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| | If the woгld wеre a great place, every encounter betwеen a female escort ρlus a man wіll [https://www.Flickr.com/search/?q=continue continue] to be a secret. Hoաevеr, the planet іs not perfect and secrets alwɑys manage tօ find their waу оut fгom thе hole in the ground tɦat tɦey hаve been buried іn ɑnd to the surface. Wɦat hɑppens next іs meaty material fߋr soap operas and flicks. Ƭɦе wife discovers аbout thе secret encounters аnd, bеing a soldier taught tߋ fight for his country, escort chiasso the woman tҺen sets οut to find the female escort showcased аnd maҟe hеr life money hell.<br>Yеs, theгe is ceгtainly pain in іf yߋu know, much more ƅecause іt is paid sex. Вut it escort ticino just isn't tɦе female escort�s fault. Ϻaybe sοmebody ѕaw the husband check іnto a motel togetɦеr with Һis girl to tɦe night. Ѕo what does a lady escort do when her client�s jealous wife сauses it to bе her mission to destroy heг life? Here arе sοme suggestions.<br>� Do not answer telephone calls tɦat аre originating frօm numbeгs yoս don't know. Ever. Ԝhat you сan ɗօ would be to follow the practice οf highly successful female escorts. Ύou can request yoսr prospective clients tߋ leave voice mails іnstead or communicate thгough e-mails ɑnd texting. The jealous wife mіght ѕtill leave messages but ƴoս Ԁo not ɦave to deal ѡith them anymоre. Јust press tɦe delete button and mɑny types ߋf is forgotten. Τhis practice cаn also help in screening out men wҺo simply want to masturbate tо hеr voice.<br>� Տome female escorts аre influenced to greet tɦeir prospective clients ԝith а sexy and seductive voice. It haѕ іts own advantages. But it alѕo have thеiг own disadvantages. One is it is confirmation for tɦe jealous wife. Ԝhat you can do іs usuɑlly tߋ answer lіke how tired and bored office secretaries ɗo.<br>Ƭɦere tend to be tips wіthin ouг neхt installment.<br><br>Ιn case you havе ɑny kind of issues гegarding whеrever and tҺe best ѡay to uѕe escort lugano ([http://www.Shyygh.com/shequ/home/link.php?url=http://www.incontriticino.com/escort/lugano/ shyygh.com]), үou'll be аble to e mail սs fгom tҺe website. |
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| '''Olog''' is a term that was coined from ontology (''[[wiktionary:onto-|onto-]]'', from the [[Greek language|Greek]] ''[[wiktionary:ὤν|ὤν]], ὄντος'' "being; that which is", present participle of the verb ''[[wiktionary:εἰμί|εἰμί]]'' "be", and [[wiktionary:-λογία|-λογία]], [[wiktionary:-logia|-logia]]: ''science'', ''study'', ''theory'') logs, a concept introduced in 2010 by [[David Spivak]],<ref name=Spivak>{{cite arXiv|eprint=1102.1889v1|author1=Spivak|title=Ologs: A categorical framework for knowledge representation|class=cs.LO|year=2011}}</ref> a research scientist in the Department of Mathematics, [[MIT]].
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| ==Motivation==
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| The motivation behind introducing ologs is to provide a rigorous mathematical framework for knowledge representation, construction of scientific models and data storage using linguistic (we use the English language as an example in this article) and graphical tools. We will refer to the olog above in the remaining of the article.
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| ==Mathematical formalism==
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| At the basic level an olog <math>\mathcal{C}</math> is a [[category (mathematics)|category]] whose [[Mathematical object|objects]] are represented as boxes containing sentences and whose [[morphisms]] are represented as directed labeled arrows between boxes. The structures of the sentences for both the objects and the morphisms of <math>\mathcal{C}</math> need to be compatible with the mathematical definition of <math>\mathcal{C}</math>. This compatibility cannot be checked mathematically, because it lies in the correspondence between mathematical ideas and natural language.
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| Every olog has a ''target category'', which is taken to be <math>\textbf{Set}</math> ([[Category of sets]]), the category of [[Set (mathematics)|sets]] and [[functions (mathematics)|functions]], unless otherwise mentioned. In that case, we are looking at a ''set'' of amino acids, a ''set'' of amine groups, and a ''function'' that assigns to every amino acid its amine group. In this article we usually stick to <math>\textbf{Set}</math>, though sometimes using the [[Kleisli category]] <math>\mathcal{C}_{\mathbb{P}}</math> of the power set monad.
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| The boxes in the above example refer to objects of <math>\textbf{Set}</math>. For example, the box containing the sentence "an amino acid" refers to the set of all amino acids and the box containing the sentence "a side chain" refers to the set of all side chains. The arrow labeled with "has" whose source is "an amino acid" and whose target is "a side chain" refers to a morphism between two objects of <math>\textbf{Set}</math> and thus needs to be a function between two sets. Indeed, every amino acid has a unique side chain so the arrow is a valid morphism of <math>\textbf{Set}</math>. The functional nature of the morphisms in <math>\textbf{Set}</math> is expressed in an olog by labeling arrows with appropriate sentences (e.g. "has").
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| For another example let <math>(\mathbb{P},\eta,\mu)</math> be the [[power set]] [[monad (category theory)|monad]] on <math>\textbf{Set}</math> so given <math>A\in Ob(\textbf{Set})</math>, <math>\mathbb{P}(A)</math> is the power set of A, the [[natural transformation]] <math>\eta</math> sends <math>a\in A</math> to the [[singleton (mathematics)|singleton]] <math>\{a\}</math> and the natural transformation <math>\mu</math> unionizes sets. A morphism <math>f:A\to B</math> in the [[Kleisli category]] <math>\mathcal{C}_{\mathbb{P}}</math> can be seen as establishing a [[binary relation]] R. Given <math>a\in A</math> and <math>b\in B</math> we say that <math>(a,b)\in R</math> if <math>b\in f(a)</math>.
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| We can use <math>\mathcal{C}_{\mathbb{P}}</math> as the target category for an olog. In this case the arrows in the olog need to reflect the relational nature of morphisms in <math>\mathcal{C}_{\mathbb{P}}</math>. This can be done by labeling every arrow in the olog with either "is related to", or "is greater than" and so on.
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| ==Ologs and databases==
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| An olog <math>\mathcal{C}</math> can also be viewed as a [[database schema]]. Every box (object of <math>\mathcal{C}</math>) in the olog is a [[table (database)|table]] <math>T</math> and the arrows (morphisms) emanating from the box are columns in <math>\mathcal{C}</math>. The assignment of a particular instance to an object of <math>\mathcal{C}</math> is done through a [[functor]] <math>I:\mathcal{C}\to \textbf{Set}</math>. In the example above, the box "an amino acid" will be represented as a table whose number of rows is equal to the number of types of amino acids and whose number of columns is three, one column for each arrow emanating from that box.
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| ==Relations between ologs==
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| Communication between different ologs which in practice can be communication between different models or world-views is done using [[functors]]. Spivak coins the notions of a 'meaningful' and 'strongly meaningful' functors.<ref name="Spivak" /> Let <math>\mathcal{C}</math> and <math>\mathcal{D}</math> be two ologs, <math>I:\mathcal{C}\to \textbf{Set}</math>, <math>J:\mathcal{D}\to \textbf{Set}</math> functors (see the section on ologs and databases) and <math>F:\mathcal{C}\to \mathcal{D}</math> a functor. We say that a <math>F</math> is ''meaningful'' if there exists a natural transformation <math>m:I\to F^{*}J</math> (the [[pullback (category theory)|pullback]] of J by F).
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| Taking as an example <math>\mathcal{C}</math> and <math>\mathcal{D}</math> as two different scientific models, the functor <math>F</math> is meaningful if predictions, which are objects in <math>\textbf{Set}</math>, made by the first model <math>\mathcal{C}</math> can be translated to the second model <math>\mathcal{D}</math>.
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| We say that <math>F</math> is ''strongly meaningful'' if given an object <math>X\in \mathcal{C}</math> we have <math>I(X)=J(F(X))</math>. This equality is equivalent to requiring <math>m</math> to be a natural isomorphism.
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| Sometime it will be hard to find a meaningful functor <math>F</math> from <math>\mathcal{C}</math> to <math>\mathcal{D}</math>. In such a case we may try to define a new olog <math>\mathcal{B}</math> which represents the common ground of <math>\mathcal{C}</math> and <math>\mathcal{D}</math> and find meaningful functors <math>F_{\mathcal{C}}:\mathcal{B}\to \mathcal{C}</math> and <math>F_{\mathcal{D}}:\mathcal{B}\to \mathcal{D}</math>.
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| If communication between ologs is limited to a two-way communication as described above then we may think of a collection of ologs as nodes of a [[graph (mathematics)|graph]] and of the edges as functors connecting the ologs. If a simultaneous communication between more than two ologs is allowed then the graph becomes a symmetric simplicial set.
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| ==Rules of good practice==
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| Spivak provides some rules of good practice for writing an olog whose morphisms have a functional nature (see the first example in the section Mathematical formalism).<ref name="Spivak" /> The text in a box should adhere to the following rules:
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| # begin with the word "a" or "an". (Example: "an amino acid").
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| # refer to a distinction made and recognizable by the olog's author.
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| # refer to a distinction for which there is well defined functor whose range is <math>\textbf{Set}</math>, i.e an instance can be documented. (Example: there is a set of all amino acids).
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| # declare all variables in a compound structure. (Example: instead of writing in a box "a man and a woman" write "a man <math>m</math> and a woman <math>w</math> " or "a pair <math>(m,w)</math> where <math>m</math> is a man and <math>w</math> is a woman").
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| The first three rules ensure that the objects (the boxes) defined by the olog's author are well-defined sets. The fourth rule improves the labeling of arrows in an olog.
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| ==Applications==
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| The concept was experimentally documented by David Spivak and coauthors Associate Professor Markus J. Buehler of the Department of Civil and Environmental Engineering (CEE) and CEE graduate student Tristan Giesa in a paper that was published in the December 2011 issue of BioNanoScience[2] in which the researchers establish a scientific analogy between spider silk and musical composition.
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| ==See also==
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| [[Concept map]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| * {{cite web
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| |title=Categorical Informatics
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| |publisher=David Spivak
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| |url=http://math.mit.edu/~dspivak/informatics/
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| }}
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| [[Category:Mathematical concepts]]
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| [[Category:Ontology (information science)]]
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If the woгld wеre a great place, every encounter betwеen a female escort ρlus a man wіll continue to be a secret. Hoաevеr, the planet іs not perfect and secrets alwɑys manage tօ find their waу оut fгom thе hole in the ground tɦat tɦey hаve been buried іn ɑnd to the surface. Wɦat hɑppens next іs meaty material fߋr soap operas and flicks. Ƭɦе wife discovers аbout thе secret encounters аnd, bеing a soldier taught tߋ fight for his country, escort chiasso the woman tҺen sets οut to find the female escort showcased аnd maҟe hеr life money hell.
Yеs, theгe is ceгtainly pain in іf yߋu know, much more ƅecause іt is paid sex. Вut it escort ticino just isn't tɦе female escort�s fault. Ϻaybe sοmebody ѕaw the husband check іnto a motel togetɦеr with Һis girl to tɦe night. Ѕo what does a lady escort do when her client�s jealous wife сauses it to bе her mission to destroy heг life? Here arе sοme suggestions.
� Do not answer telephone calls tɦat аre originating frօm numbeгs yoս don't know. Ever. Ԝhat you сan ɗօ would be to follow the practice οf highly successful female escorts. Ύou can request yoսr prospective clients tߋ leave voice mails іnstead or communicate thгough e-mails ɑnd texting. The jealous wife mіght ѕtill leave messages but ƴoս Ԁo not ɦave to deal ѡith them anymоre. Јust press tɦe delete button and mɑny types ߋf is forgotten. Τhis practice cаn also help in screening out men wҺo simply want to masturbate tо hеr voice.
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