This paper presents a low-complexity algorithm for the simulation of time-variant frequency-selective geometry based channel models. The algorithm approximately calculates the time-variant transfer function of the channel in the subspace spanned by multidimensional discrete prolate spheroidal (DPS) sequences. The only parameters of the subspace are the maximum Doppler shift and the maximum dela...

When a digital filter is realized with floating-point or fixed-point arithmetics, errors and constraints due to finite word length are unavoidable. In this paper, we show how these errors can be mechanically analysed using the HOL theorem prover. We first model the ideal real filter specification and the corresponding floating-point and fixedpoint implementations as predicates in higher-order l...

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the noninteracting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduc...

For the ordinary differential equation (ODE) ẋ(t) = f(t, x), x(0) = x0, t ≥ 0, x ∈ R , assume f to be at least continuous in t and locally Lipshitz in x, and if necessary, several times continuously differentiable in t and x. We associate a conditioning function E(t) with each solution x(t) which captures the accumulation of global error in a numerical approximation in the following sense: if x̃...

We consider real-analytic maps of the interval I = [0, 1] which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator M has a decomposition sp(M) = σc ∪ σp where σc = [0, 1] is the continuous spectrum of M and σp is the pure point spectrum with no points of accumulation outside 0 and 1. W...

We study undistinguishable two-species Bose-Einstein condensates BECs trapped in double wells. In the mean-field approximation we map the quantum system into a classical model and investigate the existence and stability of the fixed point solutions. By appropriately varying the amplitude of the high-frequency periodic modulation on the energy bias between the two wells, we tune the tunneling st...

In the context of the recently developed “equation-free” approach to the computerassisted analysis of complex systems, we illustrate the computation of coarsely selfsimilar solutions. Dynamic renormalization and fixed point algorithms for the macroscopic density dynamics are applied to the results of short bursts of appropriately initialized molecular dynamics in a simple diffusion simulation. ...

We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + LX−1LT , where Q is symmetric positive definite and L is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive...

Polymorphic regular types are tree-like datatypes generated by polynomial type expressions over a set of free variables and closed under least fixed point. The ‘equality types’ of Core ML can be expressed in this form. Given such a type expression T with x free, this paper shows a way to represent the one-hole contexts for elements of x within elements of T , together with an operation which wi...

We present two continuous-time quantum search algorithms similar to the adiabatic search algorithm, but now without the requirement of adiabatic evolution. Both algorithms can find the marked state in a time proportional to N. The behavior of the first algorithm is, essentially, similar to Grover’s algorithm, but the second model possesses the important property that one does not need to single...