Throughput capacity of two-hop relay MANETs under finite buffers

Since the seminal work of Grossglauser and Tse [1], the two-hop relay algorithm and its variants have been attractive for mobile ad hoc networks (MANETs) due to their simplicity and efficiency. However, most literature assumed an infinite buffer size for each node, which is obviously not applicable to a realistic MANET. In this paper, we focus on the exact throughput capacity study of two-hop relay MANETs under the practical finite relay buffer scenario. The arrival process and departure process of the relay queue are fully characterized, and an ergodic Markov chain-based framework is also provided. With this framework, we obtain the limiting distribution of the relay queue and derive the throughput capacity under any relay buffer size. Extensive simulation results are provided to validate our theoretical framework and explore the relationship among the throughput capacity, the relay buffer size and the number of nodes

Two-way collinear interaction of longitudinal waves in an elastic medium with quadratic nonlinearity

A numerical implementation of two-way collinear interaction of nonlinear ultrasonic longitudinal waves in an elastic medium with quadratic nonlinearity is conducted in this work. A semi-discrete central scheme is used here to solve the numerical problem. The pulse-inversion technique is applied to accentuate the generated resonant waves and remove the fundamental components. The produced resonant waves can be clearly observed in the frequency domain. Variation trends of the resonant waves together with second harmonics along the propagation path are analyzed and results show that apart from the obvious growing of the transverse component with difference frequency, the longitudinal component and the resonant wave of sum frequency have notable responses as well. The spatial distribution of resonant waves will provide necessary information for the related experiments

A Global Context Mechanism for Sequence Labeling

Sequential labeling tasks necessitate the computation of sentence representations for each word within a given sentence. With the advent of advanced pretrained language models; one common approach involves incorporating a BiLSTM layer to bolster the sequence structure information at the output level. Nevertheless, it has been empirically demonstrated (P.-H. Li et al., 2020) that the potential of BiLSTM for generating sentence representations for sequence labeling tasks is constrained, primarily due to the amalgamation of fragments form past and future sentence representations to form a complete sentence representation. In this study, we discovered that strategically integrating the whole sentence representation, which existing in the first cell and last cell of BiLSTM, into sentence representation of ecah cell, could markedly enhance the F1 score and accuracy. Using BERT embedded within BiLSTM as illustration, we conducted exhaustive experiments on nine datasets for sequence labeling tasks, encompassing named entity recognition (NER), part of speech (POS) tagging and End-to-End Aspect-Based sentiment analysis (E2E-ABSA). We noted significant improvements in F1 scores and accuracy across all examined datasets

A variable-order fractal derivative model for anomalous diffusion

This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the previous mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior, and heavy tail phenomena of the new model, and variable-order fractional derivative model are also offered

Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited

We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation with two parameter Mittag–Leffler function in the kernel to the mentioned equation. We used the contraction mapping theorem and Weissinger’s fixed point theorem to obtain existence and uniqueness of global solution in the spaces of Lebesgue integrable functions. The new representation formula of the general solution helps us to find the fixed point problem associated with the fractional Langevin equation which its contractivity constant is independent of the friction coefficient. Two examples are discussed to illustrate the feasibility of the main theoremsThe authors are thankful to the Editor(s) and reviewers of the manuscript for their helpful comments. The work of H. Fazli and H. Sun was supported by the National Key R&D Program of China (2017YFC0405203), the National Natural Science Foundation of China under Grant No. 11972148. The reserach of J. J. Nieto was partially supported by Xunta de Galicia, ED431C 2019/02, and by project MTM2016-75140-P of AEI/FEDER (Spain)S