Related papers: Local symmetries in complex networks
Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing.…
Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Biological intelligence is remarkable in its ability to produce complex behaviour in many diverse situations through data efficient, generalisable and transferable skill acquisition. It is believed that learning "good" sensory…
We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group $G$ can be utilized…
Shape had been intuitively recognized to play a dominant role in determining the global motion patterns of bio-molecular assemblies. However, it is not clear exactly how shape determines the motion patterns. What about the local…
In complex networks a common task is to identify the most important or "central" nodes. There are several definitions, often called centrality measures, which often lead to different results. Here we study extensively correlations between…
We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network…
Many nonlinear dynamical systems exhibit symmetry, affording substantial benefits for control design, observer architecture, and data-driven control. While the classical notion of group invariance enables a cascade decomposition of the…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
A measure for the maximum quantum information transfer capacity (ITC) between nodes of a spin network is defined, and shown to induce a metric on a space of equivalence classes of nodes for homogeneous chains with XX and Heisenberg…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
In this short paper, we characterize symmetric locality. In designing algorithms, compilers, and systems, data movement is a common bottleneck in high-performance computation, in which we improve cache and memory performance. We study a…
We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that…
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…