Related papers: Directed Cycles as Higher-Order Units of Informati…
Directed networks such as gene regulation networks and neural networks are connected by arcs (directed links). The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which lead to complex…
Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward…
We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
A sufficiently large information flux in recurrent neural networks, quantified by the mutual information between successive network states, is considered a prerequisite for rich information processing capabilities. This raises the question…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…
While biological vision systems rely heavily on feedback connections to iteratively refine perception, most artificial neural networks remain purely feedforward, processing input in a single static pass. In this work, we propose a…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…
We study a self-consistent approach to introduce higher-order effects in a branching process model of complex contagion on clustered networks. Branching processes operate over an infinite population such that they never circle back and…
The paper proposes the use of structured neural networks for reinforcement learning based nonlinear adaptive control. The focus is on partially observable systems, with separate neural networks for the state and feedforward observer and the…
Learning depends on changes in synaptic connections deep inside the brain. In multilayer networks, these changes are triggered by error signals fed back from the output, generally through a stepwise inversion of the feedforward processing…
The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops,…
We present several novel identities and inequalities relating the mutual information and the directed information in systems with feedback. The internal blocks within such systems are restricted only to be causal mappings, but are allowed…
When exposed to a contagion phenomenon, individuals may respond to the perceived risk of infection by adopting behavioral changes, aiming to reduce their exposure or their risk of infecting others. The social cost of such adaptive behaviors…
Tipping points are critical thresholds of parameters where tiny perturbations can lead to abrupt and large qualitative changes in the systems. Many real-world systems that exhibit tipping behavior can be represented as networks of…
Stars and cycles are basic structures in network construction. The former has been well studied in network analysis, while the latter attracted rare attention. A node together with its neighbors constitute a neighborhood star-structure…
In contrast to engineering applications, in which the structure of control laws are designed to satisfy prescribed function requirements, in biology it is often necessary to infer gene-circuit function from incomplete data on gene-circuit…
We present a theoretical formalism to study steady state information transmission in type 1 coherent feed-forward loop motif with an additive signal integration mechanism. Our construct allows a two-step cascade to be slowly transformed…