相关论文: Hierarchy of Frustrations as Supplementary Indices…

A misfit parameter is used to characterize the degree of frustration of ordered and disordered systems. It measures the increase of the ground-state energy due to frustration in comparison with that of a relevant reference state. The misfit…

We show that the emergence of systemic risk in complex systems can be understood from the evolution of functional networks representing interactions inferred from fluctuation correlations between macroscopic observables. Specifically, we…

The frustration index is a key measure for analysing signed networks, which has been underused due to its computational complexity. We use an exact optimisation-based method to analyse frustration as a global structural property of signed…

We introduce a U(1) lattice gauge theory which incorporates explicit frustration in $d>2$. We show, by identifying an appropiate order parameter and through computer simulations, the existence of a frustrated region in the phase diagram of…

Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…

As Phil Anderson noted long ago, frustration can be generally defined by measuring the fluctuations in the coupling energy across a plane boundary between two large blocks of material. Since that time, a number of groups have studied the…

A simple spin model is studied, motivated by the dynamics of traders in a market where expectation bubbles and crashes occur. The dynamics is governed by interactions which are frustrated across different scales: While ferromagnetic…

We study the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice, taking into account the exchange interactions of atomic spins at the sites of the nearest, next-nearest, and third neighbors. The…

Most of the analyses concerning signed networks have focused on the balance theory, hence identifying frustration with undirected, triadic motifs having an odd number of negative edges; much less attention has been paid to their directed…

In this work we propose a novel concept of a hierarchical confusion matrix, opening the door for popular confusion matrix based (flat) evaluation measures from binary classification problems, while considering the peculiarities of…

For the signed graph associated to a deep neural network, one can compute the frustration level, i.e., test how close or distant the graph is to structural balance. For all the pretrained deep convolutional neural networks we consider, we…

Frustration, or the competition between interacting components of a network, is often responsible for the complexity of many body systems, from social and neural networks to protein folding and magnetism. In quantum magnetic systems,…

The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such…

The resolution of geometric frustration in systems with continuous degrees of freedom often involves a cooperative inhomogeneous response and super-extensive energy scaling. In contrast, the frustration in frustrated Ising-like spin systems…

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…

The frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice are investigated taking into account the exchange interactions of atomic spins at the sites of the first (nearest), second (next-nearest) and…

Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches…

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence,…

In this paper, the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice in an external magnetic field are investigated, taking into account the exchange interactions of atomic spins at the sites of…

Aligning human-interpretable concepts with the internal representations learned by modern machine learning systems remains a central challenge for interpretable AI. We introduce a geometric framework for comparing supervised human concepts…