Dynamic knowledge graphs, which capture evolving relationships among entities over time, are becoming increasingly important in various domains such as social networks, recommendation systems, finance domain and biomedical research. This research paper investigates the effectiveness of Graph Neural Networks (GNNs) for link prediction dynamic graphs. By leveraging temporal dynamics graph, we pro...

This paper is concerned with the consensus tracking problem of high order MIMO nonlinear multi-agent systems. The agents must follow a leader node in presence of unknown dynamics and uncertain external disturbances. The communication network topology of agents is assumed to be a fixed undirected graph. A distributed adaptive control method is proposed to solve the consensus problem utilizing re...

We consider Glauber dynamics (starting from an extremal configuration) in a monotone spin system, and show that interjecting extra updates cannot increase the expected Hamming distance or the total variation distance to the stationary distribution. We deduce that for monotone Markov random fields, when block dynamics contracts a Hamming metric, single-site dynamics mixes in O(n log n) steps on ...

L-[1-11C]leucine PET can be used to measure in vivo protein synthesis in the brain. However, the relationship between regional protein synthesis and on-going neural dynamics is unclear. We use a graph theoretical approach to examine the relationship between cerebral protein synthesis (rCPS) and both static and dynamical measures of functional connectivity (measured using resting state functiona...

Dependence of charge transmission through several experimentally studied DNA duplexes on their lowest-frequency acoustic modes, combined with the molecular dynamics in picosecond characteristic time range, has been studied. Based on this analysis we were able to identify the specific acoustic modes responsible for the noticeable increase in DNA charge transmission. Other factors influencing ele...

Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial ThresholdLinear Networks (CTLNs) in order to understand how the pattern of connectivity, as encoded by a directed graph, shapes the emergent nonlinear dynamics of the corresponding network. Important aspects of t...

Quantum graphity is a background-independent model for emergent macroscopic locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly connected and the physics is invariant under the full symmetric group acting on the vertices. We present evidence that the model also has a low-energy ph...

Does the interaction graph of a finite dynamical system can force this system to have a “complex” dynamics ? In other words, given a finite interval of integers A, which are the signed digraphsG such that every finite dynamical system f : An → An with G as interaction graph has a “complex” dynamics ? If |A| ≥ 3 we prove that no such signed digraph exists. More precisely, we prove that for every...

Complex Networks can depict a clear image of real-world systems. A scenario be represented graph with interconnected layers - called multilayer network. Finding motifs give an idea the topology complex systems and help understand graphs’ dynamics. Looking at as atoms network is helpful to analyze relationship between nodes layers. This work suggests sub-graph enumeration approach find co...

We investigate the application of line-graph operator to one-dimensional spin models with periodic boundary conditions. The spins (or interactions) in original structure become interactions spins) resulting structure. identify conditions which ensure that each new is stable, is, its configuration minimises internal energy. Then, making a correspondence between configurations and binary sequence...