Relevant bibliographies by topics / Sigma matrices

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Sigma matrices'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Sigma matrices"

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Sebbar, Ahmed, and Thérèse Falliero. "CAPACITIES AND JACOBI MATRICES." Proceedings of the Edinburgh Mathematical Society 46, no. 3 (2003): 719–45. http://dx.doi.org/10.1017/s0013091502001141.

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AbstractIn this paper, we use the theorem of Burchnall and Shaundy to give the capacity of the spectrum $\sigma(A)$ of a periodic tridiagonal and symmetric matrix. A special family of Chebyshev polynomials of $\sigma(A)$ is also given. In addition, the inverse problem is considered: given a finite union $E$ of closed intervals, we study the conditions for a Jacobi matrix $A$ to exist satisfying $\sigma(A)=E$. We relate this question to Carathéodory theorems on conformal mappings.AMS 2000 Mathematics subject classification: Primary 31B15; 30C20; 39A70
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Kumar, Sandeep, and Deepa Sinha. "Spectral Analysis of Splitting Signed Graph." European Journal of Pure and Applied Mathematics 17, no. 1 (2024): 504–18. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.4798.

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An ordered pair $\Sigma = (\Sigma^{u}$,$\sigma$) is called the \textit{signed graph}, where $\Sigma^{u} = (V,E)$ is a \textit{underlying graph} and $\sigma$ is a signed mapping, called \textit{signature}, from $E$ to the sign set $\lbrace +, - \rbrace$. The \textit{splitting signed graph} $\Gamma(\Sigma)$ of a signed graph $\Sigma$ is defined as, for every vertex $u \in V(\Sigma)$, take a new vertex $u'$. Join $u'$ to all the vertices of $\Sigma$ adjacent to $u$ such that $\sigma_{\Gamma}(u'v) = \sigma(u'v), \ u \in N(v)$. The objective of this paper is to propose an algorithm for the generati
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KIM, YOUNG-ONE, and SIEYE RYU. "On the number of fixed points of a sofic shift-flip system." Ergodic Theory and Dynamical Systems 35, no. 2 (2013): 482–98. http://dx.doi.org/10.1017/etds.2013.57.

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AbstractIf $X$ is a sofic shift and $\varphi : X\rightarrow X$ is a homeomorphism such that ${\varphi }^{2} = {\text{id} }_{X} $ and $\varphi {\sigma }_{X} = { \sigma }_{X}^{- 1} \varphi $, the number of points in $X$ that are fixed by ${ \sigma }_{X}^{m} $ and ${ \sigma }_{X}^{n} \varphi , m= 1, 2, \ldots , n\in \mathbb{Z} $, is expressed in terms of a finite number of square matrices: the matrices are obtained from Krieger’s joint state chain of a sofic shift which is conjugate to $X$.
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Chen, Zhi, Zelin Zhu, Jiawei Li, Lizhen Yang, and Lei Cao. "Extreme Points of Certain Transportation Polytopes with Fixed Total Sums." Electronic Journal of Linear Algebra 37 (April 5, 2021): 256–71. http://dx.doi.org/10.13001/ela.2021.5141.

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Transportation matrices are $m\times n$ nonnegative matrices with given row sum vector $R$ and column sum vector $S$. All such matrices form the convex polytope $\mathcal{U}(R,S)$ which is called a transportation polytope and its extreme points have been classified. In this article, we consider a new class of convex polytopes $\Delta(\bar{R},\bar{S},\sigma)$ consisting of certain transportation polytopes satisfying that the sum of all elements is $\sigma$, and the row and column sum vectors are dominated componentwise by the given positive vectors $\bar{R}$ and $\bar{S}$, respectively. We char
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Preusser, Raimund. "Sandwich classification for GL n (R), O2n (R) and U2n (R,Λ) revisited". Journal of Group Theory 21, № 1 (2018): 21–44. http://dx.doi.org/10.1515/jgth-2017-0028.

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AbstractLetnbe a natural number greater than or equal to 3,Ra commutative ring and{\sigma\in\mathrm{GL}_{n}(R)}. We show that{t_{kl}(\sigma_{ij})}(resp.{t_{kl}(\sigma_{ii}-\sigma_{jj})}), where{i\neq j}and{k\neq l}can be expressed as a product of eight (resp. 24) matrices of the form{{}^{\epsilon}\sigma^{\pm 1}}, where{\epsilon\in E_{n}(R)}. We prove similar results for the orthogonal groups{\mathrm{O}_{2n}(R)}and the hyperbolic unitary groups{\mathrm{U}_{2n}(R,\Lambda)}under the assumption thatRis commutative and{n\geq 3}. This yields new, very short proofs of the Sandwich Classification Theo
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Loewy, Raphael. "Some additional notes on the spectra of non-negative symmetric 5 x 5 matrices." Electronic Journal of Linear Algebra 37, no. 37 (2021): 1–13. http://dx.doi.org/10.13001/ela.2021.5333.

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The Symmetric Non-negative Inverse Eigenvalue Problem (SNIEP) asks when is a list $ \sigma = \left( \lambda_{1}, \lambda_{2}, \dots, \lambda_{n} \right) $ of real, monotonically decreasing numbers, the spectrum of an $n \times n$, symmetric, non-negative matrix $A$. In that case, we say $\sigma$ is realizable and $A$ is a realizing matrix. Here, we consider the case $n=5$, the lowest value of $n$ for which the problem is unsolved. Let $ s_{1}(\sigma) = \sum_{i=1}^5 \lambda_{i} $ and $ s_{3}(\sigma) = \sum_{i=1}^5 {\lambda_{i}}^3 $. It is known that to complete the solution for $n=5$, it remain
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Loewy, Raphael. "Some additional notes on the spectra of non-negative symmetric 5 x 5 matrices." Electronic Journal of Linear Algebra 37, no. 37 (2021): 1–13. http://dx.doi.org/10.13001/ela.2021.5333.

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The Symmetric Non-negative Inverse Eigenvalue Problem (SNIEP) asks when is a list $ \sigma = \left( \lambda_{1}, \lambda_{2}, \dots, \lambda_{n} \right) $ of real, monotonically decreasing numbers, the spectrum of an $n \times n$, symmetric, non-negative matrix $A$. In that case, we say $\sigma$ is realizable and $A$ is a realizing matrix. Here, we consider the case $n=5$, the lowest value of $n$ for which the problem is unsolved. Let $ s_{1}(\sigma) = \sum_{i=1}^5 \lambda_{i} $ and $ s_{3}(\sigma) = \sum_{i=1}^5 {\lambda_{i}}^3 $. It is known that to complete the solution for $n=5$, it remain
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Hlavatý, Ladislav, Josef Navrátil, and Libor Šnobl. "ON RENORMALIZATION OF POISSON–LIE T-PLURAL SIGMA MODELS." Acta Polytechnica 53, no. 5 (2013): 433–37. http://dx.doi.org/10.14311/ap.2013.53.0433.

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Covariance of the one-loop renormalization group equations with respect to Poisson–Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson–Lie sigma models with truncated matrices of parameters is investigated.
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Preusser, Raimund. "Sandwich classification for O2n+1(R) and U2n+1(R,Δ) revisited". Journal of Group Theory 21, № 4 (2018): 539–71. http://dx.doi.org/10.1515/jgth-2018-0011.

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AbstractIn a recent paper, the author proved that if {n\geq 3} is a natural number, R a commutative ring and {\sigma\in GL_{n}(R)}, then {t_{kl}(\sigma_{ij})} where {i\neq j} and {k\neq l} can be expressed as a product of 8 matrices of the form {{}^{\varepsilon}\sigma^{\pm 1}} where {\varepsilon\in E_{n}(R)}. In this article we prove similar results for the odd-dimensional orthogonal groups {O_{2n+1}(R)} and the odd-dimensional unitary groups {U_{2n+1}(R,\Delta)} under the assumption that R is commutative and {n\geq 3}. This yields new, short proofs of the Sandwich Classification Theorems for
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Ganassali, Luca, Marc Lelarge, and Laurent Massoulié. "Spectral alignment of correlated Gaussian matrices." Advances in Applied Probability 54, no. 1 (2022): 279–310. http://dx.doi.org/10.1017/apr.2021.31.

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Abstract In this paper we analyze a simple spectral method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given two matrices A and B, we compute two corresponding leading eigenvectors $v_1$ and $v'_{\!\!1}$ . The algorithm returns the permutation $\hat{\pi}$ such that the rank of coordinate $\hat{\pi}(i)$ in $v_1$ and that of coordinate i in $v'_{\!\!1}$ (up to the sign of $v'_{\!\!1}$ ) are the same. We consider a model of weighted graphs where the adjacency matrix A belongs to the Gaussian orthogonal ensemble of size $N \times N$ , and B is a n
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Dissertations / Theses on the topic "Sigma matrices"

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Fournier, Bradford M. "Towards a Theory of Recursive Function Complexity: Sigma Matrices and Inverse Complexity Measures." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2072.

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This paper develops a data structure based on preimage sets of functions on a finite set. This structure, called the sigma matrix, is shown to be particularly well-suited for exploring the structural characteristics of recursive functions relevant to investigations of complexity. The matrix is easy to compute by hand, defined for any finite function, reflects intrinsic properties of its generating function, and the map taking functions to sigma matrices admits a simple polynomial-time algorithm . Finally, we develop a flexible measure of preimage complexity using the aforementioned matrix. Thi
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Najnudel, Joseph. "Sur certains objets universels liés à des changements de probabilité et des modèles de matrices aléatoires." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2011. http://tel.archives-ouvertes.fr/tel-00649552.

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Ce mémoire d'habilitation comporte deux parties. Dans la première, nous étudions une famille de mesures de probabilité construite à partir de la loi du mouvement brownien via une procédure appelée pénalisation. Nous expliquons une partie des résultats obtenus par la construction d'une mesure sigma-finie, que nous généralisons ensuite à d'autres contextes. Dans la deuxième partie, nous étudions des objets infini-dimensionnels associés à des modèles de matrices aléatoires.
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Sushma, Kumari. "Topics in random matrices and statistical machine learning." Kyoto University, 2018. http://hdl.handle.net/2433/235047.

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Ferioli, Elena. "The hybrid model matrix in industrial application: il caso Meta System S.p.A." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amslaurea.unibo.it/25086/.

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Negli ultimi decenni, nell’ambiente aziendale sta prendendo sempre più piede l’utilizzo di modelli specifici per l’approccio all’innovazione. Dei più comuni e utilizzati in letteratura, quelli analizzati in questo studio, sono lo Stage and Gate per lo sviluppo di nuovi prodotti, il Lean six-sigma per progetti di miglioramento, l’Agile per ottimizzare e velocizzare i processi, la Lean per ridurre gli sprechi e il Design Thinking per comprendere meglio i bisogni del cliente. Per sfruttare al meglio ogni modello è bene che le aziende abbiano una linea guida che illustri quando utilizzare e
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Åkesson, Emma, and David Gunnarsson. "Förstudie av transportsystem för spillmaterial : Fallstudie på INP Förpackningar AB." Thesis, Linnéuniversitetet, Institutionen för maskinteknik (MT), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-85580.

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Det finns olika tekniska lösningar för hantering, transport och återvinning av plastindustrins spillmaterial, men vilken metod som är mest lämpad för en specifik industri är svårt att avgöra. Syftet med studien var att få ökad kunskap och förståelse för hur faktorer som arbetsmiljöpåverkan, miljöpåverkan, funktion, flödeseffektivitet och investeringskostnad påverkar val av transportlösning för spillmaterial. Baserat på dessa faktorer är studiens mål att genom en förstudie presentera ett beslutsunderlag för en eventuell investering. För att finna den mest lämpade transportlösningen och förstå d
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Gennari, Elisa. "Sistemi semi-attivi per la riduzione delle vibrazioni indotte dal sisma: implementazione di un algoritmo di controllo ed applicazione ad un caso studio." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20147/.

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Il presente elaborato studia i dispositivi semi-attivi per il controllo strutturale, i quali combinano i vantaggi dei dissipatori passivi e della controparte attiva, vantando facilità nel controllo e fabbisogno energetico limitato. L'obiettivo della tesi è investigare l'efficacia degli smorzatori semi-attivi nel controllo e nella mitigazione della risposta sismica delle strutture, mostrando che la loro applicazione comporta un'efficace riduzione degli spostamenti interpiano rispetto alla struttura priva di sistemi di dissipazione. Attraverso l'analisi di un edificio in calcestruzzo armato
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Calisti, Matteo. "Misure di Hausdorff e formula dell'area in R^n." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17037/.

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La misura di Lebesgue permette di misurare il volume degli oggetti n-dimensionali di R^n, ma tutti quelli di dimensione inferiore s come le superfici sono sottoinsiemi di R^n di misura di Lebesgue nulla. Non potendo definire una nozione, ad esempio, di "area" attraverso suddivisioni successive come per la lunghezza di una curva si ricorre alla teoria della misura definendo la misura di Hausdorff s-dimensionale. Viene dapprima esposta la teoria della misura nella sua generalità, con alcune proprietà delle misure astratte e della sigma-algebra di Borel, una loro classificazione e alcuni teoremi
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Maltoni, Elia. "“Elaborazione ed implementazione di una metodologia innovativa per il miglioramento dei metodi di assemblaggio e di collaudo: il caso SCM Group S.p.A.”." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14396/.

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L'elaborato espone il contributo del candidato nel processo di elaborazione di una tecnica innovativa per il miglioramento dei metodi di assemblaggio e collaudo di MU-CN. Il modello sarà di riferimento per l’analisi delle attività a valore e spreco per tutto il gruppo aziendale. Facendo riferimento alle legioni romane: la tecnica vuole prima di tutto strutturare la strategia di attacco ovvero dichiarare come dovrebbero muoversi le legioni, poi enunciare ai singoli soldati (industrializzatori/ progettisti) come deve essere usata la spada (strumenti) ed infine quali delle spade a disposizione
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Book chapters on the topic "Sigma matrices"

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Badger, Simon, Johannes Henn, Jan Christoph Plefka, and Simone Zoia. "Solutions to the Exercises." In Lecture Notes in Physics. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-46987-9_5.

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Abstracthe sigma-matrix four-vector is defined as $$(\bar {\sigma }^{\mu })^{\dot {\alpha } \alpha } := ({\mathbb{1} },-\boldsymbol {\sigma })^{\top }$$ ( σ ̄ μ ) α ̇ α : = ( 𝟙 , − σ ) ⊤ , where $$\boldsymbol {\sigma } = (\hat \sigma _1,\hat \sigma _2, \hat \sigma _3)$$ σ = ( σ ̂ 1 , σ ̂ 2 , σ ̂ 3 ) is the list of the Pauli matrices $$\hat \sigma _i$$ σ ̂ i .
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Haake, Fritz, Sven Gnutzmann, and Marek Kuś. "Supersymmetry and Sigma Model for Random Matrices." In Quantum Signatures of Chaos. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97580-1_6.

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Zinn-Justin, Jean. "Quantum field theory: Asymptotic safety." In From Random Walks to Random Matrices. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0015.

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Chapter 15 examines the conditions under which it is possible to define renormalized quantum field theories (QFTs) consistent on all scales (a property not necessary for effective QFTs and not shared by ‘trivial’ theories like quantum electrodynamics (the triviality issue)). It has been conjectured that a necessary and, perhaps, sufficient condition is the existence of ultraviolet fixed points, a property called asymptotic safety. Examples are “asymptotically free” theories like non–Abelian gauge theories (quantum chromodynamics, or QCD) in four dimensions or the non–linear sigma model in two
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Zinn-Justin, Jean. "O(N) vector model in the ordered phase: Goldstone modes." In From Random Walks to Random Matrices. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0010.

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Chapter 10 examines the case of the spontaneous breaking of a continuous symmetry. When there is spontaneous symmetry breaking, the correlation length diverges at all temperatures in the ordered phase. Physical systems then display universal properties for all temperatures below Tc. This phenomenon is a consequence of the existence of Goldstone modes (massless bosons, in the quantum field theory terminology). Chapter 10 considers a lattice model with O(N) symmetry. In the continuum limit, it leads to the non–linear sigma model. A renormalization group can then be constructed and universal prop
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Zinn-Justin, Jean. "Quantum field theory: An effective theory." In From Random Walks to Random Matrices. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0008.

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Chapter 8 discusses effective field theory. This concept is inspired by the theory of critical phenomena in statistical physics and based on renormalization group ideas. The basic idea behind effective field theory is that one starts from a microscopic model involving an infinite number of fluctuating degrees of freedom whose interactions are characterized by a microscopic scale and in which, as a result of interactions, a length that is much larger than the microscopic scale, or, equivalently, a mass much smaller than the characteristic mass scale of the initial model, is generated. The chapt
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Hoyos L.R., Laikram A., Pérez-Ruiz D., and Puppala A.J. "Modeling unsaturated soil behavior under multiaxial stress states." In Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering. IOS Press, 2009. https://doi.org/10.3233/978-1-60750-031-5-182.

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This paper presents the results from a preliminary series of conventional triaxial compression (CTC) and triaxial compression (TC) tests conducted on compacted silty sand (SM) under constant-suction states. The experiments were conducted by using a novel, servo-controlled, true triaxial (cubical) apparatus that is suitable to test 3-in (7.5-cm) per side, cubical specimens of unsaturated soil under controlled-suction states and for a wide range of stress paths that are not achievable in a conventional cylindrical apparatus. The equipment is a mixed-boundary type of device, with the specimen sea
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Conference papers on the topic "Sigma matrices"

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Cajka, Tomas, Jiri Hricko, Lucie Rudl Kulhava, Michaela Novakova, Michaela Paucova, and Ondrej Kuda. "MetaboAtlas21: A comprehensive metabolome and lipidome atlas of mouse tissues and biofluids." In 2022 AOCS Annual Meeting & Expo. American Oil Chemists' Society (AOCS), 2022. http://dx.doi.org/10.21748/mzeg6052.

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Here, we present a specific atlas of mouse metabolome and lipidome (MetaboAtlas21) in the context of systemic energy balance (chow diet) and under chronic nutrient stress (high-fat diet). Male mice were fed a control (chow) diet for 2 months or a high-fat diet for 2 months and 10 months. Urine, plasma, feces, and 18 different tissues were collected from each animal for metabolomics and lipidomics analysis. These matrices cover digestive, excretory, respiratory, reproductive, endocrine, muscular, cardiovascular, and nervous systems. Also, chow and high-fat diet feeds were analyzed along with qu
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