Optimizing Matching Area for Underwater Gravity-Aided Inertial Navigation Based on the Convolution Slop Parameter-Support Vector Machine Combined Method

This paper focuses on the selection of matching areas in the gravity-aided inertial navigation system. Firstly, the Sobel operator was used in convolution of the gravity anomaly map to obtain the feature map. The convolution slope parameters were constructed by combining the feature map and the gravity anomaly map. The characteristic parameters, such as the difference between convolution rows and columns, convolution variance of the feature map, the pooling difference, and range of the gravity anomaly map, were combined. Based on the support vector machine algorithm, the convolution slope parameter–support vector machine combined method is proposed. Second, we selected the appropriate training sample set and set parameters to verify. The results show that compared with the pre-calibration results, the classification accuracy of the test set is more than 92%, which proves that the convolution slope parameter–support vector machine combined method can effectively distinguish between the suitable and the unsuitable area. Thirdly, we applied this method to another region. The navigation experiment was performed in the split-matching area. The average positioning error was better than 100 m, and the correct rate was more than 90%. The results show that sailing in the selected area can accurately match the trajectory and reduce the positioning error.

Lie polynomials in an algebra defined by a linearly twisted commutation relation

We present an elementary approach to characterizing Lie polynomials on the generators [Formula: see text] of an algebra with a defining relation in the form of a twisted commutation relation [Formula: see text]. Here, the twisting map [Formula: see text] is a linear polynomial with a slope parameter, which is not a root of unity. The class of algebras defined as such encompasses [Formula: see text]-deformed Heisenberg algebras, rotation algebras, and some types of [Formula: see text]-oscillator algebras, the deformation parameters of which, are not roots of unity. Thus, we have a general solution for the Lie polynomial characterization problem for these algebras.

Complexity traits and synchrony of cryptocurrencies price dynamics

In this study, we characterized the dynamics and analyzed the degree of synchronization of the time series of daily closing prices and volumes in US$ of three cryptocurrencies, Bitcoin, Ethereum, and Litecoin, over the period September 1,2015–March 31, 2020. Time series were first mapped into a complex network by the horizontal visibility algorithm in order to revel the structure of their temporal characters and dynamics. Then, the synchrony of the time series was investigated to determine the possibility that the cryptocurrencies under study co-bubble simultaneously. Findings reveal similar complex structures for the three virtual currencies in terms of number and internal composition of communities. To the aim of our analysis, such result proves that price and volume dynamics of the cryptocurrencies were characterized by cyclical patterns of similar wavelength and amplitude over the time period considered. Yet, the value of the slope parameter associated with the exponential distributions fitted to the data suggests a higher stability and predictability for Bitcoin and Litecoin than for Ethereum. The study of synchrony between the time series investigated displayed a different degree of synchronization between the three cryptocurrencies before and after a collapse event. These results could be of interest for investors who might prefer to switch from one cryptocurrency to another to exploit the potential opportunities of profit generated by the dynamics of price and volumes in the market of virtual currencies.

Analyzing Impact of a Crisis on Bank Financial Ratios

In this study we provide a practical framework and methodology for analyzing the effects of banking shocks (economic or financial in nature) on bank fundamentals, that avoids the use of complicated econometrics methods. For this, we focus our attention to the effects of the 2007-2008 global financial crisis on the four largest US banks and examine the variation of trends in the select financial ratios for those institutions using quarterly regulatory data running from 2002-Q4 to 2020-Q2. We start by plotting time series charts of those financial ratios for each bank and compare the before-crisis, transition and after-crisis periods. For this, we simply fit trend lines with three parameters of shift, slope, and volatility to the banking data. The shift parameter describes the level change of the variable when before- and after-crisis periods are compared. The slope parameter pronounces the difference in steepness of the trend lines, while the volatility parameter is associated with all three periods and describe the variation in the data during each period. Our results indicate that capital ratios, an important regulatory financial ratio, are higher across the board in the after-crisis period compared to before-crisis period, suggesting a positive shift. We don’t see significant changes in slope parameter for the capital ratio series leading us to suggest the use of dummy variable regression model where slope is treated as a fixed constant. We further show that pre-crisis and transition periods are characterized by higher volatilities that ultimately subside in the after-crisis period. Lastly, we conclude by suggesting that financial practitioners use the shift, slope and volatility parameters in understanding trends in financial time series data since it is easy to implement and interpret the results compared to more sophisticated econometric models.

An Investigation of the Slope Parameters of Reaction Times and P3 Latencies in the Sternberg Memory Scanning Task – A Fixed-Links Model Approach

The speed of retrieving information from short-term memory is thought to be captured in the slope of the linear function of reaction times (RTs) regressed on set size in the Sternberg memory scanning task (SMST). Individual differences in the slope parameter have been hypothesized to correlate with general intelligence (g). However, this correlation can usually not be found. This present study chose a fixed-links model (FLM) approach to re-evaluate the RT slope parameter on a latent level in a sample of 98 participants aged 18 to 61 years. The same was tried for P3 latencies to investigate whether or not both parameters measure the same cognitive processes in the SMST, and to assess the usability of both slopes to predict g. For RTs, a linear increase with set size was found. The RT slope correlated with g on a manifest level already. The FLM approach could significantly increase the relationship between the slope and g. For P3 latencies, no evidence for a linear increase was found. This indicates that RTs and P3 latencies do not measure the same cognitive processes in the SMST. The FLM proved suitable to investigate the association between the speed of short-term memory scanning and intelligence.

T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter α′ and re-derive the α′-corrected Buscher rules first found in ref. [42], proving the T duality invariance of the dimensionally-reduced action to that order in α′. We use Iyer and Wald’s prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the α′-corrected T duality transformations. This formula has been successfully applied to α′-corrected 4-dimensional non-extremal Reissner-Nordström black holes in ref. [21] and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.

Approximate solutions of the Schrödinger equation with energy-dependent screened Coulomb potential in D – dimensions

Within the framework of the conventional Nikiforov-Uvarov method and a new form of Greene-Aldrich approximation scheme, we solved the Schrödinger equation with the energy-dependent screened Coulomb potential. Energy eigenvalues and energy eigenfunctions were obtained both approximately and numerically at different dimensions. The energy variations with different potential parameters, quantum numbers and energy slope parameter, respectively were also discussed graphically. The major finding of this research is the effect of the energy slope parameter on the energy spectra, which is seen in the existence of two simultaneous energy values for a particular quantum state. Our special cases also agree with the results obtained from literature, when the energy slope parameter is zero.