vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Confidence interval
An approximate confidence interval for a population mean can be constructed for random variables that are not normally distributed in the population , relying on the central limit theorem , if the sample sizes and counts are big enough . The formulae are identical to the case above ( where the sample mean is actually normally distributed about the population mean ) . The approximation will be quite good with only a few dozen observations in the sample if the probability distribution of the random variable is not too different from the normal distribution ( e.g. its cumulative distribution function does not have any discontinuities and its skewness is moderate ) .
Parliamentary sovereignty
The constitutional position in New Zealand ( ... ) is clear and unambiguous . Parliament is supreme and the function of the courts is to interpret the law as laid down by Parliament . The courts do not have a power to consider the validity of properly enacted laws .
Ear
Anomalies and malformations of the pinna are common . These anomalies include chromosome syndromes such as ring 18 . Children may also present cases of abnormal ear canals and low ear implantation . In rare cases no pinna is formed ( atresia ) , or is extremely small ( microtia ) . Small pinnae can develop when the auricular hillocks do not develop properly . The ear canal can fail to develop if it does not channelise properly or if there is an obstruction . Reconstructive surgery to treat hearing loss is considered as an option for children older than five , with a cosmetic surgical procedure to reduce the size or change the shape of the ear is called an otoplasty . The initial medical intervention is aimed at assessing the baby 's hearing and the condition of the ear canal , as well as the middle and inner ear . Depending on the results of tests , reconstruction of the outer ear is done in stages , with planning for any possible repairs of the rest of the ear .
Talk:Mode (statistics)
If the population distribution is continuous , the chance of observing two or more identical values is 0 . If you discretize the data , then the result may ( of course ) depend on the details . If you have a distribution whose density function has a thin spike , it gets diluted when the intervals are much wider . The sample data show a thin spike at 15 and a robust mound around 35 . The choice of intervals does actually not conform to the advice given in the article , but it is also possible to construct an example that does conform but still displays this phenomenon . -- Lambiam 23 : 01 , 28 March 2007 ( UTC )
Planck's law
The denominator Z ( β ) , is the partition function of a single mode and makes P properly normalized :
Quadratic equation
The solutions of the quadratic equation ax + bx + c = 0 correspond to the roots of the function f ( x ) = ax + bx + c , since they are the values of x for which f ( x ) = 0 . As shown in Figure 2 , if a , b , and c are real numbers and the domain of f is the set of real numbers , then the roots of f are exactly the x-coordinates of the points where the graph touches the x-axis . As shown in Figure 3 , if the discriminant is positive , the graph touches the x-axis at two points ; if zero , the graph touches at one point ; and if negative , the graph does not touch the x-axis .
Well-defined
The question of well - definedness of a function classically arises when the defining equation of a function does not ( only ) refer to the arguments themselves , but ( also ) to elements of the arguments . This is sometimes unavoidable when the arguments are cosets and the equation refers to coset representatives .
McCulloch v. Maryland
( A ) criterion of what is constitutional , and of what is not so ... is the end , to which the measure relates as a mean . If the end be clearly comprehended within any of the specified powers , and if the measure have an obvious relation to that end , and is not forbidden by any particular provision of the Constitution , it may safely be deemed to come within the compass of the national authority . There is also this further criterion which may materially assist the decision : Does the proposed measure abridge a pre-existing right of any State , or of any individual ? If it does not , there is a strong presumption in favour of its constitutionality ...
Symmetry of second derivatives
The symmetry may be broken if the function fails to have differentiable partial derivatives , which is possible if Clairaut 's theorem is not satisfied ( the second partial derivatives are not continuous ) . The
Parameter (computer programming)
The terms parameter and argument may have different meanings in different programming languages . Sometimes they are used interchangeably , and the context is used to distinguish the meaning . The term parameter ( sometimes called formal parameter ) is often used to refer to the variable as found in the function definition , while argument ( sometimes called actual parameter ) refers to the actual input supplied at function call . For example , if one defines a function as def f ( x ) : ... , then x is the parameter , and if it is called by a = ... ; f ( a ) then a is the argument . A parameter is an ( unbound ) variable , while the argument can be a value or variable or more complex expression involving values and variables . In case of call by value , what is passed to the function is the value of the argument -- for example , f ( 2 ) and a = 2 ; f ( a ) are equivalent calls -- while in call by reference , with a variable as argument , what is passed is a reference to that variable - even though the syntax for the function call could stay the same . The specification for pass - by - reference or pass - by - value would be made in the function declaration and / or definition .
Anointing of the Sick in the Catholic Church
What in the judgment of the Catholic Church are properly described as the last rites are Viaticum , and the ritual prayers of Commendation of the Dying , and Prayers for the Dead .
Lead poisoning
The primary cause of lead 's toxicity is its interference with a variety of enzymes because it binds to sulfhydryl groups found on many enzymes . Part of lead 's toxicity results from its ability to mimic other metals that take part in biological processes , which act as cofactors in many enzymatic reactions , displacing them at the enzymes on which they act . Lead is able to bind to and interact with many of the same enzymes as these metals but , due to its differing chemistry , does not properly function as a cofactor , thus interfering with the enzyme 's ability to catalyze its normal reaction or reactions . Among the essential metals with which lead interacts are calcium , iron , and zinc .
Robert K. Merton
Lastly , the postulate of indispensability challenges the social function for customs , ideals , or institutions as a whole . Merton raises the question and doubt of whether every social institution performs a specific function . Merton believes that several institutions can provide the same function or none at all , so it is impossible to decipher what functions are vital or not to a society .
Shoplifting
Electronic article surveillance ( EAS ) are magnetic or radio - frequency tags that sound an alarm if a shoplifter leaves a store with store items that have not been paid for . EAS methods are second only to CCTV in popularity amongst retailers looking for inventory protection . EAS refers to the electronic security tags that are attached to merchandise and cause an alarm to sound on exiting the store . Some stores also have detection systems at the entrance to the bathrooms that sound an alarm if someone tries to take unpaid merchandise with them into the bathroom . Regularly , even when an alarm does sound , a shoplifter walks out casually and is not confronted if no guards are present because of the high number of false alarms , especially in malls , due to `` tag pollution '' whereby non-deactivated tags from other stores set off the alarm . This can be overcome with newer systems and a properly trained staff . Some new systems either do not alarm from `` tag pollution '' or they produce a specific alarm when a customer enters the store with a non-deactivated tag so that store personnel can remove or deactivate it so it does not produce a false alarm when exiting the store . However , with tags spider wrap may be used instead of tags . Electronic
Utilitarianism
The question then arises as to when , if at all , it might be legitimate to break the law . This is considered in The Theory of Legislation , where Bentham distinguishes between evils of the first and second orders . Those of the first order are the more immediate consequences ; those of the second are when the consequences spread through the community causing `` alarm '' and `` danger '' .
Original sin
The Orthodox Church in America makes clear the distinction between `` fallen nature '' and `` fallen man '' and this is affirmed in the early teaching of the Church whose role it is to act as the catalyst that leads to true or inner redemption . Every human person born on this earth bears the image of God undistorted within themselves . In the Orthodox Christian understanding , they explicitly deny that humanity inherited guilt from anyone . Rather , they maintain that we inherit our fallen nature . While humanity does bear the consequences of the original , or first , sin , humanity does not bear the personal guilt associated with this sin . Adam and Eve are guilty of their willful action ; we bear the consequences , chief of which is death . ''
Normal distribution
The normal distribution is sometimes informally called the bell curve . However , many other distributions are bell - shaped ( such as the Cauchy , Student 's t , and logistic distributions ) . Even the term Gaussian bell curve is ambiguous because it may be used to refer to some function defined in terms of the Gaussian function which is not a probability distribution because it is not normalized ( does not integrate to 1 ) .
Robert K. Merton
Manifest functions are the consequences that people observe or expect , or what is intended ; latent functions are those that are neither recognized nor intended . In distinguishing between manifest and latent functions , Merton argued that one must dig to discover latent functions . His example from his 1949 piece , `` Manifest and Latent Functions '' , was an analysis of political machines . Merton began by describing the negative consequences of political machines , and then changed the angle and demonstrated how the people in charge of the machines , acting in their own interest , were meeting the social needs not met by government institutions .
Robert K. Merton
Merton made it very clear however , that unanticipated consequences and latent functions are not the same . Latent functions are one type of unanticipated consequences ; functional for the designated system . According to Merton , there are also two other types of unanticipated consequences : `` those that are dysfunctional for a designated system , and these comprise the latent dysfunctions , and those which are irrelevant to the system which they affect neither functionally or dysfunctionally ... non-functional consequences '' .
Moment-generating function
An important property of the moment - generating function is that if two distributions have the same moment - generating function , then they are identical at almost all points . That is , if for all values of t ,
Quantum mechanics
In the everyday world , it is natural and intuitive to think of everything ( every observable ) as being in an eigenstate . Everything appears to have a definite position , a definite momentum , a definite energy , and a definite time of occurrence . However , quantum mechanics does not pinpoint the exact values of a particle 's position and momentum ( since they are conjugate pairs ) or its energy and time ( since they too are conjugate pairs ) ; rather , it provides only a range of probabilities in which that particle might be given its momentum and momentum probability . Therefore , it is helpful to use different words to describe states having uncertain values and states having definite values ( eigenstates ) . Usually , a system will not be in an eigenstate of the observable ( particle ) we are interested in . However , if one measures the observable , the wave function will instantaneously be an eigenstate ( or `` generalized '' eigenstate ) of that observable . This process is known as wave function collapse , a controversial and much - debated process that involves expanding the system under study to include the measurement device . If one knows the corresponding wave function at the instant before the measurement , one will be able to compute the probability of the wave function collapsing into each of the possible eigenstates . For example , the free particle in the previous example will usually have a wave function that is a wave packet centered around some mean position x ( neither an eigenstate of position nor of momentum ) . When one measures the position of the particle , it is impossible to predict with certainty the result . It is probable , but not certain , that it will be near x , where the amplitude of the wave function is large . After the measurement is performed , having obtained some result x , the wave function collapses into a position eigenstate centered at x .
Utilitarianism
Russell Hardin rejects such arguments . He argues that it is possible to distinguish the moral impulse of utilitarianism ( which is `` to define the right as good consequences and to motivate people to achieve these '' ) from our ability to correctly apply rational principles that , among other things , `` depend on the perceived facts of the case and on the particular moral actor 's mental equipment . '' The fact that the latter is limited and can change does n't mean that the former has to be rejected . `` If we develop a better system for determining relevant causal relations so that we are able to choose actions that better produce our intended ends , it does not follow that we then must change our ethics . The moral impulse of utilitarianism is constant , but our decisions under it are contingent on our knowledge and scientific understanding . ''
Mach Five
If a tire does get heavily damaged , this button causes it to regenerate . This function applies to any of the Mach 5 's four tires .
Female reproductive system
The uterus is a pear - shaped muscular organ . Its major function is to accept a fertilized ovum which becomes implanted into the endometrium , and derives nourishment from blood vessels which develop exclusively for this purpose . The fertilized ovum becomes an embryo , develops into a fetus and gestates until childbirth . If the egg does not embed in the wall of the uterus , a female begins menstruation .
Châteauneuf-du-Pape
There are no surviving plans of the castle from the 14th century . The earliest depiction is an anonymous drawing from the Album Laincel in the collection of the Musée Calvet in Avignon that dates from the second half of the 17th century . By this time the castle had not been properly maintained for three centuries and the drawing is probably an interpretation by the artist of the surviving structure . Another source of information is a plan of the village from the 1813 cadastre which indicates the position of some of the buildings but not their original function . The appearance of the donjon before its destruction in 1944 is known from old photographs .
Parameter (computer programming)
In lambda calculus , each function has exactly one parameter . What is thought of as functions with multiple parameters is usually represented in lambda calculus as a function which takes the first argument , and returns a function which takes the rest of the arguments ; this is a transformation known as currying . Some programming languages , like ML and Haskell , follow this scheme . In these languages , every function has exactly one parameter , and what may look like the definition of a function of multiple parameters , is actually syntactic sugar for the definition of a function that returns a function , etc . Function application is left - associative in these languages as well as in lambda calculus , so what looks like an application of a function to multiple arguments is correctly evaluated as the function applied to the first argument , then the resulting function applied to the second argument , etc .
Real estate contract
The contract can also specify which party pays for what closing cost ( s ) . If the contract does not specify , then there are certain customary defaults depending on law , common law ( judicial precedents ) , location , and other orders or agreements , regarding who pays for which closing costs .
Olive oil extraction
The traditional method is a valid form of producing high - quality olive oil , if after each extraction the disks are properly cleaned from the remains of paste ; if not the leftover paste will begin to ferment , thereby producing inconsistencies of flavors ( called defects ) that will contaminate the subsequently produced olive oil . A similar problem can affect the grindstones that , in order to assure perfect quality , also require cleaning after each usage .
Secession in the United States
In dramatic contrast to Article VII -- whose unanimity rule that no state can bind another confirms the sovereignty of each state prior to 1787 -- Article V does not permit a single state convention to modify the federal Constitution for itself . Moreover , it makes clear that a state may be bound by a federal constitutional amendment even if that state votes against the amendment in a properly convened state convention . And this rule is flatly inconsistent with the idea that states remain sovereign after joining the Constitution , even if they were sovereign before joining it . Thus , ratification of the Constitution itself marked the moment when previously sovereign states gave up their sovereignty and legal independence .
Robert K. Merton
Some of the crucial innovations that Merton made to sociology include the description of the unanticipated consequences of social action , of latent functions vs. manifest functions , and , as previously mentioned , of dysfunctions . According to Merton , unanticipated consequences are actions that have both intended and unintended consequences . Everyone is aware of the intended consequences , but the unintended are more difficult to recognize , and therefore , sociological analysis is required to uncover what they may be . In his 1936 essay , `` The Unanticipated Consequences of Social Action '' , Merton uncovered the wide field of human activity where things do not go as planned , and paradoxes and strange outcomes are seen . One of these outcomes is the `` self - defeating prophecy '' , which through the very fact of its being publicized , is actually wrong . Merton was able to illustrate this by referencing Karl Marx 's prediction that as societies become more modern , the wealth will be concentrated amongst fewer people , and the majority of society would suffer from poverty and misery . This prediction helped to stimulate the socialist movement , which in some countries slowed the development that Marx had predicted . The opposite of the `` self - defeating prophecy '' then , is the `` self - fulfilling prophecy '' , when an originally unfounded prophecy turns out to be correct because it is believed and acted upon .
Recursion (computer science)
The job of the recursive cases can be seen as breaking down complex inputs into simpler ones . In a properly designed recursive function , with each recursive call , the input problem must be simplified in such a way that eventually the base case must be reached . ( Functions that are not intended to terminate under normal circumstances -- for example , some system and server processes -- are an exception to this . ) Neglecting to write a base case , or testing for it incorrectly , can cause an infinite loop .
Elections in Canada
Note : Nunavut does not have political parties , and political parties in the Northwest Territories were disbanded in 1905 . MLAs in both territories are elected as independents and the legislatures function under a consensus government model .
Parameter (computer programming)
so the function f does not need to assign space for the object or copy it on returning .
Recursion (computer science)
Wrapper functions can be used to validate parameters ( so the recursive function can skip these ) , perform initialization ( allocate memory , initialize variables ) , particularly for auxiliary variables such as `` level of recursion '' or partial computations for memoization , and handle exceptions and errors . In languages that support nested functions , the auxiliary function can be nested inside the wrapper function and use a shared scope . In the absence of nested functions , auxiliary functions are instead a separate function , if possible private ( as they are not called directly ) , and information is shared with the wrapper function by using pass - by - reference .
Utilitarianism
Utilitarianism is typically taken to assess the rightness or wrongness of an action by considering just the consequences of that action . Bentham very carefully distinguishes motive from intention and says that motives are not in themselves good or bad but can be referred to as such on account of their tendency to produce pleasure or pain . He adds that , `` from every kind of motive , may proceed actions that are good , others that are bad , and others that are indifferent . '' Mill makes a similar point and explicitly says that `` motive has nothing to do with the morality of the action , though much with the worth of the agent . He who saves a fellow creature from drowning does what is morally right , whether his motive be duty , or the hope of being paid for his trouble . ''
Spec Ops: The Line
Spec Ops : The Line includes several choices for players to make . According to Williams , it was a key concept to be featured right from the start of the game 's development . The game does not feature a morality system , but instead has situations that give players some freedom of choice . The consequences of some of these choices were deliberately made unclear in an attempt to make them more realistic , encouraging players to explore the other potential options not directly presented by the game . These choices were inspired by Fallout 3 , and are often between : `` what the character knows and what the player would maybe try and do '' . To make choices more realistic , and to increase the impact of the story , the team put in a lot of morally ambiguous choices and `` bad or worse '' decisions . Williams added that absolute good choices are not practical and sometimes may not exist in real - world situations , so to reflect that combat sequences sometimes force players to make split - second decisions and accept whatever the consequences are . According to Williams , this is something that people frequently do in real - world scenarios , and they must `` live with it '' after their decision . Williams added that they hoped that the game 's players would have different feelings after making these choices , as this would show that they had created an opportunity for players to examine their own inner emotions , and that they had successfully provided different experiences for players without having a branching storyline . Replay value was also considered when the development team was designing these choices .
Child care
It is important to assess the value of caregivers because they are what truly make society function , and often their work is under - appreciated . They prepare the next generation for school , work , and decision - making . The way in which a child is nurtured at a young age and through adolescence has both psychological and developmental effects that effect their future . Not only does the child depend on caregiving , but schools and employers depend on the childcare . The government also benefits because these children turn into productive members of society . Eventually , they will be the ones running the country .