Related papers: Modeling active optical networks
We present a method for implementing an optical neural network using only linear optical resources, namely field displacement and interferometry applied to coherent states of light. The nonlinearity required for learning in a neural network…
Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
This article discusses how concepts and methods of complex networks can be applied to real-time imaging and computer vision. After a brief introduction of complex networks basic concepts, their use as means to represent and characterize…
We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a…
We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…
Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Though early studies of such processes were primarily descriptive, recent…
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple…
We derive semiclassical laser equations valid in all orders of nonlinearity. With the help of a diagrammatic representation, the perturbation series in powers of electric field can be resummed in terms of a certain class of diagrams. The…
We apply the quantum Langevin equations approach to study nonlinear light propagation through one-dimensional interacting open quantum lattice models. We write a large set of quantum Langevin equations of lattice operators obtained after…
We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be…
Recently, a perturbative model of non-linear fiber propagation in uncompensated optical transmission systems has been proposed, called GN-model [1]. Here, an extended and more detailed version of the GN-model derivation [1] is reported,…
Understanding the behaviour of complex laser systems is an outstanding challenge, especially in the presence of nonlinear interactions between modes. Hidden features, such as the gain distributions and spatial localisation of lasing modes,…
Systems whose entities interact with each other are common. In many interacting systems, it is difficult to observe the relations between entities which is the key information for analyzing the system. In recent years, there has been…
Atomic planar arrays offer a novel emerging quantum-optical many-body system in which light mediates strong interactions between the atoms. The regular lattice structure provides a cooperatively enhanced light-matter coupling and allows for…
Coupling light to ensembles of strongly interacting particles has emerged as a promising route toward achieving few photon nonlinearities. One specific way to implement this kind of nonlinearity is to interface light with highly excited…
We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the…
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…