Fission and Fusion Solutions in the (2+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation. By introducing some new constraint conditions to its N-solitons, the fifission and fusion are obtained. Numerical figures show that the two types of solutions look like the capital letter Y in spacial structures. Then, by taking a long wave limit approach and complex conjugation restrictions, some hybrid resonance solutions are generated, such as the interaction solutions between the L-order lumps and Q-fifission (fusion) solitons, as well as hybrid solutions mixed by the T-order breathers and Q-fifission (fusion) solitons. Dynamical behaviors of these solutions are analyzed theoretically and numerically. The results obtained can be helpful for understanding the fusion and fifission phenomena in many physical models, such as the organic membrane, macromolecule material and even-clump DNA, plasmas physics and so on.

Navigating Digital Borderscapes: A Case Study from Rohingya Refugee Settlements in Bangladesh

Based on a case study of the lived experiences of Rohingya refugees in Bangladesh between 2017 and 2019, this article focuses on displaced people’s digital needs and innovative efforts to navigate the challenges in their situation. The article first discusses the major barriers faced by Rohingya refugees in using various digital devices and platforms and how these obstacles adversely affect them in obtaining necessary information and humanitarian services. Our findings from the field highlight the uniquely important role that mobile repair shops in the camps play in providing online-offline hybrid solutions to circumvent restrictions imposed on the refugee community by the host government. The findings also show that different types of community leaders have emerged and that Rohingya women use digital means to push back against double discrimination. The article concludes with policy considerations related to the geopolitically transcendent issues of displacement, democracy, and digital rights.

TReMo+: Modeling Ternary and Binary ReRAM-Based Memories With Flexible Write-Verification Mechanisms

Non-volatile memory (NVM) technologies offer a number of advantages over conventional memory technologies such as SRAM and DRAM. These include a smaller area requirement, a lower energy requirement for reading and partly for writing, too, and, of course, the non-volatility and especially the qualitative advantage of multi-bit capability. It is expected that memristors based on resistive random access memories (ReRAMs), phase-change memories, or spin-transfer torque random access memories will replace conventional memory technologies in certain areas or complement them in hybrid solutions. To support the design of systems that use NVMs, there is still research to be done on the modeling side of NVMs. In this paper, we focus on multi-bit ternary memories in particular. Ternary NVMs allow the implementation of extremely memory-efficient ternary weights in neural networks, which have sufficiently high accuracy in interference, or they are part of carry-free fast ternary adders. Furthermore, we lay a focus on the technology side of memristive ReRAMs. In this paper, a novel memory model in the circuit level is presented to support the design of systems that profit from ternary data representations. This model considers two read methods of ternary ReRAMs, namely, serial read and parallel read. They are extensively studied and compared in this work, as well as the write-verification method that is often used in NVMs to reduce the device stress and to increase the endurance. In addition, a comprehensive tool for the ternary model was developed, which is capable of performing energy, performance, and area estimation for a given setup. In this work, three case studies were conducted, namely, area cost per trit, excessive parameter selection for the write-verification method, and the assessment of pulse width variation and their energy latency trade-off for the write-verification method in ReRAM.

A Relativistic Toda Lattice Hierarchy, Discrete Generalized (m,2N−m)-Fold Darboux Transformation and Diverse Exact Solutions

This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Firstly, we study some integrable properties for this system such as Hamiltonian structures, Liouville integrability and conservation laws. Secondly, we construct a discrete generalized (m,2N−m)-fold Darboux transformation based on its known Lax pair. Thirdly, we obtain some exact solutions including soliton, rational and semi-rational solutions with arbitrary controllable parameters and hybrid solutions by using the resulting Darboux transformation. Finally, in order to understand the properties of such solutions, we investigate the limit states of the diverse exact solutions by using graphic and asymptotic analysis. In particular, we discuss the asymptotic states of rational solutions and exponential-and-rational hybrid solutions graphically for the first time, which might be useful for understanding the motions of particles in lattices. Numerical simulations are used to discuss the dynamics of some soliton solutions. The results and properties provided in this paper may enrich the understanding of nonlinear lattice dynamics.

Bäcklund transformations, Lax pair and solutions of a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves

Burgers-type equations are considered as the models of certain phenomena in plasma astrophysics, ocean dynamics, atmospheric science and so on. In this paper, a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves is studied. Based on the Painlevé-Bäcklund equations, one auto-Bäcklund transformation and two hetero-Bäcklund transformations are derived. Motivated by the Burgers hierarchy, a Lax pair is given. Via two hetero-Bäcklund transformations with different constant seed solutions, we find some multiple-kink solutions, complex periodic solutions, hybrid solutions composed of the lump, periodic and multiple kink waves. Then we discuss the influence of the coefficients of the above equation on such solutions. Via the auto-Bäcklund transformation with the nontrivial seed solutions, we obtain certain lump-type solutions, kink-type solutions and recurrence relation of the above equation.

Performance Analysis of Rough Set–Based Hybrid Classification Systems in the Case of Missing Values

The paper presents a performance analysis of a selected few rough set–based classification systems. They are hybrid solutions designed to process information with missing values. Rough set-–based classification systems combine various classification methods, such as support vector machines, k–nearest neighbour, fuzzy systems, and neural networks with the rough set theory. When all input values take the form of real numbers, and they are available, the structure of the classifier returns to a non–rough set version. The performance of the four systems has been analysed based on the classification results obtained for benchmark databases downloaded from the machine learning repository of the University of California at Irvine.