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Academic literature on the topic 'Matrix partitions'

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Published: 22 June 2023

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Journal articles on the topic "Matrix partitions"

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Li, Yu, Jianfeng Wu, Chunfu Lu, Zhichuan Tang, and Chengmin Li. "Pillow Support Model with Partitioned Matching Based on Body Pressure Distribution Matrix." Healthcare 9, no. 5 (May 12, 2021): 571. http://dx.doi.org/10.3390/healthcare9050571.

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(1) Objective: Sleep problems have become one of the current serious public health issues. The purpose of this research was to construct an ideal pressure distribution model for head and neck support through research on the partitioned support surface of a pillow in order to guide the development of ergonomic pillows. (2) Methods: Seven typical memory foam pillows were selected as samples, and six subjects were recruited to carry out a body pressure distribution experiment. The average value of the first 10% of the samples in the comfort evaluation was calculated to obtain the relative ideal body pressure distribution matrix. Fuzzy clustering was performed on the ideal matrix to obtain the support surface partition. The ideal body pressure index of each partition was calculated, and a hierarchical analysis of each partition was then performed to determine the pressure sensitivity weight of each partition. Using these approaches, the key ergonomic node coordinates of the partitions of four different groups of people were extracted. The ergonomic node coordinates and the physical characteristics of the material were used to design a pillow prototype. Five subjects were recruited for each of the four groups to repeat the body pressure distribution experiment to evaluate the pillow prototype. (3) Results: An ideal support model with seven partitions, including three partitions in the supine position and four partitions in the lateral position, was constructed. The ideal body pressure distribution matrix and ideal body pressure indicators and pressure sensitivity weights for each partition were provided. The pillow that was designed and manufactured based on this model reproduced the ideal pressure distribution matrix evaluated by various groups of people. (4) Conclusion: The seven-partition ideal support model can effectively describe the head and neck support requirements of supine and lateral positions, which can provide strong support for the development of related products.
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Adm, Mohammad, Shaun Fallat, Karen Meagher, Shahla Nasserasr, Sarah Plosker, and Boting Yang. "Achievable multiplicity partitions in the inverse eigenvalue problem of a graph." Special Matrices 7, no. 1 (January 1, 2019): 276–90. http://dx.doi.org/10.1515/spma-2019-0022.

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Abstract Associated to a graph G is a set 𝒮(G) of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are free to be chosen. If G has n vertices, then the multiplicities of the eigenvalues of any matrix in 𝒮 (G) partition n; this is called a multiplicity partition. We study graphs for which a multiplicity partition with only two integers is possible. The graphs G for which there is a matrix in 𝒮 (G) with partitions [n − 2, 2] have been characterized. We find families of graphs G for which there is a matrix in 𝒮 (G) with multiplicity partition [n − k, k] for k ≥ 2. We focus on generalizations of the complete multipartite graphs. We provide some methods to construct families of graphs with given multiplicity partitions starting from smaller such graphs. We also give constructions for graphs with matrix in 𝒮 (G) with multiplicity partition [n − k, k] to show the complexities of characterizing these graphs.
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Alexandrov, A. "Matrix models for random partitions." Nuclear Physics B 851, no. 3 (October 2011): 620–50. http://dx.doi.org/10.1016/j.nuclphysb.2011.06.007.

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Feder, Tomás, and Pavol Hell. "Matrix partitions of perfect graphs." Discrete Mathematics 306, no. 19-20 (October 2006): 2450–60. http://dx.doi.org/10.1016/j.disc.2005.12.035.

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Feder, Tomás, Pavol Hell, and Oren Shklarsky. "Matrix partitions of split graphs." Discrete Applied Mathematics 166 (March 2014): 91–96. http://dx.doi.org/10.1016/j.dam.2013.10.016.

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Chen, Ji Wen, Jin Sheng Zhang, Zhi Wang, and Jing Kun Wang. "Function Module Dynamic Partition for Product Innovation Design." Applied Mechanics and Materials 58-60 (June 2011): 2095–100. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.2095.

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The reasonable functional modules partition is crucial to technical solution of function in product innovation design. Technical evolution factors are not considered in current product module partition method. The correlation of customer demand and product function unit, function unit flow correlation and function technology correlation are synthesized for function module partition in product innovation design. Based on function base expression, function chain and function structure is established to provide basis of function correlation analysis. Function correlation matrix is established by combining the correlation matrix of customer demand and product function unit, the function unit flow correlation matrix and function technology correlation matrix. The dynamic cluster analysis of fuzzy equivalence matrix is used to form function module. The function module partitions are evaluated by polymerization degree and coupling degree. The presented dynamic module partition method has strong distinguishing ability.
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Li, Yimeng, Marcello Ruta, and Matthew A. Wills. "Craniodental and Postcranial Characters of Non-Avian Dinosauria Often Imply Different Trees." Systematic Biology 69, no. 4 (November 26, 2019): 638–59. http://dx.doi.org/10.1093/sysbio/syz077.

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Abstract Despite the increasing importance of molecular sequence data, morphology still makes an important contribution to resolving the phylogeny of many groups, and is the only source of data for most fossils. Most systematists sample morphological characters as broadly as possible on the principle of total evidence. However, it is not uncommon for sampling to be focused on particular aspects of anatomy, either because characters therein are believed to be more informative, or because preservation biases restrict what is available. Empirically, the optimal trees from partitions of morphological data sets often represent significantly different hypotheses of relationships. Previous work on hard-part versus soft-part characters across animal phyla revealed significant differences in about a half of sampled studies. Similarly, studies of the craniodental versus postcranial characters of vertebrates revealed significantly different trees in about one-third of cases, with the highest rates observed in non-avian dinosaurs. We test whether this is a generality here with a much larger sample of 81 published data matrices across all major dinosaur groups. Using the incongruence length difference test and two variants of the incongruence relationship difference test, we found significant incongruence in about 50% of cases. Incongruence is not uniformly distributed across major dinosaur clades, being highest (63%) in Theropoda and lowest (25%) in Thyreophora. As in previous studies, our partition tests show some sensitivity to matrix dimensions and the amount and distribution of missing entries. Levels of homoplasy and retained synapomorphy are similar between partitions, such that incongruence must partly reflect differences in patterns of homoplasy between partitions, which may itself be a function of modularity and mosaic evolution. Finally, we implement new tests to determine which partition yields trees most similar to those from the entire matrix. Despite no bias across dinosaurs overall, there are striking differences between major groups. The craniodental characters of Ornithischia and the postcranial characters of Saurischia yield trees most similar to the “total evidence” trees derived from the entire matrix. Trees from these same character partitions also tend to be most stratigraphically congruent: a mutual consilience suggesting that those partitions yield more accurate trees. [Dinosauria; homoplasy; partition homogeneity.]
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Göbel, Andreas, Leslie Ann Goldberg, Colin McQuillan, David Richerby, and Tomoyuki Yamakami. "Counting List Matrix Partitions of Graphs." SIAM Journal on Computing 44, no. 4 (January 2015): 1089–118. http://dx.doi.org/10.1137/140963029.

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Eynard, B. "A matrix model for plane partitions." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 10 (October 15, 2009): P10011. http://dx.doi.org/10.1088/1742-5468/2009/10/p10011.

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Strahov, Eugene. "Matrix Kernels for Measures on Partitions." Journal of Statistical Physics 133, no. 5 (November 11, 2008): 899–919. http://dx.doi.org/10.1007/s10955-008-9641-9.

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Dissertations / Theses on the topic "Matrix partitions"

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Bagatini, Alessandro. "Matrix representation for partitions and Mock Theta functions." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/150232.

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Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem.
In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.
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Quéré, Romain. "Quelques propositions pour la comparaison de partitions non strictes." Phd thesis, Université de La Rochelle, 2012. http://tel.archives-ouvertes.fr/tel-00950514.

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Cette thèse est consacrée au problème de la comparaison de deux partitions non strictes (floues/probabilistes, possibilistes) d'un même ensemble d'individus en plusieurs clusters. Sa résolution repose sur la définition formelle de mesures de concordance reprenant les principes des mesures historiques développées pour la comparaison de partitions strictes et trouve son application dans des domaines variés tels que la biologie, le traitement d'images, la classification automatique. Selon qu'elles s'attachent à observer les relations entre les individus décrites par chacune des partitions ou à quantifier les similitudes entre les clusters qui composent ces partitions, nous distinguons deux grandes familles de mesures pour lesquelles la notion même d'accord entre partitions diffère, et proposons d'en caractériser les représentants selon un même ensemble de propriétés formelles et informelles. De ce point de vue, les mesures sont aussi qualifiées selon la nature des partitions comparées. Une étude des multiples constructions sur lesquelles reposent les mesures de la littérature vient compléter notre taxonomie. Nous proposons trois nouvelles mesures de comparaison non strictes tirant profit de l'état de l'art. La première est une extension d'une approche stricte tandis que les deux autres reposent sur des approches dite natives, l'une orientée individus, l'autre orientée clusters, spécifiquement conçues pour la comparaison de partitions non strictes. Nos propositions sont comparées à celles de la littérature selon un plan d'expérience choisi pour couvrir les divers aspects de la problématique. Les résultats présentés montrent l'intérêt des propositions pour le thème de recherche qu'est la comparaison de partitions. Enfin, nous ouvrons de nouvelles perspectives en proposant les prémisses d'un cadre qui unifie les principales mesures non strictes orientées individus.
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Matte, Marília Luiza. "Matrix representations for integer partitions : some consequences and a new approach." Universidade Federal do Rio Grande do Sul, 2018. http://hdl.handle.net/10183/178603.

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O presente trabalho dedica-se ao estudo de algumas consequências da representação matricial para conjuntos de partições de inteiros e funções mock theta. Na primeira parte do texto, classificamos as partições geradas por seis diferentes funções mock theta, de acordo com a soma das entradas da segunda linha das matrizes associadas, e apresentamos algumas fórmulas fechadas e identidades para essas partições. De nimos também a família ffm (q)gm 1 de funções mock theta, inspiradas pelo que chamamos de versão sem sinal da função f1(q). Fornecemos uma representação matricial análoga para as funções fm (q), o que leva a resultados interessantes a respeito das partições geradas por elas. A parte II do texto trata de uma nova abordagem que gera um conjunto diferente de partições de inteiros. A definição desse conjunto baseia-se na construção de um caminho sobre o reticulado Z2, determinado pela representao matricial para diferentes conjuntos de partições de n, e que liga a reta x + y = n a origem. As novas partições possuem apenas partes mpares distintas, com algumas restições particulares. Esse processo de construção de novas partições, chamado de Path Procedure, e aplicado a partições irrestritas, bem como para partições contadas pelas 1a e 2a Identidades de Rogers-Ramanujan e funções mock theta f5 (q) e T1(q).
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Bas, Erdeniz Ozgun. "Load-Balancing Spatially Located Computations using Rectangular Partitions." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306909831.

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Bellissimo, Michael Robert. "A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649.

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Barsukov, Alexey. "On dichotomy above Feder and Vardi's logic." Electronic Thesis or Diss., Université Clermont Auvergne (2021-...), 2022. https://tel.archives-ouvertes.fr/tel-04100704.

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On dit d'un sous-ensemble de NP qu'il présente une dichotomie s'il contient des problèmes qui sont soit résolubles en temps polynomial (dans Ptime), soit difficiles (NP-complets). La classe des problèmes de satisfaction de contraintes (CSP) finis est un sous-ensemble bien connu de NP qui présente une telle dichotomie. La classe de complexité NP n'a pas de dichotomie à moins que P = NP. Pour ces deux classes, il existe des logiques qui leur sont associées. -- NP est capturé par la logique Existentielle du second ordre (ESO) par le théorème de Fagin, c'est-à-dire qu'un problème est dans NP si et seulement s'il est exprimable par une formule ESO.-- CSP est un sous-ensemble de la logique de Feder et Vardi, le fragment monotone, monadique et sans inégalités de SNP, lui-même un fragment syntaxique de ESO (MMSNP); et, pour chaque formule de MMSNP, il existe un problème CSP équivalent via des réductions polynomiales.Ceci implique que la logique ESO, tout comme NP, n'a pas de dichotomie, à contraster avec le fait que MMSNP a une dichotomie tout comme CSP. L'objectif principal de cette thèse est d'étudier les propriétés de dichotomie de sous-ensembles de NP qui contiennent strictement CSP ou MMSNP.Feder et Vardi ont prouvé que si nous omettons une des trois propriétés qui définissent MMSNP, à savoir être monotone, monadique ou omettre les inégalités, alors la logique résultante n'a pas de dichotomie. Comme leurs preuves restent parfois sommaires, nous revisitons ces résultats et fournissons des preuves détaillées. Le fragment guardé et monotone de SNP (GMSNP) est une extension connue de MMSNP qui est obtenue en relâchant la restriction "monadique" de MMSNP. Nous définissons de manière similaire une nouvelle logique appelée MMSNP avec des inégalités gardées, en relâchant la restriction d'être "sans inégalités". Nous prouvons qu'elle est strictement plus expressive que MMSNP et qu'elle possède également une dichotomie.Il existe une logique MMSNP₂ qui étend MMSNP de la même manière que MSO₂ étend la logique monadique du second ordre (MSO). On sait que MMSNP₂ est un fragment de GMSNP et que ces deux classes ont toutes deux une dichotomie ou n'en ont pas. Nous revisitons ce résultat et le renforçons en prouvant que, en ce qui concerne le fait d'avoir une dichotomie, sans perte de généralité, on peut considérer seulement les problèmes MMSNP₂ sur des signatures à un élément, au lieu des problèmes GMSNP sur des signatures finies arbitraires.Nous cherchons à prouver l'existence d'une dichotomie pour les MMSNP₂ en construisant en temps polynomial, pour tout problème MMSNP₂, un problème MMSNP équivalent. Nous rencontrons quelques obstacles pour construire une telle équivalence. Cependant, si nous permettons aux formules MMSNP d'être composées d'un nombre dénombrable de conjonctions négatives, nous prouvons qu'une telle équivalence existe. De plus, la formule MMSNP infinie correspondante a la propriété d'être "régulière". Cette propriété de régularité signifie que, dans un certain sens, cette formule est essentiellement finie. Il est connu que les problèmes MMSNP réguliers peuvent être exprimés par CSP sur des modèles oméga-catégoriques. De plus, il existe une caractérisation de la dichotomie algébrique pour les CSP oméga-catégoriques qui décrivent des problèmes MMSNP. Si l'on parvient à étendre cette caractérisation algébrique sur les problèmes réguliers MMSNP, alors notre résultat fournirait une dichotomie algébrique pour MMSNP₂. (...)
A subset of NP is said to have a dichotomy if it contains problem that are either solvable in P-time or NP-complete. The class of finite Constraint Satisfaction Problems (CSP) is a well-known subset of NP that follows such a dichotomy. The complexity class NP does not have a dichotomy unless P = NP. For both of these classes there exist logics that are associated with them. -- NP is captured by Existential Second-Order (ESO) logic by Fagin's theorem, i.e., a problem is in NP if and only if it is expressible by an ESO sentence.-- CSP is a subset of Feder and Vardi's logic, Monotone Monadic Strict NP without inequalities (MMSNP), and for every MMSNP sentence there exists a P-time equivalent CSP problem. This implies that ESO does not have a dichotomy as well as NP, and that MMSNP has a dichotomy as well as CSP. The main objective of this thesis is to study subsets of NP that strictly contain CSP or MMSNP with respect to the dichotomy existence.Feder and Vardi proved that if we omit one of the three properties that define MMSNP, namely being monotone, monadic or omitting inequalities, then the resulting logic does not have a dichotomy. As their proofs remain sketchy at times, we revisit these results and provide detailed proofs. Guarded Monotone Strict NP (GMSNP) is a known extension of MMSNP that is obtained by relaxing the "monadic" restriction of MMSNP. We define similarly a new logic that is called MMSNP with Guarded inequalities, relaxing the restriction of being "without inequalities". We prove that it is strictly more expressive than MMSNP and that it also has a dichotomy.There is a logic MMSNP₂ that extends MMSNP in the same way as MSO₂ extends Monadic Second-Order (MSO) logic. It is known that MMSNP₂ is a fragment of GMSNP and that these two classes either both have a dichotomy or both have not. We revisit this result and strengthen it by proving that, with respect to having a dichotomy, without loss of generality, one can consider only MMSNP₂ problems over one-element signatures, instead of GMSNP problems over arbitrary finite signatures.We seek to prove the existence of a dichotomy for MMSNP₂ by finding, for every MMSNP₂ problem, a P-time equivalent MMSNP problem. We face some obstacles to build such an equivalence. However, if we allow MMSNP sentences to consist of countably many negated conjuncts, then we prove that such an equivalence exists. Moreover, the corresponding infinite MMSNP sentence has a property of being "regular". This regular property means that, in some sense, this sentence is still finite. It is known that regular MMSNP problems can be expressed by CSP on omega-categorical templates. Also, there is an algebraic dichotomy characterisation for omega-categorical CSPs that describe MMSNP problems. If one manages to extend this algebraic characterisation onto regular MMSNP, then our result would provide an algebraic dichotomy for MMSNP₂.Another potential way to prove the existence of a dichotomy for MMSNP₂ is to mimic the proof of Feder and Vardi for MMSNP. That is, by finding a P-time equivalent CSP problem. The most difficult part there is to reduce a given input structure to a structure of sufficiently large girth. For MMSNP and CSP, it is done using expanders, i.e., structures, where the distribution of tuples is close to a uniform distribution. We study this approach with respect to MMSNP₂ and point out the main obstacles. (...)
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Acosta, Jaramillo Enrique. "Leading Order Asymptotics of a Multi-Matrix Partition Function for Colored Triangulations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293410.

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We study the leading order asymptotics of a Random Matrix theory partition function related to colored triangulations. This partition function comes from a three Hermitian matrix model that has been introduced in the physics literature. We provide a detailed and precise description of the combinatorial objects that the partition function counts that has not appeared previously in the literature. We also provide a general framework for studying the leading order asymptotics of an N dimensional integral that one encounters studying the partition function of colored triangulations. The results are obtained by generalizing well know results for integrals coming from Hermitian matrix models with only one matrix that give the leading order asymptiotics in terms of a finite dimensional variational problem. We apply these results to the partition function for colored triangulations to show that the minimizing density of the variational problem is unique, and agrees with the one proposed in the physics literature. This provides the first complete mathematically rigorous description of the leading order asymptotics of this matrix model for colored triangulations.
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Shahzad, Yasser. "Micellar chromatographic partition coefficients and their application in predicting skin permeability." Thesis, University of Huddersfield, 2013. http://eprints.hud.ac.uk/id/eprint/23480/.

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The major goal for physicochemical screening of pharmaceuticals is to predict human drug absorption, distribution, elimination, excretion and toxicity. These are all dependent on the lipophilicity of the drug, which is expressed as a partition coefficient i.e. a measure of a drug’s preference for the lipophilic or hydrophilic phases. The most common method of determining a partition coefficient is the shake flask method using octanol and water as partitioning media. However, this system has many limitations when modeling the interaction of ionised compounds with membranes, therefore, unreliable partitioning data for many solutes has been reported. In addition to these concerns, the procedure is tedious and time consuming and requires a high level of solute and solvent purity. Micellar liquid chromatography (MLC) has been proposed as an alternative technique for measuring partition coefficients utilising surfactant aggregates, known as micelles. This thesis investigates the application of MLC in determining micelle-water partition coefficients (logPMW) of pharmaceutical compounds of varying physicochemical properties. The effect of mobile phase pH and column temperature on the partitioning of compounds was evaluated. Results revealed that partitioning of drugs solely into the micellar core was influenced by the interaction of charged and neutral species with the surface of the micelle. Furthermore, the pH of the mobile phase significantly influenced the partitioning behaviour and a good correlation of logPMW was observed with calculated distribution coefficient (logD) values. More interestingly, a significant change in partitioning was observed near the dissociation constant of each drug indicating an influence of ionised species on the association with the micelle and retention on the stationary phase. Elevated column temperatures confirmed partitioning of drugs considered in this study was enthalpically driven with a small change in the entropy of the system because of the change in the nature of hydrogen bonding. Finally, a quantitative structure property relationship was developed to evaluate biological relevance in terms of predicting skin permeability of the newly developed partition coefficient values. This study provides a better surrogate for predicting skin permeability based on an easy, fast and cheap experimental methodology, and the method holds the predictive capability for a wider population of drugs. In summary, it can be concluded that MLC has the ability to generate partition coefficient values in a shorter time with higher accuracy, and has the potential to replace the octanol-water system for pharmaceutical compounds.
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Thüne, Mario. "Eigenvalues of Matrices and Graphs." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-120713.

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The interplay between spectrum and structure of graphs is the recurring theme of the three more or less independent chapters of this thesis. The first chapter provides a method to relate the eigensolutions of two matrices, one being the principal submatrix of the other, via an arbitrary annihilating polynomial. This is extended to lambda-matrices and to matrices the entries of which are rational functions in one variable. The extension may be interpreted as a possible generalization of other known techniques which aim at reducing the size of a matrix while preserving the spectral information. Several aspects of an application in order to reduce the computational costs of ordinary eigenvalue problems are discussed. The second chapter considers the straightforward extension of the well known concept of equitable partitions to weighted graphs, i.e. complex matrices. It provides a method to divide the eigenproblem into smaller parts corresponding to the front divisor and its complementary factor in an easy and stable way with complexity which is only quadratic in matrix size. The exploitation of several equitable partitions ordered by refinement is discussed and a suggestion is made that preserves hermiticity if present. Some generalizations of equitable partitions are considered and a basic procedure for finding an equitable partition of complex matrices is given. The third chapter deals with isospectral and unitary equivalent graphs. It introduces a construction for unitary equivalent graphs which contains the well known GM-switching as a special case. It also considers an algebra of graph matrices generated by the adjacency matrix that corresponds to the 1-dimensional Weisfeiler-Lehman stabilizer in a way that mimics the correspondence of the coherent closure and the 2-dimensional Weisfeiler-Lehman stabilizer. The algebra contains the degree matrix, the (combinatorial, signless and normalized) Laplacian and the Seidel matrix. An easy construction produces graph pairs that are simultaneously unitary equivalent w.r.t. that algebra.
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Young, Barrington R. St A. "Efficient Algorithms for Data Mining with Federated Databases." University of Cincinnati / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1179332091.

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Books on the topic "Matrix partitions"

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Claudio, Procesi, ed. Topics in hyperplane arrangements, polytopes and box-splines. New York: Springer, 2011.

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Keating, Jon, and Nina Snaith. Random permutations and related topics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.25.

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This article considers some topics in random permutations and random partitions highlighting analogies with random matrix theory (RMT). An ensemble of random permutations is determined by a probability distribution on Sn, the set of permutations of [n] := {1, 2, . . . , n}. In many ways, the symmetric group Sn is linked to classical matrix groups. Ensembles of random permutations should be given the same treatment as random matrix ensembles, such as the ensembles of classical compact groups and symmetric spaces of compact type with normalized invariant measure. The article first describes the Ewens measures, virtual permutations, and the Poisson-Dirichlet distributions before discussing results related to the Plancherel measure on the set of equivalence classes of irreducible representations of Sn and its consecutive generalizations: the z-measures and the Schur measures.
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Concini, Corrado De, and Claudio Procesi. Topics in Hyperplane Arrangements, Polytopes and Box-Splines. Springer London, Limited, 2010.

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Guhr, Thomas. Replica approach in random matrix theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.8.

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This article examines the replica method in random matrix theory (RMT), with particular emphasis on recently discovered integrability of zero-dimensional replica field theories. It first provides an overview of both fermionic and bosonic versions of the replica limit, along with its trickery, before discussing early heuristic treatments of zero-dimensional replica field theories, with the goal of advocating an exact approach to replicas. The latter is presented in two elaborations: by viewing the β = 2 replica partition function as the Toda lattice and by embedding the replica partition function into a more general theory of τ functions. The density of eigenvalues in the Gaussian Unitary Ensemble (GUE) and the saddle point approach to replica field theories are also considered. The article concludes by describing an integrable theory of replicas that offers an alternative way of treating replica partition functions.
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Marino, Marcos. Quantum chromodynamics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.32.

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This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.
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Book chapters on the topic "Matrix partitions"

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Abed, Fidaa, Ioannis Caragiannis, and Alexandros A. Voudouris. "Near-Optimal Asymmetric Binary Matrix Partitions." In Mathematical Foundations of Computer Science 2015, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48054-0_1.

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Brietzke, Eduardo H. M., José Plínio O. Santos, and Robson da Silva. "Bijective proofs using two-line matrix representations for partitions." In Combinatory Analysis, 263–93. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7858-4_17.

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Birk, David E., and Robert L. Trelstad. "Metazoan Mesenchyme Partitions the Extracellular Space During Matrix Morphogenesis." In Biology of Invertebrate and Lower Vertebrate Collagens, 103–14. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4684-7636-1_9.

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Hackbusch, Wolfgang. "Matrix Partition." In Hierarchical Matrices: Algorithms and Analysis, 83–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47324-5_5.

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Harville, David A. "Submatrices and Partitioned Matrices." In Matrix Algebra: Exercises and Solutions, 7–10. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0181-3_2.

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Alon, Noga, Michal Feldman, Iftah Gamzu, and Moshe Tennenholtz. "The Asymmetric Matrix Partition Problem." In Web and Internet Economics, 1–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45046-4_1.

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Harville, David A. "Submatrices and Partitioned Matrices." In Matrix Algebra From a Statistician’s Perspective, 13–22. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/0-387-22677-x_2.

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Kuang, Da, Jaegul Choo, and Haesun Park. "Nonnegative Matrix Factorization for Interactive Topic Modeling and Document Clustering." In Partitional Clustering Algorithms, 215–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09259-1_7.

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Puntanen, Simo, George P. H. Styan, and Jarkko Isotalo. "Nonnegative Definiteness of a Partitioned Matrix." In Matrix Tricks for Linear Statistical Models, 305–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10473-2_15.

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Puntanen, Simo, George P. H. Styan, and Jarkko Isotalo. "Rank of the Partitioned Matrix and the Matrix Product." In Matrix Tricks for Linear Statistical Models, 121–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10473-2_6.

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Conference papers on the topic "Matrix partitions"

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Kang, Zhao, Zipeng Guo, Shudong Huang, Siying Wang, Wenyu Chen, Yuanzhang Su, and Zenglin Xu. "Multiple Partitions Aligned Clustering." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/375.

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Multi-view clustering is an important yet challenging task due to the difficulty of integrating the information from multiple representations. Most existing multi-view clustering methods explore the heterogeneous information in the space where the data points lie. Such common practice may cause significant information loss because of unavoidable noise or inconsistency among views. Since different views admit the same cluster structure, the natural space should be all partitions. Orthogonal to existing techniques, in this paper, we propose to leverage the multi-view information by fusing partitions. Specifically, we align each partition to form a consensus cluster indicator matrix through a distinct rotation matrix. Moreover, a weight is assigned for each view to account for the clustering capacity differences of views. Finally, the basic partitions, weights, and consensus clustering are jointly learned in a unified framework. We demonstrate the effectiveness of our approach on several real datasets, where significant improvement is found over other state-of-the-art multi-view clustering methods.
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Sankhavara, C. D., and H. J. Shukla. "Influence of Partition Location on Natural Convection in a Partitioned Enclosure." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72093.

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In this study, Natural convection heat transfer and fluid flow of square partitioned enclosure with two partitions protruding centrally from the end walls of an enclosure have been analysed numerically using finite element method. The enclosure has opposite isothermal walls at different temperatures. The thickness and length of the partitions is fixed and equal to 1/10 and 1/4 of width of the enclosure respectively. Computation for Rayleigh number in the range of 104 to 106 has been conducted. The influence of different thermal boundary conditions at the end walls and at the partitions is included in the investigation. ‘Standard’ boundary conditions are introduced as more appropriate to simulate situations of practical engineering interest. To solve the relevant governing equations a segregated sequential solution algorithm is used after employing Boussinesq approximation. These equations after discretization were solved by using the tridiagonal matrix algorithm. Results clearly demonstrate that partition location has a significant effect on heat transfer.
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Gobel, Andreas, Leslie Ann Goldberg, Colin McQuillan, David Richerby, and Tomoyuki Yamakami. "Counting List Matrix Partitions of Graphs." In 2014 IEEE Conference on Computational Complexity (CCC). IEEE, 2014. http://dx.doi.org/10.1109/ccc.2014.14.

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Patton, Stephen, Hamidreza Khaleghzadeh, Ravi Reddy Manumachu, and Alexey Lastovetsky. "SummaGen: Parallel Matrix-Matrix Multiplication Based on Non-rectangular Partitions for Heterogeneous HPC Platforms." In 2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). IEEE, 2019. http://dx.doi.org/10.1109/ipdpsw.2019.00017.

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Derrico, Joel B., and Gershon Buchsbaum. "Image compression application of a simultaneous Karhunen-Loeve transformation in space and color." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.fc3.

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Most color image coding techniques transform the primary color vectors, at each pixel, independently of their spatial arrangement. Since the spatial and chromatic dimensions of natural color images are not independent, efficient coding requires elimination of both spatial and chromatic correlation across chromatic bands. Global spatiochromatic decorrelation has not been utilized because of its enormous computational load.1 A more feasible local approach is presented which partitions a large image into subimages, where the computational load is reasonable. The subimages are transformed using the most significant eigenvectors generated by diagonalizing a model subimage covariance matrix found empirically by averaging subimage covariance matrices in a natural color image. These eigenvectors generate transformation masks that separate space and color information and form color image basis functions similar to mechanisms in the visual system. The masks are (i) achromatic, spatially oriented passing high spatial frequencies and (ii) color opponent, unoriented passing low spatial frequencies. By utilizing the cross correlation between space and color, this method achieves a high compression ratio (16:1) with good quality reconstruction without elaborate quantization techniques or variable word length coding.
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Qiu, Chen, and Jian S. Dai. "Constraint Stiffness Construction and Decomposition of a SPS Orthogonal Parallel Mechanism." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46811.

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This paper investigates both stiffness analysis and synthesis problems using a physical prototype of one SPS orthogonal parallel mechanism. This parallel mechanism is supported with line-type constraint limbs. In the stiffness analysis, a reciprocal relationship between motions and wrenches is used to design layouts of constraint limbs and construct the corresponding stiffness matrix. In the stiffness synthesis, the developed stiffness matrix is decomposed to obtain configurations of constraint limbs based on existing synthesis algorithms, including direct-recursion and matrix-partition approaches. It is revealed the line-vector based matrix-partition approach can establish an one-to-one correspondence between synthesized results and constraint limbs of the parallel mechanism. Subsequently both types of synthesis approaches are applied to decomposing the developed constraint stiffness matrix. The comparison results suggest the modified matrix-partition approach can obtain decomposed constraint limbs exactly the same as those used to construct the stiffness matrix.
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Fabregat-Traver, Diego, Paolo Bientinesi, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Automatic Generation of Partitioned Matrix Expressions for Matrix Operations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498598.

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Sugino, Fumihiko. "U-duality from matrix membrane partition function." In STRING THEORY; 10th Tohwa University International Symposium on String Theory. AIP, 2002. http://dx.doi.org/10.1063/1.1454380.

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Chou, Chiu-Chih, Thong Nguyen, and Jose E. Schutt-Aine. "Impact of Partition Schemes in Loewner Matrix Macromodeling." In 2020 IEEE Electrical Design of Advanced Packaging and Systems (EDAPS). IEEE, 2020. http://dx.doi.org/10.1109/edaps50281.2020.9312918.

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Adi, Prajanto Wahyu, and Pramudi Arsiwi. "Fast and Robust Watermarking Method using Walsh Matrix Partition." In 2019 International Seminar on Research of Information Technology and Intelligent Systems (ISRITI). IEEE, 2019. http://dx.doi.org/10.1109/isriti48646.2019.9034627.

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Reports on the topic "Matrix partitions"

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Brenan, J. M., K. Woods, J. E. Mungall, and R. Weston. Origin of chromitites in the Esker Intrusive Complex, Ring of Fire Intrusive Suite, as revealed by chromite trace element chemistry and simple crystallization models. Natural Resources Canada/CMSS/Information Management, 2021. http://dx.doi.org/10.4095/328981.

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To better constrain the origin of the chromitites associated with the Esker Intrusive Complex (EIC) of the Ring of Fire Intrusive Suite (RoFIS), a total of 50 chromite-bearing samples from the Black Thor, Big Daddy, Blackbird, and Black Label chromite deposits have been analysed for major and trace elements. The samples represent three textural groups, as defined by the relative abundance of cumulate silicate phases and chromite. To provide deposit-specific partition coefficients for modeling, we also report on the results of laboratory experiments to measure olivine- and chromite-melt partitioning of V and Ga, which are two elements readily detectable in the chromites analysed. Comparison of the Cr/Cr+Al and Fe/Fe+Mg of the EIC chromites and compositions from previous experimental studies indicates overlap in Cr/Cr+Al between the natural samples and experiments done at >1400oC, but significant offset of the natural samples to higher Fe/Fe+Mg. This is interpreted to be the result of subsolidus Fe-Mg exchange between chromite and the silicate matrix. However, little change in Cr/Cr+Al from magmatic values, owing to the lack of an exchangeable reservoir for these elements. A comparison of the composition of the EIC chromites and a subset of samples from other tectonic settings reveals a strong similarity to chromites from the similarly-aged Munro Township komatiites. Partition coefficients for V and Ga are consistent with past results in that both elements are compatible in chromite (DV = 2-4; DGa ~ 3), and incompatible in olivine (DV = 0.01-0.14; DGa ~ 0.02), with values for V increasing with decreasing fO2. Simple fractional crystallization models that use these partition coefficients are developed that monitor the change in element behaviour based on the relative proportions of olivine to chromite in the crystallizing assemblage; from 'normal' cotectic proportions involving predominantly olivine, to chromite-only crystallization. Comparison of models to the natural chromite V-Ga array suggests that the overall positive correlation between these two elements is consistent with chromite formed from a Munro Township-like komatiitic magma crystallizing olivine and chromite in 'normal' cotectic proportions, with no evidence of the strong depletion in these elements expected for chromite-only crystallization. The V-Ga array can be explained if the initial magma responsible for chromite formation is slightly reduced with respect to the FMQ oxygen buffer (~FMQ- 0.5), and has assimilated up to ~20% of wall-rock banded iron formation or granodiorite. Despite the evidence for contamination, results indicate that the EIC chromitites crystallized from 'normal' cotectic proportions of olivine to chromite, and therefore no specific causative link is made between contamination and chromitite formation. Instead, the development of near- monomineralic chromite layers likely involves the preferential removal of olivine relative to chromite by physical segregation during magma flow. As suggested for some other chromitite-forming systems, the specific fluid dynamic regime during magma emplacement may therefore be responsible for crystal sorting and chromite accumulation.
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