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The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
In random allocation rules, typically first an optimal fractional point is calculated via solving a linear program. The calculated point represents a fractional assignment of objects or more generally packages of objects to agents. In order…
In this paper, we study control design methods for assigning a subset of nonlinear right or left eigenvalues to a specified set of scalar-valued functions via nonlinear Sylvester equations. This framework can be viewed as a generalization…
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
This paper instantiates a convex electric powertrain design optimization framework, bridging the gap between high-level powertrain sizing and low-level components design. We focus on the electric motor and transmission of electric vehicles,…
We present superconducting quantum circuits which exhibit atomic energy spectrum and selection rules as ladder and lambda three-level configurations designed by means of genetic algorithms. These heuristic optimization techniques are…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we…
Input design is an important issue for classical system identification methods but has not been investigated for the kernel-based regularization method (KRM) until very recently. In this paper, we consider in the time domain the input…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
We consider power allocation for an access-controlled transmitter with energy harvesting capability based on causal observations of the channel fading state. We assume that the system operates in a time-slotted fashion and the channel gain…
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
The individual optimization of quantum circuit parameters is currently one of the main practical bottlenecks in variational quantum eigensolvers for electronic systems. To this end, several machine learning approaches have been proposed to…
We analyse the eigenvalue structure of the replicated transfer matrix of one-dimensional disordered Ising models. In the limit of $n \rightarrow 0$ replicas, an infinite sequence of transfer matrices is found, each corresponding to a…
The complex eigenvalues of Markov generators govern oscillatory properties of relaxation, autocorrelation, and linear response. Here we show that these eigenvalues are localized by nonequilibrium cycles of the generator, thus revealing a…
We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…
This paper has solved the inverse eigenvalue problem for "fixed-free" mass-chain systems with inerters. It is well known that for a spring-mass system wherein the adjacent masses are linked through a spring, the natural frequency assignment…