Relevant bibliographies by topics / Complex rank

Academic literature on the topic 'Complex rank'

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Published: 10 March 2023

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Journal articles on the topic "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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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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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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Dissertations / Theses on the topic "Complex rank"

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Entova, Aizenbud Inna. "Schur Weyl duality in complex rank." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104601.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 207-208).
This thesis gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with a distinguished non-zero vector 1) we give a definition of a complex tensor power of V. This is an Ind-object of the Deligne category Rep(St) equipped with a natural action of gl(V). This construction allows us to describe a duality between the abelian envelope of the category Rep(St) and a localization of the category Op/t,v (the parabolic category 0 for gl(V) associated with the pair (V, 1)). In particular, we obtain an exact contravariant functor SWt from the category Repab(St) (the abelian envelope of the category Rep(St)) to a certain quotient of the category Op/t v. This quotient, denoted by 0 p/t v, is obtained by taking the full subcategory of Op/t v consisting of modules of degree t, and localizing by the subcategory of finite dimensional modules. It turns out that the contravariant functor SWt makes Op/t v a Serre quotient of the category Repab(St)OP, and the kernel of SWt can be explicitly described. In the second part of this thesis, we consider the case when V = C[infinity] . We define the appropriate version of the parabolic category 0 and its localization, and show that the latter is equivalent to a "restricted" inverse limit of categories Op/t1CN with N tending to infinity. The Schur-Weyl functors SWt,CN then give an anti-equivalence between the category Op[infinity]/t C[infinity]and the category Repab(Se). This duality provides an unexpected tensor structure on the category Op[infinity]/t C[infinity].
by Inna Entova Aizenbud.
Ph. D.
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FENU, CATERINA. "Applications of low-rank approximation: complex networks and inverse problems." Doctoral thesis, Università degli Studi di Cagliari, 2015. http://hdl.handle.net/11584/266590.

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The use of low-rank approximation is crucial when one is interested in solving problems of large dimension. In this case, the matrix with reduced rank can be obtained starting from the singular value decomposition considering only the largest components. This thesis describes how the use of the low-rank approximation can be applied both in the analysis of complex networks and in the solution of inverse problems. In the first case, it will be explained how to identify the most important nodes or how to determine the ease of traveling between them in large-scale networks that arise in many applications. The use of low-rank approximation is presented both for undirected and directed networks, whose adjacency matrices are symmetric and nonsymmetric, respectively. As a second application, we propose how to identify inhomogeneities in the ground or the presence of conductive substances. This survey is addressed with the aid of electromagnetic induction measurements taken with a ground conductivity meter. Starting from electromagnetic data collected by this device, the electrical conductivity profile of the soil is reconstructed with the aid of a regularized damped Gauss{Newton method. The inversion method is based on the low-rank approximation of the Jacobian of the function to be inverted.
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Varduhn, Vasco [Verfasser], Ernst [Akademischer Betreuer] Rank, and Hans-Joachim [Akademischer Betreuer] Bungartz. "A Parallel, Multi-Resolution Framework for Handling Large Sets of Complex Data, from Exploration and Visualisation to Simulation / Vasco Varduhn. Gutachter: Hans-Joachim Bungartz ; Ernst Rank. Betreuer: Ernst Rank." München : Universitätsbibliothek der TU München, 2014. http://d-nb.info/1052307833/34.

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Pujari, Manisha. "Prévision de liens dans des grands graphes de terrain (application aux réseaux bibliographiques)." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD010/document.

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Nous nous intéressons dans ce travail au problème de prévision de nouveaux liens dans des grands graphes de terrain. Nous explorons en particulier les approches topologiques dyadiques pour la prévision de liens. Différentes mesures de proximité topologique ont été étudiées dans la littérature pour prédire l’apparition de nouveaux liens. Des techniques d’apprentissage supervisé ont été aussi utilisées afin de combiner ces différentes mesures pour construire des modèles prédictifs. Le problème d’apprentissage supervisé est ici un problème difficile à cause notamment du fort déséquilibre de classes. Dans cette thèse, nous explorons différentes approches alternatives pour améliorer les performances des approches dyadiques pour la prévision de liens. Nous proposons d’abord, une approche originale de combinaison des prévisions fondée sur des techniques d’agrégation supervisée de listes triées (ou agrégation de préférences). Nous explorons aussi différentes approches pour améliorer les performances des approches supervisées pour la prévision de liens. Une première approche consiste à étendre l’ensemble des attributs décrivant un exemple (paires de noeuds) par des attributs calculés dans un réseau multiplexe qui englobe le réseau cible. Un deuxième axe consiste à évaluer l’apport destechniques de détection de communautés pour l’échantillonnage des exemples. Des expérimentations menées sur des réseaux réels extraits de la base bibliographique DBLP montrent l’intérêt des approaches proposées
In this work, we are interested to tackle the problem of link prediction in complex networks. In particular, we explore topological dyadic approaches for link prediction. Different topological proximity measures have been studied in the scientific literature for finding the probability of appearance of new links in a complex network. Supervided learning methods have also been used to combine the predictions made or information provided by different topological measures. The create predictive models using various topological measures. The problem of supervised learning for link prediction is a difficult problem especially due to the presence of heavy class imbalance. In this thesis, we search different alternative approaches to improve the performance of different dyadic approaches for link prediction. We propose here, a new approach of link prediction based on supervised rank agregation that uses concepts from computational social choice theory. Our approach is founded on supervised techniques of aggregating sorted lists (or preference aggregation). We also explore different ways of improving supervised link prediction approaches. One approach is to extend the set of attributes describing an example (pair of nodes) by attributes calculated in a multiplex network that includes the target network. Multiplex networks have a layered structure, each layer having different kinds of links between same sets of nodes. The second way is to use community information for sampling of examples to deal with the problem of classe imabalance. Experiments conducted on real networks extracted from well known DBLP bibliographic database
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Oreifej, Omar. "Robust Subspace Estimation Using Low-Rank Optimization. Theory and Applications in Scene Reconstruction, Video Denoising, and Activity Recognition." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5684.

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In this dissertation, we discuss the problem of robust linear subspace estimation using low-rank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time. Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories...etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using low-rank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a two-fold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for low-rank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is ill-posed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the state-of-the-art. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using low-rank optimization. Therefore, we propose a data-driven two-stage approach, where the first stage “sparsifies” the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or de-warping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the problem of simultaneous turbulence mitigation and moving object detection. We propose a novel three-term low-rank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and L1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by L1 norm. Second, since the object's motion is linear and intrinsically different than the Gaussian-like turbulence, a Gaussian-based turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the low-rank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in miss-detections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned difficulties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camera-induced and object-induced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results. Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size ... etc. In this extremely challenging task, high-level features have recently shown a promising direction as in [53, 129], where core low-level events referred to as concepts are annotated and modeled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding high-level features are significantly noisy. In order to address this problem, we propose a novel low-rank formulation, which combines the precisely annotated videos used to train the concepts, with the rich high-level features. Our approach finds a new representation for each event, which is not only low-rank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the high-level features by a significant margin.
Ph.D.
Doctorate
Electrical Engineering and Computing
Engineering and Computer Science
Computer Engineering
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Lebiez, Judith. "'Sie rief mich aus der Nacht' : the birth complex in Nietzsche and Wagner." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/278675.

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This thesis addresses the role of the birth complex in Friedrich Nietzsche’s philosophy and in Richard Wagner’s operas. I see the birth complex as characterised by a dialectical relation between flesh and light, which is itself polarised by the tension between desire and anxiety. A structural determinant of the human relation to the world, this complex in my argument is of special importance for understanding the roles given to and assumed by women. Wagner gave the birth complex its first comprehensive elaboration through his operas. This, I contend, is the aspect of Wagner’s work that Nietzsche in his writings particularly reacted to through the ambivalent fascination it awakened in him. I argue that, even after Nietzsche’s break from Wagner, the birth complex remains central in his philosophy. The primary reference I build on here is Otto Rank’s theory of birth trauma, as set out in Das Trauma der Geburt (1924). To me, Rank’s theorisation of the trauma of birth is a translation into psychoanalytic language of Nietzsche’s philosophy, which itself arose with a translation into philosophical language of Wagner’s operas. In this thesis I build especially on Rank’s formulation of the tension between desire and anxiety and on his suggestions concerning the causes of the undoing of women. However, Rank did not take into account what I contend is a key aspect of both Nietzsche’s and Wagner’s work: the role of light in its dialectical relation with the flesh. By flesh I mean the interiority of the mother’s body and, by extension, the human body insofar as it is conceived through its relation to the maternal body. In the first main section of my PhD, I propose a theoretical understanding of the birth complex through an analysis of Nietzsche’s philosophy. I start with his writings pro and contra Wagner, showing that what Nietzsche primarily sees in Wagner’s operas is the birth complex. I then go on to argue that Nietzsche’s philosophy of life and of creativity is an exploration of the ways in which birth could be overcome. The second main section of my PhD is dedicated to Wagner, with largely text-based readings of three operas. I first discuss the extent to which death in Der fliegende Holländer and in the Freudian conception of the death drive is a mask for birth. I then tackle Tristan und Isolde and its famous celebration of night and death, in order to investigate whether love can be reduced to the birth complex. The last chapter of this section presents a close analysis of Das Rheingold and especially of its first scene and of Wagner’s indications on lighting. In a third and shorter section, I show that Hugo von Hofmannsthal’s and Richard Strauss’s Elektra pursued and reviewed this fundamental preoccupation of Nietzsche’s and Wagner’s work in proposing a further formulation of the birth complex that incorporates the scene of matricide. Finally, as a coda to the thesis, I explore the extent to which the uses of stage lighting pioneered by Adolphe Appia have been coming to terms with the birth complex.
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Albergante, L. "A PETRI NET MODEL OF LIVER RESPONSE TO VISCERAL LEISHMANIASIS: SELF-REGULATION AND COMPLEX INTERPLAY IN THE VERTEBRATE IMMUNE SYSTEM." Doctoral thesis, Università degli Studi di Milano, 2010. http://hdl.handle.net/2434/150085.

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Visceral leishmaniasis (also called "Kala-azar") is a widespread disease, which is usually fatal in the absence of treatment. Characteristic of the liver immune response to leishmaniasis is a type of inflammation (granulomatous inflammation) that leads to the formation of "granulomas". A granuloma provides a very interesting micro-environment, which is maintained by the coordination of many cells of the immune system. Due to the complexity of the immune response, only a limited amount of modeling work exists in the context of granulomatous infection, and most of the current models focus only on the formation stage of granulomas. The primary goal of this thesis is to gain insights into the process of formation and development of a granuloma. To this end, we built a model of the granuloma formation and resolution in the liver using stochastic Petri nets, and performed several in silico experiments to study the nature of the immune response to leishmaniasis, possible therapeutic options, and the role of the cells involved. Additionally, the building of the model is extensively documented, and the most important qualitative and quantitative assumptions are referenced and discussed, with the aim of presenting a “conceptual framework” to be used when facing similar problems. The model is validated against available biological data, and its robustness is assessed using sensitivity analysis.
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Bain, Raoul Harley. "The elucidation of the Rana livida complex." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq40881.pdf.

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Eastwood, S. J. "Hybrid LES – RANS of complex geometry jets." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598741.

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A promising technique for exploring jet flows is large eddy simulation (LES). However for jet LES a number of key unanswered questions remain. These include the sensitivity of solutions to the numerical scheme, subgrid scale (SGS) model and inlet conditions. Results show that for more dissipative, robust solvers often found in industry, SGS model omission can give useful results. Solutions which use no SGS model are called Numerical LES (NLES). For less dissipative codes, solutions are found to be relatively insensitive to the choice of SGS model. An industrial based solver is selected and validated further by making acoustic and hot jet predictions using the NLES approach. Encouraging agreement with measurements is shown. To relieve computational cost, the near wall modelling issue is also addressed. A novel method is used to blend a near wall Reynolds averaged Navier Stokes (RANS) method with NLES used away from the wall. Blending between the two regions makes use of the Hamilton Jacobi equation. Real engines have high bypass ratio nozzles and so the flow through these is explored. Predictions are made using the hybrid RANS-NLES strategy. Different case set ups are simulated including hot and cold jets and a range of meshes from 6 x 106 to 50 x 106 cells. For all the meshes, results show encouraging agreement with measurements. The near wall RANS modelling is helpful in preventing non-physical separation from curved surfaces highlighting the usefulness of the hybrid approach. A pylon, which attaches the engine to the wing, is shown to influence the flow development, having a significant impact on peak turbulence levels and spreading rates. Wakes, simulating those shed by upstream turbomachinery, are included in the nozzle geometry. The wakes are introduced using a body force model which prevents the need to explicitly model blade geometry. The results have demonstrated that real geometry effects are particularly influential and should be taken into account when moving towards real engine simulations.
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Colon, Laetitia. "L'hybridogenèse dans le complexe Rana klepton esculenta : apports des marqueurs génétiques." Lyon 1, 2004. http://www.theses.fr/2004LYO10143.

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Cette étude porte sur le complexe hybridogénétique de la grenouille verte Rana klepton esculenta. R. Esculenta résulte d'un croisement entre R. Lessonae et R. Ridibunda. Théoriquement, à chaque méiose, chez les R. Esculenta, le génome lessonae est éliminé, et le génotype hybride est restauré par croisement avec un mâle R. Lessonae. Il y a donc transmission clonale de l'hémigénome ridibunda et formation d'hémiclones. Le déterminisme du sexe fait qu'il y a production d'autant de mâles que de femelles hybrides. Les mâles sont cependant considérés comme n'intervenant pas dans la reproduction. Contrairement à l'attendu théorique, nos études génétiques (enzymologie et microsatellites) montrent que de nombreux têtards R. Ridibunda sont produits. Ces têtards résultent manifestement de croisement entre femelles R. Esculenta et mâles R. Esculenta. Enfin, nos résultats suggèrent que les R. Ridibunda néoformés peuvent participer à la reproduction, permettant ainsi de générer de nouveaux hémiclones
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Books on the topic "Complex rank"

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Kipps, James R. The RAND compiler kit (RACK): References manual and user's guide. Santa Monica, CA: Rand, 1991.

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Bain, Raoul Harley. The elucidation of the rana livida complex. Ottawa: National Library of Canada, 1998.

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Hillis, David M. Three new species of Leopard frogs (Rana pipiens complex) from the Mexican Plateau. Lawrence, Kansas: Museum of Natural History, University of Kansas, 1985.

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1932-, Bass Hyman, and Lam, T. Y. (Tsit-Yuen), 1942-, eds. Algebra. Providence, R.I: American Mathematical Society, 2010.

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Taylor, Tristan S. Social Status, Legal Status and Legal Privilege. Edited by Paul J. du Plessis, Clifford Ando, and Kaius Tuori. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780198728689.013.27.

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The legal categories under the Roman law of persons tell us relatively little about social status. The impact of social status on law is best understood through an examination of elite views of rank and social status. Rank and social status were closely connected as these elite markers of social esteem were requirements for admission to elite ranks. Social status bore a complex relationship to legal status: possession of the legal statuses of citizenship and free birth was a prerequisite for certain ranks, which conferred social status. Legal rules helped guide the behaviour of the social elite. Social status, rather than legal status, conferred advantages in the law, both in the structure of the legal system and through the monopoly of members of the social elite over the application of the law. These advantages could be mitigated by recourse to the patronage or petitioning of an official or the emperor.
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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0001.

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This chapter assembles a few standard definitions, fixes some notation, and reviews a few of the results about buildings and Moufang polygons. It also summarizes the basic facts about Coxeter groups and buildings, including the fundamental properties of roots, residues, apartments, and projection maps. The chapter defines a Moufang building as spherical, thick, irreducible and of rank at least 2, and a Bruhat-Tits building as a thick irreducible affine building whose building at infinity is Moufang. Furthermore, it presents a fundamental result of Tits: that an irreducible thick spherical building of rank at least 3 satisfies the Moufang condition as do all the irreducible residues of rank at least 2 of such a building. Finally, it considers a simplicial complex, the dimension of which is its cardinality minus one.
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Zein, Fouad El, and Lˆe D˜ung Tr ´ang. Mixed Hodge Structures. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0003.

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This chapter discusses mixed Hodge structures (MHS). It first defines the abstract category of Hodge structures and introduces spectral sequences. The decomposition on the cohomology of Kähler manifolds is used to prove the degeneration at rank 1 of the spectral sequence defined by the filtration F on the de Rham complex in the projective nonsingular case. The chapter then introduces an abstract definition of MHS as an object of interest in linear algebra. It then attempts to develop algebraic homology techniques on filtered complexes up to filtered quasi-isomorphisms of complexes. Finally, this chapter provides the construction of the MHS on any algebraic variety.
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Ferrari, Michel, Andrew Charles, David Dodick, Fumihiko Sakai, and Joost Haan. Oxford Textbook of Headache Syndromes. Oxford University Press, 2020. http://dx.doi.org/10.1093/med/9780198724322.001.0001.

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Headache syndromes rank among the most common presenting symptoms in general practice and neurology, affecting up to 15% of the adult population. The Oxford Textbook of Headache Syndromes provides clinicians with a definitive resource for diagnosing and managing patients with primary and secondary forms of headaches, either as isolated complaints or as part of a more complex syndrome. Split into seven key sections, with 59 chapters, this comprehensive work discusses the scientific basis and practical management of headache syndromes in a logical format. Each chapter is written by international experts in neurology who share their research and extensive experience by providing a wealth of practical advice for use in clinical situations. In addition, all content is up to date and chapters incorporate discussions on the International Classification of Headache Disorders, third edition, when relevant.
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Hildebrand, Maria, and Ulf Ekelund. The assessment of physical activity. Edited by Neil Armstrong and Willem van Mechelen. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198757672.003.0021.

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Physical activity (PA) is a complex human behaviour that comprises several dimensions, including intensity, frequency, duration, type/mode, and domain. PA outcomes can be divided into two main categories: the estimation of energy expenditure, and other quantifying metrics of PA. Subjective methods, including questionnaires and diaries, are often easy to use, cost-effective and are able to assess type of PA and to rank PA levels. However, they are prone to several limitations and are not able to provide accurate estimates of PA, energy expenditure, or intensity. Objective methods, including accelerometers and heart rate monitors, provide a reasonably accurate quantification of intensity, frequency, duration, and PA energy expenditure. When choosing a method for assessing PA several factors need to be considered, including validity, reliability, accuracy, and responsiveness, as well as the purpose of the study, the population being studied, and the outcome of interest.
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Bendersky, Joseph. Schmitt’s Diaries. Edited by Jens Meierhenrich and Oliver Simons. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199916931.013.005.

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Written between 1912 and 1979, Carl Schmitt’s diaries (published and unpublished) rank among the most illuminating documentary sources of the era. This chapter argues that the published diaries have significantly transformed perceptions of his personality, motivations, and sentiments as well as of his thoughts on crucial intellectual and political questions related to 20th century Germany. Drawing extensively on these primary sources, the chapter finds a consistency between his candid private perspectives and the ideas articulated in his major publications, thereby seriously challenging several pervasive interpretations of Schmitt’s thought and work regarding cultural pessimism, political theology, the “Conservative Revolution,” and war. While documenting his antisemitism, the diaries also confirm his often intimate, complex relationships with Jews. Among other significant insights, the chapter argues, Schmitt did not seek to undermine Weimar or realize his theories in the “Third Reich.” Few documentary collections have ever required such a momentous reevaluation of a historical figure.
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Book chapters on the topic "Complex rank"

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Lubich, Christian. "Low-Rank Dynamics." In Extraction of Quantifiable Information from Complex Systems, 381–96. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08159-5_19.

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Kebekus, Stefan, Thomas Peternell, and Andrew J. Sommese. "Manifolds with Nef Rank 1 Subsheaves in Ω X 1." In Complex Geometry, 157–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56202-0_11.

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Hounie, J. "A Radó Theorem for Locally Solvable Structures of Co-rank One." In Complex Analysis, 187–203. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0009-5_11.

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Boldi, Paolo, Flavio Furia, and Sebastiano Vigna. "Spectral Rank Monotonicity on Undirected Networks." In Complex Networks & Their Applications X, 234–46. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93409-5_20.

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Oreifej, Omar, and Mubarak Shah. "Complex Event Recognition Using Constrained Rank Optimization." In Robust Subspace Estimation Using Low-Rank Optimization, 69–93. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04184-1_6.

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Slabý, Aleš. "Behaviour of Some Rank Statistics for Detecting Changes." In Measuring Risk in Complex Stochastic Systems, 161–74. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1214-0_10.

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Faraut, Jacques. "Asympotics of Spherical Functions For Large Rank: An Introduction." In Representation Theory, Complex Analysis, and Integral Geometry, 251–75. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-4817-6_10.

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Markovsky, Ivan. "Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data." In Approximation Algorithms for Complex Systems, 255–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16876-5_12.

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Below, Alexander, Vanessa Krummeck, and Jürgen Richter-Gebert. "Complex Matroids Phirotopes and Their Realizations in Rank 2." In Algorithms and Combinatorics, 203–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55566-4_9.

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Einsiedler, Manfred, and Klaus Schmidt. "Irreducibility, Homoclinic Points and Adjoint Actions of Algebraic ℤ d -Actions of Rank One." In Nonlinear Phenomena and Complex Systems, 95–124. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0345-2_4.

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Conference papers on the topic "Complex rank"

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Menon, Prathyush P., and Christopher Edwards. "Rank constrained stabilization of complex networks." In 2008 American Control Conference (ACC '08). IEEE, 2008. http://dx.doi.org/10.1109/acc.2008.4586887.

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Boushih, Beya, and Nahla Ben Amor. "Rank aggregation using active learning in meta-searching." In 2014 Second World Conference on Complex Systems (WCCS). IEEE, 2014. http://dx.doi.org/10.1109/icocs.2014.7060911.

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Su, Zhigang, Kexiang Zhang, Yingning Peng, and Renbiao Wu. "Rank-deficient APES filter for complex spectral estimation." In 2008 IEEE Radar Conference (RADAR). IEEE, 2008. http://dx.doi.org/10.1109/radar.2008.4720954.

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Mohammadi, Eman, Q. M. Jonathan Wu, and Mehrdad Saif. "Improved rank pooling strategy for complex action recognition." In 2017 IEEE International Conference on Systems, Man and Cybernetics (SMC). IEEE, 2017. http://dx.doi.org/10.1109/smc.2017.8122801.

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Schreier, P. J., and L. L. Scharf. "Low-rank approximation of improper complex random vectors." In Conference Record. Thirty-Fifth Asilomar Conference on Signals, Systems and Computers. IEEE, 2001. http://dx.doi.org/10.1109/acssc.2001.986993.

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Cui, Tianhao, Lei Chen, Jie Xu, and Lei Xu. "Robust Sparse Low-rank Hypergraph Learning under Complex Noise." In 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2020. http://dx.doi.org/10.1109/smc42975.2020.9283388.

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Celik, Murat, Ali Baran Tasdemir, and Lale Ozkahya. "Low-Rank Representations Towards Classification Problem of Complex Networks." In 2022 30th Signal Processing and Communications Applications Conference (SIU). IEEE, 2022. http://dx.doi.org/10.1109/siu55565.2022.9864691.

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Li, Chun-Hao, Yuan-Wei Du, and Yong-He Sun. "An Approach to Rank Complex Alternatives Based on Behaviors." In 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM). IEEE, 2008. http://dx.doi.org/10.1109/wicom.2008.1804.

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Pujari, M., and R. Kanawati. "Link Prediction in Complex Networks by Supervised Rank Aggregation." In 2012 IEEE 24th International Conference on Tools with Artificial Intelligence (ICTAI 2012). IEEE, 2012. http://dx.doi.org/10.1109/ictai.2012.111.

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Pujari, Manisha, and Rushed Kanawati. "Supervised rank aggregation approach for link prediction in complex networks." In the 21st international conference companion. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2187980.2188260.

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Reports on the topic "Complex rank"

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Doostan, Alireza. Early Career Award: An Enabling Computational Framework for Uncertainty Assimilation and Propagation in Complex PDE Systems: Sparse and Low-rank Techniques (Final Report). Office of Scientific and Technical Information (OSTI), May 2019. http://dx.doi.org/10.2172/1511650.

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Olefirenko, Nadiia V., Ilona I. Kostikova, Nataliia O. Ponomarova, Kateryna O. Lebedieva, Vira M. Andriievska, and Andrey V. Pikilnyak. Training elementary school teachers-to-be at Computer Science lessons to evaluate e-tools. [б. в.], July 2020. http://dx.doi.org/10.31812/123456789/3890.

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The study purpose is to develop methodological support for students’ training for evaluation e-tools for young learners and to check its effectiveness experimentally. The module “Expert evaluation of the quality of e-tools for young learners” is offered for teachers-to-be. The determination of the weighting factor of each criterion by expert evaluations was organized. Educational principles, correlation e-tool content with the curriculum, interactivity, multimedia, assistance system, ergonomic requirements are mentioned. On the basis of the criterion rank, the significance of each criterion was calculated. The indicators to determine the level of preliminary expert evaluations of e-tools are proposed. The results are calculated with nonparametric methods of mathematical statistics, in particular, Pearson’s criterion χ2. The conclusion is the expert evaluation has different activity stages, gradually becoming a common phenomenon. Training teachers-to-be for e-tool expert evaluation at Computer Science, Mathematics, English is a complex process.
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Pikilnyak, Andrey V., Nadia M. Stetsenko, Volodymyr P. Stetsenko, Tetiana V. Bondarenko, and Halyna V. Tkachuk. Comparative analysis of online dictionaries in the context of the digital transformation of education. [б. в.], June 2021. http://dx.doi.org/10.31812/123456789/4431.

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The article is devoted to a comparative analysis of popular online dictionaries and an overview of the main tools of these resources to study a language. The use of dictionaries in learning a foreign language is an important step to understanding the language. The effectiveness of this process increases with the use of online dictionaries, which have a lot of tools for improving the educational process. Based on the Alexa Internet resource it was found the most popular online dictionaries: Cambridge Dictionary, Wordreference, Merriam–Webster, Wiktionary, TheFreeDictionary, Dictionary.com, Glosbe, Collins Dictionary, Longman Dictionary, Oxford Dictionary. As a result of the deep analysis of these online dictionaries, we found out they have the next standard functions like the word explanations, transcription, audio pronounce, semantic connections, and examples of use. In propose dictionaries, we also found out the additional tools of learning foreign languages (mostly English) that can be effective. In general, we described sixteen functions of the online platforms for learning that can be useful in learning a foreign language. We have compiled a comparison table based on the next functions: machine translation, multilingualism, a video of pronunciation, an image of a word, discussion, collaborative edit, the rank of words, hints, learning tools, thesaurus, paid services, sharing content, hyperlinks in a definition, registration, lists of words, mobile version, etc. Based on the additional tools of online dictionaries we created a diagram that shows the functionality of analyzed platforms.
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Plumhans, Laure-Anne, Elke Dall, and Klaus Schuch. Study on Austrian actors, networks and activities in the field of science diplomacy. Bringing Austrian science diplomacy to the next step: Challenges, state of play and recommendations. ZSI - Centre for Social Innovation, September 2021. http://dx.doi.org/10.22163/fteval.2021.527.

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This study examines science diplomacy in Austria. ZSI was commissioned by the BMBWF between February and September 2021 to research how science diplomacy is currently understood and implemented and how the concept can be better anchored and promoted in Austria. Using literature and desktop research, an online survey, interviews and a focus group, this report answers the following key questions: how does the Austrian science diplomacy ecosystem looks like, who are its actors, what are the challenges and how could they be addressed? The complex task of presenting the current practical implementation of science diplomacy was carried out in this study in a survey that includes more than 150 actors and ranks them according to their importance in the system. Interviews with representatives of these organizations revealed that the term is well known. The actors note that they are already carrying out activities in the direction, and are also interested in intensifying this. However, there are concerns about using the term without a specific context. Accordingly, the concept is often not explicitly mentioned in institutional presentations and activities, and practices are often in other contexts. Furthermore, actors in the system are of course aware of each other, but there is no exchange on the topic of science diplomacy in particular. The corresponding (explicit) competencies and financial resources are lacking. This study also includes case studies that look at other countries' approaches: Perspectives from Japan, Finland, and Switzerland on science diplomacy are described. These and outstanding practices from other countries, as well as interviews and findings from a focus group with Austrian stakeholders, inspire five recommendations that conclude the report.
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McClenaghan, M. B., W. A. Spirito, S. J. A. Day, M. W. McCurdy, R. J. McNeil, and S. W. Adcock. Overview of Geo-mapping for Energy and Minerals program surficial geochemistry and indicator-mineral surveys and case studies in northern Canada. Natural Resources Canada/CMSS/Information Management, 2023. http://dx.doi.org/10.4095/331421.

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As part of the Geo-mapping for Energy and Minerals (GEM) program, which ran from 2008 to 2020, the Geological Survey of Canada carried out reconnaissance-scale to deposit-scale geochemical and indicator-mineral surveys and case studies across northern Canada. In these studies, geochemical methods were used to determine the concentrations of 65 elements in lake-sediment, lake-water, stream-sediment, stream-water, and till samples across approximately 1 000 000 km2 of northern Canada. State-of the-art methods were used to examine the indicator-mineral signatures identified through regional-scale stream-sediment and till surveys. As a result of this research, areas with anomalous concentrations of elements and/or indicator minerals that are indicative of bedrock mineralization were identified, new mineral exploration models and protocols were developed, a new generation of geoscientists was trained, and knowledge was transferred to northern communities. The most immediate impact of the GEM surveys has been the stimulation of mineral exploration in Canada's north, with exploration efforts being focused on high mineral-potential areas identified in GEM regional-scale surveys. Regional- and deposit-scale studies demonstrated how transport data (till geochemistry, indicator minerals) and ice-flow indicator data can be used together to identify and understand complex ice flow and glacial transport. Detailed studies at the Izok Lake, Pine Point, Strange Lake, and Kiggavik deposits, and across the Great Bear magmatic zone, demonstrate new suites of indicator minerals that can now be used in future reconnaissance- and regional-scale stream-sediment and till surveys across Canada.
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Sett, Dominic, Christina Widjaja, Patrick Sanady, Angelica Greco, Neysa Setiadi, Saut Sagala, Cut Sri Rozanna, and Simone Sandholz. Hazards, Exposure and Vulnerability in Indonesia: A risk assessment across regions and provinces to inform the development of an Adaptive Social Protection Road Map. United Nations University - Institute for Environment and Human Security, March 2022. http://dx.doi.org/10.53324/uvrd1447.

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Risk induced by natural hazards and climate change has been accelerating worldwide, leading to adverse impacts on communities' well-being. Dealing with this risk is increasingly complex and requires cross-sectoral action. Adaptive Social Protection (ASP) has emerged as a promising approach to strengthen the resilience of communities by integrating Social Protection (SP), Disaster Risk Management (DRM) and Climate Change Adaptation (CCA) efforts. To inform this integration and thereby support the development of a functional ASP approach, the identification and provision of relevant data and information are vital. In this context, risk assessments are crucial as they establish the groundwork for the design of effective ASP interventions. However, despite the importance of risk information for ASP and the abundance of sectoral assessments, there is not yet a comprehensive risk assessment approach, a reality that also applies to Indonesia. Although the country is one of the international pioneers of the concept and has enshrined ASP at the highest national level in its development plans, this emphasis in policy and practice has been hampered by the absence of more unified assessment methods. The Hazard, Exposure and Vulnerability Assessment (HEVA) presented here takes a unique approach to develop such a cross-sectoral risk assessment and apply it throughout Indonesia. The HEVA brings together different risk understandings of key actors both internationally and domestically within SP, DRM and CCA, as well as identifying commonalities across sectors to establish a joint understanding. The HEVA not only considers risk as an overarching outcome but also focuses on its drivers, i.e. hazards, exposure and vulnerability, to identify why specific communities are at risk and thus customize ASP interventions. Subsequently, risks are assessed for Indonesia’s regions and provinces based on this cross-sectoral risk understanding. Secondary data has been acquired from various existing sectoral assessments conducted in Indonesia, and in total, data for 44 indicators has been compiled to calculate hazard, exposure and vulnerability levels for all 34 Indonesian provinces. Findings of the HEVA suggest that overall risk is high in Indonesia and no single province can be characterized as a low-risk area, demonstrating a strong relevance for ASP throughout the whole of the country. Papua, Maluku, and Central Sulawesi were identified as provinces with the highest overall risk in Indonesia. However, even Yogyakarta, which was identified as a comparatively low-risk province, still ranks among the ten most hazard-prone provinces in the country and has a demonstrated history of severe impact events. This also underlines that the composition of risk based on the interplay of hazard, exposure and vulnerability differs significantly among provinces. For example, in Papua and West Papua, vulnerability ranks as the highest in Indonesia, while hazard and exposure levels are comparatively low. In contrast, East Java and Central Java are among the highest hazard-prone provinces, while exposure and vulnerability are comparatively low. The results provide much more comprehensive insight than individual sectoral analyses can offer, facilitating the strategic development and implementation of targeted ASP interventions that address the respective key risk components. Based on lessons learned from the development and application of the HEVA approach, as well as from the retrieved results, the report provides recommendations relevant for policymakers, practitioners and researchers. First, recommendations regarding risk assessments for ASP are given, emphasizing the need to bring together sectoral understandings and to consider the interconnection of hazards, exposure and vulnerability, including their drivers and root causes, to assess current and future risk. It is also recommended to complement national level assessments with more specific local assessments. Secondly, recommendations regarding ASP option development in general are provided, including the importance of considering side effects of interventions, root causes of risks, the potential of nature-based solutions and barriers to implementation due to local capacities when designing ASP interventions. Third, recommendations regarding focal areas for ASP programmes are outlined for the case of Indonesia, such as prioritizing interventions in risk hotspots and areas characterized by high readiness for ASP solutions. At the same time, it is vital to leave no region behind as all provinces face risks that potentially jeopardize communities’ well-being.
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