“…Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…I argue that on this approach, quantum mechanics represents what Bohr called a “natural generalisation of the ordinary causal description” in the sense that the idea (which philosophers of science like Stein have argued for on the grounds of practical and epistemic necessity) that understanding a theory as a theory of physics requires that one be able to “schematise the observer” within it is elevated in quantum mechanics to the level of a postulate in the sense that interpreting the outcome of a measurement interaction, as providing us with information about the world, requires as a matter of principle, the specification of a schematic representation of an observer in the form of a ‘Boolean frame’—the Boolean algebra representing the yes-or-no questions associated with a given observable representative of a given experimental context. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.…”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Although the axis-angle representation requires vector quotient algebra (quaternions) to define rotation, this approach may be preferred for many graphics, vision, and virtual reality software applications. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…We anticipate our results to lead to better understanding of the suitability of this computational paradigm to account for the brain's functionalities and will require the development of new systematic mathematical methods beyond the methods developed for traditional Boolean algebra.…”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…The [R(j)]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of [R(j)]s. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…A new methodology based on tensor algebra that uses a higher order singular value decomposition to perform three-dimensional voxel reconstruction from a series of temporal images obtained using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is proposed. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Magnetic resonance image data were processed using SPM8 software with diffeomorphic anatomical registration via an exponentiated Lie algebra (DARTEL) algorithm. Patients with schizophrenia exhibited significantly decreased GM volumes of the insula, superior temporal gyrus (STG), gyrus rectus, and anterior cingulate cortex (ACC) compared with healthy controls. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Finally, the library can be easily extended to include additional dependencies, such as porting the algebraic operations to specific architectures, in order to exploit hardware acceleration features.…”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein–Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Tracking the passage from local to global properties is the purview of sheaf theory, a branch of mathematics at the nexus of algebra and geometry/topology. Two cognitive domains are examined: (1) learning cue-target patterns that conform to an underlying algebraic rule, and (2) visual attention requiring the integration of space-based feature maps. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…We take a special matrix Lie algebra system(non-semisimple) to construct the Lax pairs, and establish a method for deriving the nonlinear discrete integrable coupling systems(NDICS). …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Articles published in English from 2000 to August 2018 were identified using the following MeSH search terms and Boolean algebra commands: web portal AND cancer. Information obtained from bibliographic searches (title and topic of article, information in abstract, and keywords) was used to determine whether to retain each article identified in this way. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…The mathematical method employed here is a combination of operator algebra equipped with harmonic balance, which allows a clear understanding of the associated nonlinear process. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Therefore, the present study contrasted a comparably larger sample of n = 36 people who stutter with n = 34 control persons and applied the state of the art DARTEL algorithm (Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra) to analyze the available brain data. In the present data set stuttering was associated with higher gray matter volume of the right caudate and putamen region of the basal ganglia in patients. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…The model solves simultaneous mass balance equations (MBE) using simple matrix algebra. The MBEs link all concentrations and transfer processes using first-order rate constants for all processes known to be relevant for ENPs. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…They may be regarded as algebraic generalizations of the fast multipole method. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…Preprocessing was performed using the Diffeomorphic Anatomical Registration through Exponentiated Lie Algebra (DARTEL) algorithm for VBM in SPM8. Images were processed using optimized VBM. …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…RESULTS: We developed a Subsumption-based Sub-term Inference Framework (SSIF) by leveraging a novel term-algebra on top of a sequence-based representation of GO concepts along with three conditional rules (monotonicity, intersection and sub-concept rules). …”
Enlace del recurso
Enlace del recurso
Enlace del recurso

“…While half-precision has been driven largely by machine learning applications, recent algorithmic advances in numerical linear algebra have discovered beneficial use cases for half precision in accelerating the solution of linear systems of equations at higher precisions. …”
Enlace del recurso
Enlace del recurso