Miracle-dz/UniFAR-FTUs huggingface dataset:
A Generalization of A Theorem of Gleason

Since D. Hilbert proposed the famous Hilbert's fifth problem in 1900 which conjectured that every locally euclidean group is a Lie group, many mathematicians have dealt with this problem, but few satisfactory results were obtained before 1925. In 1928 Peter and Weyl [18] proved that any representation of a compact group is completely reducible and later in 1933 this problem was solved by von Neumann [17] for compact groups by using the above theorem. In the next year L. Pontrjagin [19] solved this problem for abelian groups. As a step to the final goal C. Chevalley [2] conjectured that every locally compact group with no small subgroup is a Lie group. In 1948 Kuranishi [10] obtained a very important result; that is, if a factor group over a normal abelian Lie group is a Lie group, then the whole group is a Lie group with some reasonable conditions which do not spoil the importance of this theorem. This theorem completed Iwasawa's theorem [8] which asserts that if a factor group over a normal Lie group is a Lie group, then the whole group is a Lie group. A simplified proof was given by A. M. Gleason [6] which depends only upon the preceding Kuranishi's theorem. Gleason [4] also introduced a very important idea which is called a Gleason semi-group of compact sets in this paper. By making use of this he proved many important theorems. Also Iwasawa [8] and Gleason [6] had built up the theory of generalized Lie groups (L group in the sense of Iwasawa), and from this point of view it became natural to generalize this Hilbert conjecture to the following conjecture made by Iwasawa [8] and Gleason [6]: every locally compact group is a generalized Lie group. Compared with these group-theoretical points of view, Montgomery and Zippin [13] introduced the homology theory in the theory of finite dimensional groups and obtained many important results, such as the invariance of a domain in locally connected finite dimensional groups, the determination of three or four dimensional groups, the elimination of finite groups, etc. [12, 14, 15]. Recently Gleason proved that every locally compact finite dimensional group with no small subgroup is a Lie group and using this theorem Montgomery and Zippin [16] proved that every locally compact finite dimensional group is a generalized Lie group; this gave an affirmative answer to the Hilbert's fifth problem. In a preceding paper [22] the author showed that the condition "no small normal subgroup" is equivalent to the condition "no small subgroup" and in this paper he will prove without the assumption of finite dimension that every locally compact group with no small subgroup is a Lie group. Combining these results with the Iwasawa-Gleason generalized Lie group theory we prove that every locally compact group is a generalized Lie group. This gives an 351
The Effect of Stress Hormones, Ultraviolet C, and Stilbene Precursors on Expression of Calcineurin B-like Protein (CBL) and CBL-Interacting Protein Kinase (CIPK) Genes in Cell Cultures and Leaves of Vitis amurensis Rupr

Calcium serves as a crucial messenger in plant stress adaptation and developmental processes. Plants encode several multigene families of calcium sensor proteins with diverse functions in plant growth and stress responses. Several studies indicated that some calcium sensors may be involved in the regulation of secondary metabolite production in plant cells. The present study aimed to investigate expression of calcineurin B-like proteins (CBL) and CBL-interacting protein kinase (CIPK) in response to conditions inducting biosynthesis of stilbenes in grapevine. We investigated CBL and CIPK gene expression in wild-growing grapevine Vitis amurensis Rupr. , known as a rich stilbene source, in response to the application of stilbene biosynthesis-inducing conditions, including application of stress hormones (salicylic acid or SA, methyl jasmonate or MeJA), phenolic precursors (p-coumaric acids or CA), and ultraviolet irradiation (UV-C). The influence of these effectors on the levels of 13 VaCBL and 27 VaCIPK mRNA transcripts as well as on stilbene production was analyzed by quantitative real-time RT-PCR in the leaves and cell cultures of V. amurensis. The data revealed that VaCBL4-1 expression considerably increased after UV-C treatment in both grapevine cell cultures and leaves. The expression of VaCIPK31, 41-1, and 41-2 also increased, but this increase was mostly detected in cell cultures of V. amurensis. At the same time, expression of most VaCBL and VaCIPK genes was markedly down-regulated both in leaves and cell cultures of V. amurensis, which may indicate that the CBLs and CIPKs are involved in negative regulation of stilbene accumulation (VaCBL8, 10a-2, 10a-4, 11, 12, VaCIPK3, 9-1, 9-2, 12, 21-1, 21-2, 33, 34, 35, 36, 37, 39, 40, 41-3, 41-4). The results obtained provide new information of CBL and CIPK implication in the regulation of plant secondary metabolism in response to stress hormones, metabolite precursors, and UV-C irradiation.
Extracellular Vesicles as Potential Bladder Cancer Biomarkers: Take It or Leave It?

Bladder cancer (BC) is the 10th most frequently diagnosed cancer worldwide. Although urine cytology and cystoscopy are current standards for BC diagnosis, both have limited sensitivity to detect low-grade and small tumors. Moreover, effective prognostic biomarkers are lacking. Extracellular vesicles (EVs) are lipidic particles that contain nucleic acids, proteins, and metabolites, which are released by cells into the extracellular space, being crucial effectors in intercellular communication. These particles have emerged as potential tools carrying biomarkers for either diagnosis or prognosis in liquid biopsies namely urine, plasma, and serum. Herein, we review the potential of liquid biopsies EVs’ cargo as BC diagnosis and prognosis biomarkers. Additionally, we address the emerging advantages and downsides of using EVs within this framework.
A Certain Exact Sequence

Page INTRODUCTION 51 CHAPTER I. THE SEQUENCE 2(C, A) 53 1. Definition of 2(C, A) 53 2. The secondary modular boundary operator 55 3. Induced homomorphisms of 2 55 4. Combinatorial realizability 57 CHAPTER II. THE GROUP r(A). 60 5. Definition of r(A) 60 6. Induced homomorphisms of r(A) 64 7. Relation to tensor products 67 8. "A" finitely generated 67 9. Direct systems 70 CHAPTER III. THE SEQUENCE 2(K) 71 10. Definition of 2(K) 71 11. The invariance of 2(K) 73 12. The sufficiency of 2(K) 75 13. Expression for r3(K) 75 14. Geometrical realizability 77 15. q-types 81 CHAPTER IV. THE PONTRJAGIN SQUARES 83 16. The main theorem 83 17. Secondary boundary operators 92 18. The calculation of 24(K) 97 CHAPTER V. THE SEQUENCE OF A GENERAL SPACE . 98 19. The complex K(X) 98 20. The maps K and X 101 21. The sequence 2(X) 106 APPENDIX A. ON SPACES DOMINATED BY COMPLEXES. 107 APPENDIX B. ON SEPARATION COCHAINS 108
Wnt Signaling Inhibitors and Their Promising Role in Tumor Treatment

In a continuous search for the improvement of antitumor therapies, the inhibition of the Wnt signaling pathway has been recognized as a promising target. The altered functioning of the Wnt signaling in human tumors points to the strategy of the inhibition of its activity that would impact the clinical outcomes and survival of patients. Because the Wnt pathway is often mutated or epigenetically altered in tumors, which promotes its activation, inhibitors of Wnt signaling are being intensively investigated. It has been shown that knocking down specific components of the Wnt pathway has inhibitory effects on tumor growth in vivo and in vitro. Thus, similar effects are expected from the application of Wnt inhibitors. In the last decades, molecules acting as inhibitors on the pathway’s specific molecular levels have been identified and characterized. This review will discuss the inhibitors of the canonical Wnt pathway, summarize knowledge on their effectiveness as therapeutics, and debate their side effects. The role of the components frequently mutated in various tumors that are principal targets for Wnt inhibitors is also going to be brought to the reader’s attention. Some of the molecules identified as Wnt pathway inhibitors have reached early stages of clinical trials, and some have only just been discovered. All things considered, inhibition of the Wnt signaling pathway shows potential for the development of future therapies.
Consistency Thresholds for Binary Symmetric Block Models

We consider the problem of reconstructing symmetric block models with two blocks of n vertices each and connection probabilities pn and qn for interand intra-block edge probabilities respectively. We are interested in two different notions of consistency: strong consistency means the existence of an estimation procedure which recovers the labels of all nodes correctly with probability 1 − o(1) as n → ∞, while weak consistency only asks for the estimation procedure to correctly label 2n − o(n) nodes correctly. We provide necessary and sufficient conditions on pn and qn for both notions of consistency, and we relate these conditions to the structure of the corresponding graphs. In particular, strong consistency is attainable if and only if with high probability every node has the same label as the majority of its neighbors, while weak consistency is attainable if and only if each node has, with high probability, the same label as the majority of its neighbors. We also give efficient algorithms for consistent estimators whenever one exists. Our results hold for arbitrary sequences pn and qn. ∗University of Pennsylvania. Supported by NSF grants DMS-1106999 and CCF 1320105 and DOD ONR grant N000141110140 U.T. Austin. Supported by NSF grant DMS-1106999 and DOD ONR grant N000141110140 U.C. Berkeley and the Australian National University. Supported by an Alfred Sloan Fellowship and NSF grant DMS-1208338.
Above-threshold ionization for very low electron energy

The rescattering term of the ionization amplitude in the strong-field approximation is analyzed for very low electron energy and emission in arbitrary direction, first in terms of the classical simple-man model and then in the quantum-mechanical quantum–orbit expansion of the strong-field-approximation amplitude. Particular orbits can be associated with particular patterns in the velocity map. The different roles of forward and backscattering are investigated. In addition to known features such as the LES and the fork, a characteristic and pronounced V structure in the velocity map is identified, which has been observed in recent experiments (2014 Phys. Rev. A 90 063424).
Increased soluble E‑cadherin of spheroid formation supplemented with fetal bovine serum in colorectal cancer cells

Cancer stem cells (CSCs) are known to be a major cause of metastasis, resistance and recurrence. Spheroid formation is one of the methods used to recruit CSCs utilizing an anchorage-independent environment in vitro. It was aimed to investigate the availability of spheroid formation culture methods in the research field of CSCs and resistance using 5-fluorouracil (5-FU)-resistant colorectal cancer cells. The wild type SNU-C5 and 5-FU-resistant SNU-C5 (SNU-C5/5-FUR) cells were cultured as usual (monolayer), and in 3-dimensional non-adhesive environments supplemented with fetal bovine serum (FBS) or growth factors, respectively. The characteristics of the spheroids were evaluated by morphometry, cell viability assay, western blotting, immunocytochemistry and enzyme-linked immunosorbent assay. Spheroid formation was induced in an environment supplemented with FBS, while SNU-C5/5-FUR cells only formed spheres in media supplemented with GFs. Sphere-formed cells showed slower cell proliferation than cells from monolayer, which coincided with an increased level of p21 and a decreased level of β-catenin. Markers for CSCs and drug resistance were not significantly changed after spheroid formation. Sphere-formed cells showed significantly increased levels of soluble E-cadherin, particularly in the environment supplemented with FBS. These results suggested that spheroid formation may be related to soluble E-cadherin, but is not related to CSCs or resistance markers.
Cell Phone Radiation Exposure Limits and Engineering Solutions

In the 1990s, the Institute of Electrical and Electronics Engineers (IEEE) restricted its risk assessment for human exposure to radiofrequency radiation (RFR) in seven ways: (1) Inappropriate focus on heat, ignoring sub-thermal effects. (2) Reliance on exposure experiments performed over very short times. (3) Overlooking time/amplitude characteristics of RFR signals. (4) Ignoring carcinogenicity, hypersensitivity, and other health conditions connected with RFR. (5) Measuring cellphone Specific Absorption Rates (SAR) at arbitrary distances from the head. (6) Averaging SAR doses at volumetric/mass scales irrelevant to health. (7) Using unrealistic simulations for cell phone SAR estimations. Low-cost software and hardware modifications are proposed here for cellular phone RFR exposure mitigation: (1) inhibiting RFR emissions in contact with the body, (2) use of antenna patterns reducing the Percent of Power absorbed in the Head (PPHead) and body and increasing the Percent of Power Radiated for communications (PPR), and (3) automated protocol-based reductions of the number of RFR emissions, their duration, or integrated dose. These inexpensive measures do not fundamentally alter cell phone functions or communications quality. A health threat is scientifically documented at many levels and acknowledged by industries. Yet mitigation of RFR exposures to users does not appear as a priority with most cell phone manufacturers.
Numerical investigation of unsteady heat transfer on a double wedge geometry in hypervelocity flows

In recent experiments performed at the University of Illinois, nitrogen and air flows over a double wedge geometry at Mach numbers varying from 4-7 and stagnation enthalpies varying from 2.1-8.0 MJ/kg were investigated. Selected cases from these experiments are simulated using US3D to ascertain the ability of state-of-the-art finite-volume hypersonic flow solvers to replicate experimental results. Two-dimensional simulations predict an unsteady separation and shock-shock interaction under both reacting and non-reacting conditions. The numerical solutions reach a time-periodic solution for certain experimental conditions. Good agreement is observed between experiment and two-dimensional simulations of the Mach 7 flow conditions when the simulations are limited to the experimental run-time. When run to a large number of flowtimes, the agreement is poor. Three-dimensional simulations of these free-stream conditions show non-uniformities in the wedge boundary layer during flow development.
Factor Copula Models for Spatial Data

We propose a new copula model that can be used with spatial data. Unlike the multivariate normal copula, the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process. Moreover, the proposed copula can model tail dependence and tail asymmetry. The model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature, such as the Matern model. For some choice of common factors, the joint copula density is given in closed form and therefore likelihood estimation is very fast. In the general case, one-dimensional numerical integration is needed to calculate the likelihood, but estimation is still reasonably fast even with large data sets. We use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors. We apply the proposed model to spatial temperature data and compare its performance with some popular geostatistics models. performance with some classical models that are popular in geostatistics.
Solving large‐scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh–Ritz method

Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by the matrix structures, properties of the eigen‐solutions, sizes of the problems, etc. This paper aims to remove those limitations and develop robust and universal NEP solvers for large‐scale engineering applications. The novelty lies in two aspects. First, a rational interpolation approach (RIA) is proposed based on the Keldysh theorem for holomorphic matrix functions. Comparing with the existing contour integral approach, the RIA provides the possibility to select sampling points in more general regions and has advantages in improving the accuracy and reducing the computational cost. Second, a resolvent sampling scheme using the RIA is proposed to construct reliable search spaces for the Rayleigh–Ritz procedure, based on which a robust eigen‐solver, called resolvent sampling based Rayleigh–Ritz method (RSRR), is developed for solving general NEPs. The RSRR can be easily implemented and parallelized. The advantages of the RIA and the performance of the RSRR are demonstrated by a variety of benchmark and application examples. Copyright © 2016 John Wiley & Sons, Ltd.
Lyapunov Functions and Exponential Ergodicity for Reflected Brownian Motion in the Orthant and Competing Brownian Particles

We consider semimartingale reflected Brownian motion in the positive orthant. Loosely speaking, in the interior of the orthant such process behaves like a Brownian motion with a constant drift vector and a constant covariance matrix. On each of the faces, it is reflected, not necessarily normally. Recently, conditions for its positive recurrence and existence of a stationary distribution were found. We make these results more complete. More importantly, we find several new cases when this process is exponentially ergodic. In some of these new cases, we are able to find the explicit value of the exponent of ergodicity. We find a tail estimate for the stationary distribution in all these cases. Our main tools are Lyapunov functions. We apply these results to market models of competing Brownian particles. We consider symmetric as well as asymmetric collisions.
Temporal Coupling of Subsurface and Surface Soil CO2 Fluxes: Insights From a Nonsteady State Model and Cross‐Wavelet Coherence Analysis

Inferences about subsurface CO2 fluxes often rely on surface soil respiration (Rsoil) estimates because directly measuring subsurface microbial and root respiration (collectively, CO2 production, STotal) is difficult. To evaluate how well Rsoil serves as a proxy for STotal, we applied the nonsteady state DEconvolution of Temporally varying Ecosystem Carbon componenTs model (0.01‐m vertical resolution), using 6‐hourly data from a Wyoming grassland, in six simulations that cross three soil types (clay, sandy loam, and sandy) with two depth distributions of subsurface biota. We used cross‐wavelet coherence analysis to examine temporal coherence (localized linear correlation) and offsets (lags) between STotal and Rsoil and fluxes and drivers (e.g., soil temperature and moisture). Cross‐wavelet coherence revealed higher coherence between fluxes and drivers than linear regressions between concurrent variables. Soil texture and moisture exerted the strongest controls over coherence between CO2 fluxes. Coherence between CO2 fluxes in all soil types was strong at short (~1 day) and long periods (>8 days), but soil type controlled lags, and rainfall events decoupled the fluxes at periods of 1–8 days for several days in sandy soil, up to 1 week in sandy loam, and for a month or more in clay soil. Concentrating root and microbial biomass nearer the surface decreased lags in all soil types and increased coherence up to 10% in clay soil. The assumption of high temporal coherence between Rsoil and STotal is likely valid in dry, sandy soil, but may lead to underestimates of short‐term STotal in semiarid grasslands with fine‐grained and/or wet soil.
Effects of Message Framing and Information Source on Consumers’ Attitudes toward an Amino Acid-Based Alternative Meat Curing System

Recently, meat scientists have developed an innovative amino acid-based alternative meat curing system (AAACS). However, consumer skepticism toward novel foods presents challenges regarding the acceptance of food innovations like the AAACS. Effective communication about this and other food technologies is critical. Our study was a 2 × 4 randomized factorial between-groups experiment that investigated how two peripheral cues—message frame and information source—impact attitudes toward the AAACS. We used Qualtrics to randomly assign participants to one of eight treatment groups. Each group viewed a different video about the AAACS. Then, all participants were asked about their attitudes toward the alternative meat curing system. Data were analyzed using a two-way multivariate analysis of variance (MANOVA). The two-way MANOVA determined concurrently the experimental effects of message frame and information source on information recall, trust, source expertise, source credibility, and anticipated consumption behavior. A significant MANOVA was followed up using Discriminant Function Analysis (DFA). A significant main effect was found for information source. The DFA revealed only one significant underlying function and that source expertise was the most powerful discriminating variable for information source.
Antioxidant activity and total phenolic compounds of Commiphora gileadensis extracts obtained by ultrasonic‐assisted extraction, with monitoring antiaging and cytotoxicity activities

Abstract Commiphora gileadensis (C. gileadensis) has been identified and linked with various health benefits and pharmaceutical potential for its phytochemical activities and chemical constituents. This study aimed to evaluate ultrasonic‐assisted extraction (USE) technique for total phenols content from C. gileadensis leaf compared to the hydrodistillation extraction (HDE). Our results showed that the USE operating conditions were identified as: MeOH·H2O solvent‐to‐fresh sample ratio of 80:20 (v/v); ultrasonic power/frequency at 150 W/20 kHz; and a temperature of 40 ± 1°C; subjected to acoustic waves intermittently for a calculated time (5 min) during the total programmed time of 12 min. The USE exhibited (118.71 ± 0.009 mg GAE/g DM) more amounts of all phenols than HDE (101.47 ± 0.005 mg GAE/g DM), and antioxidant (77.78 ± 0.73%, 75.27 ± 0.59% scavenging inhibition of DPPH), respectively. Anti‐aging and Cytotoxicity activities were investigated. The results of biological evaluations showed that the crude extracts of C. gileadensis significantly extended the replicative lifespan of K6001 yeast. In addition, in vitro cytotoxicity against the HepG2 cell line showed significant anticancer activity, and approximately 100 μg/mL is required to decrease viability compared with that of the control. This study is proven for a larger scale to extract and isolate compounds of C. gileadensis for potential utilization in the pharmaceutical industry. In conclusion, advanced methods afford an extract with high activity in the biological properties of the extract.