Related papers: Adaptive, locally-linear models of complex dynamic…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
The physics of behavior seeks simple descriptions of animal behavior. The field has advanced rapidly by using techniques in low dimensional dynamics distilled from computer vision. Yet, we still do not generally understand the rules which…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
Quantitative models of associative learning that explain the behavior of real animals with high precision have turned out very difficult to construct. We do this in the context of the dynamics of the thermal preference of C. elegans. For…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…
Classical swarm models, exemplified by the Cucker--Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems.…
Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is even greater when the physics underlying such systems is…
Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link internal representational structure to…
Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
We present a multidimensional data analysis framework for the analysis of ordinal response variables. Underlying the ordinal variables, we assume a continuous latent variable, leading to cumulative logit models. The framework includes…
Many dynamical systems found in biology, ranging from genetic circuits to the human brain to human social systems, are inherently computational. Although extensive research has explored their resulting functions and behaviors, the…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a…
Notwithstanding the usefulness of system dynamics in analyzing complex policy problems, policy design is far from straightforward and in many instances trial-and-error driven. To address this challenge, we propose to combine system dynamics…
Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in unsupervised way the microscopic dynamical events occurring in…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…