Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of multi-atomic ensembles directly from the computation of their one-particle density n(r). In DFT-based simulations the solution is calculated through a chain of successive self-consistent cycles; in each cycle a series of coupled equations (Kohn...

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DF...

Area-time lower bounds are derived for the VLSI computation of the (n1×n2× . . .×nd)-point multidimensional DFT (MDDFT) over different types of rings and different types of input/output protocols. First, an AT 2 = Ω ( (N log |R|) ) bound is obtained for any finite ring R, where N = ∏d k=1 nk, for any word-local protocol. The bound was previously known for the special case when R = ZM , the ring...

The planar Near-field Acoustical Holography (NAH) is a non-contact technique that can be used to estimate the vibration pattern of a planar body from the sound pressure it produces on a planar microphone array. The conventional NAH relies on the spatial Discrete Fourier Transform (DFT), requiring the microphone array to be larger than the source to reduce the spatial windowing effects due to th...

DFT(Discrete Fourier Transform) is a fundamental principle of DSP whose applications vary from Spectral analysis, Data compression, solving Partial Differential Equations, convolution and multiplication of large numbers. Despite its enormous potential in theoretically solving many DSP problems, it is of very little use in practical because of its extremely expensive hardware implementation. It ...

It is shown in this paper that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process. We show further that the chirp filter should not be realized as a transversal filter in a wide range of cases; use instead of the conventional FFT permits the computation of the DFT in a time proportional to N logz...

The electronic absorption spectra, ground-state geometries and electronic structures of symmetric and asymmetric squaraine dyes (SQD1-SQD4) were investigated using density functional theory (DFT) and time-dependent (TD-DFT) density functional theory at the B3LYP/6-311++G** level. The calculated ground-state geometries reveal pronounced conjugation in these dyes. Long-range corrected time depend...

In this paper, we present Radyban (Reliability Analysis with DYnamic BAyesian Networks), a software tool which allows to analyze systems modeled by means of Dynamic Fault Trees (DFT), by relying on automatic conversion into Dynamic Bayesian Networks (DBN). The tools aims at providing a familiar interface to reliability engineers, by allowing them to model the system to be analyzed with quite a ...

Cognitive computation, such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent Gödel encoding of the symbolic repertoire. The resulting nonlinear dynamical automata (NDA) are piecewise affine-linear maps acting on the unit square that is partitioned ...