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Given a multi-input, nonlinear, time-invariant, control-affine system and a controlled invariant, closed, embedded submanifold $\mathsf{N}$, the local transverse feedback linearization (TFL) problem seeks a coordinate and feedback…
We consider the renormalization of massive vector field interacting with charged scalar field in curved spacetime. Starting with the theory minimally coupled to external gravity and using the formulations with and without St\"uckelberg…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
We study the inverse problem of recovering a vector field in $\mathbb{R}^2$ from a set of new generalized $V$-line transforms in three different ways. First, we introduce the longitudinal and transverse $V$-line transforms for vector fields…
In this paper we propose and demonstrate the potential for unifying models and algorithms for the steady state and transient simulation of single-phase and three-phase power systems. At present, disparate algorithms and models are used for…
Vector Quantization (VQ) underpins many modern generative frameworks such as VQ-VAE, VQ-GAN, and latent diffusion models. Yet, it suffers from the persistent problem of codebook collapse, where a large fraction of code vectors remains…
Generalized fractional maps of the orders 0 < alpha < 1 are Volterra difference equations of convolution type with kernels, which differences are absolutely summable, but the series of kernels are diverging. Commonly used in applications…
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
We study the time evolution of the expectation value of the anharmonic oscillator coordinate in a coherent state as a toy model for understanding the semiclassical solutions in quantum field theory. By using the deformation quantization…
It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the…
Transition from chaotic to quasi-periodic phase in modified Lorenz model is analyzed by performing the contact transformation such that the trajectory in ${\Vec R}^3$ is projected on ${\Vec R}^2$. The relative torsion number and the…
Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of…