Digital Spectral Analysis by means of the Method of Averag Modified Periodograms Using Binary-Sign Stochastic Quantization of Signals

The method of averaging modified periodograms is one of the main methods for estimating the power spectral density (PSD). The aim of this work was the development of mathematical and algorithmic support, which can increase the computational efficiency of signals digital spectral analysis by this method.The solution to this problem is based on the use of binary-sign stochastic quantization for converting the analyzed signal into a digital code. A special feature of this quantization is the use of a randomizing uniformly distributed auxiliary signal as a stochastic continuous quantization threshold (threshold function). Taking into account the theory of discrete-event modeling the result of binary-sign quantization is interpreted as a chronological sequence of instantaneous events in which its values change. In accordance with this we have a set of time samples that uniquely determine the result of binary-sign quantization in discrete-time form. Discrete-event modeling made it possible to discretize the process of calculating PSD estimates. As a result, the calculation of PSD estimates was reduced to discrete processing of the cosine and sine Fourier transforms for window functions. These Fourier transforms are calculated analytically based on the applied window functions. The obtained mathematical equations for calculating the PSD estimates practically do not require multiplication operations. The main operations of these equations are addition and subtraction. As a consequence, the time spent on digital spectral analysis of signals is reduced.Numerical experiments have shown that the developed mathematical and algorithmic support allows us to calculate the PSD estimates by the method of averaging modified periodograms with a high frequency resolution and accuracy even for a sufficiently low signal-to-noise ratio. This result is especially important for spectral analysis of broadband signals.The developed software module is a problem-oriented component that can be used as part of metrologically significant software for the operational analysis of complex signals.

A new approach to anomalous axial vector field theory – II

This work is continuation of a stochastic quantization program reported earlier. In this paper, we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods.

A new approach to anomalous axial vector field theory

In an earlier paper, it has been shown that the ultra violet divergence structure of anomalous [Formula: see text] axial vector gauge model in the stochastic quantization scheme is different from that in the conventional quantum field theory. Also, it has been shown that the model is expected to be renormalizable. Based on the operator formalism of the stochastic quantization, a new approach to anomalous [Formula: see text] axial vector gauge model is proposed. The operator formalism provides a convenient framework for analysis of ultra violet divergences, but the computations in a realistic model become complicated. In this paper a new approach to do computations in the model is formulated directly in four dimensions. The suggestions put forward here will lead to simplification in the study of applications of the axial vector gauge theory, as well as those of other similar models.

Symplectic Quantization I: Dynamics of Quantum Fluctuations in a Relativistic Field Theory

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021).

Competence region estimation for black-box surrogate models

With advances in edge applications for industry andhealthcare, machine learning models are increasinglytrained on the edge. However, storage and memory in-frastructure at the edge are often primitive, due to costand real-estate constraints. A simple, effective methodis to learn machine learning models from quantized datastored with low arithmetic precision (1-8 bits). In thiswork, we introduce two stochastic quantization meth-ods, dithering and stochastic rounding. In dithering, ad-ditive noise from a uniform distribution is added tothe sample before quantization. In stochastic rounding,each sample is quantized to the upper level with prob-ability p and to a lower level with probability 1-p. Thekey contributions of the paper are For 3 standard machine learning models, Support Vec-tor Machines, Decision Trees and Linear (Logistic)Regression, we compare the performance loss for astandard static quantization and stochastic quantiza-tion for 55 classification and 30 regression datasetswith 1-8 bits quantization. We showcase that for 4- and 8-bit quantization overregression datasets, stochastic quantization demon-strates statistically significant improvement. We investigate the performance loss as a function ofdataset attributes viz. number of features, standard de-viation, skewness. This helps create a transfer functionwhich will recommend the best quantizer for a givendataset. We propose 2 future research areas, a) dynamic quan-tizer update where the model is trained using stream-ing data and the quantizer is updated after each batchand b) precision re-allocation under budget constraintswhere different precision is used for different features.