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Journal articles on the topic 'Generalised Cantor Set'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

OLSON, ERIC J., JAMES C. ROBINSON, and NICHOLAS SHARPLES. "Generalised Cantor sets and the dimension of products." Mathematical Proceedings of the Cambridge Philosophical Society 160, no. 1 (2015): 51–75. http://dx.doi.org/10.1017/s0305004115000584.

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AbstractIn this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the cardinality of local covers at all length-scales and at all points, and we show that a large class of homogeneous Moran sets have this property. We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lower box-counting dimensions provided that the set ‘attains’ these dimensions (analogous to ‘s-sets’ when c

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SIMON, KÁROLY, and KRYSTAL TAYLOR. "Interior of sums of planar sets and curves." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 1 (2018): 119–48. http://dx.doi.org/10.1017/s0305004118000580.

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AbstractRecently, considerable attention has been given to the study of the arithmetic sum of two planar sets. We focus on understanding the interior (A + Γ)°, when Γ is a piecewise ${\mathcal C}^2$ curve and A ⊂ ℝ2. To begin, we give an example of a very large (full-measure, dense, Gδ) set A such that (A + S1)° = ∅, where S1 denotes the unit circle. This suggests that merely the size of A does not guarantee that (A + S1)° ≠ ∅. If, however, we assume that A is a kind of generalised product of two reasonably large sets, then (A + Γ)° ≠ ∅ whenever Γ has non-vanishing curvature. As a byproduct of

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MUKHAMEDOV, FARRUKH, and OTABEK KHAKIMOV. "ON A GENERALIZED SELF-SIMILARITY IN THE p-ADIC FIELD." Fractals 24, no. 04 (2016): 1650041. http://dx.doi.org/10.1142/s0218348x16500419.

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In the present paper, we introduce a new set which defines a generalized self-similar set for contractive functions [Formula: see text] on the unit ball [Formula: see text] of [Formula: see text]-adic numbers. This set is called unconventional limit set. We prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set.

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Hosokawa, Iwao, Shin-ichi Oide, and Kiyoshi Yamamoto. "Trinomial Generalized Cantor Set Model for Isotropic Turbulence." Journal of the Physical Society of Japan 65, no. 4 (1996): 873–75. http://dx.doi.org/10.1143/jpsj.65.873.

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Cherny, A. Yu, E. M. Anitas, A. I. Kuklin, M. Balasoiu, and V. A. Osipov. "Scattering from generalized Cantor fractals." Journal of Applied Crystallography 43, no. 4 (2010): 790–97. http://dx.doi.org/10.1107/s0021889810014184.

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A fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set, is considered. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodisper

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UCHIMURA, KEISUKE. "THE SETS OF POINTS WITH BOUNDED ORBITS FOR GENERALIZED CHEBYSHEV MAPPINGS." International Journal of Bifurcation and Chaos 11, no. 01 (2001): 91–107. http://dx.doi.org/10.1142/s0218127401002018.

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We study the dynamical systems given by generalized Chebyshev mappings [Formula: see text] and show that (1) the set of points with bounded orbits of Fc(z) is connected and its complement in C∪{∞} is simply connected if and only if -4 ≤ c ≤ 2; (2) if c > 2, then the set of points with bounded orbits of Fc(z) is Cantor set. These results are the analogue of the theory of filled Julia sets of quadratic polynomials in one complex variable. We show that the mapping Fc(z) has relation to an important holomorphic map on the complex projective space P2.

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Rizkalla, Raafat Riad. "An orthonormal system on the construction of the generalized cantor set." International Journal of Mathematics and Mathematical Sciences 16, no. 4 (1993): 737–48. http://dx.doi.org/10.1155/s0161171293000924.

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This paper presents a new complete orthonormal system of functions defined on the interval[0,1]and whose supports shrink to nothing. This system related to the construction of the Cantor ternary set. We defined the canonicalmap ξand proved the equivalence between this system and the Walsh system. The generalized Cantor set with any dissection ratio is established and the constructed system is defined in the general case.

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Yang, Zhuowei, and Ping Wang. "DNA Sequences with Forbidden Words and the Generalized Cantor Set." Journal of Applied Mathematics and Physics 07, no. 08 (2019): 1687–96. http://dx.doi.org/10.4236/jamp.2019.78115.

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Soare, M. A., and R. C. Picu. "Spectral decomposition of random fields defined over the generalized Cantor set." Chaos, Solitons & Fractals 37, no. 2 (2008): 566–73. http://dx.doi.org/10.1016/j.chaos.2006.09.032.

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BLANCHARD, PAUL, ROBERT L. DEVANEY, ANTONIO GARIJO, and ELIZABETH D. RUSSELL. "A GENERALIZED VERSION OF THE MCMULLEN DOMAIN." International Journal of Bifurcation and Chaos 18, no. 08 (2008): 2309–18. http://dx.doi.org/10.1142/s0218127408021725.

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We study the family of complex maps given by Fλ(z) = zn + λ/zn + c where n ≥ 3 is an integer, λ is an arbitrarily small complex parameter, and c is chosen to be the center of a hyperbolic component of the corresponding Multibrot set. We focus on the structure of the Julia set for a map of this form generalizing a result of McMullen. We prove that it consists of a countable collection of Cantor sets of closed curves and an uncountable number of point components.

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BALANKIN, A. S., J. BORY-REYES, M. E. LUNA-ELIZARRARÁS, and M. SHAPIRO. "CANTOR-TYPE SETS IN HYPERBOLIC NUMBERS." Fractals 24, no. 04 (2016): 1650051. http://dx.doi.org/10.1142/s0218348x16500511.

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The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane. Three types of the hyperbolic analogues of the real Cantor set are identified. The complementary nature of the real Cantor dust and the real Sierpinski carpet on the hyperbolic plane are outlined. The relevance of these findings in the context of modern physics are briefly discussed.

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PAN, XUEZAI, XUDONG SHANG, MINGGANG WANG, and ZUO-FEI. "THE CANTOR SET’S MULTI-FRACTAL SPECTRUM FORMED BY DIFFERENT PROBABILITY FACTORS IN MATHEMATICAL EXPERIMENT." Fractals 25, no. 01 (2017): 1750002. http://dx.doi.org/10.1142/s0218348x17500025.

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With the purpose of researching the changing regularities of the Cantor set’s multi-fractal spectrums and generalized fractal dimensions under different probability factors, from statistical physics, the Cantor set is given a mass distribution, when the mass is given with different probability ratios, the different multi-fractal spectrums and the generalized fractal dimensions will be acquired by computer calculation. The following conclusions can be acquired. On one hand, the maximal width of the multi-fractal spectrum and the maximal vertical height of the generalized fractal dimension will

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Howard, Paul, and Eleftherios Tachtsis. "On the set-theoretic strength of the $n$-compactness of generalized Cantor cubes." Fundamenta Mathematicae 234, no. 3 (2016): 241–52. http://dx.doi.org/10.4064/fm961-1-2016.

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Chuprikov, N. L., and D. N. Zhabin. "Electron tunnelling through a self-similar fractal potential on the generalized Cantor set." Journal of Physics A: Mathematical and General 33, no. 23 (2000): 4309–16. http://dx.doi.org/10.1088/0305-4470/33/23/308.

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Nagaraj, Nithin. "Using cantor sets for error detection." PeerJ Computer Science 5 (January 14, 2019): e171. http://dx.doi.org/10.7717/peerj-cs.171.

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Error detection is a fundamental need in most computer networks and communication systems in order to combat the effect of noise. Error detection techniques have also been incorporated with lossless data compression algorithms for transmission across communication networks. In this paper, we propose to incorporate a novel error detection scheme into a Shannon optimal lossless data compression algorithm known as Generalized Luröth Series (GLS) coding. GLS-coding is a generalization of the popular Arithmetic Coding which is an integral part of the JPEG2000 standard for still image compression. G

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Macek, W. M. "Multifractality and intermittency in the solar wind." Nonlinear Processes in Geophysics 14, no. 6 (2007): 695–700. http://dx.doi.org/10.5194/npg-14-695-2007.

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Abstract. Within the complex dynamics of the solar wind's fluctuating plasma parameters, there is a detectable, hidden order described by a chaotic strange attractor which has a multifractal structure. The multifractal spectrum has been investigated using Voyager (magnetic field) data in the outer heliosphere and using Helios (plasma) data in the inner heliosphere. We have also analyzed the spectrum for the solar wind attractor. The spectrum is found to be consistent with that for the multifractal measure of the self-similar one-scale weighted Cantor set with two parameters describing uniform

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Mahapatra, Prasadini, and Divya Singh. "Scaling sets and generalized scaling sets on Cantor dyadic group." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 04 (2020): 2050019. http://dx.doi.org/10.1142/s0219691320500198.

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Scaling and generalized scaling sets determine wavelet sets and hence wavelets. In real case, wavelet sets were proved to be an important tool for the construction of MRA as well as non-MRA wavelets. However, any result related to scaling/generalized scaling sets is not available in case of locally compact abelian groups. This paper gives a characterization of scaling sets and its generalized version along with relevant examples in dual Cantor dyadic group [Formula: see text]. These results can further be generalized to arbitrary locally compact abelian groups.

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JAFARI, HOSSEIN, JYOTI GEETESH PRASAD, PRANAY GOSWAMI, and RAVI SHANKER DUBEY. "SOLUTION OF THE LOCAL FRACTIONAL GENERALIZED KDV EQUATION USING HOMOTOPY ANALYSIS METHOD." Fractals 29, no. 05 (2021): 2140014. http://dx.doi.org/10.1142/s0218348x21400144.

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In this paper, we solve the [Formula: see text]-Generalized KdV equation by local fractional homotopy analysis method (LFHAM). Further, we analyze the approximate solution in the form of non-differentiable generalized functions defined on Cantor sets. Some examples and special cases of the main results are also discussed.

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Macek, W. M., and A. Wawrzaszek. "Multifractal two-scale Cantor set model for slow solar wind turbulence in the outer heliosphere during solar maximum." Nonlinear Processes in Geophysics 18, no. 3 (2011): 287–94. http://dx.doi.org/10.5194/npg-18-287-2011.

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Abstract. To quantify solar wind turbulence, we consider a generalized two-scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We examine generalized dimensions and the corresponding multifractal singularity spectrum depending on one probability measure parameter and two rescaling parameters. In particular, we analyse time series of velocities of the slow speed streams of the solar wind measured in situ by Voyager 2 spacecraft in the outer heliosphere during solar maximum at various distanc

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Öztürk, Melike, and Çiğdem Alabaş-Uslu. "Cantor set based neighbor generation method for permutation solution representation." Journal of Intelligent & Fuzzy Systems 39, no. 5 (2020): 6157–68. http://dx.doi.org/10.3233/jifs-189086.

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Metaheuristics gained world-wide popularity and researchers have been studying them vigorously in the last two decades. A relatively less explored approach in the improvement of metaheuristics is to design new neighbor generation mechanisms. Neighbor generation mechanisms are very important in the success of any single solution-based heuristic since they directly guide the search. In this study, a neighbor generation mechanism called cantor-set based (CB) method for single solution-based heuristics which use permutation solution representation is described. The inspiration for CB method stems

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Freiberg, Uta, and Jörg-Uwe Löbus. "Zeros of eigenfunctions of a class of generalized second order differential operators on the Cantor set." Mathematische Nachrichten 265, no. 1 (2004): 3–14. http://dx.doi.org/10.1002/mana.200310133.

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22

Gaynor, Sheila M., Ryan Sun, Xihong Lin, and John Quackenbush. "Identification of differentially expressed gene sets using the Generalized Berk–Jones statistic." Bioinformatics 35, no. 22 (2019): 4568–76. http://dx.doi.org/10.1093/bioinformatics/btz277.

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Abstract Motivation Cancer genomics studies frequently aim to identify genes that are differentially expressed between clinically distinct patient subgroups, generally by testing single genes one at a time. However, the results of any individual transcriptomic study are often not fully reproducible. A particular challenge impeding statistical analysis is the difficulty of distinguishing between differential expression comprising part of the genomic disease etiology and that induced by downstream effects. More robust analytical approaches that are well-powered to detect potentially causative ge

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van den Berg, Benno, and Ieke Moerdijk. "The axiom of multiple choice and models for constructive set theory." Journal of Mathematical Logic 14, no. 01 (2014): 1450005. http://dx.doi.org/10.1142/s0219061314500056.

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We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory (hence acceptable from a constructive and generalized-predicative standpoint). In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as more gene

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SALEJDA, WŁODZIMIERZ. "LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA." International Journal of Modern Physics B 09, no. 12 (1995): 1429–51. http://dx.doi.org/10.1142/s0217979295000628.

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The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the ma

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Donoven, Casey, and Feyishayo Olukoya. "Conjugate subgroups and overgroups of Vn." International Journal of Algebra and Computation 30, no. 06 (2020): 1129–60. http://dx.doi.org/10.1142/s0218196720500344.

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We describe subgroups and overgroups of the generalized Thompson groups [Formula: see text] which arise via conjugation by rational homeomorphisms of Cantor space. We specifically consider conjugating [Formula: see text] by homeomorphisms induced by synchronizing transducers and their inverses. Our descriptions of the subgroups and overgroups use properties of the conjugating transducer to either restrict or augment the action of [Formula: see text] on Cantor space. We also consider a class [Formula: see text] of transducers containing all invertible, initial transducers. We associate to every

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BRUIN, HENK, GERHARD KELLER, and MATTHIAS ST. PIERRE. "Adding machines and wild attractors." Ergodic Theory and Dynamical Systems 17, no. 6 (1997): 1267–87. http://dx.doi.org/10.1017/s0143385797086392.

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We investigate the dynamics of unimodal maps $f$ of the interval restricted to the omega limit set $X$ of the critical point for cases where $X$ is a Cantor set. In particular, many cases where $X$ is a measure attractor of $f$ are included. We give two classes of examples of such maps, both generalizing unimodal Fibonacci maps [LM, BKNS]. In all cases $f_{|X}$ is a continuous factor of a generalized odometer (an adding machine-like dynamical system), and at the same time $f_{|X}$ factors onto an irrational circle rotation. In some of the examples we obtain irrational rotations on more complic

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Hittmeyer, Stefanie, Bernd Krauskopf та Hinke M. Osinga. "Interactions of the Julia Set with Critical and (Un)Stable Sets in an Angle-Doubling Map on ℂ\{0}". International Journal of Bifurcation and Chaos 25, № 04 (2015): 1530013. http://dx.doi.org/10.1142/s021812741530013x.

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We study a nonanalytic perturbation of the complex quadratic family z ↦ z2 + c in the form of a two-dimensional noninvertible map that has been introduced by Bamón et al. [2006]. The map acts on the plane by opening up the critical point to a disk and wrapping the plane twice around it; points inside the disk have no preimages. The bounding critical circle and its images, together with the critical point and its preimages, form the so-called critical set. For parameters away from the complex quadratic family we define a generalized notion of the Julia set as the basin boundary of infinity. We

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QIU, HUA. "Exact Hausdorff and packing measures of Cantor sets with overlaps." Ergodic Theory and Dynamical Systems 35, no. 8 (2014): 2632–68. http://dx.doi.org/10.1017/etds.2014.48.

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Let $K$ be the attractor of a linear iterated function system (IFS) $S_{j}(x)={\it\rho}_{j}x+b_{j},j=1,\ldots ,m$, on the real line $\mathbb{R}$ satisfying the generalized finite type condition (whose invariant open set ${\mathcal{O}}$ is an interval) with an irreducible weighted incidence matrix. This condition was recently introduced by Lau and Ngai [A generalized finite type condition for iterated function systems. Adv. Math.208 (2007), 647–671] as a natural generalization of the open set condition, allowing us to include many important overlapping cases. They showed that the Hausdorff and

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Sun, Ryan, Shirley Hui, Gary D. Bader, Xihong Lin, and Peter Kraft. "Powerful gene set analysis in GWAS with the Generalized Berk-Jones statistic." PLOS Genetics 15, no. 3 (2019): e1007530. http://dx.doi.org/10.1371/journal.pgen.1007530.

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Beckman, Micaela F., Farah Bahrani Mougeot, and Jean-Luc C. Mougeot. "Comorbidities and Susceptibility to COVID-19: A Generalized Gene Set Data Mining Approach." Journal of Clinical Medicine 10, no. 8 (2021): 1666. http://dx.doi.org/10.3390/jcm10081666.

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The COVID-19 pandemic has led to over 2.26 million deaths for almost 104 million confirmed cases worldwide, as of 4 February 2021 (WHO). Risk factors include pre-existing conditions such as cancer, cardiovascular disease, diabetes, and obesity. Although several vaccines have been deployed, there are few alternative anti-viral treatments available in the case of reduced or non-existent vaccine protection. Adopting a long-term holistic approach to cope with the COVID-19 pandemic appears critical with the emergence of novel and more infectious SARS-CoV-2 variants. Our objective was to identify co

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Jabo, Brice, John W. Morgan, Mayada A. Aljehani, Matthew J. Selleck, and Albert Y. Lin. "A personalized, web-based prognostic tool for resectable gastric cancer." Journal of Clinical Oncology 35, no. 15_suppl (2017): e15575-e15575. http://dx.doi.org/10.1200/jco.2017.35.15_suppl.e15575.

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e15575 Background: Gastric cancer (GC) mortality remains high, with a 5-year survival of 30 percent. For patients with resectable GC, mortality varies depending on both patient and tumor characteristics. The current study sought to develop a web-based prognostic model to assist patients and health care providers in decision making regarding either surgery-only or adjuvant chemoradiotherapy (CRT). Methods: California SEER data was used and records, including demographic, pathologic, and treatment information, for 2,583 patients diagnosed with stage IB to III GC and treated with either surgery o

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SUN, JIANSHE. "ANALYTICAL APPROXIMATE SOLUTIONS OF (N + 1)-DIMENSIONAL FRACTAL HARRY DYM EQUATIONS." Fractals 26, no. 06 (2018): 1850094. http://dx.doi.org/10.1142/s0218348x18500949.

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The new fractal models of the [Formula: see text]-dimensional and [Formula: see text]-dimensional nonlinear local fractional Harry Dym equation (HDE) on Cantor sets are derived and the analytical approximate solutions of the above two new models are obtained by coupling the fractional complex transform via local fractional derivative (LFD) and local fractional reduced differential transform method (LFRDTM). Fractional complex transform for functions of [Formula: see text]-dimensional variables is generalized and the theorems of [Formula: see text]-dimensional LFRDTM are supplementary extended.

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Egenvall, A., A. Byström, L. Roepstorff, M. Rhodin, M. Eisersiö, and H. M. Clayton. "Modelling rein tension during riding sessions using the generalised additive modelling technique." Comparative Exercise Physiology 14, no. 4 (2018): 209–21. http://dx.doi.org/10.3920/cep180017.

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General additive modelling (GAM-modelling) is an exploratory technique that can be used on longitudinal (time series) data, e.g. rein tension, over a period of time. The aim was to apply GAM-modelling to investigate changes in rein tension during a normal flatwork training session. Six riders each rode two or three of their horses (n=17 horses) during a normal flatwork/dressage training session with video recordings and rein tension measurements (128 Hz). Training sessions were classified according to rider position, stride length and whether horses were straight, bent to the left or bent to t

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Cho, Seong Beom. "Set-Wise Differential Interaction between Copy Number Alterations and Gene Expressions of Lower-Grade Glioma Reveals Prognosis-Associated Pathways." Entropy 22, no. 12 (2020): 1434. http://dx.doi.org/10.3390/e22121434.

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The integrative analysis of copy number alteration (CNA) and gene expression (GE) is an essential part of cancer research considering the impact of CNAs on cancer progression and prognosis. In this research, an integrative analysis was performed with generalized differentially coexpressed gene sets (gdCoxS), which is a modification of dCoxS. In gdCoxS, set-wise interaction is measured using the correlation of sample-wise distances with Renyi’s relative entropy, which requires an estimation of sample density based on omics profiles. To capture correlations between the variables, multivariate de

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Yüksel, Şaziye, Zehra Güzel Ergül, and Naime Tozlu. "Soft Covering Based Rough Sets and Their Application." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/970893.

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Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft u

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Shakeel, P. Mohamed, Amr Tolba, Zafer Al-Makhadmeh, and Mustafa Musa Jaber. "Automatic detection of lung cancer from biomedical data set using discrete AdaBoost optimized ensemble learning generalized neural networks." Neural Computing and Applications 32, no. 3 (2019): 777–90. http://dx.doi.org/10.1007/s00521-018-03972-2.

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Iguchi, Kazumoto. "The Saxon–Hutner Theorem, its Converse Theorem and their Applications to Localization and Delocalization Problems in Binary Quasiperiodic Lattices." International Journal of Modern Physics B 11, no. 18 (1997): 2157–82. http://dx.doi.org/10.1142/s0217979297001118.

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In this paper we discuss the application of the Saxon–Hutner theorem and its converse theorem in one-dimensional binary disordered lattices to the one-dimensional binary quasiperiodic lattices. We first summarize some basic theorems in one-dimensional periodic lattices. We discuss how the bulk and edge states are treated in the transfer matrix method. Second, we review the Saxon–Hutner theorem and prove the converse theorem, using the so-called Fricke identities. Third, we present an alternative approach for a rigorous proof of the existence of a Cantor-set spectrum in the Fibonacci lattice an

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Hare, Kathryn E., Kevin G. Hare, and Michael Ka Shing Ng. "Local Dimensions of Measures of Finite Type II: Measures Without Full Support and With Non-regular Probabilities." Canadian Journal of Mathematics 70, no. 4 (2018): 824–67. http://dx.doi.org/10.4153/cjm-2017-025-6.

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AbstractConsider a finite sequence of linear contractions Sj(x) = px + dj and probabilities pj > 0 with ∑Pj = 1. We are interested in the self-similar measure , of finite type. In this paper we study the multi-fractal analysis of such measures, extending the theory to measures arising from non-regular probabilities and whose support is not necessarily an interval.Under some mild technical assumptions, we prove that there exists a subset of supp μ of full μ and Hausdorff measure, called the truly essential class, for which the set of (upper or lower) local dimensions is a closed interval. Wi

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Tian, Yansheng, Tong Hao, Bin Cao, et al. "Clinical End-Points Associated withMycobacterium tuberculosisand Lung Cancer: Implications into Host-Pathogen Interaction and Coevolution." BioMed Research International 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/827829.

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There is a recent emerging theory that suggests a cross-link between pathogens and cancer. In this context, we examined the association between theMycobacterium tuberculosis(MTB) with its L-forms (MTB-L) and lung cancer. In the present study, we have optimized and applied a highly sensitive assay to detect the presence of MTB and MTB-L in 187 lung cancer samples and 39 samples of other cancer origins. By carefully controlling confounding factors, we have found that 62% of the lung cancer samples are MTB-L positive, while only 5.1% of the other cancer samples are MTB-L positive. Through general

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Kim, Jinchul, Ja Hyun Yeo, Jung Yong Hong, et al. "A clinical scoring system for survival prediction in advanced gastric cancer." Journal of Clinical Oncology 38, no. 4_suppl (2020): 436. http://dx.doi.org/10.1200/jco.2020.38.4_suppl.436.

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436 Background: We established a scoring system using easily approachable clinical characteristics at the timing of initiating palliative chemotherapy to achieve accurate overall survival prediction to first-line treatment consisting of fluoropyrimidines in patients with advanced gastric cancer. Methods: A total of 1,733 patients were included in the study. The dataset was split into a training (n=1156, 67%) and validation set (n=577, 33%). Top-ranked variables were identified using the Random Forest for Survival algorithm and analyzed into a Cox regression model, thereby constructing the scor

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Dixon, Paul W. "Axiomatic Construction for Language Creativity and Self-Actualization." Perceptual and Motor Skills 77, no. 1 (1993): 203–6. http://dx.doi.org/10.2466/pms.1993.77.1.203.

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Piagetian theory views intellective development in children as the unfolding of the axioms which form the basis of symbolic logic through maturation and learning. The modern derivation of set theory from these axioms may be seen as a model of how we formulate valid inferences. The axiomatic construction of the aleph null as equal to 1, which may be derived from the Cantorian algebra, can be used to extend the axiomatic basis of propositional calculus seen as the epistemological root of human knowledge by Piaget. A central postulation regarding natural languages proposed by Chomsky is the creat

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DARST, R. B., J. A. PALAGALLO, and T. E. PRICE. "GENERALIZATIONS OF THE KOCH CURVE." Fractals 16, no. 03 (2008): 267–74. http://dx.doi.org/10.1142/s0218348x08003971.

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We present an iterative method to define a two-parameter family of continuous functions fa,θ: I → ℂ such that f1/3,π/3 is the Koch curve. We consider the two-cases θ = π/3 and θ = π/4 of these generalized Koch curves fa,θ(I). In each case we determine the pivotal value of a, the largest value of a for which the corresponding curve is not simple. We give characterizations of the double points of the curve (points on the curve that have two inverse images). In the case where θ = π/3 double points are vertices of equilateral triangles. When θ = π/4 the double points form Cantor sets in the plane.

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Macías-Díaz, Jorge E., and Siegfried Macías. "An equivalence criterion for the generalized injectivity of modules with respect to algebraic classes of homomorphisms." Journal of Algebra and Its Applications 15, no. 09 (2016): 1650166. http://dx.doi.org/10.1142/s0219498816501668.

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Departing from a general definition of injectivity of modules with respect to suitable algebraic classes of morphisms, we establish conditions under which two modules are isomorphic when they are isomorphic to submodules of each other. The main result of this work extends both Bumby’s criterion for the isomorphism of injective modules and the well-known Cantor–Bernstein–Schröder’s theorem on the cardinality of sets. In the way, various properties on essential extensions, injective modules and injective hulls are generalized. The applicability of our main theorem embraces the cases of [Formula:

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Kundu, Prosenjit, Runlong Tang, and Nilanjan Chatterjee. "Generalized meta-analysis for multiple regression models across studies with disparate covariate information." Biometrika 106, no. 3 (2019): 567–85. http://dx.doi.org/10.1093/biomet/asz030.

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Summary Meta-analysis is widely popular for synthesizing information on common parameters of interest across multiple studies because of its logistical convenience and statistical efficiency. We develop a generalized meta-analysis approach to combining information on multivariate regression parameters across multiple studies that have varying levels of covariate information. Using algebraic relationships among regression parameters in different dimensions, we specify a set of moment equations for estimating parameters of a maximal model through information available from sets of parameter esti

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Steenkamp, Jan-Benedict E. M., Hans C. M. Van Trijp, and Jos M. F. Ten Berge. "Perceptual Mapping Based on Idiosyncratic Sets of Attributes." Journal of Marketing Research 31, no. 1 (1994): 15–27. http://dx.doi.org/10.1177/002224379403100102.

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The authors describe a compositional perceptual mapping procedure, unrestricted attribute-elicitation mapping (UAM), which allows consumers to describe and rate the brands in their own terminology and thus relaxes the restrictive assumptions of traditional compositional mapping techniques regarding the structure and interpretation of the set of attributes. They compare the performance of three estimation techniques for constructing a group space based on the idiosyncratic data, namely, INDSCAL, CANCOR, and generalized procrustes analysis (GPA). Their findings indicate that the three estimation

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Grineski, Sara E., Timothy W. Collins, and Ricardo Rubio. "Distributional Environmental Injustices for a Minority Group without Minority Status: Arab Americans and Residential Exposure to Carcinogenic Air Pollution in the US." International Journal of Environmental Research and Public Health 16, no. 24 (2019): 4899. http://dx.doi.org/10.3390/ijerph16244899.

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Distributional environmental injustices in residential exposure to air pollution in Arab American enclaves have not been examined. We conducted our investigation at the census tract-level across the continental United States using a set of socio-demographic variables to predict cancer risk from hazardous air pollutant (HAP) exposure. Arab enclaves had a mean cancer risk score of 44.08, as compared to 40.02 in non-enclave tracts. In terms of the specific origin groups, Moroccan enclaves had the highest cancer risk score (46.93), followed by Egyptian (45.33), Iraqi (43.13), Jordanian (41.67), an

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Royce, Trevor Joseph, Andrew Roberts, Stacie Dusetzina, and Ankit Agarwal. "Opioid prescribing patterns among generalists & oncologists for Medicare Part D beneficiaries from 2013-2017." Journal of Clinical Oncology 38, no. 15_suppl (2020): 2070. http://dx.doi.org/10.1200/jco.2020.38.15_suppl.2070.

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2070 Background: In response to the opioid crisis, recent policies aiming to reduce opioid prescribing, misuse, & abuse have generated concern that patients with cancer pain may unintentionally experience reduced access to necessary opioid therapy. It is unknown how opioid prescribing patterns have changed between generalists and oncologists during this era. Methods: We conducted a longitudinal repeated cross-sectional study estimating adjusted annual national trends in opioid prescribing among generalists & oncologists using the Medicare Part D Prescriber Public Use Files 2013-2017. P

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PARVATE, ABHAY, and A. D. GANGAL. "CALCULUS ON FRACTAL SUBSETS OF REAL LINE — I: FORMULATION." Fractals 17, no. 01 (2009): 53–81. http://dx.doi.org/10.1142/s0218348x09004181.

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A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order α, 0 < α ≤ 1, called Fα-integral, is defined, which is suitable to integrate functions with fractal support F of dimension α. Further, a derivative of order α, 0 < α ≤ 1, called Fα-derivative, is defined, which enables us to differentiate functions, like the Cantor staircase, "changing" only on a fractal set. The Fα-derivative is local unlike the classical fractional derivative. The Fα-calculus retains much of the simplicity of ordinary calculus. Several results including analog

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Sun, Ryan, and Xihong Lin. "Genetic Variant Set-Based Tests Using the Generalized Berk–Jones Statistic With Application to a Genome-Wide Association Study of Breast Cancer." Journal of the American Statistical Association 115, no. 531 (2019): 1079–91. http://dx.doi.org/10.1080/01621459.2019.1660170.

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Wan, Wenze, Bohao Zheng, Wentao Sun, et al. "Adjuvant therapy in the treatment of resected nonmetastatic gallbladder cancer of stage II-IV: A generalized propensity score analysis." Journal of Clinical Oncology 39, no. 3_suppl (2021): 471. http://dx.doi.org/10.1200/jco.2021.39.3_suppl.471.

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471 Background: The benefit of adjuvant therapy for gallbladder cancer (GBC) remains controversial due to the limited evidence. The current study was aimed to explore the efficacy of adjuvant therapy in patients with resected non-metastatic GBC and to establish a prognosis model to predict the survival benefit of GCB patients with different adjuvant therapies. Methods: Patients with resected non-metastatic GBC of stage II-IV were selected from the Surveillance, Epidemiology, and End Results database and divided into non-radiotherapy and chemotherapy (NCRT) group, chemotherapy (CT) group, and c

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