Statistical physics of network structure and information dynamics

In the last two decades, network science has proven to be an invaluable tool for the analysis of empirical systems across a wide spectrum of disciplines, with applications to data structures admitting a representation in terms of complex networks. On the one hand, especially in the last decade, an increasing number of applications based on geometric deep learning have been developed to exploit, at the same time, the rich information content of a complex network and the learning power of deep architectures, highlighting the potential of techniques at the edge between applied math and computer science. On the other hand, studies at the edge of network science and quantum physics are gaining increasing attention, e.g., because of the potential applications to quantum networks for communications, such as the quantum Internet. In this work, we briefly review a novel framework grounded on statistical physics and techniques inspired by quantum statistical mechanics which have been successfully used for the analysis of a variety of complex systems. The advantage of this framework is that it allows one to define a set of information-theoretic tools which find widely used counterparts in machine learning and quantum information science, while providing a grounded physical interpretation in terms of a statistical field theory of information dynamics. We discuss the most salient theoretical features of this framework and selected applications to protein-protein interaction networks, neuronal systems, social and transportation networks, as well as potential novel applications for quantum network science and machine learning.

Results of the Water Quality Study Within the Luga­-Balt-­2 International Project

The authors noted the transboundary nature of anthropogenic impact on the environment, including that on water bodies, which needs to be studied in an international format. (Research purpose) To determine the water state of the Urpolanjoki River in the Mikkeli area in Finland and the Luga River in Russia in order to prepare proposals for improvement. (Materials and methods) Water quality was specified by 11 parameters by sampling and analyzing them in the laboratory. Additionally, 1South-Eastern Finland University of Applied Sciences carried out online monitoring using the YSI 6920-V2 continuous water probe. The authors used standard methods of processing statistical, field data. (Results and discussion) The authors revealed good, stable during the entire monitoring period, water quality in the Urpolanjoki River. The authors showed that the water quality in the Luga River deteriorates downstream, in particular, due to the agricultural and livestock farms’ activities near the river basin. Thus, the Kjeldahl nitrogen and total phosphorus content at the upstream point is 10.8 milligrams and 119 micrograms per liter, respectively, and at the downstream point, it is only 1.6 milligrams and 28 micrograms, respectively. (Conclusions) It was determined that the analyzed indicators correspond to the category of good quality: the level of water oxygen saturation fluctuated within 88.76-117.83 per cent during the monitoring period; the color was 30 milligrams per liter on the platinum-cobalt scale, which means a low humus content in the water; the presence of solids in the water ranged from 1.1 to 2.4 milligrams per liter; the total phosphorus content in water is below 9.2 micrograms per liter, that is, within the normal limits. During the monitoring of the Luga River, a clear influence of nearby agricultural enterprises and settlements was detected.

Unraveling the effects of multiscale network entanglement on empirical systems

Complex systems are large collections of entities that organize themselves into non-trivial structures, represented as networks. One of their key emergent properties is robustness against random failures or targeted attacks —i.e., the networks maintain their integrity under removal of nodes or links. Here, we introduce network entanglement to study network robustness through a multiscale lens, encoded by the time required for information diffusion through the system. Our measure’s foundation lies upon a recently developed statistical field theory for information dynamics within interconnected systems. We show that at the smallest temporal scales, the node-network entanglement reduces to degree, whereas at extremely large scales, it measures the direct role played by each node in keeping the network connected. At the meso-scale, entanglement plays a more important role, measuring the importance of nodes for the transport properties of the system. We use entanglement as a centrality measure capturing the role played by nodes in keeping the overall diversity of the information flow. As an application, we study the disintegration of empirical social, biological and transportation systems, showing that the nodes central for information dynamics are also responsible for keeping the network integrated.

Quantum field theory (QFT) at finite temperature: Equilibrium properties

Some equilibrium properties in statistical quantum field theory (QFT), that is, relativistic QFT at finite temperature are reviewed. Study of QFT at finite temperature is motivated by cosmological problems, high energy heavy ion collisions, and speculations about possible phase transitions, also searched for in numerical simulations. In particular, the situation of finite temperature phase transitions, or the limit of high temperature (an ultra-relativistic limit where the temperature is much larger than the physical masses of particles) are discussed. The concept of dimensional reduction emerges, in many cases, statistical properties of finite-temperature QFT in (1, d − 1) dimensions can be described by an effective classical statistical field theory in (d − 1) dimensions. Dimensional reduction generalizes a property already observed in the non-relativistic example of the Bose gas, and indicates that quantum effects are less important at high temperature. The corresponding technical tools are a mode-expansion of fields in the Euclidean time variable, singling out the zero modes of boson fields, followed by a local expansion of the resulting (d − 1)-dimensional effective field theory (EFT). Additional physical intuition about QFT at finite temperature in (1, d−1) dimensions can be gained by considering it as a classical statistical field theory in d dimensions, with finite size in one dimension. This identification makes an analysis of finite temperature QFT in terms of the renormalization group (RG), and the theory of finite-size effects of the classical theory, possible. These ideas are illustrated with several simple examples, the φ4 field theory, the non-linear σ-model, the Gross–Neveu model and some gauge theories.

Correction to: Statistical field theory of the transmission of nerve impulses

An amendment to this paper has been published and can be accessed via the original article.

Interface Roughening in Two Dimensions

Roughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

Topological excitations in statistical field theory at the upper critical dimension

We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.