@article{KraemerGelbrechtPavithranetal.2022,
  author    = {Kr{\"a}mer, Hauke Kai and Gelbrecht, Maximilian and Pavithran, Induja and Sujith, Ravindran and Marwan, Norbert},
  title     = {Optimal state space reconstruction via Monte Carlo decision tree search},
  series = {Nonlinear Dynamics},
  volume    = {108},
  journal   = {Nonlinear Dynamics},
  number    = {2},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0924-090X},
  doi       = {10.1007/s11071-022-07280-2},
  pages     = {1525 -- 1545},
  year      = {2022},
  abstract  = {A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally, we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.},
  language  = {en}
}
@article{WeidlichPolyvyanyyMendlingetal.2011,
  author    = {Weidlich, Matthias and Polyvyanyy, Artem and Mendling, Jan and Weske, Mathias},
  title     = {Causal behavioural profiles - efficient computation, applications, and evaluation},
  series = {Fundamenta informaticae},
  volume    = {113},
  journal   = {Fundamenta informaticae},
  number    = {3-4},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0169-2968},
  doi       = {10.3233/FI-2011-614},
  pages     = {399 -- 435},
  year      = {2011},
  abstract  = {Analysis of behavioural consistency is an important aspect of software engineering. In process and service management, consistency verification of behavioural models has manifold applications. For instance, a business process model used as system specification and a corresponding workflow model used as implementation have to be consistent. Another example would be the analysis to what degree a process log of executed business operations is consistent with the corresponding normative process model. Typically, existing notions of behaviour equivalence, such as bisimulation and trace equivalence, are applied as consistency notions. Still, these notions are exponential in computation and yield a Boolean result. In many cases, however, a quantification of behavioural deviation is needed along with concepts to isolate the source of deviation. In this article, we propose causal behavioural profiles as the basis for a consistency notion. These profiles capture essential behavioural information, such as order, exclusiveness, and causality between pairs of activities of a process model. Consistency based on these profiles is weaker than trace equivalence, but can be computed efficiently for a broad class of models. In this article, we introduce techniques for the computation of causal behavioural profiles using structural decomposition techniques for sound free-choice workflow systems if unstructured net fragments are acyclic or can be traced back to S-or T-nets. We also elaborate on the findings of applying our technique to three industry model collections.},
  language  = {en}
}