Related papers: Solving a directed percolation inverse problem
We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
We study entanglement percolation in qubit-based planar quantum network models of arbitrary topology, where neighboring nodes are initially connected by pure states with quenched disorder in their entanglement. To address this, we develop a…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are…
This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
Nowadays massive amount of data are available for analysis in natural and social systems. Inferring system structures from the data, i.e., the inverse problem, has become one of the central issues in many disciplines and interdisciplinary…
Inverse rendering, the process of inferring scene properties from images, is a challenging inverse problem. The task is ill-posed, as many different scene configurations can give rise to the same image. Most existing solutions incorporate…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization…
We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…