PATTERN FORMATION AND PHASE TRANSITION OF CONNECTIVITY IN TWO DIMENSIONS

This dissertation is devoted to the study and analysis of different types of emergent behavior in physical systems. Emergence is a phenomenon that has fascinated researchers from various fields of science and engineering. From the emergence of global pandemics to the formation of reaction-diffusion patterns, the main feature that connects all these diverse systems is the appearance of a complex global structure as a result of collective interactions of simple underlying components. This dissertation will focus on two types of emergence in physical systems: emergence of long-range connectivity in networks and emergence and analysis of complex patterns. The most prominent theory which deals with the emergence of long-range connectivity is the percolation theory. This dissertation employs many concepts from the percolation theory to study connectivity transitions in various systems. Ordinary percolation theory is founded upon two main assumptions, namely locality and independence of the underlying components. In Chapters 2 and 3, we relax these assumptions in different manners and show that relaxing these assumptions leads to irregular behaviors such as appearance of different universality classes and, in some instances, violation of universality. Chapter 2 deals with relaxing the assumption of locality of interactions. In this Chapter, we define a hierarchy of various measures of robust connectivity. We study the phase transition of these robustness metrics as a function of site/bond occupation/removal probability on the square lattice. Furthermore, we perform extensive numerical analysis and extract these robustness metrics\u27 critical thresholds and critical behaviors. We show that some of these robustness metrics do not fall under the regular percolation universality class. The extensive numerical results in this work can serve as a foundation for any researcher who aims to design/study various degrees of connectivity in networks. In Chapter 3, we study the non-equilibrium phase transition of long-range connectivity in a multi-particle interacting system on the square lattice. The interactions between different particles translate to relaxing the assumption of independence in the percolation theory. Using extensive numerical simulations, we show that the phase transition observed in this system violates the regular concept of universality. However, it conforms well with the concept of weak-universality recently introduced in the literature. We observe that by varying inter-particle interaction strength in our model, one can control the critical behavior of this phase transition. These observations could be pivotal in studying phase transitions and universality classes. Chapter 4 focuses on the analysis of reaction-diffusion patterns. We utilize a multitude of machine learning algorithms to analyze reaction-diffusion patterns. In particular, we address two main problems using these techniques, namely, pattern regression and pattern classification. Given an observed instance of a pattern with a known generative function, in the pattern regression task, we aim to predict the specific set of reaction-diffusion parameters (i.e. diffusion constant) which can reproduce the observed pattern. We employ supervised learning techniques to successfully solve this problem and show the performance of our model in some real-world instances. We also address the task of pattern classification. In this task, we are interested in grouping different instances of similar patterns together. This task is usually performed visually by the researcher studying certain natural phenomena. However, this method is tedious and can be inconsistent among different researchers. We utilize supervised and unsupervised machine learning algorithms to classify patterns of the Gray-Scott model. We show that our methods show outstanding performance both in supervised and unsupervised settings. The methods introduced in this Chapter could bridge the gaps between researchers studying patterns in different fields of science and engineering

Resilience Evaluation and Enhancement in Mobile Ad Hoc Networks

Understanding network behavior that undergoes challenges is essential to constructing a resilient and survivable network. Due to the mobility and wireless channel properties, it is more difficult to model and analyze mobile ad hoc networks under various challenges. We provide a comprehensive model to assess the vulnerability of mobile ad hoc networks in face of malicious attacks. We analyze comprehensive graph-theoretical properties and network performance of the dynamic networks under attacks against the critical nodes using both synthetic and real-world mobility traces. Motivated by Minimum Spanning Tree and small-world networks, we propose a network enhancement strategy by adding long-range links. We compare the performance of different enhancement strategies by evaluating a list of robustness measures. Our study provides insights into the design and construction of resilient and survivable mobile ad hoc networks

Avalanches and the edge-of-chaos in neuromorphic nanowire networks

The brain's efficient information processing is enabled by the interplay between its neuro-synaptic elements and complex network structure. This work reports on the neuromorphic dynamics of nanowire networks (NWNs), a brain-inspired system with synapse-like memristive junctions embedded within a recurrent neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, thus satisfying criteria for criticality. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos. Dynamical states at the edge-of-chaos are found to optimise information processing for increasingly complex learning tasks. Overall, these results reveal a rich repertoire of emergent, collective dynamics in NWNs which may be harnessed in novel, brain-inspired computing approaches

Nanoparticle devices for brain-inspired computing.

The race towards smarter and more efficient computers is at the core of our technology industry and is driven by the rise of more and more complex computational tasks. However, due to limitations such as the increasing costs and inability to indefinitely keep shrinking conventional computer chips, novel hardware architectures are needed. Brain-inspired, or neuromorphic, hardware has attracted great interest over the last decades. The human brain can easily carry out a multitude of tasks such as pattern recognition, classification, abstraction, and motor control with high efficiency and extremely low power consumption. Therefore, it seems logical to take inspiration from the brain to develop new systems and hardware that can perform interesting computational tasks faster and more efficiently. Devices based on percolating nanoparticle networks (PNNs) have shown many features that are promising for the creation of low-power neuromorphic systems. PNN devices exhibit many emergent brain-like properties and complex electrical activity under stimulation. However, so far PNNs have been studied using simple two-contact devices and relatively slow measuring systems. This limits the capabilities of PNNs for computing applications and questions such as whether the brain-like properties continue to be observed at faster timescales, or what are the limits for operation of PNN devices remain unanswered. This thesis explores the design, fabrication, and testing of the first successful multi- contact PNN devices. A novel and simple fabrication technique for the creation of working electrical contacts to nanoparticle networks is presented. Extensive testing of the multi-contact PNN devices demonstrated that electrical stimulation of multiple input contacts leads to complex switching activity. Complex switching activity exhibited different patterns of switching behaviour with events occurring on all contacts, on few contacts, or only on a single contact. The device behaviour is investigated for the first time at microsecond timescales, and it is found that the PNNs exhibit stochastic spiking behaviour that originates in single tunnel gaps and is strikingly similar to that observed in biological neurons. The stochastic spiking behaviour of PNNs is then used for the generation of high quality random numbers which are fundamental for encryption and security. Together the results presented in this thesis pave the way for the use of PNNs for brain-inspired computing and secure information processing

Properties of Opportunistic Routing in the Argo Underwater Sensor Network

Underwater Acoustic Sensor Networks (UASN) represent a novel technology for monitoring the underwater environment. However, underwater communications through acoustic modems rise several networking challenges for UASN. In our work, we study the possibility to use Opportunistic Routing to overcome the limitations posed by the acoustic communication channel in UASN. For our study, we used a real-world mobility dataset obtained from the Argo project. In particular, we used data produced by the 51 free-drifting floats deployed on the Mediterranean Sea for approximately one year to build a fictitious network called the Argo Underwater Sensor Network. Then we analyse some important properties of the underwater network we built. Specifically, we analyse the network degree, density, properties of the connected components, properties of contact and inter-contact time while varying the connectivity degree of the whole network. We then consider four known opportunistic routing algorithms, namely Epidemic, PROPHET, SprayAndWait and Direct Delivery, with the goal of measuring their performance in real conditions for UASN. We finally discuss the opportunities arising from the adoption of opportunistic routing in UASN showing that, even in a very sparse and strongly disconnected network, it is still possible to build a limited but working networking framework

The structure and dynamics of multilayer networks

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201