Related papers: A Max-Flow approach to Random Tensor Networks
Randomized neural networks (NNs) are an interesting alternative to conventional NNs that are more used for data modeling. The random vector functional-link (RVFL) network is an established and theoretically well-grounded randomized learning…
We consider the problem of finding the value of a maximum flow over time in a network with uniform edge lengths where the edge capacities change at specific time instants. To solve this problem, we show how to construct a condensed version…
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it…
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the…
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a…
The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their…
Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
On the lattice, a renormalization group (RG) flow for two-dimensional partition functions expressed as a tensor network can be obtained using the tensor network renormalization (TNR) algorithm [G. Evenbly, G. Vidal, Phys. Rev. Lett. 115…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…
Convolution Neural Networks (CNN) are well-suited to model the nonlinear relationship between the microscale geometry of porous media and the corresponding flow distribution, thereby accurately and efficiently coupling the flow behavior at…
We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not…
We consider the problem of optimising the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum internet, where the repeaters may perform a probabilistic bell-state measurement and we may impose a…
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…
Entanglement spectrum of finite-size correlated electron systems are investigated using the Gutzwiller projection technique. The product of largest eigenvalue and rank of the block reduced density matrix, which is a measure of distance of…