Miracle-dz/UniFAR-FTUs huggingface dataset:
On polynomial solutions of differential equations

A general method of obtaining linear diﬀerential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the ”projectivized” representation possessing an invariant subspace and the spectral problem for a certain linear diﬀerential operator with variable coeﬃcients. It is shown in general that polynomial solutions of partial diﬀerential equations occur; in the case of Lie superalge-bras there are polynomial solutions of some matrix diﬀerential equations, quantum algebras give rise to polynomial solutions of ﬁnite–diﬀerence equations. Particularly, known classical orthogonal polynomials will appear when considering SL (2 , R ) acting on
Observation of fast and slow modes associated with ICRF heating in the TFR tokamak by CO2 laser scattering

Using a CO2 forward-scattering experiment during ICRF heating in a D2-H2 plasma, fast and slow waves associated with the heating mechanism are observed. The fast wave, with long wavelength, is observed through a coupling between the fast wave and drift waves. A measure of the corresponding electric field is given. When approaching the ion-ion hybrid layer, the fast wave is slowed down and an electric field increase is observed (swelling) . Afterwards, the fast wave undergoes conversion and becomes a slow one, which is directly observed and analysed. Its corresponding electric field is measured. ‘Sawtooth relaxations’ are also observed on this signal. The importance of the hybrid layer and the rotational transform in the process is outlined.
A factorization theorem for lozenge tilings of a hexagon with triangular holes

In this paper we present a combinatorial generalization of the fact that the number of plane partitions that fit in a $2a\times b\times b$ box is equal to the number of such plane partitions that are symmetric, times the number of such plane partitions for which the transpose is the same as the complement. We use the equivalent phrasing of this identity in terms of symmetry classes of lozenge tilings of a hexagon on the triangular lattice. Our generalization consists of allowing the hexagon have certain symmetrically placed holes along its horizontal symmetry axis. The special case when there are no holes can be viewed as a new, simpler proof of the enumeration of symmetric plane partitions.
Premaximum Spectroscopic Diversity of Hydrogen-poor Superluminous Supernovae

We search for the reasons behind the spectroscopic diversity of hydrogen-poor superluminous supernovae (SLSNe-I) in the premaximum phase. Our analysis is a continuation of the paper of Könyves-Tóth & Vinkó, who disclosed two new subtypes of SLSNe-I characterized by the presence/absence of a W-shaped absorption feature in their premaximum spectra between 4000 and 5000 Å (called Type W and Type 15bn, respectively). However, the physical cause of this bimodality is still uncertain. Here we present premaximum spectral synthesis of 27 SLSNe-I with special attention to the photospheric temperature (T phot) and velocity (v phot) evolution. We find that a T phot limit of 12,000 K separates the Type W and Type 15bn SLSNe-I: Type W objects tend to show T phot ≥ 12,000 K, while Type 15bn ones have T phot ≤ 12,000 K. This is consistent with the chemical composition of the studied objects. Another difference between these groups may be found in their ejecta geometry: Type W SLSNe-I may show null polarization, implying spherical symmetry, while the polarization of Type 15bn objects may increase in time. This suggests a two-component model with a spherical outer carbon–oxygen layer and an asymmetric inner layer containing heavier ions. The two subgroups may have different light-curve evolution as well, since six Type W objects show early bumps, unlike Type 15bn SLSNe-I. This feature, however, needs further study, as it is based on only a few objects at present.
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory

Introduction Property A for the curve complex Amenability for the actions of the mapping class group on the boundary of the curve complex Indecomposability of equivalence relations generated by the mapping class group Classification of the mapping class groups in terms of measure equivalence I Classification of the mapping class groups in terms of measure equivalence II Appendix A. Amenability of a group action Appendix B. Measurability of the map associating image measures Appendix C. Exactness of the mapping class group Appendix D. The cost and $\ell^{2}$-Betti numbers of the mapping class group Appendix E. A group-theoretic argument for Chapter 5 Bibliography Index.
Double-Bosonisation and the Construction of {$U_q(g)$}

We introduce a quasitriangular Hopf algebra or `quantum group' $U(B)$, the {\em double-bosonisation}, associated to every braided group $B$ in the category of $H$-modules over a quasitriangular Hopf algebra $H$, such that $B$ appears as the `positive root space', $H$ as the `Cartan subalgebra' and the dual braided group $B^*$ as the `negative root space' of $U(B)$. The choice $B=f$ recovers Lusztig's construction of $U_q(g)$, where $f$ is Lusztig's algebra associated to a Cartan datum; other choices give more novel quantum groups. As an application, our construction provides a canonical way of building up quantum groups from smaller ones by repeatedly extending their positive and negative root spaces by linear braided groups; we explicitly construct $U_q(sl_3)$ from $U_q(sl_2)$ by this method, extending it by the quantum-braided plane $A_q^2$. We provide a fundamental representation of $U(B)$ in $B$. A projection from the quantum double, a theory of double biproducts and a Tannaka-Krein reconstruction point of view are also provided.
Echocardiographic Evidence of Cardiac Atrophy in the Critically Ill

OBJECTIVES: The purpose of this explorative study is to determine if critically ill patients experience cardiac atrophy that can be quantified as a loss of left ventricular mass (LVM) and thus detected by echocardiography. DESIGN: Retrospective single-center cohort study. SETTING: Patients admitted to a tertiary medical center in Boston, MA. PATIENTS: Adult critically ill patients with ICU length of stay greater than or equal to 5 days. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: We conducted a retrospective cohort study of 68 patients, of which 42 were included in the final analysis (mean age 60.9 ± 19.2 yr; 47.6% male). The median length of ICU stay was 11.3 days (interquartile range, 6.8–20.1 d). A decrease in mean LVM over the course of admission for critical illness was observed (median 189.11 g [162.82–240.20 g] vs 176.69 g [142.37–226.26 g]; p = 0.01). After adjusting for sex, age, fluid balance, ICU type, dietary orders, time between echocardiograms, and vasopressor use, this decrease in LVM remained consistent (mean difference, –21.30 g; 95% CI, –41.85 to –0.74; p = 0.04). Relative wall thickness (RWT) did not change during admission. CONCLUSIONS: These data reveal that a loss of LVM is present in patients over their ICU stay without a corresponding change in RWT, consistent with cardiac atrophy. Future prospective studies are needed to confirm these findings and identify possible sequelae of this finding.
Fatou's Lemma in Its Classic Form and Lebesgue's Convergence Theorems for Varying Measures with Applications to MDPs

The classic Fatou lemma states that the lower limit of a sequence of integrals of functions is greater or equal than the integral of the lower limit. It is known that Fatou's lemma for a sequence of weakly converging measures states a weaker inequality because the integral of the lower limit is replaced with the integral of the lower limit in two parameters, where the second parameter is the argument of the functions. This paper provides sufficient conditions when Fatou's lemma holds in its classic form for a sequence of weakly converging measures. The functions can take both positive and negative values. The paper also provides similar results for sequences of setwise converging measures. It also provides Lebesgue's and monotone convergence theorems for sequences of weakly and setwise converging measures. The obtained results are used to prove broad sufficient conditions for the validity of optimality equations for average-cost Markov decision processes.
Incidence of primary bone sarcomas in Iranian population (2008-2015): A national population-based study

Background: Epidemiological characteristics of bone sarcomas are variant in different populations, however, there is no previous study on primary bone sarcomas among Iranian population. This study aimed to evaluate the incidence, age, sex distribution, histologic type, and location of malignant bone sarcomas, based on the Iran National Cancer Registry (INCR). Methods: This was a national population-based study using INCR data from March 20, 2008, to March 20, 2015, on patients who were diagnosed with primary bone sarcomas of the appendicular (C-code:40) and axial skeleton (C-code 41), excluding skull and face bones. Primary bone sarcomas were classified according to the International Classification of Diseases for Oncology (ICD-O-3: C40–C41). Results: A total of 4112 patients (59.5% males and 40.5% females) with a mean age of 36 years were included in the study. 60.38% of patients were between 10 to 44 years old. The overall age-standardized incidence rates (ASIR) was 8.23 (males=9.67 and females=6.80) per million person-years. Osteosarcoma chondrosarcoma and Ewing sarcoma were the three main histology subtypes with the ASIR of 2.36, 1.26, and 1.08 per million person-years. Long bones of the lower limb were the most affected area, with the ASIR of 3.18 (95% CI: 3.02-3.33) per million. We found an increasing trend in the incidence of bone sarcomas in Iran from 8.59 in 2007 to 11.37 per million person-year in 2015. Conclusion: This study provided the epidemiological features of bone sarcomas, including the histological type of sarcoma, tumors’ location, and patients’ age and gender in the Iranian population for the first time.
Escaping local minima with local derivative-free methods: a numerical investigation

ABSTRACT We investigate the potential of applying a state-of-the-art, local derivative-free solver, Py-BOBYQA to global optimization problems. In particular, we demonstrate the potential of a restarts procedure – as distinct from multistart methods – to allow Py-BOBYQA to escape local minima (where ordinarily it would terminate at the first local minimum found). We also introduce an adaptive variant of restarts which yields improved performance on global optimization problems. As Py-BOBYQA is a model-based trust-region method, we compare largely with other global optimization methods for which (global) models are important, such as Bayesian optimization and response surface methods; we also consider state-of-the-art representative deterministic and stochastic codes, such as DIRECT and CMA-ES. We find numerically that the restarts procedures in Py-BOBYQA are effective at helping it to escape local minima, when compared to using no restarts in Py-BOBYQA. Additionally, we find that Py-BOBYQA with adaptive restarts has comparable performance with global optimization solvers for all accuracy/budget regimes, in both smooth and noisy settings. In particular, Py-BOBYQA variants are best performing for smooth and multiplicative noise problems in high-accuracy regimes. As a by-product, some preliminary conclusions can be drawn on the relative performance of the global solvers we have tested with default settings.
Random error growth in NMC's global forecasts

Abstract The three-dimensional structure of random error growth in the National Meteorological Center's Medium-Range Forecast Model is investigated in an effort to identify the sources of error growth. The random error growth is partitioned into two types: external error growth, which is due to model deficiencies, and internal error growth, which is the self-growth of errors in the initial conditions. Forecasts from winter 1987, summer 1990, and winter 1992 are compared to assess seasonal variations in regional error growth as well as forecast model improvement. The following is found: In the tropics, large external error growth at the 200-mb level is closely associated with deep convection. There is evidence of significant model improvements in the tropics at the 850-mb level between 1987 and 1992. The spatial structure of the external error growth in the midlatitudes suggests that the representation of orography in the model, especially over Antarctica and the Rockies, is a significant source of errors.
Definitive equations for the fluid resistance of spheres

For calculation of terminal velocities it is convenient to express the Reynolds' number, Re, of a moving sphere as a function of the dimensionless group ψRe2, where ψ is the drag coefficient. The following equations have been fitted by the method of least squares to critically selected data from a number of experimenters: Re = ψRe2/24 -0.00023363(ψRe2)2 + 0.0000020154(ψRe2)3 - 0.0000000069105(ψRe2)4 for Re<4 or ψRe2<140. This tends to Stokes' law for low values of Re. It is specially suited to calculation of the sedimentation of air-borne particles. The upper limit corresponds to a sphere weighing 1.5 μg. falling in the normal atmosphere, that is, one having a diameter of 142 μ for unit density. logRe=-1.29536+0.986 (logψRe2)-0.046677 (logψRe2)2+0.0011235 (logψRe2)3 for 3<Re<10,000 or 100<ψRe2<4.5. 107. Correction for slip in gases should be applied to Stokes' law by the following expression, based on the best results available: 1 + l/a[1.257 + 0.400exp(-1.10a/l)], where the mean free path l is given by η/0. 499σc. This conveniently transforms to the following for the sedimentation of particles in air at pressure p cm. mercury 1 + l/pa[6.32. 10-4 + 2.01. 10-4exp(-2190ap)]
Characterization and response of two potato receptor-like kinases to cyst nematode infection

ABSTRACT Plant-parasitic cyst nematodes (Heterodera and Globodera spp.) secrete CLAVATA3/EMBRYO SURROUNDING REGION-RELATED (CLE) effector proteins, which act as ligand mimics of plant CLE peptides to promote successful nematode infection. Previous studies of the Arabidopsis-beet cyst nematode (BCN; H. schachtii) pathosystem showed that Arabidopsis CLE receptors including CLAVATA1 (CLV1), CLV2, and RECEPTOR-LIKE PROTEIN KINASE 2 (RPK2) are required for BCN CLE signaling. Studies further revealed that nematode CLE signaling through GmCLV2 and StCLV2, an Arabidopsis CLV2 orthologue from soybean (Glycines max) and potato (Solanum tuberosum), respectively, is required for the soybean cyst nematode (SCN; H. glycines) and the potato cyst nematode (PCN; G. rostochiensis) to induce disease in their respective host plant. In this study, we identified and characterized two additional potato receptors, StRPK2 and StCLV1, homologues of Arabidopsis RPK2 and CLV1, for a role in PCN parasitism. Using promoter-reporter lines we showed that both StRPK2 and StCLV1 are expressed in the potato root but vary in their spatial expression patterns. Interestingly, StRPK2 but not StCLV1 was found to be expressed and upregulated at PCN infection sites. Nematode infection assays on StRPK2-knockdown lines revealed a decrease in nematode infection. Collectively, our results suggest that parallel CLE signaling pathways involving StCLV2 and StRPK2 are important for PCN parasitism and that manipulation of nematode CLE signaling may represent a viable means to engineer nematode resistance in crop plants including potato.
Solar cycle effects on parallel electric field acceleration of auroral electron beams

We present the occurrence frequency of downgoing auroral electron beams in magnetic local time and invariant latitude, and the dependence on solar cycle, as indicated by F10.7, on whether the ionospheric foot point of the satellite is illuminated or dark, and on the energy flux carried by the electrons. As previously reported, we find that the occurrence of electron beams peaks in the premidnight local time sector and that solar illumination at the foot point (solar zenith angle) reduces both the occurrence and energy of the electron beams. The effect of solar maximum conditions (indicated by F10.7) is almost as large as the effect of the solar zenith angle. The characteristic energy of the electron beams is dependent on the energy flux carried, in addition to both solar zenith angle and F10.7. The beam energy (and therefore the parallel potential drop) is ~1.6 times higher for during solar minimum than during solar maximum for both dark and illuminated foot points. The beam energy during dark solar minimum conditions is a factor of ~3 more than during sunlit minimum conditions. The “area” covered by intense aurora is also reduced during solar maximum, for both sunlit and dark conditions. There is no evidence that the statistical results are due to the fact that acceleration via parallel electric fields moves to lower latitudes during solar maximum.
Generating functions for intersection numbers on moduli spaces of curves

Using the connection between intersection theory on the Deligne-Mumford spaces and the edge scaling of the GUE matrix model (see math.CO/9903176, math.AG/0101147), we express the n-point functions for the intersection numbers as n-dimensional error-function-type integrals and also give a derivation of Witten's KdV equations using the higher Fay identities of Adler, Shiota, and van Moerbeke.
COBE Differential Microwave Radiometer Constraints on an Inflation Model with Nonminimal Scalar Field

We derive the power spectra of the scalarand tensor-type structures generated in a chaoticinflation model based on nonminimally coupled scalar field with a self-interaction. By comparin contributions of both structures to the anisotropy of the cosmic microwave background radiation with t four-year COBE differential microwave radiometer data on quadrupole anisotropy we derive constrai on the ratio of self-coupling and nonminimal coupling constants, and the expansion rate in the inflat era. The requirement for a successful amount of inflation further constrains the relative amount o tensor-type contribution. [S0031-9007(98)07925-3]
Prevalence of benign focal liver lesions and non-hepatocellular carcinoma malignant lesions in liver cirrhosis

Abstract Liver cirrhosis is associated with an increased risk of developing hepatocellular carcinoma (HCC). However, other benign and malignant liver lesions may co-exist or may be the only focal liver lesion (FLL) detected. Compared to HCC, comparatively little is known about the frequency and natural history of benign FLL in patients with established liver cirrhosis. This review analyses the prevalence and frequency of benign and malignant FLL others than hepatocellular carcinoma (HCC) in liver cirrhosis including imaging and autopsy studies. Understanding these data should be helpful in avoiding misdiagnoses.
New advances in management and treatment of multidrug-resistant Klebsiella pneumoniae

ABSTRACT Introduction The management of multidrug-resistant (MDR) Klebsiella pneumoniae (KP) represents a major challenge in the field of infectious diseases. It is associated with a high rate of nosocomial infections with a mortality rate that reaches approximately 50%, even when using an effective antimicrobial therapy. Therefore, combined actions addressing infection control and antibiotic stewardship are required to delay the emergence of resistance. Since new antimicrobial agents targeting MDR-GNB bacteria have been produced during the last years and are now available for physicians to treat MDR, it is fundamental to choose appropriate antimicrobial therapy for K. pneumoniae infection. Areas covered The PubMed database was searched to review the most significant recent literature on the topic, including data from articles coming from endemic areas and from the current European and American Guidelines. Expert opinion We explore the most effective strategies for prevention of MDR-KP spread and the currently available treatment options, focusing on comparing old strategies and new compounds. We reviewed data concerning newly developed drugs that could play an important role in the future; we also propose a treatment algorithm that could be useful for physicians in daily clinical practice.
Meditation Mobile App Developed for Patients With and Survivors of Cancer: Feasibility Randomized Controlled Trial

Background To address the unmet need for a commercial cancer-specific meditation app, we leveraged a long-standing partnership with a consumer-based app (ie, Calm) to develop the first commercial meditation app prototype adapted specifically for the needs of patients with cancer. Input was obtained at both the individual user and clinic levels (ie, patients with and survivors of cancer and health care providers). Objective This study aimed to determine the feasibility of a cancer-specific meditation app prototype. Methods Patients with and survivors of cancer who were recruited and enrolled in the feasibility randomized controlled trial were asked to use the prototype app daily (≥70 minutes per week) for 4 weeks. Participants completed web-based weekly questionnaires and a final poststudy questionnaire and were asked to participate in an optional web-based poststudy interview. The questionnaires and interviews covered the following feasibility categories: acceptability, demand, practicality, and adaptation. Results A total of 36 patients with and survivors of cancer completed the baseline questionnaire, 18 completed the final questionnaire, and 6 completed the optional interviews. Weekly and poststudy questionnaires indicated high overall enjoyment, ease of use, and satisfaction with the app content, aesthetics, and graphics. The objective use data indicated that the average total app use rate was 73.39 (SD 7.12) minutes per week. Interviews (N=6) revealed positive and mixed responses to the app prototype and informative differences related to preferences for narrators, emotional content, and meditation teaching but an overall appreciation for the variety of options. Conclusions The most likely candidates for moving from cancer-specific meditation apps to dissemination are through partnering with the industry, in which name recognition and market distribution are already established (even showing a base of users from the targeted population with cancer). This study established the feasibility of a cancer-specific mobile meditation app prototype for patients with and survivors of cancer, using a commercially available app. The quantitative and qualitative data demonstrated the acceptability, demand, practicality, and adaptation of the prototype. Improvements suggested by the participants will be considered in the final app design before testing the efficacy of the app in a future study. Trial Registration Clinicaltrials.gov NCT05459168; https://clinicaltrials.gov/ct2/show/record/NCT05459168