A method for inferring hierarchical dynamics in stochastic processes

Complex systems may often be characterized by their hierarchical dynamics. In this paper do we present a method and an operational algorithm that automatically infer this property in a broad range of systems; discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections that impose Markovian dynamics on the coarser level. These projections, which we call Markov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, so a priori knowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes; a finite state automaton and an iterated map.Comment: 16 pages, 12 figure

Perception and Hierarchical Dynamics

In this paper, we suggest that perception could be modeled by assuming that sensory input is generated by a hierarchy of attractors in a dynamic system. We describe a mathematical model which exploits the temporal structure of rapid sensory dynamics to track the slower trajectories of their underlying causes. This model establishes a proof of concept that slowly changing neuronal states can encode the trajectories of faster sensory signals. We link this hierarchical account to recent developments in the perception of human action; in particular artificial speech recognition. We argue that these hierarchical models of dynamical systems are a plausible starting point to develop robust recognition schemes, because they capture critical temporal dependencies induced by deep hierarchical structure. We conclude by suggesting that a fruitful computational neuroscience approach may emerge from modeling perception as non-autonomous recognition dynamics enslaved by autonomous hierarchical dynamics in the sensorium

Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics

We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a magnetic field, which allows us to analyse the resulting phase transitions in detail. For the triangular plaquette model (TPM), we find for the coupled-replica system a phase transition between high- and low-overlap phases, occuring at a coupling eps*(T), which vanishes in the low-temperature limit. Using computational path sampling techniques, we show that a single TPM also displays space-time transitions between active and inactive dynamical phases. These first-order dynamical transitions occur at a critical counting field s_c(T)>=0 that appears to vanish at zero temperature, in a manner reminiscent of the thermodynamic overlap transition. In order to extend the ideas to three dimensions we introduce the square pyramid model which also displays both overlap and activity transitions. We discuss a possible common origin of these various phase transitions, based on long-lived (metastable) glassy states.Comment: 12 pages, 9 fig

Population–reaction model and microbial experimental ecosystems for understanding hierarchical dynamics of ecosystems

Understanding ecosystem dynamics is crucial as contemporary human societies face ecosystem degradation. One of the challenges that needs to be recognized is the complex hierarchical dynamics. Conventional dynamic models in ecology often represent only the population level and have yet to include the dynamics of the sub-organism level, which makes an ecosystem a complex adaptive system that shows characteristic behaviors such as resilience and regime shifts. The neglect of the sub-organism level in the conventional dynamic models would be because integrating multiple hierarchical levels makes the models unnecessarily complex unless supporting experimental data are present. Now that large amounts of molecular and ecological data are increasingly accessible in microbial experimental ecosystems, it is worthwhile to tackle the questions of their complex hierarchical dynamics. Here, we propose an approach that combines microbial experimental ecosystems and a hierarchical dynamic model named population–reaction model. We present a simple microbial experimental ecosystem as an example and show how the system can be analyzed by a population–reaction model. We also show that population–reaction models can be applied to various ecological concepts, such as predator–prey interactions, climate change, evolution, and stability of diversity. Our approach will reveal a path to the general understanding of various ecosystems and organisms

Velocity and hierarchical spread of epidemic outbreaks in scale-free networks

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.Comment: 4 pages, 4 figures, final versio

Approaches for advancing scientific understanding of macrosystems

The emergence of macrosystems ecology (MSE), which focuses on regional- to continental-scale ecological patterns and processes, builds upon a history of long-term and broad-scale studies in ecology. Scientists face the difficulty of integrating the many elements that make up macrosystems, which consist of hierarchical processes at interacting spatial and temporal scales. Researchers must also identify the most relevant scales and variables to be considered, the required data resources, and the appropriate study design to provide the proper inferences. The large volumes of multi-thematic data often associated with macrosystem studies typically require validation, standardization, and assimilation. Finally, analytical approaches need to describe how cross-scale and hierarchical dynamics and interactions relate to macroscale phenomena. Here, we elaborate on some key methodological challenges of MSE research and discuss existing and novel approaches to meet them