Related papers: Entropy bounds for Glass networks
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system.…
Guessing random additive noise decoding (GRAND) is a code-agnostic decoding method that iteratively guesses the noise pattern affecting the received codeword. The number of noise sequences to test depends on the noise realization. Thus,…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
We discuss the need for discretization to evaluate the configurational entropy in a general model. We also discuss the prescription using restricted partition function formalism to study the stationary limit of metastable states. We…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
A general method is presented for modeling high entropy alloys as ensembles of randomly sampled, ordered configurations on a given lattice. Statistical mechanics is applied post hoc to derive the ensemble properties as a function of…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behaviour of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very…
Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This…
We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with…
In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…
We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
Channel decoding is a challenging task in communication channels exhibiting memory effects. In this work, we apply the recently proposed decoding paradigm of guessing random additive noise decoding (GRAND) to channels with memory, focusing…
We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand…
The injective norm is a natural generalization to tensors of the operator norm of a matrix. In quantum information, the injective norm is one important measure of genuine multipartite entanglement of quantum states, where it is known as the…