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Journal articles on the topic 'Matrix partitions'

Author: Grafiati

Published: 22 June 2023

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1

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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4

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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5

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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6

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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7

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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9

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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10

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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11

Feder, Tomás, Pavol Hell, Sulamita Klein, Loana Tito Nogueira, and Fábio Protti. "List matrix partitions of chordal graphs." Theoretical Computer Science 349, no. 1 (December 2005): 52–66. http://dx.doi.org/10.1016/j.tcs.2005.09.030.

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12

Abed, Fidaa, Ioannis Caragiannis, and Alexandros A. Voudouris. "Near-Optimal Asymmetric Binary Matrix Partitions." Algorithmica 80, no. 1 (November 2, 2016): 48–72. http://dx.doi.org/10.1007/s00453-016-0238-4.

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13

Feder, Tomás, Pavol Hell, and Kim Tucker-Nally. "Digraph matrix partitions and trigraph homomorphisms." Discrete Applied Mathematics 154, no. 17 (November 2006): 2458–69. http://dx.doi.org/10.1016/j.dam.2006.02.009.

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Feder, Tomás, Pavol Hell, and Wing Xie. "Matrix Partitions with Finitely Many Obstructions." Electronic Notes in Discrete Mathematics 28 (March 2007): 371–78. http://dx.doi.org/10.1016/j.endm.2007.01.057.

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15

Joshi, Prajakta Bharat, and Mayamma Joseph. "𝒫-energy of graphs." Acta Universitatis Sapientiae, Informatica 12, no. 1 (July 1, 2020): 137–57. http://dx.doi.org/10.2478/ausi-2020-0009.

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AbstractGiven a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.

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16

Walker, Grant. "Horizontal partitions and Kleshchev's algorithm." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 1 (July 1996): 55–60. http://dx.doi.org/10.1017/s0305004100074661.

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We shall work with rational Mn(K)-modules, where K is an infinite field of prime characteristic p > 0, and Mn(K) is the full matrix semigroup of n × n matrices over K. Recall that equivalence classes of simple rational Mn(K)-modules are parametrized by the set of all partitions λ = (λ1, λ2, …, λl) of length l = l(λ) ≤ n, and that the socle L(λ) of the Schur module (or dual Weyl module) H0(λ) is a simple Mn(K)-module whose highest weight corresponds to the partition λ.

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17

Kong, Xu. "A concise proof to the spectral and nuclear norm bounds through tensor partitions." Open Mathematics 17, no. 1 (May 16, 2019): 365–73. http://dx.doi.org/10.1515/math-2019-0028.

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Abstract On estimations of the lower and upper bounds for the spectral and nuclear norm of a tensor, Li established neat bounds for the two norms based on regular tensor partitions, and proposed a conjecture for the same bounds to be hold based on general tensor partitions [Z. Li, Bounds on the spectral norm and the nuclear norm of a tensor based on tensor partition, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1440-1452]. Later, Chen and Li provided a solution to the conjecture [Chen B., Li Z., On the tensor spectral p-norm and its dual norm via partitions]. In this short paper, we present a concise and different proof for the validity of the conjecture, which also offers a new and simpler proof to the bounds of the spectral and nuclear norms established by Li for regular tensor partitions. Two numerical examples are provided to illustrate tightness of these bounds.

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18

HOLZRICHTER, MICHAEL, and SUELY OLIVEIRA. "A GRAPH BASED DAVIDSON ALGORITHM FOR THE GRAPH PARTITIONING PROBLEM." International Journal of Foundations of Computer Science 10, no. 02 (June 1999): 225–46. http://dx.doi.org/10.1142/s0129054199000162.

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The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing fill-in in matrix factorizations and load-balancing for parallel algorithms. Spectral graph partitioning algorithms partition a graph using the eigenvector associated with the second smallest eigenvalue of a matrix called the graph Laplacian. The focus of this paper is the use graph theory to compute this eigenvector more quickly.

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19

Benatia, Akrem, Weixing Ji, Yizhuo Wang, and Feng Shi. "Sparse matrix partitioning for optimizing SpMV on CPU-GPU heterogeneous platforms." International Journal of High Performance Computing Applications 34, no. 1 (November 14, 2019): 66–80. http://dx.doi.org/10.1177/1094342019886628.

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Sparse matrix–vector multiplication (SpMV) kernel dominates the computing cost in numerous applications. Most of the existing studies dedicated to improving this kernel have been targeting just one type of processing units, mainly multicore CPUs or graphics processing units (GPUs), and have not explored the potential of the recent, rapidly emerging, CPU-GPU heterogeneous platforms. To take full advantage of these heterogeneous systems, the input sparse matrix has to be partitioned on different available processing units. The partitioning problem is more challenging with the existence of many sparse formats whose performances depend both on the sparsity of the input matrix and the used hardware. Thus, the best performance does not only depend on how to partition the input sparse matrix but also on which sparse format to use for each partition. To address this challenge, we propose in this article a new CPU-GPU heterogeneous method for computing the SpMV kernel that combines between different sparse formats to achieve better performance and better utilization of CPU-GPU heterogeneous platforms. The proposed solution horizontally partitions the input matrix into multiple block-rows and predicts their best sparse formats using machine learning-based performance models. A mapping algorithm is then used to assign the block-rows to the CPU and GPU(s) available in the system. Our experimental results using real-world large unstructured sparse matrices on two different machines show a noticeable performance improvement.

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20

Dyer, Martin, Leslie Ann Goldberg, and David Richerby. "Counting 4×4 matrix partitions of graphs." Discrete Applied Mathematics 213 (November 2016): 76–92. http://dx.doi.org/10.1016/j.dam.2016.05.001.

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21

Dalfó, Cristina, and Miquel Àngel Fiol. "A general method to obtain the spectrum and local spectra of a graph from its regular partitions." Electronic Journal of Linear Algebra 36, no. 36 (July 12, 2020): 446–60. http://dx.doi.org/10.13001/ela.2020.5225.

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It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also the local spectra, of a graph from the quotient matrices of some of its regular partitions, is proposed. Moreover, from such partitions, the $C$-local multiplicities of any class of vertices $C$ is also determined, and some applications of these parameters in the characterization of completely regular codes and their inner distributions are described. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.

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Whittle, Gabriel, Daniel Wong-McSweeney, Joshua Meggitt, and Andrew Elliott. "Towards a low cost method for measuring the airborne sound insulation of partitions." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 2 (February 1, 2023): 5037–44. http://dx.doi.org/10.3397/in_2022_0728.

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BS EN ISO 10140-2 outlines a method for estimating the airborne sound insulation of a partition using adjacent rooms. In this paper, a new method is presented by which the airborne sound insulation is obtained without the need for a transmission suite. Using a stand-alone partition, a representative blocked pressure field is applied numerically to a measured frequency response function matrix characterising the partition. The incident and transmitted powers are determined from the blocked pressure and velocity field on the source and receiver sides, respectively. Results of several partitions measured using the proposed methodology will be compared against estimates obtained according to BS EN ISO 10140-2.

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De Schuymer, Bart, Hans De Meyer, and Bernard De Baets. "Optimal Strategies for Symmetric Matrix Games with Partitions." Bulletin of the Belgian Mathematical Society - Simon Stevin 16, no. 1 (February 2009): 67–89. http://dx.doi.org/10.36045/bbms/1235574193.

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24

Klotz, Jerome H. "Restricted partitions and matrix counts for Cochran's test." Journal of Nonparametric Statistics 17, no. 7 (October 2005): 867–72. http://dx.doi.org/10.1080/10485250500319367.

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25

Staudacher, Matthias. "Master Partitions for Large N Matrix Field Theories." Communications in Mathematical Physics 206, no. 1 (September 1, 1999): 23–32. http://dx.doi.org/10.1007/s002200050696.

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26

Valadkhan, Payam. "List matrix partitions of graphs representing geometric configurations." Discrete Applied Mathematics 260 (May 2019): 237–43. http://dx.doi.org/10.1016/j.dam.2019.01.013.

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27

Liu, Yu Wen, Huang Hsing Pan, Chao Shun Chang, and Kun Sheng Pann. "Properties of Coconut Fiber/Rubber Cement Board for Building Partitions." Advanced Materials Research 338 (September 2011): 566–71. http://dx.doi.org/10.4028/www.scientific.net/amr.338.566.

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Due to recycling of scrapped tire rubbers and coconut fibers, a new building material composited of rubber particles, coconut fibers and cement is applied to building partitions. A lightweight coconut fiber/rubber cement board (LCRCB) consists of rubber/cement board as a sandwich layer and coconut fiber/cement as the matrix, where the sandwich layer containing three fractions of the rubber from 30% to 50%, and the matrix with a constant ratio of 15% coconut fibers in volume. Results show that the measured properties of LCRCB are found with water absorption between 13.8% and 15.4%, unit weight of 1400-1480 kgf/m3, bending strength of 1.97 MPa and coefficients of thermal conductivity in 0.261~0.286 kcal/m•oC•hr,. After the impact test, LCRCBs show no cracks, detachment, pinholes and the split on the impacted surface. Besides, LCRCB satisfies the 2nd degree requirements of incombustibility based on national standards. To be a building partition, LCRCB also shows no smoke toxicity in burning.

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Sivakumar, B. "MATRIX UNITS FOR THE GROUP ALGEBRA kGf = k((ℤ2 × ℤ2) ≀ Sf)." Asian-European Journal of Mathematics 02, no. 02 (June 2009): 255–77. http://dx.doi.org/10.1142/s1793557109000212.

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The irreducible representations of the group Gf := (ℤ2 × ℤ2) ≀ Sf are indexed by 4-partitions of f, i.e., by the set {[α]3[β]2[γ]1[δ]0|α ⊢ u3, β ⊢ u2, γ ⊢ u1, δ ⊢ u0, u0 + u1 + u2 + u3 = f}. This set is in 1 - 1 correspondence with partitions of 4f whose 4-core is empty. In this paper we construct the inequivalent irreducible representations of Gf. We also compute a complete set of seminormal matrix units for the group algebra kGf.

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Mishra, Dhananjay, Krishna Shah, and Ankur Jain. "Investigation of the Impact of Radiative Shielding by Internal Partitions Walls on Propagation of Thermal Runaway in a Matrix of Cylindrical Li-Ion Cells." Journal of The Electrochemical Society 168, no. 12 (December 1, 2021): 120507. http://dx.doi.org/10.1149/1945-7111/ac3715.

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Understanding the nature of onset and propagation of thermal runaway in a Li-ion battery pack is critical for ensuring safety and reliability. This paper presents thermal runaway simulations to understand the impact of radiative heat transfer on thermal runaway onset and propagation in a pack of cylindrical Li-ion cells during transportation/storage. It is shown that radiative properties of the internal partition walls between cells commonly found in battery packs for transportation/storage play a key role in determining whether thermal runaway propagation occurs or not. Surface emissivity of the internal partitions is shown to drive a key balance between radiative heat absorbed from the trigger cell and emitted to neighboring cells. It is shown that a high thermal conductivity partition may greatly help dissipate the radiatively absorbed heat, and therefore prevent onset and propagation. Therefore, choosing an appropriate emissivity of the internal partitions may offer an effective thermal management mechanism to minimize thermal runaway. Emissivity of the cells is also shown to play a key role in radiative heat transfer within the battery pack. This work contributes towards the fundamental understanding of heat transfer during thermal runaway in a battery pack, and offers practical design guidelines for improved safety and reliability.

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Craveiro, Irene Magalhães, Adriana Wagner, and Deborah Domingues. "Parity Indices and Two-Line Matrix Representation for Partitions." TEMA (São Carlos) 16, no. 3 (January 28, 2016): 253. http://dx.doi.org/10.5540/tema.2015.016.03.0253.

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<p>In this work we present a solution for Andrews's Problem 5 [1], by establishing a bijection between the sets and defined in Fine's Theorem [8] and the sets of partitions indexed by their lower parity index [1]. We provide two combinatorial interpretations for [1], determining another solution for Problem 5. We also solve Andrews's Problem 6, conjectured in [1].</p>

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Duane Porter, A., and Nick Mousouris. "Partitions of a skew matrix over a finite field." Linear and Multilinear Algebra 17, no. 3-4 (August 1985): 309–23. http://dx.doi.org/10.1080/03081088508817663.

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32

Pate, Thomas H. "Partitions, irreducible characters, and inequalities for generalized matrix functions." Transactions of the American Mathematical Society 325, no. 2 (February 1, 1991): 875–94. http://dx.doi.org/10.1090/s0002-9947-1991-0998356-3.

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Mujica, V., E. Squitieri, and P. Nieto. "Generalized virial partitions and the one-particle density matrix." Journal of Molecular Structure: THEOCHEM 501-502 (April 2000): 115–23. http://dx.doi.org/10.1016/s0166-1280(99)00420-0.

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34

Borodin, Alexei, Vadim Gorin, and Eugene Strahov. "Product Matrix Processes as Limits of Random Plane Partitions." International Mathematics Research Notices 2020, no. 20 (January 16, 2019): 6713–68. http://dx.doi.org/10.1093/imrn/rny297.

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AbstractWe consider a random process with discrete time formed by squared singular values of products of truncations of Haar-distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives determinantal formulas for (dynamical) correlation functions and a contour integral representation for the correlation kernel. The relation with the Schur processes implies that the continuous limit of marginals for q-distributed plane partitions coincides with the joint law of squared singular values for products of truncations of Haar-distributed random unitary matrices. We provide structural reasons for this coincidence that may also extend to other classes of random matrices.

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Igusa, K., and G. Todorov. "Preprojective partitions and the determinant of the Hom matrix." Proceedings of the American Mathematical Society 94, no. 2 (February 1, 1985): 189. http://dx.doi.org/10.1090/s0002-9939-1985-0784160-0.

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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." Ramanujan Journal 23, no. 1-3 (April 21, 2010): 265–95. http://dx.doi.org/10.1007/s11139-009-9207-8.

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Xu, Wei Hong, Min Zhu, Ya Ruo Jiang, Yu Shan Bai, and Yan Yu. "The Spectral Clustering Based on the Most Similar Relation Diagram." Advanced Materials Research 403-408 (November 2011): 2577–80. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.2577.

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In this paper we present a spectral clustering method based on the MSRD (Most Similar Relation Diagram). The feature of this method is that both the constructing of the adjacency matrix and the clustering are achieved by spectral algorithm. Experiment on an artificial datasets demonstrate that our method can generate balanced partition and detect the manifold clusters no matter the unnormalized or normalized Laplassian is used and can generate partitions with different features if different MSRD is used. Experiments on some real datasets proved that our method is valid and effective.

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Djidjev, Hristo N., Georg Hahn, Susan M. Mniszewski, Christian F. A. Negre, and Anders M. N. Niklasson. "Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics." Algorithms 12, no. 9 (September 7, 2019): 187. http://dx.doi.org/10.3390/a12090187.

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The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.

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Apandi, Tri Herdiawan, Roby Bayu Maulana, Rian Piarna, and Dwi Vernanda. "MENGANALISIS KEMUNGKINAN KETERLAMBATAN PEMBAYARAN SPP DENGAN ALGORITMA C4.5 (STUDI KASUS POLITEKNIK TEDC BANDUNG)." Jurnal Techno Nusa Mandiri 16, no. 2 (September 5, 2019): 93–98. http://dx.doi.org/10.33480/techno.v16i2.659.

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Payment of tuition as one of the sources of funds, plays an important role in the sustainability of the operations of higher education. The problem that arises is that students are not often late to make payments in a timely manner. One of the factors causing the many cases of late payment of tuition fees due to lack of policy and decisive action on the part of the campus when students are late in making payments, besides the factors of parents and students also have an influence on the delay. The purpose of this study is to classify students who are late and timely in making SPP payments using the C4.5 algorithm. From the total sample used then divided into 4 partitions, partition 1 for 90% training data and 10% testing data, partition 2 for 80% training data and 20% testing data, and partition 3 for 70% training data and 30% testing data , and partition 4 for 60% training data and 40% testing data. The classification results of the C4.5 algorithm are evaluated and validated with cross validation and confusion matrix to determine the accuracy of the C4.5 algorithm in predicting late SPP payments. Based on the comparison of the results of evaluations and validations conducted, it shows that data partition 2 has a better level of accuracy than the other partitions, which is 75%. Keywords: Data Mining, Decision Tree (C4.5), SPP.

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Hariono, Maywan, Rollando Rollando, Jasson Karamoy, Pandu Hariyono, M. Atmono, Maria Djohan, Wiwy Wiwy, et al. "Bioguided Fractionation of Local Plants against Matrix Metalloproteinase9 and Its Cytotoxicity against Breast Cancer Cell Models: In Silico and In Vitro Study." Molecules 25, no. 20 (October 14, 2020): 4691. http://dx.doi.org/10.3390/molecules25204691.

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Matrix metalloproteinase9 (MMP9) is known to be highly expressed during metastatic cancer where most known potential inhibitors failed in the clinical trials. This study aims to select local plants in our state, as anti-breast cancer agent with hemopexin-like domain of MMP9 (PEX9) as the selective protein target. In silico screening for PEX9 inhibitors was performed from our in house-natural compound database to identify the plants. The selected plants were extracted using methanol and then a step-by-step in vitro screening against MMP9 was performed from its crude extract, partitions until fractions using FRET-based assay. The partitions were obtained by performing liquid–liquid extraction on the methanol extract using n-hexane, ethylacetate, n-butanol, and water representing nonpolar to polar solvents. The fractions were made from the selected partition, which demonstrated the best inhibition percentage toward MMP9, using column chromatography. Of the 200 compounds screened, 20 compounds that scored the binding affinity −11.2 to −8.1 kcal/mol toward PEX9 were selected as top hits. The binding of these hits were thoroughly investigated and linked to the plants which they were reported to be isolated from. Six of the eight crude extracts demonstrated inhibition toward MMP9 with the IC50 24 to 823 µg/mL. The partitions (1 mg/mL) of Ageratum conyzoides aerial parts and Ixora coccinea leaves showed inhibition 94% and 96%, whereas their fractions showed IC50 43 and 116 µg/mL, respectively toward MMP9. Using MTT assay, the crude extract of Ageratum exhibited IC50 22 and 229 µg/mL against 4T1 and T47D cell proliferations, respectively with a high safety index concluding its potential anti-breast cancer from herbal.

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41

Wang, Zecong, Hamid Parvin, Sultan Noman Qasem, Bui Anh Tuan, and Kim-Hung Pho. "Cluster ensemble selection using balanced normalized mutual information." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 3033–55. http://dx.doi.org/10.3233/jifs-191531.

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A bad partition in an ensemble will be removed by a cluster ensemble selection framework from the final ensemble. It is the main idea in cluster ensemble selection to remove these partitions (bad partitions) from the selected ensemble. But still, it is likely that one of them contains some reliable clusters. Therefore, it may be reasonable to apply the selection phase on cluster level. To do this, a cluster evaluation metric is needed. Some of these metrics have been recently introduced; each of them has its limitations. The weak points of each method have been addressed in the paper. Subsequently, a new metric for cluster assessment has been introduced. The new measure is named Balanced Normalized Mutual Information (BNMI) criterion. It balances the deficiency of the traditional NMI-based criteria. Additionally, an innovative cluster ensemble approach has been proposed. To create the consensus partition considering the elected clusters, a set of different aggregation-functions (called also consensus-functions) have been utilized: the ones which are based upon the co-association matrix (CAM), the ones which are based on hyper graph partitioning algorithms, and the ones which are based upon intermediate space. The experimental study indicates that the state-of-the-art cluster ensemble methods are outperformed by the proposed cluster ensemble approach.

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Bedford, Tim. "Generating special Markov partitions for hyperbolic toral automorphisms using fractals." Ergodic Theory and Dynamical Systems 6, no. 3 (September 1986): 325–33. http://dx.doi.org/10.1017/s0143385700003527.

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AbstractWe show that given some natural conditions on a 3 × 3 hyperbolic matrix of integers A(det A = 1) there exists a Markov partition for the induced map A(x + ℤ3) = A(x)+ℤ3 on T3 whose transition matrix is (A−1)t. For expanding endomorphisms of T2 we construct a Markov partition so that there is a semiconjugacy from a full (one-sided) shift.

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Bessenrodt, Christine, and Richard P. Stanley. "Smith normal form of a multivariate matrix associated with partitions." Journal of Algebraic Combinatorics 41, no. 1 (May 13, 2014): 73–82. http://dx.doi.org/10.1007/s10801-014-0527-4.

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Močkoř, Jiří. "Relational Variants of Lattice-Valued F-Transforms." Axioms 9, no. 1 (December 19, 2019): 1. http://dx.doi.org/10.3390/axioms9010001.

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Two categories of lower and upper lattice-valued F-transforms with fuzzy relations as morphisms are introduced, as generalisations of standard categories of F-transforms with maps as morphisms. Although F-transforms are defined using special structures called spaces with fuzzy partitions, it is shown that these categories are identical to the relational variants of the two categories of semimodule homomorphisms where these fuzzy partitions do not occur. This a priori independence of the F-transform on spaces with fuzzy partitions makes it possible, for example, to use a simple matrix calculus to calculate F-transforms, or to determine the image of F-transforms in relational morphisms of the two categories.

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Hariono, Maywan, Rollando Rollando, I. Yoga, Abraham Harjono, Alfonsus Suryodanindro, Michael Yanuar, Thomas Gonzaga, et al. "Bioguided Fractionation of Local Plants against Matrix Metalloproteinase9 and Its Cytotoxicity against Breast Cancer Cell Models: In Silico and In Vitro Study (Part II)." Molecules 26, no. 5 (March 8, 2021): 1464. http://dx.doi.org/10.3390/molecules26051464.

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In our previous work, the partitions (1 mg/mL) of Ageratum conyzoides (AC) aerial parts and Ixora coccinea (IC) leaves showed inhibitions of 94% and 96%, respectively, whereas their fractions showed IC50 43 and 116 µg/mL, respectively, toward Matrix Metalloproteinase9 (MMP9), an enzyme that catalyzes a proteolysis of extracellular matrix. In this present study, we performed IC50 determinations for AC n-hexane, IC n-hexane, and IC ethylacetate partitions, followed by the cytotoxicity study of individual partitions against MDA-MB-231, 4T1, T47D, MCF7, and Vero cell lines. Successive fractionations from AC n-hexane and IC ethylacetate partitions led to the isolation of two compounds, oxytetracycline (OTC) and dioctyl phthalate (DOP). The result showed that AC n-hexane, IC n-hexane, and IC ethylacetate partitions inhibit MMP9 with their respective IC50 as follows: 246.1 µg/mL, 5.66 µg/mL, and 2.75 × 10−2 µg/mL. Toward MDA-MB-231, 4T1, T47D, and MCF7, AC n-hexane demonstrated IC50 2.05, 265, 109.70, and 2.11 µg/mL, respectively, whereas IC ethylacetate showed IC50 1.92, 57.5, 371.5, and 2.01 µg/mL, respectively. The inhibitions toward MMP9 by OTC were indicated by its IC50 18.69 µM, whereas DOP was inactive. A molecular docking study suggested that OTC prefers to bind to PEX9 rather than its catalytic domain. Against 4T1, OTC showed inhibition with IC50 414.20 µM. In conclusion, this study furtherly supports the previous finding that AC and IC are two herbals with potential to be developed as triple-negative anti-breast cancer agents.

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Van Cutsem, Bernard, and Bernard Ycart. "Renewal-type behavior of absorption times in Markov chains." Advances in Applied Probability 26, no. 4 (December 1994): 988–1005. http://dx.doi.org/10.2307/1427901.

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This paper studies the absorption time of an integer-valued Markov chain with a lower-triangular transition matrix. The main results concern the asymptotic behavior of the absorption time when the starting point tends to infinity (asymptotics of moments and central limit theorem). They are obtained using stochastic comparison for Markov chains and the classical theorems of renewal theory. Applications to the description of large random chains of partitions and large random ordered partitions are given.

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Van Cutsem, Bernard, and Bernard Ycart. "Renewal-type behavior of absorption times in Markov chains." Advances in Applied Probability 26, no. 04 (December 1994): 988–1005. http://dx.doi.org/10.1017/s0001867800026720.

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This paper studies the absorption time of an integer-valued Markov chain with a lower-triangular transition matrix. The main results concern the asymptotic behavior of the absorption time when the starting point tends to infinity (asymptotics of moments and central limit theorem). They are obtained using stochastic comparison for Markov chains and the classical theorems of renewal theory. Applications to the description of large random chains of partitions and large random ordered partitions are given.

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Zhao, Chenyue, Hosein Alizadeh, Behrouz Minaei, Majid Mohamadpoor, Hamid Parvin, and Mohammad Reza Mahmoudi. "Social Network Optimization for Cluster Ensemble Selection." Fundamenta Informaticae 176, no. 1 (October 31, 2020): 79–102. http://dx.doi.org/10.3233/fi-2020-1964.

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This paper studies the cluster ensemble selection problem for unsupervised learning. Given a large ensemble of clustering solutions, our goal is to select a subset of solutions to form a smaller yet better performing cluster ensemble than using all available solutions. The common way of aggregating the chosen solutions is accumulating the information of the selected results to a similarity matrix. This paper suggests transforming the similarity matrix to a modularity matrix and then applying a new consensus function which optimizes modularity measure in it. We represent the modularity maximization problem as a 0-1 quadratic program which can be exactly solved for small datasets. We also established a new greedy algorithm, namely sum linkage, to optimize the objective function specially for large scale datasets in a very short time. We show that the proposed consensus partition gets much closer to the actual cluster structure than the partitions obtained from the direct application of common cluster ensemble methods. The promising results compared with other most cited consensus functions show the excellent efficiency of the proposed method.

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MARTIN, PAUL. "TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTION." Journal of Knot Theory and Its Ramifications 03, no. 01 (March 1994): 51–82. http://dx.doi.org/10.1142/s0218216594000071.

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We give the definition of the Partition Algebra Pn(Q). This is a new generalisation of the Temperley–Lieb algebra for Q-state n-site Potts models, underpinning their transfer matrix formulation on arbitrary transverse lattices. In Pn(Q) subalgebras appropriate for building the transfer matrices for all transverse lattice shapes (e.g. cubic) occur. For [Formula: see text] the Partition algebra manifests either a semi-simple generic structure or is one of a discrete set of exceptional cases. We determine the Q-generic and Q-independent structure and representation theory. In all cases (except Q = 0) simple modules are indexed by the integers j ≤ n and by the partitions λ ˫ j. Physically they may be associated, at least for sufficiently small j, to 2j 'spin' correlation functions. We exhibit a subalgebra isomorphic to the Brauer algebra.

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Lu, Zhigang, and Hong Shen. "An accuracy-assured privacy-preserving recommender system for internet commerce." Computer Science and Information Systems 12, no. 4 (2015): 1307–26. http://dx.doi.org/10.2298/csis140725056l.

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Recommender systems, tool for predicting users? potential preferences by computing history data and users? interests, show an increasing importance in various Internet applications such as online shopping. As a well-known recommendation method, neighbourhood-based collaborative filtering has attracted considerable attentions recently. The risk of revealing users? private information during the process of filtering has attracted noticeable research interests. Among the current solutions, the probabilistic techniques have shown a powerful privacy preserving effect. The existing methods deploying probabilistic methods are in three categories, one [19] adds differential privacy noises in the covariance matrix; one [1] introduces the randomisation in the neighbour selection process; the other [29] applies differential privacy in both the neighbour selection process and covariance matrix. When facing the k Nearest Neighbour (kNN) attack, all the existing methods provide no data utility guarantee, for the introduction of global randomness. In this paper, to overcome the problem of recommendation accuracy loss, we propose a novel approach, Partitioned Probabilistic Neighbour Selection, to ensure a required prediction accuracy while maintaining high security against the kNN attack. We define the sum of k neighbours? similarity as the accuracy metric ?, the number of user partitions, across which we select the k neighbours, as the security metric ?. We generalise the k Nearest Neighbour attack to the ?k Nearest Neighbours attack. Differing from the existing approach that selects neighbours across the entire candidate list randomly, our method selects neighbours from each exclusive partition of size k with a decreasing probability. Theoretical and experimental analysis show that to provide an accuracy-assured recommendation, our Partitioned Probabilistic Neighbour Selection method yields a better trade-off between the recommendation accuracy and system security.

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