Tridiagonalized GUE matrices are a matrix model for labeled mobiles

It is well-known that the number of planar maps with prescribed vertex degree distribution and suitable labeling can be represented as the leading coefficient of the $\frac{1}{N}$-expansion of a joint cumulant of traces of powers of an $N$-by-$N$ GUE matrix. Here we undertake the calculation of this leading coefficient in a different way. Firstly, we tridiagonalize the GUE matrix in the manner of Trotter and Dumitriu-Edelman and then alter it by conjugation to make the subdiagonal identically equal to $1$. Secondly, we apply the cluster expansion technique (specifically, the Brydges-Kennedy-Abdesselam-Rivasseau formula) from rigorous statistical mechanics. Thirdly, by sorting through the terms of the expansion thus generated we arrive at an alternate interpretation for the leading coefficient related to factorizations of the long cycle $(12\cdots n)\in S_n$. Finally, we reconcile the group-theoretical objects emerging from our calculation with the labeled mobiles of Bouttier-Di Francesco-Guitter.Comment: 42 pages, LaTeX, 17 figures. The present paper completely supercedes arXiv1203.3185 in terms of methods but addresses a different proble

Prompted Opinion Summarization with GPT-3.5

Large language models have shown impressive performance across a wide variety of tasks, including text summarization. In this paper, we show that this strong performance extends to opinion summarization. We explore several pipeline methods for applying GPT-3.5 to summarize a large collection of user reviews in a prompted fashion. To handle arbitrarily large numbers of user reviews, we explore recursive summarization as well as methods for selecting salient content to summarize through supervised clustering or extraction. On two datasets, an aspect-oriented summarization dataset of hotel reviews (SPACE) and a generic summarization dataset of Amazon and Yelp reviews (FewSum), we show that GPT-3.5 models achieve very strong performance in human evaluation. We argue that standard evaluation metrics do not reflect this, and introduce three new metrics targeting faithfulness, factuality, and genericity to contrast these different methods.Comment: Accepted to ACL (Findings) 202

Correlation of Early Outcomes and Intradiscal Interleukin-6 Expression in Lumbar Fusion Patients.

OBJECTIVE: To determine if there is correlation between intradiscal levels of interleukin-6 (IL-6) and early outcome measures in patients undergoing lumbar fusion for painful disc degeneration. METHODS: Intervertebral disc tissue was separated into annulus fibrosus/nucleus pulposus and cultured separately in vitro in serum-free medium (Opti-MEM). Conditioned media was collected after 48 hours. The concentration of IL-6 was quantified using enzyme-linked immunosorbent assay. Pearson correlation coefficients quantified relationships between IL-6 levels and pre- and postoperative visual analogue scale (VAS) back pain and Oswestry Disability Index (ODI), as well as change in VAS/ODI. RESULTS: Sixteen discs were harvested from 9 patients undergoing anterior lumbar interbody fusion (mean age, 47.4 years; range, 21-70 years). Mean preoperative and 6-month postoperative VAS were 8.1 and 3.7, respectively. Mean preoperative and postoperative ODI were 56.2 and 25.6, respectively. There were significant positive correlations between IL-6 expression and postoperative VAS (ρ = 0.38, p = 0.048) and ODI (ρ = 0.44, p = 0.02). No significant correlations were found between intradiscal IL-6 expression and preoperative VAS (ρ = -0.12, p = 0.54). Trends were seen associating IL-6 expression and change in VAS/ODI (ρ = -0.35 p = 0.067; ρ = -0.34, p = 0.08, respectively). A trend associated IL-6 and preoperative ODI (ρ = 0.36, p = 0.063). CONCLUSION: The direct association between IL-6 expression and VAS/ODI suggests patients with elevated intradiscal cytokine expression may have worse early outcomes than those with lower expression of IL-6 after surgery for symptomatic disc degeneration

Conflicts between reindeer herding and an expanding caribou herd in Alaska

The reindeer industry has existed in Alaska since 1892. This industry has largely been concentrated on the Seward Peninsula, Alaska because suitable habitat has been available and caribou have been absent here for over 100 years. Until recently, reindeer meat and velvet antler production consistently generated millions of dollars in revenue critical to the economies of rural Alaskan communities. From 1976 to 1996 the Western Arctic Caribou Herd (WACH) increased from about 75 000 to 463 000 animals. Concurrently, seasonal range use of the WACH shifted westward onto traditional reindeer ranges of the Seward Peninsula. Reindeer herders lost 75-100% of their herds through commingling and out¬migration with wild caribou. This loss of over 12 000 reindeer represents a potential economic value of 13 million dollars. Sustainable meat and velvet antler production and the economies of western Alaskan are likely to be affected by these changes

Coupled-Mode Theory of Field Enhancement in Complex Metal Nanostructures

We describe a simple yet rigorous theoretical model capable of analytical estimation of plasmonic field enhancement in complex metal structures. We show that one can treat the complex structures as coupled multi-pole modes with highest enhancements obtained due to superposition of high order modes in small particles. The model allows one to optimize the structures for the largest possible field enhancements, which depends on the quality factor Q of the metal and can be as high as Q^2 for two spherical particles. The "hot spot" can occur either in the nano-gaps between the particles or near the smaller particles. We trace the optimum field enhancement mechanism to the fact that the extended dipole modes of larger particles act as the efficient antennas while the modes in the gaps or near the smaller particles act as the compact sub-wavelength cavities. We also show how easily our approach can be extended to incorporate large numbers of particles in intricate arrangements.Comment: 23 pages, 7 figure

Epiphyte type and sampling height impact mesofauna communities in Douglas-fir trees

Branches and boles of trees in wet forests are often carpeted with lichens and bryophytes capable of providing periodically saturated habitat suitable for microfauna, animals that include tardigrades, rotifers, nematodes, mites, and springtails. Although resident microfauna likely exhibit habitat preferences structured by fine-scale environmental factors, previous studies rarely report associations between microfaunal communities and habitat type (e.g., communities that develop in lichens vs. bryophytes). Microfaunal communities were examined across three types of epiphyte and three sampling heights to capture gradients of microenvironment. Tardigrades, rotifers, and nematodes were significantly more abundant in bryophytes than fruticose lichen or foliose lichen. Eight tardigrade species and four tardigrade taxa were found, representing two classes, three orders, six families, and eight genera. Tardigrade community composition was significantly different between bryophytes, foliose lichen, fruticose lichen, and sampling heights. We show that microenvironmental factors including epiphyte type and sampling height shape microfaunal communities and may mirror the environmental preferences of their epiphyte hosts

Reference Intervals: Strengths, Weaknesses, and Challenges

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Characterization of Pulmonary Metastases in Children With Hepatoblastoma Treated on Children\u27s Oncology Group Protocol AHEP0731 (The Treatment of Children With All Stages of Hepatoblastoma): A Report From the Children\u27s Oncology Group.

Purpose To determine whether the pattern of lung nodules in children with metastatic hepatoblastoma (HB) correlates with outcome. Methods Thirty-two patients with metastatic HB were enrolled on Children\u27s Oncology Group Protocol AHEP0731 and treated with vincristine and irinotecan (VI). Responders to VI received two additional cycles of VI intermixed with six cycles of cisplatin/fluorouracil/vincristine/doxorubicin (C5VD), and nonresponders received six cycles of C5VD alone. Patients were imaged after every two cycles and at the conclusion of therapy. All computed tomography scans and pathology reports were centrally reviewed, and information was collected regarding lung nodule number, size, laterality, timing of resolution, and pulmonary surgery. Results Among the 29 evaluable patients, only 31% met Response Evaluation Criteria in Solid Tumors (RECIST) for measurable metastatic disease. The presence of measurable disease by RECIST, the sum of nodule diameters greater than or equal to the cumulative cohort median size, bilateral disease, and ≥ 10 nodules were each associated with an increased risk for an event-free survival event ( P = .48, P = .08, P = .065, P = .03, respectively), with nodule number meeting statistical significance. Ten patients underwent pulmonary resection/metastasectomy at various time points, the benefit of which could not be determined because of small patient numbers. Conclusion Children with metastatic HB have a poor prognosis. Overall tumor burden may be an important prognostic factor for these patients. Lesions that fail to meet RECIST size criteria (ie, those \u3c 10 mm) at diagnosis may contain viable tumor, whereas residual lesions at the end of therapy may constitute eradicated tumor/scar tissue. Patients may benefit from risk stratification on the basis of the burden of lung metastatic disease at diagnosis

Reliability, Flexibility, and Environmental Impact of Alternative Arterial Offset Optimization Objective Functions

A wide variety of alternative optimization objective functions, such as minimizing stops, minimizing delay, and maximizing arrivals on green, has been reported in the literature. An extensive literature evaluates these alternative objective functions with models. This paper reports on the field deployment of these alternative optimization functions, developed with high resolution controller data, to adjust offsets on an arterial system of eight coordinated signals. The deployment consisted of a 1-week base data collection and four 1-week deployments of offset plans developed with four alternative optimization objective functions. Travel times of anonymous probe vehicles were measured during the study period to evaluate the impact of these alternative optimization functions on corridor travel time. All objective functions were successful in reducing median corridor travel time significantly. Median travel time decreased by more than 1 min in both directions on the 5-mi corridor. Travel time reliability, as quantified by the difference between 75th and 25th percentile travel times, was improved for the busiest portion of the day. A lower bound of the estimated annual savings on user costs was $472,817, with an associated reduction in carbon dioxide emissions of 197 tons per year. </jats:p

Truthmakers and modality

This paper attempts to locate, within an actualist ontology, truthmakers for modal truths: truths of the form or . In section 1 I motivate the demand for substantial truthmakers for modal truths. In section 2 I criticise Armstrong’s account of truthmakers for modal truths. In section 3 I examine essentialism and defend an account of what makes essentialist attributions true, but I argue that this does not solve the problem of modal truth in general. In section 4 I discuss, and dismiss, a theistic account of the source of modal truth proposed by Alexander Pruss. In section 5 I offer a means of (dis)solving the problem