A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms

We study growth of higher Sobolev norms of solutions to the one-dimensional periodic nonlinear Schrodinger equation (NLS). By a combination of the normal form reduction and the upside-down I-method, we establish \|u(t)\|_{H^s} \lesssim (1+|t|)^{\alpha (s-1)+} with \alpha = 1 for a general power nonlinearity. In the quintic case, we obtain the above estimate with \alpha = 1/2 via the space-time estimate due to Bourgain [4], [5]. In the cubic case, we concretely compute the terms arising in the first few steps of the normal form reduction and prove the above estimate with \alpha = 4/9. These results improve the previously known results (except for the quintic case.) In Appendix, we also show how Bourgain's idea in [4] on the normal form reduction for the quintic nonlinearity can be applied to other powers.Comment: 24 pages. Small modification in Section 1, to appear in J. Anal. Mat

Photo-heating and the fate of hard photons during the reionisation of HeII by quasars

We use a combination of analytic and numerical arguments to consider the impact of quasar photo-heating during HeII reionisation on the thermal evolution of the intergalactic medium (IGM). We demonstrate that rapid (\Delta z 10^4 K) photo-heating is difficult to achieve across the entire IGM unless quasar spectra are significantly harder than implied by current observational constraints. Although filtering of intrinsic quasar radiation through dense regions in the IGM does increase the mean excess energy per HeII photo-ionisation, it also weakens the radiation intensity and lowers the photo-ionisation rate, preventing rapid heating over time intervals shorter than the local photo-ionisation timescale. Moreover, the hard photons responsible for the strongest heating are more likely to deposit their energy inside dense clumps. The abundance of such clumps is, however, uncertain and model-dependent, leading to a fairly large uncertainty in the photo-heating rates. Nevertheless, although some of the IGM may be exposed to a hardened and weakened ionising background for long periods, most of the IGM must instead be reionised by the more abundant, softer photons and with accordingly modest heating rates (\Delta T < 10^4 K). The repeated ionisation of fossil quasar HeIII regions does not increase the net heating because the recombination times in these regions typically exceed the IGM cooling times and the average time lag between successive rounds of quasar activity. Detailed line-of-sight radiative transfer simulations confirm these expectations and predict a rich thermal structure in the IGM during HeII reionisation. [Abridged]Comment: 20 pages, 6 figures, accepted by MNRA

Detrimental Contexts in Open-Domain Question Answering

For knowledge intensive NLP tasks, it has been widely accepted that accessing more information is a contributing factor to improvements in the model's end-to-end performance. However, counter-intuitively, too much context can have a negative impact on the model when evaluated on common question answering (QA) datasets. In this paper, we analyze how passages can have a detrimental effect on retrieve-then-read architectures used in question answering. Our empirical evidence indicates that the current read architecture does not fully leverage the retrieved passages and significantly degrades its performance when using the whole passages compared to utilizing subsets of them. Our findings demonstrate that model accuracy can be improved by 10% on two popular QA datasets by filtering out detrimental passages. Additionally, these outcomes are attained by utilizing existing retrieval methods without further training or data. We further highlight the challenges associated with identifying the detrimental passages. First, even with the correct context, the model can make an incorrect prediction, posing a challenge in determining which passages are most influential. Second, evaluation typically considers lexical matching, which is not robust to variations of correct answers. Despite these limitations, our experimental results underscore the pivotal role of identifying and removing these detrimental passages for the context-efficient retrieve-then-read pipeline. Code and data are available at https://github.com/xfactlab/emnlp2023-damaging-retrievalComment: Findings of EMNLP 202

Almost sure well-posedness of the cubic nonlinear Schr\"odinger equation below L^2(T)

We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear Schr\"odinger equation (NLS) with initial data below L^2. In particular, we exhibit nonlinear smoothing when the initial data are randomized. Then, we prove local well-posedness of NLS almost surely for the initial data in the support of the canonical Gaussian measures on H^s(T) for each s > -1/3, and global well-posedness for each s > -1/12.Comment: 36 pages. Deterministic multilinear estimates are now summarized in Sec. 3. We use X^{s, b} with b = 1/2+ instead of Z^{s, 1/2}. To appear in Duke Math.

A cognitive architecture for emergency response

Plan recognition, cognitive workload estimation and human assistance have been extensively studied in the AI and human factors communities, resulting in many techniques being applied to domains of various levels of realism. These techniques have seldom been integrated and evaluated as complete systems. In this paper, we report on the development of an assistant agent architecture that integrates plan recognition, current and future user information needs, workload estimation and adaptive information presentation to aid an emergency response manager in making high quality decisions under time stress, while avoiding cognitive overload. We describe the main components of a full implementation of this architecture as well as a simulation developed to evaluate the system. Our evaluation consists of simulating various possible executions of the emergency response plans used in the real world and measuring the expected time taken by an unaided human user, as well as one that receives information assistance from our system. In the experimental condition of agent assistance, we also examine the effects of different error rates in the agent's estimation of user's stat or information needs

Physical activity differences by birthplace and sex in youth of Mexican Heritage

Journal ArticleBackground: One of the goals of Healthy People 2020 is to increase physical activity (PA) and reduce health disparities among different racial and ethnic segments of the U.S. population. Few studies have been conducted to examine PA differences by birthplace and sex in youth of Mexican heritage. Methods: Participants were 101 youth (43 boys, 58 girls, 59% U.S.-born, 41% Mexico-born) who wore a sealed New Lifestyles NL-1000 pedometer for 7 consecutive days. Results: Mexico-born youth took more steps, on average, than their U.S.-born counterparts (P = .038). However, moderate-to-vigorous intensity (MVI) time did not differ between Mexico- and U.S.-born youth (P = .146). By contrast to birthplace, sex-related differences were more consistent, as boys took more steps (P = .005) and accumulated more MVI time (P = .043) than girls. Only 4% of our sample met either one or both of the PA recommendations. Conclusions: We conclude that PA may differ by birthplace and by sex in youth of Mexican heritage, as U.S.-born girls were the least active segment of our sample. Culturally sensitive interventions to increase daily PA must become a higher public health priority for youth of Mexican heritage, in particular, for U.S.-born girls of Mexican heritage

Knowledge Corpus Error in Question Answering

Recent works in open-domain question answering (QA) have explored generating context passages from large language models (LLMs), replacing the traditional retrieval step in the QA pipeline. However, it is not well understood why generated passages can be more effective than retrieved ones. This study revisits the conventional formulation of QA and introduces the concept of knowledge corpus error. This error arises when the knowledge corpus used for retrieval is only a subset of the entire string space, potentially excluding more helpful passages that exist outside the corpus. LLMs may mitigate this shortcoming by generating passages in a larger space. We come up with an experiment of paraphrasing human-annotated gold context using LLMs to observe knowledge corpus error empirically. Our results across three QA benchmarks reveal an increased performance (10% - 13%) when using paraphrased passage, indicating a signal for the existence of knowledge corpus error. Our code is available at https://github.com/xfactlab/emnlp2023-knowledge-corpus-errorComment: Findings of EMNLP 202

Intensity Mapping with Carbon Monoxide Emission Lines and the Redshifted 21 cm Line

We quantify the prospects for using emission lines from rotational transitions of the CO molecule to perform an `intensity mapping' observation at high redshift during the Epoch of Reionization (EoR). The aim of CO intensity mapping is to observe the combined CO emission from many unresolved galaxies, to measure the spatial fluctuations in this emission, and use this as a tracer of large scale structure at very early times in the history of our Universe. This measurement would help determine the properties of molecular clouds -- the sites of star formation -- in the very galaxies that reionize the Universe. We further consider the possibility of cross-correlating CO intensity maps with future observations of the redshifted 21 cm line. The cross spectrum is less sensitive to foreground contamination than the auto power spectra, and can therefore help confirm the high redshift origin of each signal. Furthermore, the cross spectrum measurement would help extract key information about the EoR, especially regarding the size distribution of ionized regions. We discuss uncertainties in predicting the CO signal at high redshift, and discuss strategies for improving these predictions. Under favorable assumptions, and feasible specifications for a CO survey mapping the CO(2-1) and CO(1-0) lines, the power spectrum of CO emission fluctuations and its cross spectrum with future 21 cm measurements from the MWA are detectable at high significance.Comment: 19 pages, 8 figures, submitted to Ap