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In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
The maximum likelihood estimates of an ARMA model can be obtained by the Kalman filter based on the state-space representation of the model. This paper presents an algorithm for computing gradient of the log-likelihood by an extending the…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
The linear system $|D|$ of a divisor $D$ on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it - they serve as the landmarks for us to compute the f-vector of the complex and find all…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are…
This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian…
A regression-based framework for interpretable multi-way data imputation, termed Kernel Regression via Tensor Trains with Hadamard overparametrization (KReTTaH), is introduced. KReTTaH adopts a nonparametric formulation by casting…
Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
In this work, the Einstein notation is utilized to synthesize state and parameter transition matrices, by solving a set of ordinary differential equations. Additionally, for the system identification problem, it has been demonstrated that…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
The Corner Transfer Matrix Renormalization Group (CTMRG) algorithm is modified to measure the magnetization at the boundary of the system, including the corners of the square-shaped lattice. Using automatic differentiation, we calculate the…
Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…
This paper proposes a tensor-based parameter estimation algorithm for sensing in an intelligent reflecting surface-assisted system. We present a higher-order singular value decomposition-based solution that exploits the tensor structure of…