Object Identification by Signal Gain and Correlation

In this study, “ring rotation invariant transform” techniques are used to add more salient feature to the original images. The “ring rotation invariant transform” can solve image rotation problem, which transfers a ring signal to several signal vectors in the complex domain, whereby to generate invariant magnitude. Matrix correlation is employed to combine these magnitudes to generate the various discriminators, by which to identify objects. For managing image-shifting problem, one pixel in sample image is compared with surrounding pixels of unknown image. The comparison approaching in this study is by the basis of pixel-to-pixel-comparisons.

A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

Electroencephalogram Image under Complex Domain Analysis Algorithm to Analyze Neurological Status Epilepticus and Poor Prognostic Factors of Children

This study was to adopt the electroencephalogram (EEG) image to analyze the neurological status epilepticus (SE) and adverse prognostic factors of children using the complex domain analysis algorithm, aiming at providing a theoretical basis for the clinical treatment of children with SE. 24-hour EEG was adopted to diagnose 197 children with SE. The patients were divided into an experimental group (100 cases) and a control group (97 cases) using a random number table method. The EEGs of children in the experimental group were analyzed using the compound domain analysis algorithm, and those in the control group were diagnosed by a professional doctor. The indicators of children in two groups were compared to analyze the effect of the compound domain analysis algorithm in diagnosing diseases through EEG. The prognostic scores of 197 children were scored one month after they were diagnosed, treated, and discharged, and the adverse prognostic factors were analyzed. As a result, EEG can accurately and effectively analyze the brain diseases in children. The sensitivity and specificity of the complex domain analysis algorithm for the detection of epilepsy EEG were much higher than those of the EEG automatic detection algorithm based on time-domain waveform similarity and the EEG automatic detection algorithm based on convolutional neural network (CNN), and the average running time was opposite, showing obvious difference ( P < 0.05 ).The average accuracy, sensitivity, and specificity of children in the experimental group were 96.11%, 97.10%, and 95.19%, respectively; and those in the control group were 88.83%, 90.14%, and 87.82%, respectively, so there was an obvious difference in accuracy between two groups ( P < 0.05 ). There were 57 cases with good prognosis and 140 cases with poor prognosis; there were 70 males with good prognosis and 19 poor prognoses and 69 women with good prognosis and 19 poor prognoses. Among 121 patients with infections, 84 cases had good prognosis and 37 cases had poor prognosis; 39 cases of irregular medication had good prognosis in 31 cases and a poor prognosis in 8 cases; and 37 cases had no obvious cause, including 25 cases with good prognosis and 12 cases with poor prognosis. In short, the EEG diagnosis and treatment effect of the compound domain analysis algorithm were better than those of professional doctors; the gender of the patient had no effect on the poor prognosis, and the pathogenic factors had an impact on the poor prognosis of the patient.

Generalized Quantum Integro-Differential Fractional Operator with Application of 2D-Shallow Water Equation in a Complex Domain

In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.

A GENERALIZATION OF THE SHIFT OPERATOR

Several approaches are known to generalize the shift operator in the complex domain. Specific generalization procedures lead to significantly different operators of the shift type even in one specific area of complex analysis. In this paper, a certain general operator of the shift type is defined. The properties of this operator are studied and the question of the continuity of this definition is considered. The properties of a certain operator to a certain extent re-peat the properties of the previously studied operators of the shift type. This allows us to speak of the possibility of extending the main results on spectral synthesis in the complex domain to convolutional equations of a more general form.

Symmetry Breaking of a Time-2D Space Fractional Wave Equation in a Complex Domain

(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional differential operator is used together with a symmetric operator to define a new fractional symmetric operator. Then by applying the new operator, we formulate a generalized time-2D space fractional wave equation. We shall utilize the two concepts: subordination and majorization to present our results; (3) Results: we obtain different formulas of analytic solutions using the geometric analysis. The solution suggests univalent (1-1) in the open unit disk. Moreover, under certain conditions, it was starlike and dominated by a chaotic function type sine. In addition, the authors formulated a fractional time wave equation by using the Atangana–Baleanu fractional operators in terms of the Riemann–Liouville and Caputo derivatives.