What's the difference between group and quaternion?
Group
Definition:
(n.) A cluster, crowd, or throng; an assemblage, either of persons or things, collected without any regular form or arrangement; as, a group of men or of trees; a group of isles.
(n.) An assemblage of objects in a certain order or relation, or having some resemblance or common characteristic; as, groups of strata.
(n.) A variously limited assemblage of animals or plants, having some resemblance, or common characteristics in form or structure. The term has different uses, and may be made to include certain species of a genus, or a whole genus, or certain genera, or even several orders.
(n.) A number of eighth, sixteenth, etc., notes joined at the stems; -- sometimes rather indefinitely applied to any ornament made up of a few short notes.
(n.) To form a group of; to arrange or combine in a group or in groups, often with reference to mutual relation and the best effect; to form an assemblage of.
Example Sentences:
(1) A group of interested medical personnel has been identified which has begun to work together.
(2) Once treatment began, no significant changes occurred in Group 1, but both PRA and A2 rose significantly in Groups 2 and 3.
(3) This trend appeared to reverse itself in the low dose animals after 3 hr, whereas in the high dose group, cardiac output continued to decline.
(4) All transplants were performed using standard techniques, the operation for the two groups differing only as described above.
(5) after operation for hip fracture, and merits assessment in other high-risk groups of patients.
(6) Seventeen patients (Group 1) had had no previous surgery, while 13 (Group 2) had had multiple previous operations.
(7) The effects of sessions, individual characteristics, group behavior, sedative medications, and pharmacological anticipation, on simple visual and auditory reaction time were evaluated with a randomized block design.
(8) Urinary ANF immunoreactivity was significantly enhanced by candoxatril in both groups (P less than 0.05 and P less than 0.01 in groups 1 and 2, respectively), with a more pronounced effect evident at the higher dose (P less than 0.01).
(9) The second group only with Haloperidol (same dose).
(10) A change in the pattern of care of children with IDDM, led to a pronounced decrease in hospital use by this patient group.
(11) If the method was taken into routine use in a diagnostic laboratory, the persistence of reverse passive haemagglutination reactions would enable grouping results to be checked for quality control purposes.
(12) We considered the days of the disease and the persistence of symptoms since the admission as peculiar parameters between the two groups.
(13) A group I subset (six animals), for which predominant cultivable microbiota was described, had a mean GI of 2.4.
(14) The half-life of 45Ca in the various calcium fractions of both types of bone was 72 hours in both the control and malnourished groups except the calcium complex portion of the long bone of the control group, which was about 100 hours.
(15) Between 22 HLA-identical siblings and 16 two-haplotype different siblings, a significant difference in concordance of reactions for the B-cell groups was noted.
(16) The cumulative incidence of grade II and III acute GVHD in the 'low dose' cyclosporin group was 42% compared to 51% in the 'standard dose' group (P = 0.60).
(17) The intrauterine mean active pressure (MAP) in the nulliparous group was 1.51 kPa (SD 0.45) in the first stage and 2.71 kPa (SD 0.77) in the second stage.
(18) Biden will meet with representatives from six gun groups on Thursday, including the NRA and the Independent Firearms Owners Association, which are both publicly opposed to stricter gun-control laws.
(19) Another interested party, the University of Miami, had been in talks with the Beckham group over the potential for a shared stadium project.
(20) However, the groups often paused less and responded faster than individual rats working under identical conditions.
Quaternion
Definition:
(n.) The number four.
(n.) A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
(n.) A word of four syllables; a quadrisyllable.
(n.) The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
(v. t.) To divide into quaternions, files, or companies.
Example Sentences:
(1) During visually guided movements, arm follows gaze, and the nine-dimensional rotatory configuration space for eye-head-arm-synergies (three degrees of freedom for each system) is reduced to a two-dimensional plane in the space of quaternion vectors.
(2) Many testable predictions made by quaternion models also turn up in models based on other mathematics.
(3) Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion.
(4) The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements.
(5) In other words, angular eye positions in space (expressed as quaternions) were constrained to a two-dimensional surface.
(6) Findings 1 and 3 show that saccadic control signals accurately reflect the properties of three-dimensional rotations, as predicted by a new quaternion model of the saccadic system; models that approximate rotational kinematics using vectorial addition and integration do not predict these findings.
(7) Tweed and Vilis (Journal of Neurophysiology, 58, 832-849, 1987) have argued that quaternion algebra provides the most appropriate description of the rotations of the eye, and have derived a three-dimensional model of gaze control based on quaternion operations.
(8) A canonical unitary representation of the Euclidean group on the range space of the Gabor transform is constructed from mathematical properties of the Euclidean group and the quaternions.
(9) The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position.
(10) In this paper we present algorithms for computing eye position quaternions and eye angular velocity (not the derivative of position in three dimensions) from two search coils (not necessarily orthogonal) on one eye in two or three magnetic fields, and for locating primary position using quaternions.
(11) In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions.