Boundary-Aware Hashing for Hamming Space Retrieval

Hamming space retrieval is a hot area of research in deep hashing because it is effective for large-scale image retrieval. Existing hashing algorithms have not fully used the absolute boundary to discriminate the data inside and outside the Hamming ball, and the performance is not satisfying. In this paper, a boundary-aware contrastive loss is designed. It involves an exponential function with absolute boundary (i.e., Hamming radius) information for dissimilar pairs and a logarithmic function to encourage small distance for similar pairs. It achieves a push that is bigger than the pull inside the Hamming ball, and the pull is bigger than the push outside the ball. Furthermore, a novel Boundary-Aware Hashing (BAH) architecture is proposed. It discriminatively penalizes the dissimilar data inside and outside the Hamming ball. BAH enables the influence of extremely imbalanced data to be reduced without up-weight to similar pairs or other optimization strategies because its exponential function rapidly converges outside the absolute boundary, making a huge contrast difference between the gradients of the logarithmic and exponential functions. Extensive experiments conducted on four benchmark datasets show that the proposed BAH obtains higher performance for different code lengths, and it has the advantage of handling extremely imbalanced data.

On a special class of modified integral operators preserving some exponential functions

<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id="M1">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id="M2">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} _{0}^{+} $\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>

Radius of Star-Likeness for Certain Subclasses of Analytic Functions

In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition ℜfzgz>0, for some analytic function, g, with ℜz+1−2nzgz>0,∀n∈N. We calculate the radius constants for different classes of analytic functions, including, for example, for the class of star-like functions connected with the exponential functions, i.e., the lemniscate of Bernoulli, the sine function, cardioid functions, the sine hyperbolic inverse function, the Nephroid function, cosine function and parabolic star-like functions. The results obtained are sharp.

Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.

Rollover of Liquid Natural Gas in a Storage Tank: A Numerical Simulation

In the filling and transportation processes of liquefied natural gas (LNG), the safety of LNG storage tanks is compromised because of rollover phenomenon. As such, the rollover factors of LNG in a storage tank should be identified to prevent or weaken the rollover intensity of LNG. In this study, the rollover behavior of LNG in a storage tank is numerically simulated. The density of the two layers in a LNG storage tank is related to temperature in our numerical model. It is found that the greater the significant initial density difference (range of 1-12 kg·m-3) is, the more obvious the LNG rollover will be. A density difference of 7.5 kg·m-3 is found as the critical density difference in the present work. When the initial density difference exceeds the critical density difference, the LNG rollover coefficients increase dramatically. Moreover, an LNG rollover model with two daughter models is proposed, which are divided by the critical initial density difference, i.e., a cubic relationship between rollover coefficients and the initial density difference when the density difference is less than 7.5 kg·m-3 and secondly, a linear relationship between the rollover coefficient and the double exponential functions when the density difference is larger than 7.5 kg·m-3.

A population-based method to determine the time-integrated activity in molecular radiotherapy

Background The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [177Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient. Methods Renal biokinetics of [177Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. Results The function $$A_{1} { }\beta { }e^{{ - \left( {\lambda_{1} + \lambda_{{{\text{phys}}}} } \right)t}} + A_{1} { }\left( {1 - \beta } \right){ }e^{{ - \left( {\lambda_{{{\text{phys}}}} } \right)t}}$$ A 1 β e - λ 1 + λ phys t + A 1 1 - β e - λ phys t with shared parameter $$\beta$$ β was selected as the function most supported by the data with an Akaike weight of 97%. Parameters $$A_{1}$$ A 1 and $$\lambda_{1}$$ λ 1 were fitted individually for every patient while parameter $$\beta { }$$ β was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037. Conclusions The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.

Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications

The improved tan(φ/2)-expansion, simplest equation, and extended (G′/G)-expansion methods are employed to construct the exact solutions involving parameters of the Van der Waals equation arising in the material industry. This model explains the phase separation phenomenon. Understanding the prominent dynamic and static properties of this model and other models of this type is of great importance for the physical phenomena encountered in many areas of industry. Therefore, for such models, it is also important to obtain guiding solutions in obtaining new information. Many explicit wave solutions consisting of trigonometric, hyperbolic, rational, and exponential functions are found by using analytical techniques. The obtained solutions were verified with Maple by placing them back into the original equations. Moreover, graphical demonstrations for some of the obtained solutions are given.

Application of exponential functions in weighted residuals method in structural mechanics. Part 3: infinite cylindrical shell under concentrated forces

Solution for cylindrical shell under concentrated force is a fundamental problem which allow to consider many other cases of loading and geometries. Existing solutions were based on simplified assumptions, and the ranges of accuracy of them still remains unknown. The common idea is the expansion of them into Fourier series with respect to circumferential coordinate. This reduces the problem to 8th order even differential equation as to axial coordinate. Yet the finding of relevant 8 eigenfunctions and exact relation of 8 constant of integrations with boundary conditions are still beyond the possibilities of analytical treatment. In this paper we apply the decaying exponential functions in Galerkin-like version of weighted residual method to above-mentioned 8th order equation. So, we construct the sets of basic functions each to satisfy boundary conditions as well as axial and circumferential equilibrium equations. The latter gives interdependencies between the coefficients of circumferential and axial displacements with the radial ones. As to radial equilibrium, it is satisfied only approximately by minimizations of residuals. In similar way we developed technique for application of Navier like version of WRM. The results and peculiarities of WRM application are discussed in details for cos2j concentrated loading, which methodologically is the most complicated case, because it embraces the longest distance over the cylinder. The solution for it clearly exhibits two types of behaviors – long-wave and short-wave ones, the analytical technique of treatment of them was developed by first author elsewhere, and here was successfully compared. This example demonstrates the superior accuracy of two semi analytical WRM methods. It was shown that Navier method while being simpler in realization still requires much more (at least by two orders) terms than exponential functions.

Relation of Some Known Functions in terms of Generalized Meijer G -Functions

The aim of this paper is to prove some identities in the form of generalized Meijer G -function. We prove the relation of some known functions such as exponential functions, sine and cosine functions, product of exponential and trigonometric functions, product of exponential and hyperbolic functions, binomial expansion, logarithmic function, and sine integral, with the generalized Meijer G -function. We also prove the product of modified Bessel function of first and second kind in the form of generalized Meijer G -function and solve an integral involving the product of modified Bessel functions.