Related papers: A Markovian Model of the Evolving World Input-Outp…
This paper studies the statistical properties of the web of import-export relationships among world countries using a weighted-network approach. We analyze how the distributions of the most important network statistics measuring…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
Trade is a fundamental pillar of economy and a form of social organization. Its empirical characterization at the worldwide scale is represented by the World Trade Web (WTW), the network built upon the trade relationships between the…
Markovian evolving graphs are dynamic-graph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamic-network…
The number of observable degrees of freedom is typically limited in experiments. Here, we consider discrete Markov networks in which an observer has access to a few visible transitions and the waiting times between these transitions.…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
Financial networks are dynamic. To assess their systemic importance to the world-wide economic network and avert losses we need models that take the time variations of the links and nodes into account. Using the methodology of classical…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
Current concepts of neural networks have emerged over two centuries of progress beginning with the neural doctrine to the idea of neural cell assemblies. Presently the model of neural networks involves distributed neural circuits of nodes,…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the…
In this chapter, an input-output economic model with multiple interactive economic systems is considered. The model captures the multi-dimensional nature of the economic sectors or industries in each economic system, the interdependencies…
There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the…
This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via…
Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov random network and characterizes a novel phenomenon of intermittent…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…