Journal articles: 'Complex rank'

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Bikram, Banerjee. "Chern rank of complex bundle." Commentationes Mathematicae Universitatis Carolinae 60, no. 3 (November 25, 2019): 401–13. http://dx.doi.org/10.14712/1213-7243.2019.015.

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Błaszczak-Świątkiewicz, Katarzyna. "New Selective Progesterone Receptor Modulators and Their Impact on the RANK/RANKL Complex Activity." Molecules 25, no. 6 (March 13, 2020): 1321. http://dx.doi.org/10.3390/molecules25061321.

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Breast cancer depends on women’s age. Its chemotherapy and hormone therapy lead to the loss of bone density and disruption of the skeleton. The proteins RANK and RANKL play a pivotal role in the formation of osteoclasts. It is also well established that the same proteins (RANK and RANKL) are the main molecules that play an important role in mammary stem cell biology. Mammary stem cells guarantee differentiation of the epithelial mammary cells, the growth of which is regulated by the progesterone-induced RANKL signaling pathway. The crosstalk between progesterone receptor, stimulated by progesterone and its analogues results in RANKL to RANK binding and activation of cell proliferation and subsequently unlimited expansion of the breast cancer cells. Therefore downstream regulation of this signaling pathway is desirable. To meet this need, a new class of selective estrogen receptor modulators (SPRMs) with anti- and mesoprogestin function were tested as potential anti-RANK agents. To establish the new feature of SPRMs, the impact of tested SPRMs on RANK-RANKL proteins interaction was tested. Furthermore, the cells proliferation upon RANKL stimulation, as well as NFkB and cyclin D1 expression, induced by tested SPRMs were analyzed. Conducted experiments proved NFkB expression inhibition as well as cyclin D1 expression limitation under asoprisnil and ulipristal treatment. The established paracrine anti-proliferative activity of antiprogestins together with competitive interaction with RANK make this class of compounds attractive for further study in order to deliver more evidence of their anti-RANK activity and potential application in the breast cancer therapy together with its accompanied osteoporosis.

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Ballico, Edoardo, and Alessandra Bernardi. "Real and Complex Rank for Real Symmetric Tensors with Low Ranks." Algebra 2013 (March 21, 2013): 1–5. http://dx.doi.org/10.1155/2013/794054.

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We study the case of a real homogeneous polynomial whose minimal real and complex decompositions in terms of powers of linear forms are different. We prove that if the sum of the complex and the real ranks of is at most , then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines.

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Chen, Na, and Viktor K. Prasanna. "Learning to Rank Complex Semantic Relationships." International Journal on Semantic Web and Information Systems 8, no. 4 (October 2012): 1–19. http://dx.doi.org/10.4018/jswis.2012100101.

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This paper presents a novel ranking method for complex semantic relationship (semantic association) search based on user preferences. The authors’ method employs a learning-to-rank algorithm to capture each user’s preferences. Using this, it automatically constructs a personalized ranking function for the user. The ranking function is then used to sort the results of each subsequent query by the user. Query results that more closely match the user’s preferences gain higher ranks. Their method is evaluated using a real-world RDF knowledge base created from Freebase linked-open-data. The experimental results show that the authors’ method significantly improves the ranking quality in terms of capturing user preferences, compared with the state-of-the-art.

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Li, Qun. "Constant rank theorem in complex variables." Indiana University Mathematics Journal 58, no. 3 (2009): 1235–56. http://dx.doi.org/10.1512/iumj.2009.58.3574.

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Yamaguchi, Toshihiro. "Examples of Rational Toral Rank Complex." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/867247.

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ETINGOF, PAVEL. "REPRESENTATION THEORY IN COMPLEX RANK, I." Transformation Groups 19, no. 2 (March 25, 2014): 359–81. http://dx.doi.org/10.1007/s00031-014-9260-2.

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8

Etingof, Pavel. "Representation theory in complex rank, II." Advances in Mathematics 300 (September 2016): 473–504. http://dx.doi.org/10.1016/j.aim.2016.03.025.

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Intermont, Michele, Brenda Johnson, and Randy McCarthy. "The rank filtration and Robinson’s complex." Journal of Pure and Applied Algebra 212, no. 4 (April 2008): 735–52. http://dx.doi.org/10.1016/j.jpaa.2007.07.009.

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10

Achar, Pramod N., and Anne-Marie Aubert. "On Rank 2 Complex Reflection Groups." Communications in Algebra 36, no. 6 (May 27, 2008): 2092–132. http://dx.doi.org/10.1080/00927870801949559.

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Mizukami, Junko, Giichi Takaesu, Hiroyuki Akatsuka, Hiroaki Sakurai, Jun Ninomiya-Tsuji, Kunihiro Matsumoto, and Naoki Sakurai. "Receptor Activator of NF-κB Ligand (RANKL) Activates TAK1 Mitogen-Activated Protein Kinase Kinase Kinase through a Signaling Complex Containing RANK, TAB2, and TRAF6." Molecular and Cellular Biology 22, no. 4 (February 15, 2002): 992–1000. http://dx.doi.org/10.1128/mcb.22.4.992-1000.2002.

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ABSTRACT The receptor activator of NF-κB (RANK) and its ligand RANKL are key molecules for differentiation and activation of osteoclasts. RANKL stimulates transcription factors AP-1 through mitogen-activated protein kinase (MAPK) activation, and NF-κB through IκB kinase (IKK) activation. Tumor necrosis factor receptor-associated factor 6 (TRAF6) is essential for activation of these kinases. In the interleukin-1 signaling pathway, TAK1 MAPK kinase kinase (MAPKKK) mediates MAPK and IKK activation via interaction with TRAF6, and TAB2 acts as an adapter linking TAK1 and TRAF6. Here, we demonstrate that TAK1 and TAB2 participate in the RANK signaling pathway. Dominant negative forms of TAK1 and TAB2 inhibit NF-κB activation induced by overexpression of RANK. In 293 cells stably transfected with full-length RANK, RANKL stimulation facilitates the formation of a complex containing RANK, TRAF6, TAB2, and TAK1, leading to the activation of TAK1. Furthermore, in murine monocyte RAW 264.7 cells, dominant negative forms of TAK1 and TAB2 inhibit NF-κB activation induced by RANKL and endogenous TAK1 is activated in response to RANKL stimulation. These results suggest that the formation of the TRAF6-TAB2-TAK1 complex is involved in the RANK signaling pathway and may regulate the development and function of osteoclasts.

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Xu, Feng, Qi Zhou, Dein Wong, and Fenglei Tian. "Complex unit gain graphs of rank 2." Linear Algebra and its Applications 597 (July 2020): 155–69. http://dx.doi.org/10.1016/j.laa.2020.03.023.

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13

Chiose, Ionuţ. "The Kähler Rank of Compact Complex Manifolds." Journal of Geometric Analysis 26, no. 1 (February 3, 2015): 603–15. http://dx.doi.org/10.1007/s12220-015-9564-z.

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14

Lumley, T., and A. J. Scott. "Two-sample rank tests under complex sampling." Biometrika 100, no. 4 (July 29, 2013): 831–42. http://dx.doi.org/10.1093/biomet/ast027.

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15

Amara, Zouheir, and Mourad Oudghiri. "Finite rank perturbations of complex symmetric operators." Journal of Mathematical Analysis and Applications 495, no. 1 (March 2021): 124720. http://dx.doi.org/10.1016/j.jmaa.2020.124720.

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16

Woźniczka, Magdalena, and Katarzyna Błaszczak-Świątkiewicz. "New Generation of Meso and Antiprogestins (SPRMs) into the Osteoporosis Approach." Molecules 26, no. 21 (October 27, 2021): 6491. http://dx.doi.org/10.3390/molecules26216491.

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Receptor activator of nuclear factor κB (RANK) and its ligand (RANKL) play key roles in bone metabolism and the immune system. The RANK/RANKL complex has also been shown to be critical in the formation of mammary epithelia cells. The female hormones estradiol and progesterone closely control the action of RANKL with RANK. Blood concentration of these sex hormones in the postmenopausal period leads to an increase in RANK/RANKL signaling and are a major cause of women’s osteoporosis, characterized by altered bone mineralization. Knowledge of the biochemical relationships between hormones and RANK/RANKL signaling provides the opportunity to design novel therapeutic agents to inhibit bone loss, based on the anti-RANKL treatment and inhibition of its interaction with the RANK receptor. The new generation of both anti- and mesoprogestins that inhibit the NF-κB-cyclin D1 axis and blocks the binding of RANKL to RANK can be considered as a potential source of new RANK receptor ligands with anti-RANKL function, which may provide a new perspective into osteoporosis treatment itself as well as limit the osteoporosis rise during breast cancer metastasis to the bone.

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17

Tyrtyshnikov, Eugene E. "Tensor decompositions and rank increment conjecture." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 4 (August 26, 2020): 239–46. http://dx.doi.org/10.1515/rnam-2020-0020.

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AbstractSome properties of tensor ranks and the non-closeness issue of sets with given restrictions on the rank of tensors entering those sets are studied. It is proved that the rank of the d-dimensional Laplacian equals d. The following conjecture is formulated: for any tensor of non-maximal rank there exists a nonzero decomposable tensor (tensor of rank 1) such that the rank increases by one after adding this tensor. In the general case, it is proved that this property holds algebraically almost everywhere for complex tensors of fixed size whose rank is strictly less than the generic rank.

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18

Ballico, E. "An upper bound for the real tensor rank and the real symmetric tensor rank in terms of the complex ranks." Linear and Multilinear Algebra 62, no. 11 (September 24, 2013): 1546–52. http://dx.doi.org/10.1080/03081087.2013.839671.

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19

Krejsek, Jan, Martina Koláčková, Vladimír Lonský, Manuela Trojáčková Kudlová, Jiří Manďák, Pavel Kuneš, Karolína Jankovičová, Dana Vlášková, and Ctirad Andrýs. "RANK/RANKL Expression Is Induced by Cardiac Surgical Operation." Acta Medica (Hradec Kralove, Czech Republic) 52, no. 4 (2009): 149–53. http://dx.doi.org/10.14712/18059694.2016.121.

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Background: Cardiac surgery provokes a systemic inflammatory response in any patient. This complex body reaction involves also RANK/RANKL molecules which have been recently identified as principal regulators of bone metabolism. Aims: To follow the changes in the expression of RANK/RANKL molecules on innate immune cells of cardiac surgical patients. Patients and Methods: Twenty-six patients undergoing cardiac surgical were assigned to undergo coronary artery bypass grafting using either cardiopulmonary bypass (“on-pump”) or modified “miniinvasive on-pump”. The expression of RANK/RANKL was performed by flow cytometry. Results: Significantly increased expression of RANK on monocytes of “miniinvasive on-pump” patients was found at the 1st, the 3nd, and 7th postoperative days. The similar pattern was found also for monocyte RANKL expression. In addition, RANKL expression was significantly increased at the 3rd postoperative day in “on-pump” patient. No significant differences between “miniinvasive on-pump” and “on-pump” cardiac surgical patients were found. Conclusion: The expression of both RANK and RANKL molecules is significantly enhanced on monocytes of “miniinvasive on-pump” cardiac surgical patients.

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20

Lai, Sheng-Hong, Jen-Chi Lee, and I.-Hsun Tsai. "Extended complex Yang–Mills instanton sheaves." International Journal of Geometric Methods in Modern Physics 17, no. 04 (March 2020): 2050061. http://dx.doi.org/10.1142/s0219887820500619.

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In the search of Yang–Mills (YM) instanton sheaves with topological charge two, the rank of [Formula: see text] matrix in the monad construction can be dropped from the bundle case with rank [Formula: see text] to either rank [Formula: see text] [S. H. Lai, J. C. Lee and I. H. Tsai, Yang–Mills instanton sheaves, Ann. Phys. 377 (2017) 446] or 0 on some points of [Formula: see text] of the sheaf cases. In this paper, we first show that the sheaf case with rank [Formula: see text] does not exist for the previous construction of [Formula: see text] complex YM instantons [S. H. Lai, J. C. Lee and I. H. Tsai, Biquaternions and ADHM construction of concompact [Formula: see text] Yang–Mills instantons, Ann. Phys. 361 (2015) 14]. We then show that in the new “extended complex YM instantons” discovered in this paper, rank [Formula: see text] can be either 2 on the whole [Formula: see text] (bundle) with some given ADHM data or 1, 0 on some points of [Formula: see text] with other ADHM data (sheaves). These extended [Formula: see text] complex YM instantons have no real instanton counterparts. Finally, the potential applications to real physics systems are noted in the end of the paper.

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21

Lu, Jun. "Bayesian Low-Rank Interpolative Decomposition for Complex Datasets." Studies in Engineering and Technology 9, no. 1 (June 30, 2022): 1. http://dx.doi.org/10.11114/set.v9i1.5624.

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In this paper, we introduce a probabilistic model for learning interpolative decomposition (ID), which is commonly used for feature selection, low-rank approximation, and identifying hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Prior densities with support on the specified subspace are used to address the constraint for the magnitude of the factored component of the observed matrix. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on a variety of real-world datasets including CCLE EC50, CCLE IC50, CTRP EC50, and MovieLens 100K datasets with different sizes, and dimensions, and show that the proposed Bayesian ID GBT and GBTN models lead to smaller reconstructive errors compared to existing randomized approaches.

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22

Li, Dehe, and Shujie Zhai. "Real Hypersurfaces in Complex Grassmannians of Rank Two." Mathematics 9, no. 24 (December 14, 2021): 3238. http://dx.doi.org/10.3390/math9243238.

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It is known that there does not exist any Hopf hypersurface in complex Grassmannians of rank two of complex dimension 2m with constant sectional curvature for m≥3. The purpose of this article is to extend the above result, and without the Hopf condition, we prove that there does not exist any locally conformally flat real hypersurface for m≥3.

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23

Toma, Matei. "On the Kähler Rank of Compact Complex Surfaces." Bulletin de la Société mathématique de France 136, no. 2 (2008): 243–60. http://dx.doi.org/10.24033/bsmf.2556.

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24

Chiose, Ionuţ, and Matei Toma. "On compact complex surfaces of Kähler rank one." American Journal of Mathematics 135, no. 3 (2013): 851–60. http://dx.doi.org/10.1353/ajm.2013.0022.

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25

Ko, Eungil, and Ji Lee. "On rank one perturbations of complex symmetric operators." Filomat 29, no. 8 (2015): 1795–809. http://dx.doi.org/10.2298/fil1508795k.

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In this paper we study the decomposability of rank one perturbations of complex symmetric operators R = T+u?v. Also we investigate some conditions for which R satisfies a-Weyl?s theorem. Finally, we characterize some conditions for R to be hyponormal. As consequences, we provide several cases for such operators.

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26

Marcus, Marvin, and Susan Franklin. "Rank and inertia of a complex hadamard Power∗." Linear and Multilinear Algebra 32, no. 2 (August 1992): 149–66. http://dx.doi.org/10.1080/03081089208818158.

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27

Dehghan, Afshin, Omar Oreifej, and Mubarak Shah. "Complex event recognition using constrained low-rank representation." Image and Vision Computing 42 (October 2015): 13–21. http://dx.doi.org/10.1016/j.imavis.2015.06.007.

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Luo, Minnan, Xiaojun Chang, Zhihui Li, Liqiang Nie, Alexander G. Hauptmann, and Qinghua Zheng. "Simple to complex cross-modal learning to rank." Computer Vision and Image Understanding 163 (October 2017): 67–77. http://dx.doi.org/10.1016/j.cviu.2017.07.001.

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Lee, Ruenn-Huah, and Tee-How Loo. "Hopf Hypersurfaces in Complex Grassmannians of Rank Two." Results in Mathematics 71, no. 3-4 (September 7, 2016): 1083–107. http://dx.doi.org/10.1007/s00025-016-0601-4.

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Yoon, K. Paul. "A probabilistic approach to rank complex fuzzy numbers." Fuzzy Sets and Systems 80, no. 2 (June 1996): 167–76. http://dx.doi.org/10.1016/0165-0114(95)00193-x.

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31

BERNDT, JÜRGEN, and YOUNG JIN SUH. "HYPERSURFACES IN NONCOMPACT COMPLEX GRASSMANNIANS OF RANK TWO." International Journal of Mathematics 23, no. 10 (October 2012): 1250103. http://dx.doi.org/10.1142/s0129167x12501030.

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Consider a Riemannian manifold N equipped with an additional geometric structure, such as a Kähler structure or a quaternionic Kähler structure, and a hypersurface M in N. The geometric structure induces a decomposition of the tangent bundle TM of M into subbundles. A natural problem is to classify all hypersurfaces in N for which the second fundamental form of M preserves these subbundles. This problem is reasonably well understood for Riemannian symmetric spaces of rank one, but not for higher rank symmetric spaces. A general treatment of this problem for higher rank symmetric spaces is out of reach at present, and therefore it is desirable to understand this problem better in a few special cases. Due to some conceptual differences between symmetric spaces of compact type and of noncompact type it appears that one needs to consider these two cases separately. In this paper we investigate this problem for the rank two symmetric space SU 2, m/S(U2Um) of noncompact type.

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32

Kalinov, Daniil. "Finite-Dimensional Representations of Yangians in Complex Rank." International Mathematics Research Notices 2020, no. 20 (February 18, 2019): 6967–98. http://dx.doi.org/10.1093/imrn/rnz005.

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Abstract We classify the “finite-dimensional” irreducible representations of the Yangians $Y(\mathfrak{g}\mathfrak{l}_t)$ and $Y(\mathfrak{s}\mathfrak{l}_t)$. These are associative ind-algebras in the Deligne category $\textrm{Rep}(GL_t)$, which generalize the regular Yangians $Y(\mathfrak{g}\mathfrak{l}_n)$ and $Y(\mathfrak{s}\mathfrak{l}_n)$ to complex rank. They were first defined in the paper [14]. Here we solve [14, Problem 7.2]. We work with the Deligne category $\textrm{Rep}(GL_t)$ using the ultraproduct approach introduced in [7] and [16].

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Dana, M., and Kh D. Ikramov. "On rank-one corrections of complex symmetric matrices." Journal of Mathematical Sciences 141, no. 6 (March 2007): 1614–17. http://dx.doi.org/10.1007/s10958-007-0070-0.

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Kohli, SarvrajSingh, and VirinderSingh Kohli. "Role of RANKL-RANK/osteoprotegerin molecular complex in bone remodeling and its immunopathologic implications." Indian Journal of Endocrinology and Metabolism 15, no. 3 (2011): 175. http://dx.doi.org/10.4103/2230-8210.83401.

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35

Walter, Thomas S., Changzhen Liu, Peng Huang, Shiqian Zhang, Lucy R. Wedderburn, Bin Gao, Raymond J. Owens, David I. Stuart, Peifu Tang, and Jingshan Ren. "Crystallization and preliminary X-ray analysis of mouse RANK and its complex with RANKL." Acta Crystallographica Section F Structural Biology and Crystallization Communications 65, no. 6 (May 22, 2009): 597–600. http://dx.doi.org/10.1107/s1744309109015735.

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36

Schlauer, Jan. "Nomenclature of the Drosera anglica complex revisited." Carnivorous Plant Newsletter 39, no. 2 (June 1, 2010): 46. http://dx.doi.org/10.55360/cpn392.js729.

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As noted before (Carniv. Pl. Newslett. 37:118-119, 2008), there can be only one legitimate name for all hybrids (including hybridogenic stabilized segregates) between two taxa at the rank that distinguishes the two parent taxa. In the case of Drosera linearis and D. rotundifolia as the parents (which are distinguished at species rank), this name is D. anglica. This has led to the relegation of the back-cross that has been known for a long time at the illegitimate rank of species (as D. 3 obovata) to a variety of D. anglica.

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Ausloos, Marcel, Rudi Cloots, Adam Gadomski, and Nikolay K. Vitanov. "Ranking structures and rank–rank correlations of countries: The FIFA and UEFA cases." International Journal of Modern Physics C 25, no. 11 (October 15, 2014): 1450060. http://dx.doi.org/10.1142/s0129183114500600.

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Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank–rank, similar or not, correlations based on the case of European countries ranked by UEFA and FIFA from different soccer competitions. The first question to be answered is whether an empirical and simple law is obtained for such (self-) organizations of complex sociological systems with such different measuring schemes. It is found that the power law form is not the best description contrary to many modern expectations. The stretched exponential is much more adequate. Moreover, it is found that the measuring rules lead to some inner structures in both cases.

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van Dam, Peter A., Yannick Verhoeven, Julie Jacobs, An Wouters, Wiebren Tjalma, Filip Lardon, Tim Van den Wyngaert, et al. "RANK-RANKL Signaling in Cancer of the Uterine Cervix: A Review." International Journal of Molecular Sciences 20, no. 9 (May 2, 2019): 2183. http://dx.doi.org/10.3390/ijms20092183.

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RANK ligand (RANKL) is a member of the tumor necrosis factor alpha superfamily of cytokines. It is the only known ligand binding to a membrane receptor named receptor activator of nuclear factor-kappa B (RANK), thereby triggering recruitment of tumor necrosis factor (TNF) receptor associated factor (TRAF) adaptor proteins and activation of downstream pathways. RANK/RANKL signaling is controlled by a decoy receptor called osteoprotegerin (OPG), but also has additional more complex levels of regulation. The existing literature on RANK/RANKL signaling in cervical cancer was reviewed, particularly focusing on the effects on the microenvironment. RANKL and RANK are frequently co-expressed in cervical cancer cells lines and in carcinoma of the uterine cervix. RANKL and OPG expression strongly increases during cervical cancer progression. RANKL is directly secreted by cervical cancer cells, which may be a mechanism they use to create an immune suppressive environment. RANKL induces expression of multiple activating cytokines by dendritic cells. High RANK mRNA levels and high immunohistochemical OPG expression are significantly correlated with high clinical stage, tumor grade, presence of lymph node metastases, and poor overall survival. Inhibition of RANKL signaling has a direct effect on tumor cell proliferation and behavior, but also alters the microenvironment. Abundant circumstantial evidence suggests that RANKL inhibition may (partially) reverse an immunosuppressive status. The use of denosumab, a monoclonal antibody directed to RANKL, as an immunomodulatory strategy is an attractive concept which should be further explored in combination with immune therapy in patients with cervical cancer.

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Mortini, Raymond, and Rudolf Rupp. "A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane." Journal of Function Spaces and Applications 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/905650.

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We determine, via classroom proofs, the maximal ideal space, the Bass stable rank as well as the topological and dense stable rank of the uniform closure of all complex-valued functions continuously differentiable on neighborhoods of a compact planar set and holomorphic in the interior of . In this spirit, we also give elementary approaches to the calculation of these stable ranks for some classical function algebras on .

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SOBERON-CHAVEZ, SOCORRO. "RANK 2 VECTOR BUNDLES OVER A COMPLEX QUADRIC SURFACE." Quarterly Journal of Mathematics 36, no. 2 (1985): 159–72. http://dx.doi.org/10.1093/qmath/36.2.159.

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41

Javed, Sajid, Arif Mahmood, Thierry Bouwmans, and Soon Ki Jung. "Spatiotemporal Low-Rank Modeling for Complex Scene Background Initialization." IEEE Transactions on Circuits and Systems for Video Technology 28, no. 6 (June 2018): 1315–29. http://dx.doi.org/10.1109/tcsvt.2016.2632302.

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42

Entova Aizenbud, Inna. "On representations of rational Cherednik algebras of complex rank." Representation Theory of the American Mathematical Society 18, no. 12 (November 24, 2014): 361–407. http://dx.doi.org/10.1090/s1088-4165-2014-00459-x.

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Cubadda, Gianluca. "Complex Reduced Rank Models For Seasonally Cointegrated Time Series." Oxford Bulletin of Economics and Statistics 63, no. 4 (September 2001): 497–511. http://dx.doi.org/10.1111/1468-0084.00231.

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44

Corrêa, M. "Rank two nilpotent co-Higgs sheaves on complex surfaces." Geometriae Dedicata 183, no. 1 (January 19, 2016): 25–31. http://dx.doi.org/10.1007/s10711-016-0141-9.

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BERNDT, JÜRGEN, HYUNJIN LEE, and YOUNG JIN SUH. "CONTACT HYPERSURFACES IN NONCOMPACT COMPLEX GRASSMANNIANS OF RANK TWO." International Journal of Mathematics 24, no. 11 (October 2013): 1350089. http://dx.doi.org/10.1142/s0129167x13500894.

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46

Lee, Hyunjin, and Young Jin Suh. "Cyclic parallel hypersurfaces in complex Grassmannians of rank 2." International Journal of Mathematics 31, no. 02 (December 24, 2019): 2050014. http://dx.doi.org/10.1142/s0129167x20500147.

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The object of the paper is to study cyclic parallel hypersurfaces in complex (hyperbolic) two-plane Grassmannians which have a remarkable geometric structure as Hermitian symmetric spaces of rank 2. First, we prove that if the Reeb vector field belongs to the orthogonal complement of the maximal quaternionic subbundle, then the shape operator of a cyclic parallel hypersurface in complex hyperbolic two-plane Grassmannians is Reeb parallel. By using this fact, we classify all cyclic parallel hypersurfaces in complex hyperbolic two-plane Grassmannians with non-vanishing geodesic Reeb flow. Next, we give a non-existence theorem for cyclic Hopf hypersurfaces in complex two-plane Grassmannians.

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Carlini, Enrico, Emanuele Ventura, and Cheng Guo. "Real and complex Waring rank of reducible cubic forms." Journal of Pure and Applied Algebra 220, no. 11 (November 2016): 3692–701. http://dx.doi.org/10.1016/j.jpaa.2016.05.007.

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48

Huang, Shuai, Sidharth Gupta, and Ivan Dokmanic. "Solving Complex Quadratic Systems With Full-Rank Random Matrices." IEEE Transactions on Signal Processing 68 (2020): 4782–96. http://dx.doi.org/10.1109/tsp.2020.3011016.

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49

Deck, Thomas. "Finite Rank Hankel Operators over the Complex Wiener Space." Potential Analysis 22, no. 1 (February 2005): 85–100. http://dx.doi.org/10.1007/s11118-004-6458-2.

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Jang, Yuria, Hong Moon Sohn, Young Jong Ko, Hoon Hyun, and Wonbong Lim. "Inhibition of RANKL-Induced Osteoclastogenesis by Novel Mutant RANKL." International Journal of Molecular Sciences 22, no. 1 (January 4, 2021): 434. http://dx.doi.org/10.3390/ijms22010434.

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Abstract:

Background: Recently, it was reported that leucine-rich repeat-containing G-protein-coupled receptor 4 (LGR4, also called GPR48) is another receptor for RANKL and was shown to compete with RANK to bind RANKL and suppress canonical RANK signaling during osteoclast differentiation. The critical role of the protein triad RANK–RANKL in osteoclastogenesis has made their binding an important target for the development of drugs against osteoporosis. In this study, point-mutations were introduced in the RANKL protein based on the crystal structure of the RANKL complex and its counterpart receptor RANK, and we investigated whether LGR4 signaling in the absence of the RANK signal could lead to the inhibition of osteoclastogenesis.; Methods: The effects of point-mutated RANKL (mRANKL-MT) on osteoclastogenesis were assessed by tartrate-resistant acid phosphatase (TRAP), resorption pit formation, quantitative real-time polymerase chain reaction (qPCR), western blot, NFATc1 nuclear translocation, micro-CT and histomorphological assay in wild type RANKL (mRANKL-WT)-induced in vitro and in vivo experimental mice model. Results: As a proof of concept, treatment with the mutant RANKL led to the stimulation of GSK-3β phosphorylation, as well as the inhibition of NFATc1 translocation, mRNA expression of TRAP and OSCAR, TRAP activity, and bone resorption, in RANKL-induced mouse models; and Conclusions: The results of our study demonstrate that the mutant RANKL can be used as a therapeutic agent for osteoporosis by inhibiting RANKL-induced osteoclastogenesis via comparative inhibition of RANKL. Moreover, the mutant RANKL was found to lack the toxic side effects of most osteoporosis treatments.

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