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Автор: Grafiati
Опубліковано: 14 березня 2023

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1

Koshi, J. M., and R. A. Goldstein. "Context-dependent optimal substitution matrices." Protein Engineering Design and Selection 8, no. 7 (July 1, 1995): 641–45. http://dx.doi.org/10.1093/protein/8.7.641.

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2

Hautus, M. L. J. "Substitution of matrices over rings." Linear Algebra and its Applications 226-228 (September 1995): 353–70. http://dx.doi.org/10.1016/0024-3795(95)00155-k.

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3

BARBÉ, ANDRÉ M. "FRACTALS BY NUMBERS." Fractals 03, no. 04 (December 1995): 651–61. http://dx.doi.org/10.1142/s0218348x95000588.

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Анотація:
We introduce an extension of an earlier defined simple, number-based matrix substitution system for obtaining fractal matrices, by considering cyclic substitutions. The elements of the resulting matrices are related to representations of their addresses in a mixed number base. The Hutchinson operator for the limit form of a geometrical representation of the fractal matrix is derived. It is shown that the class of fractal limit sets obtainable from cyclic substitutions does not extend the class obtainable from the simple substitutions.
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4

Barlowe, Scott, Heather B. Coan, and Robert T. Youker. "SubVis: an interactive R package for exploring the effects of multiple substitution matrices on pairwise sequence alignment." PeerJ 5 (June 27, 2017): e3492. http://dx.doi.org/10.7717/peerj.3492.

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Understanding how proteins mutate is critical to solving a host of biological problems. Mutations occur when an amino acid is substituted for another in a protein sequence. The set of likelihoods for amino acid substitutions is stored in a matrix and input to alignment algorithms. The quality of the resulting alignment is used to assess the similarity of two or more sequences and can vary according to assumptions modeled by the substitution matrix. Substitution strategies with minor parameter variations are often grouped together in families. For example, the BLOSUM and PAM matrix families are commonly used because they provide a standard, predefined way of modeling substitutions. However, researchers often do not know if a given matrix family or any individual matrix within a family is the most suitable. Furthermore, predefined matrix families may inaccurately reflect a particular hypothesis that a researcher wishes to model or otherwise result in unsatisfactory alignments. In these cases, the ability to compare the effects of one or more custom matrices may be needed. This laborious process is often performed manually because the ability to simultaneously load multiple matrices and then compare their effects on alignments is not readily available in current software tools. This paper presents SubVis, an interactive R package for loading and applying multiple substitution matrices to pairwise alignments. Users can simultaneously explore alignments resulting from multiple predefined and custom substitution matrices. SubVis utilizes several of the alignment functions found in R, a common language among protein scientists. Functions are tied together with the Shiny platform which allows the modification of input parameters. Information regarding alignment quality and individual amino acid substitutions is displayed with the JavaScript language which provides interactive visualizations for revealing both high-level and low-level alignment information.
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5

BALDI, PIERRE. "Substitution Matrices and Hidden Markov Models." Journal of Computational Biology 2, no. 3 (January 1995): 487–91. http://dx.doi.org/10.1089/cmb.1995.2.487.

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6

Dosztányi, Zs, and A. E. Torda. "SUBSTITUTION MATRICES BASED ON FORCE FIELDS." Biochemical Society Transactions 28, no. 5 (October 1, 2000): A146. http://dx.doi.org/10.1042/bst028a146.

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7

G., Renganayaki, and Achuthsankar S. Nair. "Hubsm: A Novel Amino Acid Substitution Matrix for Comparing Hub Proteins." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 8 (August 30, 2017): 212. http://dx.doi.org/10.23956/ijarcsse.v7i8.53.

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Анотація:
Sequence alignment algorithms and database search methods use BLOSUM and PAM substitution matrices constructed from general proteins. These de facto matrices are not optimal to align sequences accurately, for the proteins with markedly different compositional bias in the amino acid. In this work, a new amino acid substitution matrix is calculated for the disorder and low complexity rich region of Hub proteins, based on residue characteristics. Insights into the amino acid background frequencies and the substitution scores obtained from the Hubsm unveils the residue substitution patterns which differs from commonly used scoring matrices .When comparing the Hub protein sequences for detecting homologs, the use of this Hubsm matrix yields better results than PAM and BLOSUM matrices. Usage of Hubsm matrix can be optimal in database search and for the construction of more accurate sequence alignments of Hub proteins.
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8

Aledo, Pablo, and Juan Carlos Aledo. "Proteome-Wide Structural Computations Provide Insights into Empirical Amino Acid Substitution Matrices." International Journal of Molecular Sciences 24, no. 1 (January 2, 2023): 796. http://dx.doi.org/10.3390/ijms24010796.

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Анотація:
The relative contribution of mutation and selection to the amino acid substitution rates observed in empirical matrices is unclear. Herein, we present a neutral continuous fitness-stability model, inspired by the Arrhenius law (qij=aije−ΔΔGij). The model postulates that the rate of amino acid substitution (i→j) is determined by the product of a pre-exponential factor, which is influenced by the genetic code structure, and an exponential term reflecting the relative fitness of the amino acid substitutions. To assess the validity of our model, we computed changes in stability of 14,094 proteins, for which 137,073,638 in silico mutants were analyzed. These site-specific data were summarized into a 20 square matrix, whose entries, ΔΔGij, were obtained after averaging through all the sites in all the proteins. We found a significant positive correlation between these energy values and the disease-causing potential of each substitution, suggesting that the exponential term accurately summarizes the fitness effect. A remarkable observation was that amino acids that were highly destabilizing when acting as the source, tended to have little effect when acting as the destination, and vice versa (source → destination). The Arrhenius model accurately reproduced the pattern of substitution rates collected in the empirical matrices, suggesting a relevant role for the genetic code structure and a tuning role for purifying selection exerted via protein stability.
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9

LIU, XIN, and WEI-MOU ZHENG. "AN AMINO ACID SUBSTITUTION MATRIX FOR PROTEIN CONFORMATION IDENTIFICATION." Journal of Bioinformatics and Computational Biology 04, no. 03 (June 2006): 769–82. http://dx.doi.org/10.1142/s0219720006002156.

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Анотація:
Amino acid substitution matrices play an essential role in protein sequence alignment, a fundamental task in bioinformatics. Most widely used matrices, such as PAM matrices derived from homologous sequences and BLOSUM matrices derived from aligned segments of PROSITE, did not integrate conformation information in their construction. There are a few structure-based matrices, which are derived from limited data of structure alignment. Using databases PDB_SELECT and DSSP, we create a database of sequence-conformation blocks which explicitly represent sequence-structure relationship. Members in a block are identical in conformation and are highly similar in sequence. From this block database, we derive a conformation-specific amino acid substitution matrix CBSM60. The matrix shows an improved performance in conformational segment search and homolog detection.
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10

Vilim, R. B., R. M. Cunningham, B. Lu, P. Kheradpour, and F. J. Stevens. "Fold-specific substitution matrices for protein classification." Bioinformatics 20, no. 6 (February 5, 2004): 847–53. http://dx.doi.org/10.1093/bioinformatics/btg492.

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11

Hourai, Y., T. Akutsu, and Y. Akiyama. "Optimizing substitution matrices by separating score distributions." Bioinformatics 20, no. 6 (January 29, 2004): 863–73. http://dx.doi.org/10.1093/bioinformatics/btg494.

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12

Henikoff, S., and J. G. Henikoff. "Amino acid substitution matrices from protein blocks." Proceedings of the National Academy of Sciences 89, no. 22 (November 15, 1992): 10915–19. http://dx.doi.org/10.1073/pnas.89.22.10915.

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13

Trivedi, Rakesh, and Hampapathalu Adimurthy Nagarajaram. "Substitution scoring matrices for proteins ‐ An overview." Protein Science 29, no. 11 (October 12, 2020): 2150–63. http://dx.doi.org/10.1002/pro.3954.

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14

Henikoff, Steven, and Jorja G. Henikoff. "Performance evaluation of amino acid substitution matrices." Proteins: Structure, Function, and Genetics 17, no. 1 (September 1993): 49–61. http://dx.doi.org/10.1002/prot.340170108.

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15

Desbene-Monvernay, Annie, Ouzama Karazoun, Jacques Berthelot, and Paul-Louis Desbene. "Modelisation de la bromation au moyen de TBABr3 de matrices organiques complexes: suivi de la bromation de carbazoles à l'aide de la voltampérométrie et de la chromatographie liquide hautes performances." Canadian Journal of Chemistry 70, no. 3 (March 1, 1992): 870–76. http://dx.doi.org/10.1139/v92-115.

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Анотація:
To determine the degree of substitution of complex matrices, the bromination of various carbazoles by tetrabutylammonium tribromide has been used as a model of a substitution reaction. This has allowed us to test the validity of the voltamperometric titration of tribromide ions and species formed (Br− and H+ ions). The results obtained for various substrate/reagent ratios are in excellent agreement with those of high performance liquid chromatography. The electrochemical titration can be considered as reliable, fast, and very easy to use. It permits us to follow the bromination kinetics and to determine the degree of substitution of complex organic matrices. Keywords: bromination, tetrabutylammonium tribromide, voltamperometric titration (Br3−, Br−, H+), degree of substitution.
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16

Yu, Y. K., J. C. Wootton, and S. F. Altschul. "The compositional adjustment of amino acid substitution matrices." Proceedings of the National Academy of Sciences 100, no. 26 (December 8, 2003): 15688–93. http://dx.doi.org/10.1073/pnas.2533904100.

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17

Altschul, Stephen F., John C. Wootton, E. Michael Gertz, Richa Agarwala, Aleksandr Morgulis, Alejandro A. Schaffer, and Yi-Kuo Yu. "Protein database searches using compositionally adjusted substitution matrices." FEBS Journal 272, no. 20 (October 2005): 5101–9. http://dx.doi.org/10.1111/j.1742-4658.2005.04945.x.

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18

Cui, Ting, Chenhui Jin, and Zhiyin Kong. "On Compact Cauchy Matrices for Substitution-Permutation Networks." IEEE Transactions on Computers 64, no. 7 (July 1, 2015): 2098–102. http://dx.doi.org/10.1109/tc.2014.2346180.

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19

Avishai, Yshai, Daniel Berend, and Vadim Tkachenko. "Trace Maps." International Journal of Modern Physics B 11, no. 30 (December 10, 1997): 3525–42. http://dx.doi.org/10.1142/s0217979297001763.

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Анотація:
Trace maps for products of transfer matrices prove to be an important tool in the investigation of electronic spectra and wave functions of one-dimensional quasiperiodic systems. These systems belong to a general class of substitution sequences. In this work we review the various stages of development in constructing trace maps for products of (2×2) matrices generated by arbitrary substitution sequences. The dimension of the underlying space of the trace map obtained by means of this construction is the minimal possible, namely 3r-3 for an alphabet of size r≥2. In conclusion, we describe some results from the spectral theory of discrete Schrödinger operators with substitution potentials.
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20

Liu, Xin, and Ya-Pu Zhao. "Substitution Matrices of Residue Triplets Derived from Protein Blocks." Journal of Computational Biology 17, no. 12 (December 2010): 1679–87. http://dx.doi.org/10.1089/cmb.2008.0035.

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21

Henikoff, Jorja G., and Steven Henikoff. "Using substitution probabilities to improve position-specific scoring matrices." Bioinformatics 12, no. 2 (1996): 135–43. http://dx.doi.org/10.1093/bioinformatics/12.2.135.

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22

Altschul, Stephen F. "Amino acid substitution matrices from an information theoretic perspective." Journal of Molecular Biology 219, no. 3 (June 1991): 555–65. http://dx.doi.org/10.1016/0022-2836(91)90193-a.

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23

Pokarowski, Piotr, Andrzej Kloczkowski, Szymon Nowakowski, Maria Pokarowska, Robert L. Jernigan, and Andrzej Kolinski. "Ideal amino acid exchange forms for approximating substitution matrices." Proteins: Structure, Function, and Bioinformatics 69, no. 2 (November 1, 2007): 379–93. http://dx.doi.org/10.1002/prot.21509.

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24

Li, Jing, and Wei Wang. "Detailed assessment of homology detection using different substitution matrices." Chinese Science Bulletin 51, no. 13 (July 2006): 1538–45. http://dx.doi.org/10.1007/s11434-006-1538-x.

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25

Kim, Matthew, Kelly Shin, Clara Lim, and Selcuk Koyuncu. "A short note on determinantal representation of stable polynomials." Journal of Mathematics Research 12, no. 5 (September 15, 2020): 43. http://dx.doi.org/10.5539/jmr.v12n5p43.

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In this paper we provide some results that replace the condition ”real-zero” by the properties so-called x-substitution and y-substitution. We show that using these properties, we can still write the determinantal representation of a stable polynomial in terms of identity and Hermitian matrices.
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26

Prlić, Andreas, Francisco S. Domingues, and Manfred J. Sippl. "Structure-derived substitution matrices for alignment of distantly related sequences." Protein Engineering, Design and Selection 13, no. 8 (August 2000): 545–50. http://dx.doi.org/10.1093/protein/13.8.545.

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27

Arvestad, Lars, and William J. Bruno. "Estimation of Reversible Substitution Matrices from Multiple Pairs of Sequences." Journal of Molecular Evolution 45, no. 6 (December 1997): 696–703. http://dx.doi.org/10.1007/pl00006274.

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28

Lin, Kuang, Alex C. W. May, and William R. Taylor. "Amino Acid Substitution Matrices from an Artificial Neural Network Model." Journal of Computational Biology 8, no. 5 (October 2001): 471–81. http://dx.doi.org/10.1089/106652701753216495.

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29

Eskin, Eleazar, William Stafford Noble, and Yoram Singer. "Using Substitution Matrices to Estimate Probability Distributions for Biological Sequences." Journal of Computational Biology 9, no. 6 (December 2002): 775–91. http://dx.doi.org/10.1089/10665270260518263.

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30

Yamada, Kazunori, and Kentaro Tomii. "Revisiting amino acid substitution matrices for identifying distantly related proteins." Bioinformatics 30, no. 3 (November 26, 2013): 317–25. http://dx.doi.org/10.1093/bioinformatics/btt694.

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31

Mount, D. W. "Comparison of the PAM and BLOSUM Amino Acid Substitution Matrices." Cold Spring Harbor Protocols 2008, no. 6 (June 1, 2008): pdb.ip59. http://dx.doi.org/10.1101/pdb.ip59.

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32

Tafrikan, Mohammad, and Mohammad Ghani. "Iterative Method of Thomas Algorithm on The Case Study of Energy Equation." Postulat : Jurnal Inovasi Pendidikan Matematika 3, no. 1 (July 26, 2022): 14. http://dx.doi.org/10.30587/postulat.v3i1.4346.

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Implicit method is one of the finite difference method and is widely used for discretization some of ordinary or partial differential equations, such like: advection equation, heat transfer equation, burger equation, and many others. Implicit method is unconditionally stable and has been proved with the approximation of Von-Neumann stability criterion. Actually, implicit method is always identical to block matrices (tri-diagonal matrices or penta-diagonal matrices). These matrices can be solved numerically by Thomas algorithm including Gauss elimination using pivot or not, backward or forward substitution. Furthermore, it can be also solved using LU decomposition method with the elimination of lower triangle matrices first and then the elimination of upper triangle matrices. In this research, Thomas algorithm is used to solve numerically for the problem of convective flow on boundary layer, especially for energy equation with the variation of Prandtl number ( ).
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33

Pagon, Dusan. "Performing Operations with Matrices on Spreadsheets." Mathematics Teacher 91, no. 4 (April 1998): 338–41. http://dx.doi.org/10.5951/mt.91.4.0338.

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Although created mainly for other purposes, spreadsheets appear to be useful in mathematics education. For instance, Russell (1992) writes about spreadsheet activities in middle school mathematics in his book with the same title. In a Mathematics Teacher article, Hunt (1995) describes how he uses spreadsheets to teach students synthetic substitution, synthetic division, and Newton's method. Our experience shows that the same tool can be useful for performing matru operations and, further on, for introducing students to basic concepts of linear algebra. The interested reader can find additional examples of using spreadsheets in high school mathematics in Sjostrand's (1994) book, which deals with Excel spreadsheets.
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34

SUMNER, JEREMY G. "MULTIPLICATIVELY CLOSED MARKOV MODELS MUST FORM LIE ALGEBRAS." ANZIAM Journal 59, no. 2 (October 2017): 240–46. http://dx.doi.org/10.1017/s1446181117000359.

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Анотація:
We prove that the probability substitution matrices obtained from a continuous-time Markov chain form a multiplicatively closed set if and only if the rate matrices associated with the chain form a linear space spanning a Lie algebra. The key original contribution we make is to overcome an obstruction, due to the presence of inequalities that are unavoidable in the probabilistic application, which prevents free manipulation of terms in the Baker–Campbell–Haursdorff formula.
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35

Saidi, Rabie, Mondher Maddouri, and Engelbert Mephu Nguifo. "Protein sequences classification by means of feature extraction with substitution matrices." BMC Bioinformatics 11, no. 1 (2010): 175. http://dx.doi.org/10.1186/1471-2105-11-175.

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36

YAP, Von Bing. "A unified approach to the transition matrices of DNA substitution models." Mathematical Biosciences 242, no. 2 (April 2013): 111–16. http://dx.doi.org/10.1016/j.mbs.2012.12.008.

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37

Get’man, E. I., Yu A. Oleksii, S. V. Radio, and L. I. Ardanova. "Determining the phase stability of luminescent materials based on the solid solutions of oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5], where Ln = La−Yb." Fine Chemical Technologies 15, no. 5 (November 14, 2020): 54–62. http://dx.doi.org/10.32362/2410-6593-2020-15-5-54-62.

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Анотація:
Objectives. This study aimed to predict the limits of substitution and stability of luminescent materials based on low-temperature modifications of solid solutions (spatial group P21/c) with lutetium oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5], where Ln represents the rare-earth elements (REEs) of the La–Yb series.Methods. The V.S. Urusov’s crystal energy theory of isomorphous substitutions and a crystallochemical approach in the regular solid solution approximation were used to calculate the energies of the mixing (interaction parameters) of the solid solutions.Results. Using the V.S. Urusov’s theory, we calculated the energies of mixing (interaction parameters) in the systems under study. The dependences of the decomposition temperatures of solid solutions on the REE number and composition (x) were obtained and used to create a diagram of the thermodynamic stability of the solid solutions, allowing us to predict the substitution limits depending on the temperature or determine the decomposition temperature using the given substitution limits.Conclusions. The results of the study can be useful when choosing the ratio of components in matrices (host materials) and the amount of the activator (dopant) in the new luminescent, laser, and other materials based on low-temperature modifications of solid solutions of “mixed” REE oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5].
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38

Moreno-Manzano, Victoria, Maravillas Mellado-López, Maria Jose Morera-Esteve, Ana Alastrue-Agudo, Viviana Bisbal-Velasco, Jerónimo Forteza-Vila, Ángel Serrano-Aroca, and César David Vera-Donoso. "Human adipose-derived mesenchymal stem cells accelerate decellularized neobladder regeneration." Regenerative Biomaterials 7, no. 2 (December 22, 2019): 161–69. http://dx.doi.org/10.1093/rb/rbz049.

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Abstract Decellularized natural bladder matrices (neobladders) represent an exciting means to regenerate the bladder following bladder cancer-associated cystectomy. In this study, we compare the evolution of decellularized matrices with recellularized matrices by seeding it with human adipose-derived mesenchymal stem cells (ADSC) after implantation following partial cystectomy in rats. We discovered significant anatomical differences since 10 days after neobladder implantation with the ADSC-containing matrices promoting a significant recovery of mature p63- and cytokeratin 7-positive urothelium. We also discovered significantly induced expression of the vimentin mesoderm marker in the submucosal layer in ADSC-seeded matrices. Interestingly, we found a higher expression of smooth muscle actin in transversal and longitudinal smooth muscle layers with ADSC-seeded matrices. Furthermore, ADSC also showed increased vascularization and nerve innervation of the neobladder as determined by the distribution of CD31 and S100β reactivity, respectively. We believe that ADSC and their paracrine-acting pro-regenerative secretome within decellularized matrices represent an efficient bladder substitution strategy; however, we require a fuller understanding of the mechanisms involved before clinical studies can begin.
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39

BARBÉ, A., and G. SKORDEV. "SUBSTITUTIONS GENERATING THE FRACTAL MATRICES OF THE p-ADIC VALUATION OF THE BINOMIAL AND LEGENDRE-POLYNOMIAL COEFFICIENTS." Fractals 17, no. 04 (December 2009): 407–26. http://dx.doi.org/10.1142/s0218348x09004600.

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We consider the fractal matrix which describes the divisibility properties of the coefficients of the Legendre polynomials by prime powers, and derive a block matrix substitution system that generates it. Central in the development is a similar substitution for a particular matrix of binomial coefficients.
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40

Sandri, Monica, Anna Tampieri, Luca Bertinetti, and Adele Boskey. "In Vitro Bio-Mineralization Process." Key Engineering Materials 361-363 (November 2007): 543–46. http://dx.doi.org/10.4028/www.scientific.net/kem.361-363.543.

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The present work describes the development of biomimetic composites materials for bone tissue substitution and repair. At this purpose a biomimetic approach was used and apatitic phases were nucleated on macromolecular matrices like natural collagen, which act as template and induce peculiar physico-chemical features in the mineral phase.
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41

Vlach, M. "LU decomposition and forward-backward substitution of recursive bordered block diagonal matrices." IEE Proceedings G (Electronic Circuits and Systems) 132, no. 1 (1985): 24. http://dx.doi.org/10.1049/ip-g-1.1985.0005.

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42

Vishnepolsky, Boris, Grigol Managadze, Maya Grigolava, and Malak Pirtskhalava. "Evaluation performance of substitution matrices, based on contacts between residue terminal groups." Journal of Biomolecular Structure and Dynamics 30, no. 2 (June 2012): 180–90. http://dx.doi.org/10.1080/07391102.2012.677769.

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43

GAHRAMANOV, ILMAR, and ELMAR ASGEROV. "A REMARK ON THE TRACE-MAP FOR THE SILVER MEAN SEQUENCE." Modern Physics Letters B 27, no. 15 (May 21, 2013): 1350107. http://dx.doi.org/10.1142/s0217984913501078.

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In this work, we study the Silver mean sequence based on substitution rules by means of a transfer-matrix approach. Using transfer-matrix method, we find a recurrence relation for the traces of general transfer-matrices which characterizes electronic properties of the quasicrystal in question. We also find an invariant of the trace-map.
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44

Ardanova, Lyudmyla I., Evgeni I. Get'man, Serhii V. Radio, Ian M. Hill, and Aleksey V. Ignatov. "Isomorphous Substitutions in Luminescent Materials Based on ScVO4." Key Engineering Materials 865 (September 2020): 37–42. http://dx.doi.org/10.4028/www.scientific.net/kem.865.37.

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The aim of the paper is to define the limits of substitution and phase stability for solidsolutions of orthovanadates with zircon structure Sc1–xLnxVO4, where Ln is a rare-earth element(REE), Ln = Ce – Lu. The mixing energies (interaction parameters) and critical decompositiontemperatures of Sc1–xLnxVO4 solid solutions with the zircon structure were calculated using thecrystal-energy theory of isomorphous miscibility. Diagram of thermodynamic stability visualizingthe substitution limits (x) by the decomposition temperature or the decomposition temperature bythe substitution limits, the dependencies of the decomposition temperatures on the REE atomicnumbers is presented. This diagram also allows assessing areas of stability, instability, andmetastability for Sc1–xLnxVO4 solid solutions. Results of calculations were compared with literaturedata on thermodynamic stability of solid solutions and on substitution limits. The results of thisstudy can be used in the development of new luminescent materials based on ScVO4 modified withREE, in the selection of REE for matrix and activator, in defining optimal proportions of REE inSc1–xLnxVO4 matrices.
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45

VOORHEES, BURTON. "FRACTAL DIMENSION, PROBABILITY AND ENTROPY IN MATRIX AND SUMMATION SUBSTITUTION SYSTEMS." Fractals 07, no. 03 (September 1999): 283–99. http://dx.doi.org/10.1142/s0218348x99000293.

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The box-count method is used to obtain fractal dimensions, limiting probabilities and relative entropies for fractal and fractal-like objects generated by matrix and summation substitution systems. Results are based on the fact that a transition matrix formalism can be developed for these systems, yielding box counts at each iteration. The transition matrix is non-negative, and many results on non-negative matrices can be applied. The formalism developed is, up to a multiplicative constant, equivalent to a Markov process.
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46

Le, Si Quang, Nicolas Lartillot, and Olivier Gascuel. "Phylogenetic mixture models for proteins." Philosophical Transactions of the Royal Society B: Biological Sciences 363, no. 1512 (October 7, 2008): 3965–76. http://dx.doi.org/10.1098/rstb.2008.0180.

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Standard protein substitution models use a single amino acid replacement rate matrix that summarizes the biological, chemical and physical properties of amino acids. However, site evolution is highly heterogeneous and depends on many factors: genetic code; solvent exposure; secondary and tertiary structure; protein function; etc. These impact the substitution pattern and, in most cases, a single replacement matrix is not enough to represent all the complexity of the evolutionary processes. This paper explores in maximum-likelihood framework phylogenetic mixture models that combine several amino acid replacement matrices to better fit protein evolution. We learn these mixture models from a large alignment database extracted from HSSP, and test the performance using independent alignments from TreeBase . We compare unsupervised learning approaches, where the site categories are unknown, to supervised ones, where in estimations we use the known category of each site, based on its exposure or its secondary structure. All our models are combined with gamma-distributed rates across sites. Results show that highly significant likelihood gains are obtained when using mixture models compared with the best available single replacement matrices. Mixtures of matrices also improve over mixtures of profiles in the manner of the CAT model. The unsupervised approach tends to be better than the supervised one, but it appears difficult to implement and highly sensitive to the starting values of the parameters, meaning that the supervised approach is still of interest for initialization and model comparison. Using an unsupervised model involving three matrices, the average AIC gain per site with TreeBase test alignments is 0.31, 0.49 and 0.61 compared with LG (named after Le & Gascuel 2008 Mol. Biol. Evol. 25 , 1307–1320), WAG and JTT, respectively. This three-matrix model is significantly better than LG for 34 alignments (among 57), and significantly worse for 1 alignment only. Moreover, tree topologies inferred with our mixture models frequently differ from those obtained with single matrices, indicating that using these mixtures impacts not only the likelihood value but also the output tree. All our models and a PhyML implementation are available from http://atgc.lirmm.fr/mixtures .
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47

Norn, Christoffer, Ingemar André, and Douglas L. Theobald. "A thermodynamic model of protein structure evolution explains empirical amino acid substitution matrices." Protein Science 30, no. 10 (July 30, 2021): 2057–68. http://dx.doi.org/10.1002/pro.4155.

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48

Trindade, Daniela, Nuno Alves, and Carla Moura. "From Animal to Human: (Re)using Acellular Extracellular Matrices for Temporomandibular Disc Substitution." Journal of Functional Biomaterials 13, no. 2 (May 18, 2022): 61. http://dx.doi.org/10.3390/jfb13020061.

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Current treatments for temporomandibular joint (TMJ) disc dysfunctions are not fully effective and lack regenerative capacity. Therefore, the search for tissue-engineered materials for TMJ disc substitution is critical to fill this gap. Decellularization presents tremendous potential, as it is possible to obtain an extracellular matrix with an adequate biomechanical structure and biochemical components. However, its application to the TMJ disc is still in progress, since there are few studies in the literature, and those that exist have many gaps in terms of characterisation, which is decisive to ensure its success. Ultimately, we intend to emphasize the importance of the decellularization technique for the development of an engineered TMJ disc.
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49

Baussand, J., and A. Carbone. "Inconsistent Distances in Substitution Matrices can be Avoided by Properly Handling Hydrophobic Residues." Evolutionary Bioinformatics 4 (January 2008): EBO.S885. http://dx.doi.org/10.4137/ebo.s885.

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50

Jia, Kejue, Mesih Kilinc, Benjamin R. Litterer, and Robert L. Jernigan. "Protsubs: a series of substitution matrices reflecting relationships between protein evolution and structure." Biophysical Journal 121, no. 3 (February 2022): 322a. http://dx.doi.org/10.1016/j.bpj.2021.11.1156.

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