting out…
A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
It has been established in both high and low spacetime dimensions that existing constructions of entanglement islands, at least in the study of black holes, are all in the context of massive gravity. In fact, later studies realized that the…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a…
Identifying an entanglement island requires exquisite control over the entropy of quantum fields, which is available only in toy models. Here we present a set of sufficient conditions that guarantee the existence of an island and place an…
A wiggle is an embedded curve in the plane that is the attractor of an iterated function system associated to a complex parameter z. We show the space of wiggles is disconnected -- i.e. there is a wiggle island.
Large-scale system development companies are increasingly adopting agile methods. While this adoption may improve lead-times, such companies need to balance two trade-offs: (i) the need to have a uniform, consistent development method on…
Recent progress in our understanding of the black hole information paradox has lead to a new prescription for calculating entanglement entropies, which involves special subsystems in regions where gravity is dynamical, called…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
This article presents the mathematical background of general interactive systems. The first principle of designing a large system is to _divide and conquer_, which implies that we could possibly reduce human error if we divided a large…
The term islands in linguistics refers to phrases from which extracting an element results in ungrammaticality (Ross, 1967). Grammatical subjects are considered islands because extracting a sub-part of a subject results in an ill-formed…