Related papers: Geometric Entropy and Retrieval Phase Transitions …

Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very…

We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on…

The holographic bit threads are an insightful tool to investigate the holographic entanglement entropy and other quantities related to the bipartite entanglement in AdS/CFT. We mainly explore the geodesic bit threads in various static…

We discuss a class of quantum theories which exhibit a sharply increased memory storage capacity due to emergent gapless degrees of freedom. Their realization, both theoretical and experimental, is of great interest. On the one hand, such…

In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…

We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. This theory allows to reformulate Bachmann's classification of PTs for finite-size systems in terms of geometric properties of…

Inspired by the holographic computation of large interval entanglement entropy of two dimensional conformal field theory at high temperature, it was proposed that the thermal entropy is related to the entanglement entropy as…

In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We disclose the properties of phases mostly from the holographic topological entanglement…

We study the holographic construction of timelike entanglement entropy (tEE) in black hole backgrounds in Lorentzian geometries. The holographic tEE is realized through extremal surfaces consisting of spacelike and timelike branches that…

In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…

Computing the holographic entanglement entropy proposed by Ryu-Takayanagi shows that thermal energy near boundary region in $AdS_3$ gain maximum of the temperature. The absolute maxima of temperature is $T^{Max}_{E}= \frac{4G_3…

We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…

Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical…

A new nonparametric approach for system identification has been recently proposed where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this…

We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions.We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical…

In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method from [Crane et al. 2013] can be reformulated…

We propose a systematic scheme to reach the properties of two-dimensional (2D) statistical and quantum systems by studying the effective (1+1)-dimensional theory that is constructed from the tensor network representation. On on hand, we…

Standard thermodynamic treatments of quantum field theory in the presence of black-hole backgrounds reproduce the black hole entropy by usually specializing to the leading order of the heat-kernel or the high-temperature expansion. By…

Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In…

Statistical mechanics of spin glasses is one of the main strands toward a comprehension of information processing by neural networks and learning machines. Tackling this approach, at the fairly standard replica symmetric level of…