Robustness of spatial networks and networks of networks

Many complex networks have recently been recognized to involve significant interdependence between different systems. Motivation comes primarily from infrastructures like power grids and communications networks, but also includes areas such as the human brain and finance. Interdependence implies that when components in one system fail, they lead to failures in the same system or other systems. This can then lead to additional failures finally resulting in a long cascade that can cripple the entire system. Furthermore, many of these networks, in particular infrastructure networks, are embedded in space and thus have unique spatial properties that significantly decrease their resilience to failures. Here we present a review of novel results on interdependent spatial networks and how cascading processes are affected by spatial embedding. We include various aspects of spatial embedding such as cases where dependencies are spatially restricted and localized attacks on nodes contained in some spatial region of the network. In general, we find that spatial networks are more vulnerable when they are interdependent and that they are more likely to undergo abrupt failure transitions than interdependent non-embedded networks. We also present results on recovery in spatial networks, the nature of cascades due to overload failures in these networks, and some examples of percolation features found in real-world traffic networks. Finally, we conclude with an outlook on future possible research directions in this area.     

Spatial brain networks

The human brain is a wonderfully complex organ characterized by heterogeneous connectivity between cellular and tissue units. This complexity supports the rich repertoire of dynamics and function that is characteristic of human cognition. While studies of brain connectivity have provided important insight into healthy cognition as well as its alteration in psychiatric disorders and neurological disease, an understanding of how this connectivity is embedded into the 3-dimensional space of the skull has remained elusive. In this article, we will motivate the importance of studying the brain as a spatially embedded network, particularly for understanding the rules of its development and alterations to those rules that may occur in neurodevelopmental disorders such as schizophrenia. We will review recent evidence for well-defined wiring rules in the brain, informed by notions of wiring minimization, spatially localized modules, and hierarchically nested topology. We will then discuss potential drivers of these rules in the form of evolution, genetics, energy, and the need for computational complexity. Finally, we will conclude with a discussion of emerging frontiers in the study of spatial brain networks, both in theory and modeling, and their potential to enhance our understanding of mental health.     

Body area networks at radio frequencies: Creeping waves and antenna analysis

On-body communication technology development requires a better knowledge of antenna radiation and wave propagation along the body, in both near and far fields. Therefore, Green's functions associated with penetrable cylinders are briefly reviewed, considering frequencies at which the body is not much larger than the wavelength and with a particular attention given to the near fields. A unified approach based on current sheets is provided and an acceleration technique is proposed. This is validated with the help of an FDTD software, which also allows the analysis of non-canonical cross-sections. The properties of creeping waves launched by sources parallel and perpendicular to the body are studied, in particular from the point of view of their phase velocity, and a very simple fitting model is proposed. It is also explained how the Green function can be exploited to analyze antennas very efficiently with the help of an integral-equation approach.     

Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex, non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity, and interference.     

Multi-radius geographical spatial networks: Statistical characteristics and application to wireless sensor networks

In this paper, a new kind of complex network model named multi-radius geographical spatial networks is proposed. We investigate statistical characteristics of this model and then map wireless sensor networks (WSNs) to it based on an efficient mechanism of broadcasting radius adjustment. Analysis and simulation show that WSNs working under this mechanism obtain longer lifetime and faster data delivering speed than those in traditional uniform radius WSNs.     

In social complex systems,the whole can be more or less than (the sum of) the parts

We discuss in a statistical physics framework the idea that “the whole is less than the parts”, as sometimes advocated by sociologists in view of the intrinsic complexity of humans, and try to reconcile this idea with the statistical physicists wisdom according to which “the whole is more than the sum of its parts” due to collective phenomena. We consider a simple mean-field model of interacting agents having an intrinsic complexity modeled by a large number of internal configurations. We show, by analytically solving the model, that interactions between agents lead, in some parameter range, to a ‘standardization’ of agents in the sense that all agents collapse in the same internal state, thereby drastically suppressing their complexity. Slightly generalizing the model, we find that agents standardization may lead to a global order if appropriate interactions are included. Hence, in this simple model, both agents standardization and collective organization may be viewed as two sides of the same coin.     

Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.     

The transport network of a leaf

Modern leaves, the energy factories of plants, are the products of a 400-million-year evolutionary race towards improved efficiency and robustness. As such they have evolved two sophisticated transport systems, the xylem and the phloem, which irrigate the surface of the leaf blade, distribute water and nutrients, and collect the products of photosynthesis. In this review, we discuss the development and function of these two networks. Additionally, with a focus on the global topological and architectural features, we present an overview of the evolution of reticulation through the lens of transport network optimization theory and analyze some aspects of the physics of flow.     

Superposition of fiber Bragg and LPG gratings for embedded strain measurement

When a fiber Bragg grating strain sensor is embedded inside a structure, the interaction of the sensor with the host material can lead to spurious results if the radial strain is neglected. In this article, we use numerical simulations to show that the axial and radial strains can be simultaneously measured with a single fiber in which a Bragg grating and a long-period grating are superimposed. Moreover, we present an optimal architecture of the sensor.     

Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have unordered discrete values, but many networks exhibit assortative mixing by some ordered (discrete or continuous) attribute, such as age or geographical location. In such cases, the identification of discrete communities may be difficult or impossible. We consider how the notion of community structure can be generalized to networks that have assortative mixing by ordered attributes. We propose a method of generating synthetic networks with ordered communities and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that current community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.     

Topological efficiency in three-dimensional gallery networks of termite nests

Transport networks are a key component of human and natural societies that enable efficient communication at a low cost. Here, we study the topological efficiency of the three-dimensional networks of galleries in termite nests and how spatial constraints affect the organisation of these networks. Cubitermes termite nests have far better than random transportation efficiency, but they do not reach theoretical optimal performance. We rather suggest a multiobjective process where a number of additional requirements, such as resilience to external attacks and the presence of spatial constraints, limit the ability of the system to achieve maximal transportation performance.     

Analyzing complex networks evolution through Information Theory quantifiers

A methodology to analyze dynamical changes in complex networks based on Information Theory quantifiers is proposed. The square root of the Jensen-Shannon divergence, a measure of dissimilarity between two probability distributions, and the MPR Statistical Complexity are used to quantify states in the network evolution process. Three cases are analyzed, the Watts-Strogatz model, a gene network during the progression of Alzheimer's disease and a climate network for the Tropical Pacific region to study the El Niño/Southern Oscillation (ENSO) dynamic. We find that the proposed quantifiers are able not only to capture changes in the dynamics of the processes but also to quantify and compare states in their evolution.     

空间网络上的随机游走

本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足p_ijα d_ij^-α (α≥ 0),其中d_ij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α₀ 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α₀单调增加,并趋近最优值1.5.     

A new method of spatial compounding imaging

A new method of spatial compound imaging is presented that improves image quality without the usual requirement to decrease the frame rate. The new method of imaging utilizes three transducers for data acquisition. The transducer located at the center of the transducer system is a phased array probe that acts as both transmitter and receiver. The other transducers are unfocused pistons that act only as receivers. Envelope data acquired by each transducer are combined to form a final image with improved quality (speckle contrast, target detectability and lateral resolution). It is shown that the improvement in speckle contrast depends on the correlation between individual images acquired by the transducers. The effective aperture approach is used for analytic estimation of the correlation between images in order to optimize the lateral separation between transducers. Using simulations, several compounding strategies have been performed to find the strategy that maximizes image quality. The central frequency of 2.5 MHz is used in simulations. Quantitative analysis of simulated B-mode images shows that the new method of imaging efficiently improves visibility, detectability, and lateral resolution of low contrast regions. The image frame rate is preserved because multiple scans are not required for the spatial compounding.     

Thermoelectric transport and Peltier cooling of cold atomic gases

This brief review presents the emerging field of mesoscopic physics with cold atoms, with an emphasis on thermal and ‘thermoelectric’ transport, i.e. coupled transport of particles and entropy. We review in particular the comparison between theoretically predicted and experimentally observed thermoelectric effects in such systems. We also show how combining well-designed transport properties and evaporative cooling leads to an equivalent of the Peltier effect with cold atoms, which can be used as a new cooling procedure with improved cooling power and efficiency compared to the evaporative cooling currently used in atomic gases. This could lead to a new generation of experiments probing strong correlation effects of ultracold fermionic atoms at low temperatures.     

Modeling Structural and Magnetic Phase Transitions in Iron-Nickel Nanoparticles

Martensitic phase transformations and magnetovolume effects in iron-nickel alloys are intimately related. The term Invar is widely used to characterize the unusual physical properties accompanying structural and magnetic instabilities such as those observed in the vicinity of the critical composition Fe 65 Ni 35 . We discuss the crossover from bulk iron-nickel alloys to nanoparticles with respect to structural and magnetic behavior. By employing molecular-dynamics and Monte Carlo methods, we find the absence of structural instabilities in defect-free particles, a linear scaling of the austenitic transformation temperature with the reciprocal cluster radius, as well as a decrease of the magnetic transition temperature with decreasing particle size.     

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-$T_{\mathrm{c}}$ superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.     

Proximity networks and epidemics

Disease spread in most biological populations requires the proximity of agents. In populations where the individuals have spatial mobility, the contact graph is generated by the “collision dynamics” of the agents, and thus the evolution of epidemics couples directly to the spatial dynamics of the population. We first briefly review the properties and the methodology of an agent-based simulation (EPISIMS) to model disease spread in realistic urban dynamic contact networks. Using the data generated by this simulation, we introduce the notion of dynamic proximity networks which takes into account the relevant time-scales for disease spread: contact duration, infectivity period, and rate of contact creation. This approach promises to be a good candidate for a unified treatment of epidemic types that are driven by agent collision dynamics. In particular, using a simple model, we show that it can account for the observed qualitative differences between the degree distributions of contact graphs of diseases with short infectivity period (such as air-transmitted diseases) or long infectivity periods (such as HIV).