Related papers: Minimal state space realizations in Jacobson norma…
Given stable rational matrix functions $G$ and $K$, a procedure is presented to compute a stable rational matrix solution $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\sup_{|z|\leq 1}\|X(z)\|\leq 1$.…
In this paper, we consider linear state-space models with compressible innovations and convergent transition matrices in order to model spatiotemporally sparse transient events. We perform parameter and state estimation using a dynamic…
This paper provides a novel approach for finding sparse state-space realizations of linear systems (e.g., controllers). Sparse controllers are commonly used in distributed control, where a controller is synthesized with some sparsity…
In this work, we propose how to load and manipulate chiral states in a Josephson junction ring in the so called transmon regimen. We characterise these states by their symmetry properties under time reversal and parity transformations. We…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…
Given a controllable discrete-time linear system C, a shortest basis for C is a set of linearly independent generators for C with the least possible lengths. A basis B is a shortest basis if and only if it has the predictable span property…
Let $\mathrm{JT}_\lambda$ be the Jacobi-Trudi matrix corresponding to the partition $\lambda$, so $\det\mathrm{JT}_\lambda$ is the Schur function $s_\lambda$ in the variables $x_1,x_2,\dots$. Set $x_1=\cdots=x_n=1$ and all other $x_i=0$.…
We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…
We consider continuous-time, finite-horizon, optimal quadratic control of semi-Markov jump linear systems (S-MJLS), and develop principled approximations through Markov-like representations for the holding-time distributions. We adopt a…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the…
The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…
Let $K$ be a complete discretely valued field with perfect residue field $k$. If $X \to \mathbb{P}^1_K$ is a $\mathbb{Z}/d$-cover with $\text{char } k \nmid d$, we compute the minimal regular normal crossings model $\mathcal{X}$ of $X$ as…
We define a compact local Smith-McMillan form of a rational matrix $R(\lambda)$ as the diagonal matrix whose diagonal elements are the nonzero entries of a local Smith-McMillan form of $R(\lambda)$. We show that a recursive rank search…
In this short letter, I present a powerful application in dimensionality reduction of the lesser-used Jacobi-Davidson algorithm for the generalized eigenvalue decomposition. When combined with matrix-free implementations of relevant…
We introduce a concept of $autoregressive$ (AR)state-space realization that could be applied to all transfer functions $\boldsymbol{T}(L)$ with $\boldsymbol{T}(0)$ invertible. We show that a theorem of Kalman implies each Vector…
In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…
Higher-fidelity entry simulations can be enabled by integrating finer thermo-chemistry models into compressible flow physics. One such class of models are State-to-State (StS) kinetics, which explicitly track species populations among…
We express the positive partial transpose (PPT) separability criterion for symmetric states of multi-qubit systems in terms of matrix inequalities based on the recently introduced tensor representation for spin states. We construct a matrix…