A Unique Vector Sum (Rudolf K. Meyer)

SIAM Review ◽  
1994 ◽  
Vol 36 (3) ◽  
pp. 495-496
Author(s):  
William C. Waterhouse ◽  
A. A. Jagers
Keyword(s):  
Vector Sum ◽  
Unique Vector

A Unique Vector Sum

SIAM Review ◽  
1993 ◽  
Vol 35 (3) ◽  
pp. 488-488
Author(s):  
Rudolf X. Meyer
Keyword(s):  
Vector Sum ◽  
Unique Vector

Spatial orientation of the angular vestibulo-ocular reflex

1999 ◽  
Vol 9 (3) ◽  
pp. 163-172
Author(s):  
Bernard Cohen ◽  
Susan Wearne ◽  
Mingjia Dai ◽  
Theodore Raphan
Keyword(s):  
Spatial Orientation ◽  
Optokinetic Nystagmus ◽  
Vestibular Nuclei ◽  
Velocity Storage ◽  
Gravitational Acceleration ◽  
Ocular Reflex ◽  
Eye Rotation ◽  
Slow Velocity ◽  
Vestibulo Ocular Reflex ◽  
Vector Sum

During vestibular nystagmus, optokinetic nystagmus (OKN), and optokinetic afternystagmus (OKAN), the axis of eye rotation tends to align with the vector sum of linear accelerations acting on the head. This includes gravitational acceleration and the linear accelerations generated by translation and centrifugation. We define the summed vector of gravitational and linear accelerations as gravito-inertial acceleration (GIA) and designate the phenomenon of alignment as spatial orientation of the angular vestibuloocular reflex (aVOR). On the basis of studies in the monkey, we postulated that the spatial orientation of the aVOR is dependent on the slow (velocity storage) component of the aVOR, not on the short latency, compensatory aVOR component, which is in head-fixed coordinates. Experiments in which velocity storage was abolished by midline medullary section support this postulate. The velocity storage component of the aVOR is likely to be generated in the vestibular nuclei, and its spatial orientation was shown to be controlled through the nodulus and uvula of the vestibulo-cerebellum. Separate regions of the nodulus/uvula appear to affect the horizontal and vertical/torsional components of the response differently. Velocity storage is weaker in humans than in monkeys, but responds in a similar fashion in both species. We postulate that spatial orientation of the aVOR plays an important role in aligning gaze with the GIA and in maintaining balance during angular locomotion.

scholarly journals Impact or push-off lameness presentation is not altered by the type of track surface where horses are trotted

2015 ◽  
Vol 67 (6) ◽  
pp. 1475-1482 ◽  
Author(s):  
M.S. Azevedo ◽  
F.D.D.L. Côrte ◽  
K.E. Brass ◽  
M. Gallio ◽  
S.L Dau ◽  
...  
Keyword(s):  
Inertial Sensors ◽  
Concrete Surface ◽  
Variation Coefficient ◽  
Soft Ground ◽  
Loose Sand ◽  
Significance Level ◽  
Tukey Test ◽  
Minimum Height ◽  
Track Surface ◽  
Vector Sum

This study aimed to evaluate the influence of the track surface on which horses are examined, regarding the phase of lameness presentation. Ten horses with lameness in at least one limb were evaluated with wireless inertial sensors on three track surfaces (concrete, loose sand and grass). Six crossover track sequences were established. The variables vector sum, maximum and minimum height of the head and pelvis, variation coefficient of the maximum and minimum height of the head and pelvis were analyzed using ANOVA, followed by Tukey test to compare means between track surface and sequence, at 5% significance level. The lameness phase (impact or pushoff) was analyzed considering the proportion of affected animals. There were no differences on vector sum, maximum and minimum height or variation coefficient of head and pelvis. Difference was observed on the number of strides registered on sand compared to grass and concrete (p <0.0001) for fore and hindlimbs. Impact lameness on forelimbs was presented by a larger number of animals on the concrete surface; pushoff lameness was more evident on the grass surface. In the hindlimbs, impact lameness was more evident on the grass surface, while pushoff lameness was in greater number of animals on concrete surfaces. The track sequence on which horses were trotted during evaluation does not seem to be a factor, but the number of lame horses and the phase of lameness manifestation can vary between track surfaces, as some horses showed impact lameness on soft ground and elevation lameness on hard ground.

A 28-GHz Low-Power Vector-Sum Phase Shifter Using Biphase Modulator and Current Reused Technique

2018 ◽  
Vol 28 (11) ◽  
pp. 1014-1016 ◽  
Author(s):  
Yu-Teng Chang ◽  
Zhe-Wei Ou ◽  
Hamid Alsuraisry ◽  
Abdulhamid Sayed ◽  
Hsin-Chia Lu
Keyword(s):  
Low Power ◽  
Phase Shifter ◽  
Vector Sum

Interisland movements of Peary caribou (Rangifer tarandus pearyi) on western Queen Elizabeth Islands, Arctic Canada

1977 ◽  
Vol 55 (6) ◽  
pp. 1029-1037 ◽  
Author(s):  
Frank L. Miller ◽  
Richard H. Russell ◽  
Anne Gunn
Keyword(s):  
Seasonal Changes ◽  
Horizontal Plane ◽  
Rangifer Tarandus ◽  
Maximum Distance ◽  
Arctic Canada ◽  
Complete Evaluation ◽  
Spray Method ◽  
Annual Range ◽  
Vector Sum

To verify that Peary caribou were making seasonal interisland movements, we used an aerial dye-spray method. In April 1974, about 230 caribou were dye-marked green, and about 200 were marked red on Prince Patrick and Eglinton islands respectively. Aerial searches in June and July 1974 located 41 sightings of dye-marked animals. Of animals marked on Prince Patrick Island 4 were seen on Melville Island, 3 on Eglinton Island, and 16 on Prince Patrick. Of sightings of animals marked on Eglinton Island, there were 6 on Prince Patrick Island and 12 on Eglinton. Maximum distance travelled (vector sum on horizontal plane) by marked caribou was 450 km, from Prince Patrick Island to eastern Melville Island. The study indicates that high proportions of the caribou population seasonally range over two or more islands of the western Queen Elizabeth Group. Therefore, complete evaluation of annual range requirements on an island basis should take into consideration seasonal changes in numbers of caribou that are due to interisland movements.

1. On a Particular Case of the Symbolic Cubic

1882 ◽  
Vol 11 ◽  
pp. 342-354
Author(s):  
Gustav Plarr
Keyword(s):  
Vector Function ◽  
Image Position ◽  
Vector Sum

§ 1. The method by which Hamilton has established the symbolical cubicand more particularly the relationis founded on a generalisation of the resultwhere ϕ represents a linear and vector function, and ϕ' its conjugate according to the definitionIn the most general case of ϕρ the expression of this function is reducible to a vector sum of three terms of the form αSα1ρ, and the directions which ϕρ is susceptible of representing are generally not limited in space.

scholarly journals IMAGES OF MENTAL VISUALIZATION IN BIOETHICS

2021 ◽  
pp. 140-152
Author(s):  
Вячеслав Иванович Моисеев
Keyword(s):  
Local Community ◽  
Three Dimensional ◽  
Unit Vector ◽  
Vector Model ◽  
Vector Representation ◽  
Three Dimensional Objects ◽  
The Status ◽  
The Subject ◽  
Vector Sum ◽  
Sum Vector

В статье даётся краткий очерк антиномической природы биоэтического дискурса и возможностей его геометрической визуализации. Рассматриваются два варианта визуализации. Первый связан с представлением той или иной ситуации как системы полярностей, которая в свою очередь моделируется в рамках векторной модели. В простейшем случае тезис и антитезис рассматриваются как два перпендикулярных вектора, а синтез – как их векторная сумма. В этом случае можно ввести и более количественную оценку «меры многомерности» полярной системы – как величины проекции её векторного представления на суммарный вектор. С использованием этих конструкций разбирается один пример из биоэтики, связанный со столкновением принципов милосердия и правдивости (проблема «лжи во спасение»). Деяние (действие или бездействие) интерпретируется как своеобразный оператор на событиях, который переводит одни события в другие. Предполагается, что субъект в своих деяниях рассматривает различные возможности и выбирает те из них, которые максимизируют ту или иную ценностную меру субъекта, в данном случае – меру векторной проекции полярного вектора ситуации на суммарный вектор – вектор синтеза базисных полярностей. Второй вариант визуализации связан с понятием антиномий в биоэтике – таких противоречий, которые не являются формально-логическими ошибками. В отличие от последних, в антиномиях как тезис, так и антитезис имеют свой момент оправдания в рамках тех или иных условий. Используется также понятие «антинома» – логического субъекта антиномии, который предицируется тезисом и антитезисом антиномии. Редукции антиномии соответствуют двум крайним аспектам антинома, которые называются его «редуктами» – по аналогии с редукцией волновой функции в квантовой механике. Приводятся различные примеры антиномов: биоэты, глоболоки, холомеры. В биоэтах один редукт выражает в большей мере биологические (биоредукт), второй – этические (эторедукт) определения антинома. В глоболоках выделяются глобальный (глоборедукт) и локальный (локоредукт) виды редуктов: первый выражает более глобальные (универсальные) этические определения, второй – более локальные, связанные с ценностями и нормами того или иного сообщества. Наконец, холомеры – вид антиномов, где антиномически соединяются определения целого (холоредукт) и части (мероредукт). Даётся их интерпретация как многомерных ментальных объектов в некотором обобщённом пространстве, так что крайние их аспекты (редукции антиномии) можно представить как проекции более многомерного состояния. В заключении делается предположение о связи биоэтических проблем с идеей ментальной многомерности, что составляет основу возможной визуализации как интерпретации ментальной многомерности на векторном её представлении. The article provides a brief outline of the antinomic nature of bioethical discourse and the possibilities of its geometric visualization. Two visualization options are considered. The first is associated with the representation of a particular situation as a system of polarities, which in turn is modeled in the framework of a vector model. In the simplest case, the thesis and the antithesis are considered as two orthogonal vectors P1 and P2, and the synthesis is considered as their vector sum S = P1+P2. In this case, we can also introduce a more quantitative estimate of the “measure of multidimensionality” M(P) of the polar system – as the magnitude of the projection of its vector representation P on the sum vector S, i.e. M(P) = (P,es), where es = S/|S| is the unit vector of the vector S, and (P,es) is the scalar product of the vectors P and es. Using these constructs, the author analyzes one example from bioethics related to the clash of the principles of mercy and truthfulness (the problem of “lying for salvation”). An act (action or omission) is interpreted as a kind of an operator on events that transforms some events into others. It is assumed that the subject considers various possibilities in their actions and chooses those that maximize a particular value measure of the subject, in our case, the measure M(P) of the vector projection of the polar vector P of the situation on the sum vector S – the vector of synthesis of basic polarities. The second version of visualization is related to the concept of antinomies – such contradictions that are not formal logical errors – in bioethics. In contrast to errors, in antinomies, both the thesis and the antithesis have their moment of justification within the framework of certain conditions. The concept “antinome” is also used; it is the logical subject of antinomy, which is predicated by the thesis and the antithesis of antinomy. Antinomy reductions correspond to two extreme aspects of the antinome, which are called its “reducts” – by analogy with the reduction of the wave function in quantum mechanics. Various examples of antinomes are given: bioets, globolocs, and holomers. In bioets, one reduct expresses the biological (bioreduct) definition of the antinome, another the ethical (ethoreduct) one. In globolocs, global (globoreduct) and local (locoreduct) types of reducts are distinguished: the former expresses more global (universal) ethical definitions, the latter more local ones, related to the values and norms of a particular local community. Finally, holomers are a kind of antinomes in which the definitions of the whole (holoreduct) and the part (meroreduct) are antinomically connected. They are interpreted as multidimensional mental objects in some generalized space, so that their extreme aspects (antinomy reductions) can be represented as generalized projections of a more multidimensional state within certain constricted conditions (reduction intervals). In this case, it is possible to geometrically visualize such states as, for example, three-dimensional objects in space, through which antinomes can be modeled, and their reducts as two-dimensional projections of a three-dimensional body on certain projection planes (intervals of reducts). In this case, one of the central tasks of bioethics is to determine the boundaries of the demarcation of some intervals from others. For example, in solving the problem of abortion and the status of the human embryo, such a demarcation is expressed in the search for a time point that would separate the phase of a more biological definition (bioreduct) of the embryo from its more ethical state (ethoreduct). In conclusion, the author suggests that bioethical problems are connected with the idea of mental multidimensionality, which forms the basis of a possible visualization as an interpretation of mental multidimensionality in its vector representation.

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