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Aiyangar, A. K., Vivanco, J., Au, A. G., Anderson, P. A., Smith, E. L., & Ploeg, H. L. (2014). Dependence of Anisotropy of Human Lumbar Vertebral Trabecular Bone on Quantitative Computed TomographyBased Apparent Density. J. Biomech. Eng.Trans. ASME, 136(9), 10 pp.
Abstract: Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical propertydensity relationships have presented results for the superiorinferior (SI), or “ onaxis” direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) densitydependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCTbased apparent density of HVTB and its apparent compressive mechanical propertieselastic modulus (Eapp), yield strength (sigma(y)), and yield strain (epsilon(y))in the SI and TR directions for future clinical QCTbased continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, rho(CT). Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, rho(app), showed significant correlation with rho(CT) [rho(CT) = 1.0568 x rho(app), r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (Eapp) and yield strength (sigma(y)) were linearly related to the rho(CT) in the axial direction [ESI = 1493.8 x (rho(CT)), r = 0.77, p < 0.01; sigma(Y,SI) = 6.9 x (rho(CT)) = 0.13, r = 0.76, p < 0.01] while a powerlaw relation provided the best fit in the transverse direction [ETR 3349.1 x (rho(CT))(1.94), r = 0.89, p < 0.01; sigma(Y,TR) 18.81 x (rho(CT)) 1.83, r = 0.83, p < 0.01]. No significant correlation was found between epsilon(y) and rho(CT) in either direction. Eapp and sigma(y) in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, epsilon(y) exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CTbased densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.

Lobos, F., Goles, E., Ruivo, E. L. P., de Oliveira, P. P. B., & Montealegre, P. (2018). Mining a Class of Decision Problems for Onedimensional Cellular Automata. J. Cell. Autom., 13(56), 393–405.
Abstract: Cellular automata are locally defined, homogeneous dynamical systems, discrete in space, time and state variables. Within the context of onedimensional, binary, cellular automata operating on cyclic configurations of odd length, we consider the general decision problem: if the initial configuration satisfies a given property, the lattice should converge to the fixedpoint of all 1s ((1) over right arrow), or to (0) over right arrow, otherwise. Two problems in this category have been widely studied in the literature, the parity problem [1] and the density classification task [4]. We are interested in determining all cellular automata rules with neighborhood sizes of 2, 3, 4 and 5 cells (i.e., radius r of 0.5, 1, 1.5 and 2.5) that solve decision problems of the previous type. We have demonstrated a theorem that, for any given rule in those spaces, ensures the non existence of fixed points other than (0) over right arrow and (1) over right arrow for configurations of size larger than 2(2r), provided that the rule does not support different fixed points for any configuration with size smaller than or equal to 2(2r). In addition, we have a proposition that ensures the convergence to only (0) over right arrow or (1) over right arrow of any initial configuration, if the rule complies with given conditions. By means of theoretical and computational approaches, we determined that: for the rule spaces defined by radius 0.5 and r = 1, only 1 and 2 rules, respectively, converge to (1) over right arrow or (0) over right arrow, to any initial configuration, and both recognize the same language, and for the rule space defined by radius r = 1.5, 40 rules satisfy this condition and recognize 4 different languages. Finally, for the radius 2 space, out of the 4,294,967,296 different rules, we were able to significantly filter it out, down to 40,941 candidate rules. We hope such an extensive mining should unveil new decision problems of the type widely studied in the literature.

Mahajan, S. M., & Asenjo, F. A. (2015). Hot Fluids and Nonlinear Quantum Mechanics. Int. J. Theor. Phys., 54(5), 1435–1449.
Abstract: A hot relativistic fluid is viewed as a collection of quantum objects that represent interacting elementary particles. We present a conceptual framework for deriving nonlinear equations of motion obeyed by these hypothesized objects. A uniform phenomenological prescription, to affect the quantum transition from a corresponding classical system, is invoked to derive the nonlinear Schrodinger, KleinGordon, and PauliSchrodinger and FeynmanGellMaan equations. It is expected that the emergent hypothetical nonlinear quantum mechanics would advance, in a fundamental way, both the conceptual understanding and computational abilities, particularly, in the field of extremely high energydensity physics.

MontalvaMedel, M., de Oliveira, P. P. B., & Goles, E. (2018). A portfolio of classification problems by onedimensional cellular automata, over cyclic binary configurations and parallel update. Nat. Comput., 17(3), 663–671.
Abstract: Decision problems addressed by cellular automata have been historically expressed either as determining whether initial configurations would belong to a given language, or as classifying the initial configurations according to a property in them. Unlike traditional approaches in language recognition, classification problems have typically relied upon cyclic configurations and fully paralell (twoway) update of the cells, which render the action of the cellular automaton relatively less controllable and difficult to analyse. Although the notion of cyclic languages have been studied in the wider realm of formal languages, only recently a more systematic attempt has come into play in respect to cellular automata with fully parallel update. With the goal of contributing to this effort, we propose a unified definition of classification problem for onedimensional, binary cellular automata, from which various known problems are couched in and novel ones are defined, and analyse the solvability of the new problems. Such a unified perspective aims at increasing existing knowledge about classification problems by cellular automata over cyclic configurations and parallel update.

Vivanco, J. F., Burgers, T. A., GarciaRodriguez, S., Crookshank, M., Kunz, M., MacIntyre, N. J., et al. (2014). Estimating the density of femoral head trabecular bone from hip fracture patients using computed tomography scan data. Proc. Inst. Mech. Eng. Part HJ. Eng. Med., 228(6), 616–626.
Abstract: The purpose of this study was to compare computed tomography density (rho(CT)) obtained using typical clinical computed tomography scan parameters to ash density (rho(ash)), for the prediction of densities of femoral head trabecular bone from hip fracture patients. An experimental study was conducted to investigate the relationships between rho(ash) and rho(CT) and between each of these densities and rho(bulk) and rho(dry). Seven human femoral heads from hip fracture patients were computed tomographyscanned ex vivo, and 76 cylindrical trabecular bone specimens were collected. Computed tomography density was computed from computed tomography images by using a calibration Hounsfield unitsbased equation, whereas rho(bulk), rho(dry) and rho(ash) were determined experimentally. A large variation was found in the mean Hounsfield units of the bone cores (HUcore) with a constant bias from rho(CT) to rho(ash) of 42.5 mg/cm(3). Computed tomography and ash densities were linearly correlated (R2 = 0.55, p < 0.001). It was demonstrated that rho(ash) provided a good estimate of rho(bulk) (R2 = 0.78, p < 0.001) and is a strong predictor of rho(dry) (R2 = 0.99, p < 0.001). In addition, the rho(CT) was linearly related to rho(bulk) (R2 = 0.43, p < 0.001) and rho(dry) (R2 = 0.56, p < 0.001). In conclusion, mineral density was an appropriate predictor of rho(bulk) and rho(dry), and rho(CT) was not a surrogate for rho(ash). There were linear relationships between rho(CT) and physical densities; however, following the experimental protocols of this study to determine rho(CT), considerable scatter was present in the rho(CT) relationships.
