Related papers: Dynamical correlation functions from complex time …
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the…
We present a technique to resolve a Gaussian density matrix and its time evolution through known expectation values in position and momentum. Further we find the full spectrum of this density matrix and apply the technique to a chain of…
The evolution of non-interacting bosons in the presence of repeated projective measurements is studied. Following the established approach, this monitored evolution is characterized by the first detected return and the first detected…
Investigating relation between various structural patterns found in real-world networks and stability of underlying systems is crucial to understand importance and evolutionary origin of such patterns. We evolve multiplex networks,…
As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit…
Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly…
We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1+1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a…
We introduce an approach for approximate real-time evolution of quantum systems using Tensor Renormalization Group (TRG) methods originally developed for imaginary time. We use Higher- Order TRG (HOTRG) to generate a coarse-grained time…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
The myriad microscopic interactions among the individual organisms that constitute an ecological system collectively give rise, at the macroscopic scale, to evolutionary trends. The ability to detect the directionality of such trends is…
In general, convolutional neural networks (CNNs) are easy to train, but their essential properties, such as generalization error and adversarial robustness, are hard to control. Recent research demonstrated that singular values of…
Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the…
We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction…
We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context, to compute dynamical correlation functions of correlated systems. We…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing…
Traditional energy-based learning models associate a single energy metric to each configuration of variables involved in the underlying optimization process. Such models associate the lowest energy state to the optimal configuration of…
The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models by forecasting populations with and without intervention. These model ensembles commonly assume stable coexistence of…
This paper proposes a new methodology to predict and update the residual useful lifetime of a system using a sequence of degradation images. The methodology integrates tensor linear algebra with traditional location-scale regression widely…