All-optical wavelength-tunable narrow-linewidth fiber laser

Parameter regulations of narrow-linewidth fiber lasers in frequency domain has drawn considerable interests for widespread applications in the light quantum computing, precise coherent detection, and generation of micro-waves. All-optical methods provide compact, precise and fast accesses to achieving these lasers with wavelength-tunability. Here, the optical-thermal effects of graphene is utilized to precisely control operations of free-running lasers with a tuning speed of 140 MHz/ms. Assisted by the single-longitude-mode operation and linewidth suppression of stimulated Brillouin backscattering, we obtain an optical-controllable ~750 Hz fiber laser with a wavelength-tuning range of 3.7 nm

A row analogue of Hecke column insertion

We introduce a new row insertion algorithm on decreasing tableaux and increasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivial variation of Hecke column insertion which generalizes EG column insertion. Similar to Hecke column insertion, our row insertion is bijective and respects Hecke equivalence, and therefore recovers the expansions of Grothendieck symmetric functions into Grassmannian Grothendieck functions. In future work, we will use this row insertion to establish an expansion of products between Lascoux polynomials and certain Grothendieck polynomials, which cannot be done by Hecke column insertion

Investigating chromium cycling in global oxygen deficient zones with chromium isotopes

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2021.Chromium (Cr) isotopes have shown great potential as a paleo-redox proxy to trace the redox conditions of ancient oceans and atmosphere. However, its cycling in modern environments is poorly constrained. In my thesis, I attempt to fill in the gap of our understanding of chromium cycling in the modern ocean, with a focus on the redox processes in global oxygen deficient zones (ODZs). Firstly, we developed a method to analyze Cr isotopes of different Cr redox species. Tests on processing conditions demonstrated its robustness in obtaining accurate Cr isotope data. It is applicable to both frozen and fresh samples. This method allows us to investigate the redox cycling of Cr that is hard to unravel by existing total Cr methods. Secondly, in the Eastern Tropical North Pacific (ETNP), Eastern Tropical South Pacific (ETSP) and Arabian Sea ODZs, their total dissolved Cr profiles show preferential reduction of isotopically light Cr(VI) to Cr(III), which is scavenged and exported to deeper oceans. Applying our new method to ETNP and ETSP ODZ seawater samples, we observed Cr(VI) reduction in both ODZs with a similar fractionation factor. This indicates similar mechanisms may be controlling Cr(VI) reduction in the two ODZs. Cr(III) maximum coincides with Fe(II) and secondary nitrite maximums in the upper core of both ODZs. Shipboard incubations with spiked Fe(II) showed fast Cr(VI) reduction occurring in the ETNP ODZ. But neither Fe(II) nor microbes were reducing Cr(VI) directly. Thirdly, we calculated the isotope effects of Cr scavenging in the ETNP and ETSP ODZs. Thetwo ODZs show a similar isotope partitioning during Cr scavenging. And spatial variability is observed in the ETNP ODZ. Our calculated scavenged Cr isotope ratio is lighter than that of the total dissolved Cr from the same depth. It is also comparable to that of reducing or anoxic sediments, which implies that Cr isotopes can be used as an archive for local redox conditions.This research was supported by an anonymous MIT Fellowship, Praceis Presidential Fellowship, Frederick A. Middleton Fellowship, the US National Science Foundation (NSF Award No. OCE-1459287, OCE-1736996, OCE-1924050 and DEB-1542240) and the Center for Microbial Oceanography: Research and Education (C-MORE, NSF-OIA Award No. EF-0424599)

When do you need Chain-of-Thought Prompting for ChatGPT?

Chain-of-Thought (CoT) prompting can effectively elicit complex multi-step reasoning from Large Language Models~(LLMs). For example, by simply adding CoT instruction ``Let's think step-by-step'' to each input query of MultiArith dataset, GPT-3's accuracy can be improved from 17.7\% to 78.7\%. However, it is not clear whether CoT is still effective on more recent instruction finetuned (IFT) LLMs such as ChatGPT. Surprisingly, on ChatGPT, CoT is no longer effective for certain tasks such as arithmetic reasoning while still keeping effective on other reasoning tasks. Moreover, on the former tasks, ChatGPT usually achieves the best performance and can generate CoT even without being instructed to do so. Hence, it is plausible that ChatGPT has already been trained on these tasks with CoT and thus memorized the instruction so it implicitly follows such an instruction when applied to the same queries, even without CoT. Our analysis reflects a potential risk of overfitting/bias toward instructions introduced in IFT, which becomes more common in training LLMs. In addition, it indicates possible leakage of the pretraining recipe, e.g., one can verify whether a dataset and instruction were used in training ChatGPT. Our experiments report new baseline results of ChatGPT on a variety of reasoning tasks and shed novel insights into LLM's profiling, instruction memorization, and pretraining dataset leakage