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A<sc>bstract</sc> In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory. 

A homology class [Formula: see text] of a complex flag variety [Formula: see text] is called a line degree if the moduli space [Formula: see text] of 0-pointed stable maps to X of degree d is also a flag variety [Formula: see text]. We prove a quantum equals classical formula stating that any n-pointed (equivariant, [Formula: see text]-theoretic, genus zero) Gromov–Witten invariant of line degree on X is equal to a classical intersection number computed on the flag variety [Formula: see text]. We also prove an n-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov–Witten invariants of the variety of complete flags [Formula: see text]. Our formulas make it straightforward to compute the big quantum [Formula: see text]-theory ring [Formula: see text] modulo the ideal [Formula: see text] generated by degrees d larger than line degrees. 

This work seeks to leverage Processing-with-storage-technology (PWST) to accelerate a key bioinformatics kernel calledk-mer counting, which involves processing large files of sequence data on the disk to build a histogram of fixed-size genome sequence substrings and thereby entails prohibitively high I/O overhead. In particular, this work proposes a set of accelerator designs called Abakus that offer varying degrees of tradeoffs in terms of performance, efficiency, and hardware implementation complexity. The key to these designs is a set of domain-specific hardware extensions to accelerate the key operations fork-mer counting at various levels of the SSD hierarchy, with the goal of enhancing the limited computing capabilities of conventional SSDs, while exploiting the parallelism of the multi-channel, multi-way SSDs. Our evaluation suggests that Abakus can achieve 8.42×, 6.91×, and 2.32× speedup over the CPU-, GPU-, and near-data processing solutions. 

Abstract MotivationDriven by technological advances, the throughput and cost of mass spectrometry (MS) proteomics experiments have improved by orders of magnitude in recent decades. Spectral library searching is a common approach to annotating experimental mass spectra by matching them against large libraries of reference spectra corresponding to known peptides. An important disadvantage, however, is that only peptides included in the spectral library can be found, whereas novel peptides, such as those with unexpected post-translational modifications (PTMs), will remain unknown. Open modification searching (OMS) is an increasingly popular approach to annotate modified peptides based on partial matches against their unmodified counterparts. Unfortunately, this leads to very large search spaces and excessive runtimes, which is especially problematic considering the continuously increasing sizes of MS proteomics datasets. ResultsWe propose an OMS algorithm, called HOMS-TC, that fully exploits parallelism in the entire pipeline of spectral library searching. We designed a new highly parallel encoding method based on the principle of hyperdimensional computing to encode mass spectral data to hypervectors while minimizing information loss. This process can be easily parallelized since each dimension is calculated independently. HOMS-TC processes two stages of existing cascade search in parallel and selects the most similar spectra while considering PTMs. We accelerate HOMS-TC on NVIDIA’s tensor core units, which is emerging and readily available in the recent graphics processing unit (GPU). Our evaluation shows that HOMS-TC is 31× faster on average than alternative search engines and provides comparable accuracy to competing search tools. Availability and implementationHOMS-TC is freely available under the Apache 2.0 license as an open-source software project at https://github.com/tycheyoung/homs-tc.