“…This study applied the Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) voxel-based morphometry (VBM) to determine if gray matter deficits in TBM are associated with acute presentations and chronic cognitive impairment. …”
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“…To view the disease states in terms of symmetry in the manner of abstract algebra is considered important for the future systematization of clinical medicine. …”
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“…The latest algorithm called as Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) has been introduced for VBA as the function of statistical parametric mapping (SPM8), and improved registration has been achieved by SPM8 with DARTEL. …”
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“…We evaluated the degree of hippocampal atrophy (z‐score—referred to as ZAdvance hereafter), using a free software program—the voxel‐based specific regional analysis system for Alzheimer's disease (VSRAD) based on statistical parametric mapping 8 plus Diffeomorphic Anatomical Registration Through an Exponentiated Lie algebra. RESULTS: Routine magnetic resonance imaging findings were as follows: silent brain infarction, n = 24 (11.3%); deep white matter lesions, n = 72 (33.8%); periventricular hyperintensities, n = 35 (16.4%); and cerebral microbleeds, n = 14 (6.6%). …”
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“…Qualitative comparative analysis by operating Boolean algebra and drawing Venn diagrams was used to visualize our findings. …”
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“…BACKGROUND: Students’ ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. …”
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“…Students’ development of more sophisticated concepts of fractions, beyond the part-whole concept, lays the groundwork for the later study of important mathematical topics, such as algebra, ratios, and proportions, which are foundational understandings for most STEM-related fields. …”
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“…There are 13 possible relations between two intervals according to Allen’s interval algebra. Conventional interval trees are routinely used to identify the genomic intervals satisfying a coarse relation with a query interval, but cannot support efficient query for more refined relations such as all Allen’s relations. …”
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“…RESULTS: We achieve our goal through the definition of a domain-specific language (DSL), Kendrick, that relies on a very general mathematical definition of epidemiological concerns as stochastic automata that are combined using tensor-algebra operators. A very large class of epidemiological concerns, including multi-species, spatial concerns, control policies, sex or age structures, are supported and can be defined independently of each other and combined into models to be simulated by different methods. …”
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“…Although the potential of artificial intelligence/machine learning is profound, present marketing promises and hype exceeds its stage of development, analogous to the seventieth century mathematical “boom” with algebra. Nevertheless robotic systems augmented by machine learning may eventually improve robot-assisted retinal surgery and could potentially transform the discipline. …”
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“…The development of models of environmental variables that determine the spatial distribution of the elements that make up T. cruzi transmission by spatial analysis, followed by map algebra and networking, are the next steps toward interpreting and dealing with the new profile of Chagas disease with its many peculiarities. …”
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“…We conducted voxel-based morphometric analysis with diffeomorphic anatomical registration using an exponentiated Lie algebra algorithm. Region of interest analysis was performed on the fronto-cingulate region to identify whether gray matter volume (GMV) differed between the two groups. …”
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“…CONCLUSION: The feasibility of developing a CPS using geometric models and standard vector algebra has been investigated. This study outlines a framework for potential clinical implementation of a CPS for noncoplanar radiotherapy.…”
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“…The least squares solution to the system of embryo transfer equations was determined using linear algebra. This analysis was repeated for ages 35 to 42 years old at oocyte retrieval. …”
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“…The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from commutative algebra and therefore only an implicit bound was known that depends on parameters r, s, t and [Formula: see text] , where [Formula: see text] is the largest entry of the constraint matrix. …”
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“…We confirm this finding by applying for the first time an alternative method to estimate the neural signal, based on transfer function analysis and phasor algebra. Altogether, our results demonstrate the feasibility of using a rhythmic mental task to impose an oscillatory state useful to separate true brain functional responses from those of non‐cerebral origin. …”
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“…Furthermore, we obtain a cosine distance measure between Fermatean fuzzy sets by using the relationship between the similarity and distance measures, then we extend the technique for order of preference by similarity to the ideal solution method to the proposed cosine distance measure, which can deal with the related decision-making problems not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods.…”
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“…The results showed that straw degradation rate, endoglucanase activity, and filter paper enzyme activity of M44 generally decreased with increasing culture algebra. The activities of xylanase, laccase, and lignin peroxidase, as well as VFA content, showing a single-peak curve change with first an increase and then decrease. …”
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“…Symmetry Operations. 2.1a. Operator Algebra. 2.1b. Symmetry Operator Algebra. 2.2. Groups. 2.2a. …”
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