Related papers: Composing Behaviors of Networks
It is common for people to access multiple social networks, for example, using phone, email, and social media. Together, the multi-layer social interactions form a "integrated social network." How can we extend well developed knowledge…
Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Petri Nets (PN) are widely used for modeling concurrent and distributed systems, but face challenges in modeling adaptive systems. To address this, we have formalized "rewritable" PT nets (RwPT) using Maude, a declarative language with…
This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical…
We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…
In the late 1970s, C.A. Petri introduced partially ordered event occurrences (runs), then called \emph{processes}, as the appropriate model to describe the individual evolutions of distributed systems. Here, we present a unified framework…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
Structure-preserving bisimilarity is a truly concurrent behavioral equivalence for finite Petri nets, which relates markings (of the same size only) generating the same causal nets, hence also the same partial orders of events. The process…
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…
We show how a particular variety of hierarchical nets, where the firing of a transition in the parent net must correspond to an execution in some child net, can be modelled utilizing a functorial semantics from a free category --…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
We consider data with multiple observations or reports on a network in the case when these networks themselves are connected through some form of network ties. We could take the example of a cognitive social structure where there is another…
Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…