Related papers: Generalized Replica Manifolds I: Surgery and Avera…
In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as…
Renormalized entanglement entropy can be defined using the replica trick for any choice of renormalization scheme; renormalized entanglement entropy in holographic settings is expressed in terms of renormalized areas of extremal surfaces.…
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra…
We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g.,…
We extend the approach of Casini, Huerta and Myers to a new calculation of the Renyi entropy of a general CFT in d dimensions with a spherical entangling surface, in terms of certain thermal partition functions. We apply this approach to…
Recently variational models with priors involving first and second order derivatives resp. differences were successfully applied for image restoration. There are several ways to incorporate the derivatives of first and second order into the…
Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…
Will further scaling up of machine learning models continue to bring success? A significant challenge in answering this question lies in understanding generalization gap, which is the impact of overfitting. Understanding generalization gap…
We calculate the entanglement entropy between two (maximally-extended) spacetime regions of static black hole, seperated by horizon. As a first case, we consider the Schwarzschild black hole, and then we extend the calculations to the…
This manuscript is a review of the main results obtained in a series of papers involving the present authors and their collaborator J.L. Cardy over the last two years. In our work we have developed and applied a new approach for the…
Entanglement entropy is an essential metric for characterizing quantum many-body systems, but its numerical evaluation for neural network representations of quantum states has so far been inefficient and demonstrated only for the restricted…
A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a…
Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…
Symmetry-resolved entanglement, capturing the refined structure of quantum entanglement in systems with global symmetries, has attracted a lot of attention recently. In this manuscript, introducing the notion of symmetry-resolved…
Neural operators are neural network-based surrogate models for approximating solution operators of parametric partial differential equations, enabling efficient many-query computations in science and engineering. Many applications,…
We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
We reconstruct all (2+1)D quantum double models of finite groups from their boundary symmetries through the repeated application of a gauging procedure, extending the existing construction for abelian groups. We employ the recently proposed…
We introduce "Replicated Entanglement Entropy (REE)" as the entanglement entropy of a subspace in a replicated theory. We calculate this quantity by replicating the original theory in two steps along the same entangling region and taking…
Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the RG flow. After introducing a new generalized temperature which satisfies the thermodynamics-like law even in the IR regime, we find that the…