A rigorous method for simulations of quantum dynamics is introduced on the basis of concatenation of semiclassical thawed Gaussian propagation steps. The time-evolving state is represented as a linear superposition of closely overlapping Gaussians that evolve in time according to their characteristic equations of motion, integrated by fourth-order Runge-Kutta or velocity Verlet. The expansion c...

Attention is focused on continuous-space shift-invariant systems with continuous system maps and inputs and outputs that are elements of L∞(IR ). It is shown that infinite superposition can fail in this important setting. It is also shown that continuous shift-invariant linear mappings need not commute with the operation of integration (even when the two composite operations are well defined). ...

Trajectory based methods approximate nonlinear dynamical systems by superposition of dimensionally reduced linear systems. The linear systems are obtained by linearisations at multiple points along a state-trajectory. They are combined in a weighted sum and the combinations are switched appropriately to approximate the dynamic behaviour of the nonlinear system. Weights assigned at a specimen po...

Clarifying the nature of quantum state |Ψ⟩ is at root problems with insight into counter-intuitive postulates. We provide a direct—and math-axiom free—empirical derivation this object as an element vector space. Establishing linearity structure—quantum superposition—is based on set-theoretic creation ensemble formations and invokes following three principia: (I) statics, (II) doctrine number in...

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on “superposition-structured” models where multiple structural constraints are imposed. To efficiently solve these “superpo...

This paper investigates one eigenvalue decomposition-based source number estimation method, and three information-based source number estimation methods, namely the Akaike Information Criterion (AIC), Minimum Description Length (MDL) and Bayesian Information Criterion (BIC), and improves BIC as Improved BIC (IBIC) to make it more efficient and easier for calculation. The performances of the abo...

Linear and nonlinear device models are the building blocks of most RF and microwave designs. S-parameters are often used to represent linear devices. As a “black-box” model, they can easily be obtained using a vector network analyzer and distributed for simulation. S-parameters use superposition to equate the linear relationship between incident and refl ected waves at all of the device’s ports...

In this thesis, we propose one approach to compute the multi-valued density via the existing level set method in computing multi-valued velocity of WKB system in high frequency wave dynamics and a superposition property is proved and numerically validated, too. Several novel level set methods are developed and analyzed for computing multi-valued solutions to the Euler-Poisson equations and the ...

We present a systematic quantitative analysis of power-law force relaxation and investigate logarithmic superposition of force response in relaxed porcine airway smooth muscle (ASM) strips in vitro. The term logarithmic superposition describes linear superposition on a logarithmic scale, which is equivalent to multiplication on a linear scale. Additionally, we examine whether the dynamic respon...