Related papers: Partial Order on the set of Boolean Regulatory Fun…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support…
This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…
Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate…
This paper studies linear time-invariant descriptor systems which are not necessarily regular. We introduce the notion of partial detectability and characterize this concept by means of a simple rank criterion involving the system…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
In this paper we present the mathematical description and analysis of a fractional-order regulated system in the state space. A little historical background of our results in the analysis and synthesis of the fractional-order dynamical…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the…
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput…
We investigate the use of an extension of rule-based modelling for cellular signalling to create a structured space of model variants. This enables the incremental development of rule sets that start from simple mechanisms and which, by a…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic terms. Our treatment starts from the…
There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…
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,…
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The…