Related papers: Gnutella: Topology Dynamics On Phase Space
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
We study the formation of topological textures in a nonequilibrium phase transition of an overdamped classical O(3) model in 2+1 dimensions. The phase transition is triggered through an external, time-dependent effective mass, parameterized…
Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one…
In this paper, we revisit the stability region of a cellular time division duplex (TDD) network. We characterize the queuing stability region of a network model that consists of two types of communications: (i) users communicating with the…
The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between…
Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on learning a useful discretization of the phase space of a…
The phase diagram of the Blume--Capel model on a semi--infinite simple cubic lattice with a (100) free surface is studied in the pair approximation of the cluster variation method. Six main topologies are found, of which two are new, due to…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
Studies on the large scale peer-to-peer (P2P) network like Gnutella have shown the presence of large number of free riders. Moreover, the open and decentralized nature of P2P network is exploited by malicious users who distribute…
Exact string solutions are presented, providing backgrounds where a dynamical change of topology is occuring. This is induced by the time variation of a modulus field. Some lessons are drawn concerning the region of validity of effective…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
We prove that for a broad class of permutation-equivariant learning rules (including SGD, Adam, and others), the training process induces a bi-Lipschitz mapping between neurons and strongly constrains the topology of the neuron distribution…
Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of…
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…