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Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time…
In this work, we proposed and experimentally demonstrated a photonic simulator for XY models, which is a typical kind of classical spin models. By encoding the XY spins on the phase term of the input light field, the corresponding XY…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
Modeling the wave nature of light and the propagation and diffraction of electromagnetic fields is crucial for the accurate simulation of many phenomena, yet wave simulations are significantly more computationally complex than classical…
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…
We are concerned with numerical simulations of quantum optical circuits under certain realistic conditions, specifically that photon quantum states are not perfectly indistinguishable. The partial photon distinguishability presents a…
In this paper, we propose and evaluate a novel algorithm for performing spectrum sensing on linear modulations based on second-order cyclic features of the received signals. The proposed approach has similar computational complexity to that…
Alternative machine learning approaches that are computationally light with low latency and can work with only a small training dataset are needed for applications where the insatiable demand of deep learning methods for computing power and…
Accurately modeling power distribution grids is crucial for designing effective monitoring and decision making algorithms. This paper addresses the partial observability issue of data-driven distribution modeling in order to improve the…
The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest.…
Fourier Ptychographic Microscopy (FPM) is a computational technique that achieves a large space-bandwidth product imaging. It addresses the challenge of balancing a large field of view and high resolution by fusing information from multiple…
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear…
We show that the density matrix of a spin-l system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of 4l+1 different spin directions. It is thus possible to represent the…
Most of current Convolution Neural Network (CNN) based methods for optical flow estimation focus on learning optical flow on synthetic datasets with groundtruth, which is not practical. In this paper, we propose an unsupervised optical flow…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…