Abstract:
In spite of the breakthrough in non-perturbative chiral gauge theories during the last decade, the present formulation has stubborn artefacts. Independently of the fermion representation one is confronted with unwanted CP violation and infinitely many undetermined weight factors. Renormalization group identifies the culprit. We demonstrate the procedure on Weyl fermions in a real representation.

Abstract:
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.

Abstract:
A continuous-time equivalent without frequency dependent elements for analysis of SC networks is derived by using the mixed bilinear-LDI transformation.

Abstract:
Numerical and phantom simulations were used to illustrate the effects of frequency-offsets and non-uniform magnitude modulation with this sequence in a typical perfusion protocol. In vivo data was post-processed to analyse the h-EPI’s sensitivity to the frequency-offsets.The centric phase-order was shown to be highly sensitive to frequency-offsets due to its symmetrical phase slope. Resulting artefacts include blurring, and splitting of the image into two identical copies along the phase-encode direction. It was also shown that frequency-offsets can introduce signal loss and ghosting of the right ventricle signal into the myocardium. The in vivo results were confirmed by numerical and phantom simulations. Magnitude modulation effects were found to be small.Imaging first-pass myocardial perfusion with an hybrid centric echo-planar-imaging sequence can be corrupted with ghosting and splitting of the image due to frequency-offsets.

Abstract:
We describe an approach to online analysis of micro-rheology data using a multi-scale time-correlation method. The method is particularly suited to process high-volume data streams and compress the relevant information in real time. Using this, we can obtain complex moduli of visco-elastic media without suffering from the high-frequency artefacts that are associated with the truncation errors in the most widely used versions of micro-rheology. Moreover, the present approach obviates the need to choose the time interval for data acquisition beforehand. We test our approach first on an artificial data set and then on experimental data obtained both for an optically trapped colloidal probe in water and a similar probe in poly-ethylene glycol solutions at various concentrations. In all cases, we obtain good agreement with the bulk rheology data in the region of overlap. We compare our method with the conventional Kramers-Kronig transform approach and find that the two methods agree over most of the frequency regime. For the same data set, the present approach is superior to Kramers-Kronig at high frequencies and can be made to perform at least comparable at low frequencies.

Abstract:
Measurable spectra are theoretically very often derived from complicated many-body Green's functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct effective potentials and kernels for the direct calculation of electronic spectra. In particular, the potential that yields the spectral function needed to describe photoemission turns out to be dynamical but {\it local} and {\it real}. As example we illustrate this ``photoemission potential'' for sodium and aluminium, modelled as homogeneous electron gas, and discuss in particular its frequency dependence stemming from the nonlocality of the corresponding self-energy. We also show that our approach leads to a very short derivation of a kernel that is known to well describe absorption and energy-loss spectra of a wide range of materials.

Abstract:
Image and video compression introduces distortions (artefacts) to the coded image. The mostprominent artefacts added are blockiness and blurriness. Many existing quality meters arenormally distortion-specific. This paper proposes an objective quality meter for quantifying thecombined blockiness and blurriness distortions in frequency domain. The model first applies edgedetection and cancellation, then spatial masking to mimic the characteristics of the human visualsystem. Blockiness is then estimated by transforming image into frequency domain, followed byfinding the ratio of harmonics to other AC components. Blurriness is determined by comparing thehigh frequency coefficients of the reference and coded images due to the fact that blurrinessreduces the high frequency coefficients. Then, both blockiness and blurriness distortions arecombined for a single quality metric. The meter is tested on blocky and blurred images from theLIVE image database, with a correlation coefficient of 95-96%.

Abstract:
In frequency hopping spread spectrum (FHSS) systems, two major problems are timing synchronization and frequency estimation. A blind estimation scheme is presented for estimating frequency and transition time without using reference signals. The scheme is robust in the sense that it can avoid the unbalanced sampling block problem that occurs in existing maximum likelihood-based schemes, which causes large errors in one of the estimates of frequency. The proposed scheme has a lower computational cost than the maximum likelihood-based greedy search method. The estimated parameters are also used for the subsequent time and frequency tracking. The simulation results demonstrate the efficacy of the proposed approach.

Abstract:
A new representation of the Fourier transform in terms of time and scale localization is discussed that uses a newly coined A-wavelet transform (Grigoryan 2005). The A-wavelet transform uses cosine- and sine-wavelet type functions, which employ, respectively, cosine and sine signals of length . For a given frequency , the cosine- and sine-wavelet type functions are evaluated at time points separated by on the time-axis. This is a two-parameter representation of a signal in terms of time and scale (frequency), and can find out frequency contents present in the signal at any time point using less computation. In this paper, we extend this work to provide further signal information in a better way and name it as -wavelet transform. In our proposed work, we use cosine and sine signals defined over the time intervals, each of length , , and are nonnegative integers, to develop cosine- and sine-type wavelets. Using smaller time intervals provides sharper frequency localization in the time-frequency plane as the frequency is inversely proportional to the time. It further reduces the computation for evaluating the Fourier transform at a given frequency. The A-wavelet transform can be derived as a special case of the -wavelet transform. 1. Introduction There are two domains for representing a signal: time and frequency domains. Depending upon the information required, either representation can be used. Fourier analysis has been the main technique for transforming a signal from one representation into another. In spite of the fact that the Fourier analysis is an ideal solution for deterministic and stationary signals, it is hardly of any use for time-varying signals or nonstationary signals, because analysis of these types of signals compromises between their transition and long term behaviors. For these types of signals, a transform is desired to represent the signal in a two-parameter form. The very first such transform in literature is the short time Fourier transform (STFT) [1]. This transform uses a time-window function to decompose the signal into segments and then the Fourier analysis is carried out on individual segments. The STFT provides local features that are present in the signal in a limited form because it uses the time-window function of fixed width for all frequency contents and thus it is unable to extract the required information in any given signal. So, a transform that can represent the signal in two-parameter form and uses the time-window function of different lengths is needed. Application of the short time Fourier transform multiple times

Abstract:
While Quantum Gravity remains elusive and Quantum Field Theory retains the interpretational difficulties of Quantum Mechanics, we have introduced an alternate approach to the unification of particles, fields, space and time, suggesting that the concept of matter as space without time provides a framework which unifies matter with spacetime and in which we anticipate the development of complete theories (ideally a single unified theory) describing observed 'particles, charges, fields and forces' solely with the geometry of our matter-space-time universe.