The perturbation bound of the extended vertical linear complementarity problem

In this paper, we discuss the perturbation analysis of the extended vertical linear complementarity problem (EVLCP). Under the assumption of the row $\mathcal{W}$-property, several absolute and relative perturbation bounds of EVLCP are given, which can be reduced to some existing results. Some numerical examples are given to show the proposed bounds

The error and perturbation bounds for the absolute value equations with some applications

To our knowledge, so far, the error and perturbation bounds for the general absolute value equations are not discussed. In order to fill in this study gap, in this paper, by introducing a class of absolute value functions, we study the error bounds and perturbation bounds for two types of absolute value equations (AVEs): Ax-B|x|=b and Ax-|Bx|=b. Some useful error bounds and perturbation bounds for the above two types of absolute value equations are presented. By applying the absolute value equations, we also obtain the error and perturbation bounds for the horizontal linear complementarity problem (HLCP). In addition, a new perturbation bound for the LCP without constraint conditions is given as well, which are weaker than the presented work in [SIAM J. Optim., 2007, 18: 1250-1265] in a way. Besides, without limiting the matrix type, some computable estimates for the above upper bounds are given, which are sharper than some existing results under certain conditions. Some numerical examples for the AVEs from the LCP are given to show the feasibility of the perturbation bounds

Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO4_{4}

The spin-1/2 triangular lattice antiferromagnet YbMgGaO$_{4}$ has attracted recent attention as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin-liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field polarized state of YbMgGaO$_{4}$ to obtain better microscopic insights on its exchange interactions. Terahertz spectroscopy in this fashion functions as high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4T, informed by the analysis of the terahertz spectroscopy linewidths, yields stringent constraints on $g$-factors and exchange interactions. Our results paint YbMgGaO$_{4}$ as an easy-plane XXZ antiferromagnet with the combined and necessary presence of sub-leading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained $g$-factors are substantially different from previous reports. This works establishes the hierarchy of exchange interactions in YbMgGaO$_{4}$ from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology

Efficient Alignment Algorithms for DNA Sequencing Data

The DNA Next Generation Sequencing (NGS) technologies produce data at a low cost, enabling their application to many ambitious fields such as cancer research, disease control, personalized medicine etc. However, even after a decade of research, the modern aligners and assemblers are far from providing efficient and error free genome alignments and assemblies respectively. This is due to the inherent nature of the genome alignment and assembly problem, which involves many complexities. Many algorithms to address this problem have been proposed over the years, but there still is a huge scope for improvement in this research space. Many new genome alignment algorithms are proposed over time and one of the key differentiator among these algorithms is the efficiency of the genome alignment process. I present a new algorithm for efficiently finding Maximal Exact Matches (MEMs) between two genomes: E-MEM (Efficient computation of maximal exact matches for very large genomes). Computing MEMs is one of the most time consuming step during the alignment process. E-MEM can be used to find MEMs which are used as seeds in genome aligner to increase its efficiency. The E-MEM program is the most efficient algorithm as of today for computing MEMs and it surpasses all competition by large margins. There are many genome assembly algorithms available for use, but none produces perfect genome assemblies. It is important that assemblies produced by these algorithms are evaluated accurately and efficiently.This is necessary to make the right choice of the genome assembler to be used for all the downstream research and analysis. A fast genome assembly evaluator is a key factor when a new genome assembler is developed, to quickly evaluate the outcome of the algorithm. I present a fast and efficient genome assembly evaluator called LASER (Large genome ASsembly EvaluatoR), which is based on a leading genome assembly evaluator QUAST, but significantly more efficient both in terms of memory and run time. The NGS technologies limit the potential of genome assembly algorithms because of short read lengths and nonuniform coverage. Recently, third generation sequencing technologies have been proposed which promise very long reads and a uniform coverage. However, this technology comes with its own drawback of high error rate of 10 - 15% consisting mostly of indels. The long read sequencing data is useful only after error correction obtained using self read alignment (or read overlapping) techniques. I propose a new self read alignment algorithm for Pacific Biosciences sequencing data: HISEA (Hierarchical SEed Aligner), which has very high sensitivity and precision as compared to other state-of-the-art aligners. HISEA is also integrated into Canu assembly pipeline. Canu+HISEA produces better assemblies than Canu with its default aligner MHAP, at a much lower coverage