Related papers: From sources to initial data and back again: on bu…
The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…
A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged…
We consider a class of wild initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We identify the closure of this class in the natural $L^1$-topology…
The 2D Euler equations is the basic example of fluid models for which a microcanical measure can be constructed from first principles. This measure is defined through finite-dimensional approximations and a limiting procedure. Creutz's…
Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…
Individual-level data (microdata) that characterizes a population, is essential for studying many real-world problems. However, acquiring such data is not straightforward due to cost and privacy constraints, and access is often limited to…
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for non-structured data is exponential on the number of qubits. Several works address this…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
In modern data analysis, information is frequently collected from multiple sources, often leading to challenges such as data heterogeneity and imbalanced sample sizes across datasets. Robust and efficient data integration methods are…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
We consider a generalization of the fundamental $k$-means clustering for data with incomplete or corrupted entries. When data objects are represented by points in $\mathbb{R}^d$, a data point is said to be incomplete when some of its…
Recently Horodecki et al. [Phys. Rev. Lett. 90, 100402 (2003)] introduced an important quantum information processing paradigm, in which two parties sharing many copies of the same bipartite quantum state distill local pure states, by means…
Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic…
Traditional perturbative statistical disclosure control (SDC) approaches such as microaggregation, noise addition, rank swapping, etc, perturb the data in an ``ad-hoc" way in the sense that while they manage to preserve some particular…
The differential capacitance comprises the most relevant thermodynamic information about an electrochemical system. Classical approaches to describe electrochemical capacitance have difficulties to combine the treatment of the ionic…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Despite the rich and fruitful history of the integrability approach to string theory on the $AdS_3\times S^3\times T^4$ background, it has not been possible to extract many concrete predictions from integrability, except in a strict…
This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York,…
Quantum information processing provides remarkable advantages over its classical counterpart. Quantum optical systems are proved to be sufficient for realizing general quantum tasks, which however often rely on single photon sources. In…
These lectures review recent developments in our understanding of the emergence of local bulk physics in AdS/CFT. The primary topics are sufficient conditions for a conformal field theory to have a semiclassical dual, bulk reconstruction,…