WordNet

based on or subject to individual discretion or preference or sometimes impulse or caprice; "an arbitrary decision"; "the arbitrary rule of a dictator"; "an arbitrary penalty"; "of arbitrary size and shape"; "an arbitrary choice"; "arbitrary division of the group into halves"
of or relating to the mental faculties
able to exist under more than one set of conditions; "a facultative parasite can exist as a parasite or a saprophyte"
granting a privilege or permission or power to do or not do something; "a facultative enactment"
not compulsory; "facultative courses in the sciences"
possible but not necessary; left to personal choice
not subject to individual determination (同)unarbitrary

PrepTutorEJDIC

随意の,任意の,気まぐれな(capricious) / 独裁的な,独断的な,専横な(despotic)
選択が自合の,随意の
随意に,気ままに

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/02/20 23:57:06」(JST)

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The word "tree" is assigned only arbitrarily to the concept of a perennial woody plant.

Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle".^[1]

Arbitrary decisions are not necessarily the same as random decisions. For example, during the 1973 oil crisis, Americans were allowed to purchase gasoline only on odd-numbered days if their license plate was odd, and on even-numbered days if their license plate was even. The system was well-defined and not random in its restrictions; however, since license plate numbers are completely unrelated to a person's fitness to purchase gasoline, it was still an arbitrary division of people. Similarly, schoolchildren are often organized by their surname in alphabetical order, a non-random yet still arbitrary method, at least in cases where surnames are irrelevant.

Law

Arbitrary comes from the Latin arbitrarius, the source of arbiter; someone who is tasked to judge some matter.^[2] An arbitrary legal judgment is a decision made at the discretion of the judge, not one that is fixed by law.^[3] In some countries, a prohibition of arbitrariness is enshrined into the constitution. Article 9 of the Swiss Federal Constitution theoretically overrides even democratic decisions in prohibiting arbitrary government action.^[4] The US Supreme Court has overturned laws for having "no rational basis." A recent study of the U.S. asylum system suggests that arbitrariness in decision-making might be the cause of large disparities in outcomes between different adjudicators, a phenomenon described as refugee roulette.

Article 330 of the Russian penal code defines 'Arbitrariness' as a specific crime, but with a very broad definition encompassing any 'actions contrary to the order presented by a law'.^[5]

Philosophy

Arbitrary actions are closely related to teleology, the study of purpose. Actions lacking a telos, a goal, are necessarily arbitrary. With no end to measure against, there can be no standard applied to choices, so all decisions are alike. Note that arbitrary or random methods in the standard sense of arbitrary may not qualify as arbitrary choices philosophically, if they were done in furtherance of a larger purpose; in the examples above, discipline in school and avoiding overcrowding at gas stations.

Nihilism is the philosophy that believes that there is no purpose in the universe, and that every choice is arbitrary.^[6] According to nihilism, the universe contains no value and is essentially meaningless. Because the universe and all of its constituents contain no higher goal for us to make subgoals from, all aspects of human life and experiences are completely arbitrary. There is no right or wrong decision, thought or practice, and whatever choice a human being makes is just as meaningless and empty as any other choice he or she could have made.

Many brands of theism, the belief in a deity or deities, believe that everything has a purpose and that nothing is arbitrary. In these philosophies, God created the universe for a reason, and every event flows from that. Even seemingly random events cannot escape God's hand and purpose. This is somewhat related to the argument from design, the argument for God's existence because a purpose can be found in the universe.

Arbitrariness is also related to ethics, the philosophy of decision-making. Even if a person has a goal, they may choose to attempt to achieve it in ways that may be considered arbitrary. Rationalism holds that knowledge comes about through intellectual calculation and deduction; many rationalists (though not all) apply this to ethics as well. All decisions should be made through reason and logic, not via whim or how one "feels" what is right. Randomness may occasionally be acceptable as part of a subtask in furtherance of a larger goal, but not in general.

In semiotics, the general theory of signs, sign systems and sign processes, Saussure introduced the notion of arbitrariness according to which there is no necessary connection between the material sign (or signifier) and the entity it refers to or denotes as its meaning (or signified) as a mental concept or real object.

Mathematics

In mathematics, arbitrary normally means "any;" for instance, an arbitrary division of a set or an arbitrary permutation of a sequence. Its use implies generality and that a statement does not only apply to special cases – "you may select any choice possible, and this statement will still hold." A simple example would be "Given an arbitrary integer, multiplying it by two will result in an even number."

Even further, the implication is that generality will hold even if you have an opponent choose the item in question. In some ways arbitrary is here synonymous with worst-case.^[7]

References

^ http://www.thefreedictionary.com/arbitrariness
^ Online Etymology Dictionary: "'deciding by one's own discretion,' from L. arbitrarius, from arbiter (see arbiter). The original meaning gradually to mean ‘capricious’ (1646) and ‘despotic’ (1642).”
^ Curtis, Thomas. The London Encyclopaedia, page 565 (1829): “Arbitrary, and the words more immediately connected with it, signify that the decision of the arbiter is made in consequence of his own uncontrolled will, or in consequence of reasons which do not appear.”
^ Federal Constitution of the Swiss Federation. The Federal Authorities of the Swiss Confederation.
^ "Article 330. Arbitrariness". The Criminal Code Of The Russian Federation. Arbitrariness, that is the unauthorized commission of actions contrary to the order presented by a law or any other normative legal act,
^ Magnus, Bernd (1971). "Nihilism, Reason, and "The Good"." The Review of Metaphysics. 25 (2):292–310.
^ Tel, Gérard (2000). Introduction to distributed algorithms. Cambridge University Press. p. 245.

External links

The dictionary definition of arbitrary at Wiktionary

UpToDate Contents

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1. 一過性脳虚血発作の定義 definition of transient ischemic attack
2. 証拠、p値、および仮説検定 proof p values and hypothesis testing
3. 診断的検査の評価 evaluating diagnostic tests
4. プレカット括約筋切開術：有効性および合併症に関するほかの視点 precut sphincterotomy another perspective on efficacy and complications
5. プレカット括約筋切開術：適応および手技に対する別視点 precut sphincterotomy another perspective on indications and techniques

English Journal

Generating fibre orientation maps in human heart models using Poisson interpolation.

Wong J1, Kuhl E.Author information 1a Department of Mechanical Engineering , Stanford University , Stanford , CA 94305 , USA.AbstractSmoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately - 70° in the outer wall to +80° in the inner wall. However, the creation of fibre orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here, we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fibre orientations, quickly, efficiently and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however, the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, in which it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data-sets, which are sparse but uniformly distributed.
Computer methods in biomechanics and biomedical engineering.Comput Methods Biomech Biomed Engin.2014 Aug;17(11):1217-26. doi: 10.1080/10255842.2012.739167. Epub 2012 Dec 5.
Smoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately - 70° in the outer wall to +80° in the i
PMID 23210529

A mathematical model for cell differentiation, as an evolutionary and regulated process.

Prokharau PA1, Vermolen FJ, García-Aznar JM.Author information 1a Delft Institute of Applied Mathematics, Delft University of Technology , HB 07.290, Mekelweg 4, 2628 CD , Delft , The Netherlands.AbstractWe introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.
Computer methods in biomechanics and biomedical engineering.Comput Methods Biomech Biomed Engin.2014 Aug;17(10):1051-70. doi: 10.1080/10255842.2012.736503. Epub 2012 Oct 31.
We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitr
PMID 23113617

Simulating the scanning of a focused beam through scattering media using a numerical solution of Maxwell's equations.

Elmaklizi A, Schäfer J, Kienle A.Erratum inJ Biomed Opt. 2014 Jul;19(7):079801. AbstractA highly efficient method based on Maxwell's theory was developed, which enables the calculation of the scanning of a focused beam through scattering media. Maxwell's equations were numerically solved in two dimensions using finite difference time domain simulations. The modeling of the focused beam was achieved by applying the angular spectrum of plane waves method. The scanning of the focused beam through the scattering medium was accomplished by saving the results of the near field obtained from one simulation set of plane waves incident at different angles and by an appropriate post processing of these data. Thus, an arbitrary number of focus positions could be simulated without the need to further solve Maxwell's equations. The presented method can be used to efficiently study the light propagation of focused beam through scattering media which is important, for example, for different kinds of scanning microscopes.
Journal of biomedical optics.J Biomed Opt.2014 Jul;19(7):071404. doi: 10.1117/1.JBO.19.7.071404.
A highly efficient method based on Maxwell's theory was developed, which enables the calculation of the scanning of a focused beam through scattering media. Maxwell's equations were numerically solved in two dimensions using finite difference time domain simulations. The modeling of the focused beam
PMID 24395650

Improving the air coupling of bulk piezoelectric transducers with wedges of power-law profiles: A numerical study.

Remillieux MC1, Anderson BE2, Le Bas PY3, Ulrich TJ4.Author information 1Geophysics Group EES-17, Los Alamos National Laboratory, MS D446, Los Alamos, NM 87545, USA. Electronic address: mcr1@lanl.gov.2Geophysics Group EES-17, Los Alamos National Laboratory, MS D446, Los Alamos, NM 87545, USA. Electronic address: bea@lanl.gov.3Geophysics Group EES-17, Los Alamos National Laboratory, MS D446, Los Alamos, NM 87545, USA. Electronic address: pylb@lanl.gov.4Geophysics Group EES-17, Los Alamos National Laboratory, MS D446, Los Alamos, NM 87545, USA. Electronic address: tju@lanl.gov.AbstractAn air-coupled ultrasonic transducer is created by bonding a bulk piezoelectric element onto the surface of a thick plate with a wedge of power-law profile. The wedge is used to improve the ultrasonic radiation efficiency. The power-law profile provides a smooth, impedance-matching transition for the mechanical energy to be transferred from the thick plate to the air, through the large-amplitude flexural waves observed in the thinnest region of the wedge. The performance of the proposed transducer is examined numerically and compared to that of a design where the piezoelectric element is isolated and where it is affixed to a thin plate of uniform thickness. The numerical analysis is first focused on the free-field radiation of the transducers. Then, time-reversal experiments are simulated by placing the transducers inside a cavity of arbitrary shape with some perfectly reflecting boundaries. In addition to time-reversal mirrors, the proposed concept could be integrated in the design of phased arrays and parametric arrays.
Ultrasonics.Ultrasonics.2014 Jul;54(5):1409-16. doi: 10.1016/j.ultras.2014.02.017. Epub 2014 Mar 4.
An air-coupled ultrasonic transducer is created by bonding a bulk piezoelectric element onto the surface of a thick plate with a wedge of power-law profile. The wedge is used to improve the ultrasonic radiation efficiency. The power-law profile provides a smooth, impedance-matching transition for th
PMID 24636675

Japanese Journal

Reflective boundary condition with arbitrary boundary shape for compact-explicit finite-difference time-domain method

Yamashita Osamu,Tsuchiya Takao,Iwaya Yukio,Otani Makoto,Inoguchi Yasushi
Jpn. J. Appl. Phys. 54(7S1), 07HC02, 2015-06-03
… In this paper, we propose the reflective boundary condition with an arbitrary boundary shape for the compact-explicit finite-difference time-domain (CE-FDTD) method. … The boundary condition with the arbitrary boundary shape is first formulated using an extension of the standard FDTD method. … The validity of the proposed boundary condition with arbitrary boundary shape was confirmed through the numerical experiments. …
NAID 150000111003