Related papers: Higher-order correlations for group actions
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
The problem of controlling higher-order interactions in neural networks is addressed with techniques commonly applied in the cluster analysis of quantum many-particle systems. For multi-neuron synaptic weights chosen according to a…
Systems of active particles can show a large variety of collective behavior. In theory, two aspects determine the collective behavior: the model at the particle level and the parameter regime. While many studies consider a single model and…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
We argue that the coordination of the activities of individual complex agents enables a system to develop and sustain complexity at a higher level. We exemplify relevant mechanisms through computer simulations of a toy system, a coupled map…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
We develop a new analysis for the length of controlled bad sequences in well-quasi-orderings based on Higman's Lemma. This leads to tight multiply-recursive upper bounds that readily apply to several verification algorithms for…
Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that…
In this paper, we consider the coordination control of a group of autonomous mobile agents with multiple leaders. Different interconnection topologies are investigated. At first, a necessary and sufficient condition is proved in the case of…
We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.
We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case, with two recent infinite-volume…
In this paper we introduce two new Hawkes processes, namely, compound and regime-switching compound Hawkes processes, to model the price processes in limit order books. We prove Law of Large Numbers and Functional Central Limit Theorems…
In this paper we are concerned with the two-stage contact process introduced in \cite{Krone1999} on a high-dimensional lattice. By comparing this process with an auxiliary model which is a linear system, we obtain two limit theorems for…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…
Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet,…
This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or…
We describe new universality classes associated to generic higher character Lifshitz critical behaviors for systems with arbitrary short range competing interactions. New renormalization-group arguments are proposed for anisotropic and…
This paper proposes an approach to addresses the control challenges posed by a fault-induced uncertainty in both the dynamics and control input effectiveness of a class of hierarchical nonlinear systems in which the high-level dynamics is…
Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation…