Local linear spatial regression

A local linear kernel estimator of the regression function x\mapsto g(x):=E[Y_i|X_i=x], x\in R^d, of a stationary (d+1)-dimensional spatial process {(Y_i,X_i),i\in Z^N} observed over a rectangular domain of the form I_n:={i=(i_1,...,i_N)\in Z^N| 1\leq i_k\leq n_k,k=1,...,N}, n=(n_1,...,n_N)\in Z^N, is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is assumed to satisfy some very general mixing conditions, generalizing classical time-series strong mixing concepts. The size of the rectangular domain I_n is allowed to tend to infinity at different rates depending on the direction in Z^N.Comment: Published at http://dx.doi.org/10.1214/009053604000000850 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Closed-form Absorption Probability of Certain D=5 and D=4 Black Holes and Leading-Order Cross-Section of Generic Extremal p-branes

We obtain the closed-form absorption probabilities for minimally-coupled massless scalars propagating in the background of D=5 single-charge and D=4 two-charge black holes. These are the only two examples of extremal black holes with non-vanishing absorption probabilities that can be solved in closed form for arbitrary incident frequencies. In both cases, the absorption probability vanishes when the frequency is below a certain threshold, and we discuss the connection between this phenomenon and the behaviour of geodesics in these black hole backgrounds. We also obtain leading-order absorption cross-sections for generic extremal p-branes, and show that the expression for the cross-section as a function of frequency coincides with the leading-order dependence of the entropy on the temperature in the corresponding near-extremal p-branes.Comment: Latex (3 times), 20 page

Euclidean-signature Supergravities, Dualities and Instantons

We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.Comment: Latex, 50 pages, typos corrected and references adde

Hybrid Long Document Summarization using C2F-FAR and ChatGPT: A Practical Study

Text summarization is a downstream natural language processing (NLP) task that challenges the understanding and generation capabilities of language models. Considerable progress has been made in automatically summarizing short texts, such as news articles, often leading to satisfactory results. However, summarizing long documents remains a major challenge. This is due to the complex contextual information in the text and the lack of open-source benchmarking datasets and evaluation frameworks that can be used to develop and test model performance. In this work, we use ChatGPT, the latest breakthrough in the field of large language models (LLMs), together with the extractive summarization model C2F-FAR (Coarse-to-Fine Facet-Aware Ranking) to propose a hybrid extraction and summarization pipeline for long documents such as business articles and books. We work with the world-renowned company getAbstract AG and leverage their expertise and experience in professional book summarization. A practical study has shown that machine-generated summaries can perform at least as well as human-written summaries when evaluated using current automated evaluation metrics. However, a closer examination of the texts generated by ChatGPT through human evaluations has shown that there are still critical issues in terms of text coherence, faithfulness, and style. Overall, our results show that the use of ChatGPT is a very promising but not yet mature approach for summarizing long documents and can at best serve as an inspiration for human editors. We anticipate that our work will inform NLP researchers about the extent to which ChatGPT's capabilities for summarizing long documents overlap with practitioners' needs. Further work is needed to test the proposed hybrid summarization pipeline, in particular involving GPT-4, and to propose a new evaluation framework tailored to the task of summarizing long documents

Measuring Adaptive Behaviors in Individuals with Autism Enrolled in Project-Based Therapy

As the number of individuals with Autism Spectrum Disorder (ASD) entering adulthood increases, this population faces limited resources to foster independent living. Therefore, it is crucial to explore innovative interventions that help this population develop the skills necessary to live more independently. This exploratory prospective cohort study evaluated the effectiveness of Autistry Studios, which focuses on improving adaptive behavior skills for adults and adolescents with ASD using project-based therapy. The study used the Brief Adaptive Behavior Scale (BABS), a novel quantitative assessment, to track the development of adaptive behaviors in individuals with ASD within the domains of Executive Functioning (EF), Socialization (SOC), and Self-Regulation (SR). The BABS specifically measures Frequency of adaptive behaviors (FRQ), the Lowest Level of Assistance (LoALow) required, and the Highest Level of Assistance (LoAHigh) required while engaging in project-based therapy. Paired-samples t-tests compared the mean of BABS scores for 11 participants across nine sessions at Autistry Studios. LoALow and LoAHigh Total scores improved significantly from session one to nine. Additional analyses found significant differences in the LoALow and LoAHigh scores in the domains of EF and SOC. Cohen’s d effect sizes for the difference between session one and nine for LoALow and LoAHigh scores were large to very large, suggesting practical improvement in all domains. The results indicate that Autistry’s pre-vocational, project-based therapy program is effective in improving adaptive behavior skills in adults and adolescents with ASD, as measured by the BABS assessment