Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Griffiths phases and localization in hierarchical modular networks

We study variants of hierarchical modular network models suggested by Kaiser and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional brain connectivity, using extensive simulations and quenched mean-field theory (QMF), focusing on structures with a connection probability that decays exponentially with the level index. Such networks can be embedded in two-dimensional Euclidean space. We explore the dynamic behavior of the contact process (CP) and threshold models on networks of this kind, including hierarchical trees. While in the small-world networks originally proposed to model brain connectivity, the topological heterogeneities are not strong enough to induce deviations from mean-field behavior, we show that a Griffiths phase can emerge under reduced connection probabilities, approaching the percolation threshold. In this case the topological dimension of the networks is finite, and extended regions of bursty, power-law dynamics are observed. Localization in the steady state is also shown via QMF. We investigate the effects of link asymmetry and coupling disorder, and show that localization can occur even in small-world networks with high connectivity in case of link disorder.Comment: 18 pages, 20 figures, accepted version in Scientific Report

Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios

Modeling social resilience: Questions, answers, open problems

Resilience denotes the capacity of a system to withstand shocks and its ability to recover from them. We develop a framework to quantify the resilience of highly volatile, non-equilibrium social organizations, such as collectives or collaborating teams. It consists of four steps: (i) \emph{delimitation}, i.e., narrowing down the target systems, (ii) \emph{conceptualization}, .e., identifying how to approach social organizations, (iii) formal \emph{representation} using a combination of agent-based and network models, (iv) \emph{operationalization}, i.e. specifying measures and demonstrating how they enter the calculation of resilience. Our framework quantifies two dimensions of resilience, the \emph{robustness} of social organizations and their \emph{adaptivity}, and combines them in a novel resilience measure. It allows monitoring resilience instantaneously using longitudinal data instead of an ex-post evaluation

Complex network analysis and nonlinear dynamics

This chapter aims at reviewing complex network and nonlinear dynamical models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary introduces some applications of complex networks to economics, finance, epidemic spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issue

Safe Connectivity Maintenance in Underactuated Multi-Agent Networks for Dynamic Oceanic Environments

Autonomous Multi-Agent Systems are increasingly being deployed in environments where winds and ocean currents can exert a significant influence on their dynamics. Recent work has developed powerful control policies for single agents that can leverage flows to achieve their objectives in dynamic environments. However, in the context of multi-agent systems, these flows can cause agents to collide or drift apart and lose direct inter-agent communications, especially when agents have low propulsion capabilities. To address these challenges, we propose a Hierarchical Multi-Agent Control approach that allows arbitrary single agent performance policies that are unaware of other agents to be used in multi-agent systems, while ensuring safe operation. We first develop a safety controller solely dedicated to avoiding collisions and maintaining inter-agent communication. Subsequently, we design a low-interference safe interaction (LISIC) policy that trades-off the performance policy and the safety controller to ensure safe and optimal operation. Specifically, when the agents are at an appropriate distance, LISIC prioritizes the performance policy, while smoothly increasing the safety controller when necessary. We prove that under mild assumptions on the flows experienced by the agents our approach can guarantee safety. Additionally, we demonstrate the effectiveness of our method in realistic settings through an extensive empirical analysis with underactuated Autonomous Surface Vehicles (ASV) operating in dynamical ocean currents where the assumptions do not always hold.Comment: 8 pages, submitted to 2023 IEEE 62th Annual Conference on Decision and Control (CDC) Nicolas Hoischen and Marius Wiggert contributed equally to this wor

Financial stability from a network perspective

This thesis consists of six chapters related to applications of network analysis’ methods for financial stability. The first chapter introduces the network perspective as a new mapping technique for studying and understanding financial markets’architecture. The second chapter breaks down the Colombian sovereign securities market into different layers of interaction corresponding to distinct trading and registering platforms. The third chapter addresses an overlooked issue: How to measure the importance of financial market infrastructures within their corresponding network. The fourth chapter studies the connective and hierarchical structure of the Colombian non-collateralized money market, and uses an information retrieval algorithm for identifying those financial institutions that simultaneously excel at borrowing and lending central bank’s liquidity (i.e. superspreaders). The fifth chapter addresses –for the first time- the question regarding the presence of a modular hierarchy in financial networks, and discusses the main implications for financial stability. The sixth chapter explicitly models the role of financial market infrastructures as financial markets’ “plumbing”, and recognizes that traditional analysis of financial institutions networks is of a virtual or logical nature. The third chapter is published in the Journal of Financial Market Infrastructures (Vol.2 (3), 2014), whereas the fourth chapter is published in the Journal of Financial Stability (Vol.15, 2014)