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Semantic subtyping is an approach to define subtyping relations for type systems featuring union and intersection type connectives. It has been studied only for strict languages, and it is unsound for non-strict semantics. In this work, we…
Previous work has presented our ongoing e orts to define a "reference semantics" for the UML, that is, a mathematically defined system model that is envisaged to cover all of the UML eventually, and that also carefully avoids the…
We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
We investigate the data-driven discovery of constitutive closures in nonlinear reaction-diffusion systems with known governing PDE structures. Our objective is to robustly recover diffusion and reaction laws from spatiotemporal observations…
Symbolic systems are powerful frameworks for modeling cognitive processes as they encapsulate the rules and relationships fundamental to many aspects of human reasoning and behavior. Central to these models are systematicity,…
This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data . basis method is a qualitative approach to the analysis of linear models and construction of the symmetry groups of attractors of…
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…
We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied…
The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of…
Given a natural language instruction and an input scene, our goal is to train a model to output a manipulation program that can be executed by the robot. Prior approaches for this task possess one of the following limitations: (i) rely on…
Procedural models (i.e. symbolic programs that output visual data) are a historically-popular method for representing graphics content: vegetation, buildings, textures, etc. They offer many advantages: interpretable design parameters,…
A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…