Entropy Bounds: New Insights

In this paper we review the fundamental concepts of entropy bounds put forward by Bousso and its relation to the holographic principle. We relate covariant entropy with logarithmic distance of separation of nearby geodesics. We also give sufficient arguments to show that the origin of entropy bounds is not indeed thermodynamic, but statistical.

Existence of two-solitary waves with logarithmic distance for the nonlinear Klein–Gordon equation

We consider the focusing nonlinear Klein–Gordon (NLKG) equation [Formula: see text] for [Formula: see text] and [Formula: see text] subcritical for the [Formula: see text] norm. In this paper, we show the existence of a solution [Formula: see text] of the equation such that [Formula: see text] where [Formula: see text] are two solitary waves of the equation with translations [Formula: see text] satisfying [Formula: see text] This behavior is due to the strong interactions between solitary waves which is in contrast with the previous work [R. Côte and Y. Martel, Multi-travelling waves for the nonlinear Klein–Gordon equation, Trans. Amer. Math. Soc. 370(10) (2018) 7461–7487] on multi-solitary waves of the (NLKG), devoted to the case of solitary waves with different speeds. This work is motivated by previous similar existence results for the nonlinear Schrödinger and generalized Korteweg–de Vries equations.

Multiple Positional Self-Attention Network for Text Classification

Self-attention mechanisms have recently caused many concerns on Natural Language Processing (NLP) tasks. Relative positional information is important to self-attention mechanisms. We propose Faraway Mask focusing on the (2m + 1)-gram words and Scaled-Distance Mask putting the logarithmic distance punishment to avoid and weaken the self-attention of distant words respectively. To exploit different masks, we present Positional Self-Attention Layer for generating different Masked-Self-Attentions and a following Position-Fusion Layer in which fused positional information multiplies the Masked-Self-Attentions for generating sentence embeddings. To evaluate our sentence embeddings approach Multiple Positional Self-Attention Network (MPSAN), we perform the comparison experiments on sentiment analysis, semantic relatedness and sentence classification tasks. The result shows that our MPSAN outperforms state-of-the-art methods on five datasets and the test accuracy is improved by 0.81%, 0.6% on SST, CR datasets, respectively. In addition, we reduce training parameters and improve the time efficiency of MPSAN by lowering the dimension number of self-attention and simplifying fusion mechanism.

Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework.

Best predictors in logarithmic distance between positive random variables

The metric properties of the set in which random variables take their values lead to relevant probabilistic concepts. For example, the mean of a random variable is a best predictor in that it minimizes the L2 distance between a point and a random variable. Similarly, the median is the same concept but when the distance is measured by the L1 norm. Also, a geodesic distance can be defined on the cone of strictly positive vectors in ℝn in such a way that, the minimizer of the distance between a point and a collection of points is their geometric mean. That geodesic distance induces a distance on the class of strictly positive random variables, which in turn leads to an interesting notions of conditional expectation (or best predictors) and their estimators. It also leads to different versions of the Law of Large Numbers and the Central Limit Theorem. For example, the lognormal variables appear as the analogue of the Gaussian variables for version of the Central Limit Theorem in the logarithmic distance.

INDUCED AND LOGARITHMIC DISTANCES WITH MULTI-REGION AGGREGATION OPERATORS

This paper introduces the induced ordered weighted logarithmic averaging IOWLAD and multiregion induced ordered weighted logarithmic averaging MR-IOWLAD operators. The distinctive characteristic of these operators lies in the notion of distance measures combined with the complex reordering mechanism of inducing variables and the properties of the logarithmic averaging operators. The main advantage of MR-IOWLAD operators is their design, which is specifically thought to aid in decision-making when a set of diverse regions with different properties must be considered. Moreover, the induced weighting vector and the distance measure mechanisms of the operator allow for the wider modeling of problems, including heterogeneous information and the complex attitudinal character of experts, when aiming for an ideal scenario. Along with analyzing the main properties of the IOWLAD operators, their families and specific cases, we also introduce some extensions, such as the induced generalized ordered weighted averaging IGOWLAD operator and Choquet integrals. We present the induced Choquet logarithmic distance averaging ICLD operator and the generalized induced Choquet logarithmic distance averaging IGCLD operator. Finally, an illustrative example is proposed, including real-world information retrieved from the United Nations World Statistics for global regions.

Optimization calculation of well function W (u, r/B) based on BP neural network

In order to obtain the calculation result of the well function W (u, r/B) in the groundwater more quickly and the obtained result is more accurate than the approximation obtained by the conventional interpolation. Based on the selection of BP neural network structure and the selection of parameters, the corresponding BP neural network model was established to study the well function W (u, r/B). The results show that the partial data of well function are trained by BP neural network, and the prediction result is faster and more accurate than the approximate solution obtained by the equal logarithmic distance trapezoidal segmentation method. It can be seen that using BP neural network to learn and train, the network model obtained is used for solving and calculation, which is a convenient, fast and accurate calculation method.