Related papers: A method for inferring hierarchical dynamics in st…
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…
Scientific inference involves obtaining the unknown properties or behavior of a system in the light of what is known, typically, without changing the system. Here we propose an alternative to this approach: a system can be modified in a…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of theQmatrix for the discrete state…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…