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Model pathway diagrams for the representation of mathematical models

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Liskov Cook I discuss of tool because mathematical model to treat them as 2 to
such that this is the a series of talks during them as so into 12 and 16 the started to have some preliminary ideas when we get in contact with its Council of functionality then in 2 thousand 17 last year's I presented at the next step in the evolution of of of the use of formalization together of the sick would of image I houses in Allen and during the last year so all the store
will make new steps in this direction and so I want to present our results in this point so this is basically an MMS stays governed than so I started this a
classical picture of research Dr. in mathematical modeling and simulation so he has started on the 1 hand and software on the other hand as a doctor could use input parameters output so the Lancet it's good to store them in the repositories or to publish even to dada like open doctor and the software produces the actual output so simulations or analysis as he's unit and the last talk so the discussion is held 2 sides software so there will be other presentation the on that topic and also there's a discussion should be open or software or this open source of light strategy for science you heard about something about you a study master the basis of the citation and reference to mobile hopefully now I show home from the suffer sustainably Institute they give a lecture on how to produce good software and we also see that even in the likeness of
association be you have a lot of infrastructure related to start and software and here you see a lot of talks or presentations of related to these topics researched Dr.
halted soft hour hard to archive things and also of the of the poster by ago it's 1 I think in the poster session after my talk on the topic science so
this movement on dada publications citations refer citation is governed by the 4th 11 activity which started at also by docks to
histamine also indictments of Institute and you never invade worked out some guidelines how to vote starter publication and thought a citation was including software and principle they developed this makes the dada findable accessibility into opera-loving and the use of the sub-summit by if she happens appears and the find a B means you need some composer two-piece accessible means not always so that you can find a license to do with but also that the format should be open at this it it's not import if you if you have to stop for example some script of a puppet to soft and you don't know the format then it's not a big step for the of us if it if you don't know the documentation what what is stored in the form of an and operator into usable is to go on the claims to use everything of this button so what is
the state of dada publication and citation it's just so after the last and the rest is also the tied to full of his principles and things to side and the tip who can assign you Iose persistent identifiers to objects the storage the US we performed showcase so the made the preprint of the publication of its users and software and produces dada and then the entire linked to get and you for the software the got and you I thought about set and he couldn't I think if they everything together and now also the find articles published and also of this you Eyes interlinked the other things so he tried to follow this principle the to be transparent to to in encourage use in scientific publications but the at the beginning and on the last element days I get in touch you have passed in these funds they also say of this is important step but you can do more so he gave a presentation ridges on cannot stores a doctor but you could also stores of his early days and on the tip of whole part heart and soul his
claim was published was talking so yes article the doctor the software 3 D objects like to geometry scientifically dual switch visualize assimilation dada and so on and me to go about about this principle out for my community this semantic simulation of of the electronic devices and what an article who state encourage people to do this the state at what this is state of the art and publication and dada citation softer citation this course this is not really developed in my community and also maiden showcase from an article how it could be enhanced by publishing visualizations of assimilation so this is being all it comes from the cooperation of in the it's not rocket on undead that part of research Dr. so I can take the the
speech about software on mark and then we say that the there's something is missing if we look on mathematical modeling simulation you cannot understand said Dr. of all the soft of automated the sightings at the commodities and so all architectures at modest part of the such out of the classical such doctor and so the type to find a foot and if it is to be searched out of the question is what it's about format for mathematical models and this this question of developed the 1st step in this direction namely formalizing moderates and finding about of former early and 2nd airport users of these search dot our point of view but
on on science is that was a mentioned in the talk of Andreas crewmen when but to get more and more articles so he sort it yeah yeah they get 120 thousand articles and master such incident private doctor basal it's impossible virtue you get so here's a state of the art in these sperm and the schools and sold some people like so when I was a new that it can also brought a position paper and save you must go from a document based voxels in in in science to a knowledge-based blood flow and published the meaning of this year and yes some excerpts from this position paper the document or intent workflows and science have been reached already exceeded the limits of adequacy as highlighted for example bodies and discussions on is increasing on a foundation of scientific is demand the schools which under the US show instead in in this talk and so reproducibility crisis so the optical staunch so everything you need to completely understand them the 2nd point this this system this a number of articles you cannot get everything off this information in your brain and have to read every article Sawczuk Asian reading and processing of scientific literature this currently tying up an extremely high cognitive capacity so there's a limit you cannot be this more than a certain number of articles but they all you can item so in the classic of it and the last point this this a sort of say we have scientific articles so usually loses clever techniques to get the content of to find something that represent knowledge but for scientific articles are very hard to understand for machines and for example here the moderates so that the question is if you want to go further we need mission support for for the knowledge ridges included in all articles and not only to related to the objects in to people choose them and so solution but
our our our vision is that's stored knowledge graph on knowledge-based scholarly communications entire intending to every objects to each other and watched only to be presented in a mixture of natural language and references to other objects so this is this vision to go to knowledge cost like we do it in the TPD out Okidata and so on OK so this is the 2nd motivation if you want to listen mathematical modeling and simulation we need the I've made had out about the also need some that format for 1 know the question is what I
Matematica waters could be regarded as the such dada and how to represent so usually the communicate the models in a mixture of nectar language of formulas but this is illegal was a porch because we can vote with them so this is result of science but this doesn't scare in the sense of and the the look for our for a machine action of a representation of the modeling and so we got some ideas
I presented last year's MMS days on that may need to use some feel the calf based on cost based representation of the model and you the ideas from denounced them as this together input from other ASEAN like part of a star market and also I just discussed ideas was of CIA involved in the last year so he gave different presentations of our porch on Cook Conference on 1 information at the tip that's a key but a medical knowledge management conference I also presented as to to my community and also to the mathematics communities and it also of the what of all ideas and the 2 articles for example 1 and appeared in lecture channels of artificial intelligence which is false this or what he publication whole tools to ought to be present models and also be presented this to my community and optical and Quantum Electronics in a smaller a version who
and as I said I presented this idea on the news of confidence in that I'm session on model representation to give of this past year on on how to handle assimilation data and to get discussion on
that and also of 1 of the participants adopted this idea and presented his model on the next day but also by moral pass diagram so I have a feeling that that's the thing that that actually are going and what the started on the as this seems to be also interesting to my at the Applied community so I come bank how to
the present mathematical models that means the
use of I said as the in a
mixture of natural language and formulas in our case study last year and also this year is a fund was support quarter the fun was about what it describes the motion of carriers and their conductance is are charged particles by incest consistent and that a static field so this basically creations govern the behavior of all your electronic devices or computer chips and you'll see a typical except for of presentation of this model modern and then the set the of 1 day to be present from as tools to but I showed last year
is by the field the cast this is sort of say the mating oil parrots of somewhat all components to each other
and the presented each component in a certain which is the the language and this except the look the feel the calf of 2 because and to model last year so this is not very helpful I think you it is a crucial showed that this approach could Vodafone and
also behind every of these points there is some formalization in the MMT language for example here for the
displacement vector you can see he a court's snippets of these fine if you're really and so the plug of our said
there's no distinction between quantities and loss and everything has admitted it messed and mixed up so I mean last year I get the discussion the so called
Western market in the system biology is it's all because and and modern passed the action Party diagrams also in this and so we looked in the us being there but it's been us and to edit this year to partition of eventually creations and this wanted
parsley diagrams from and this is so not a presentation of the diagram diagrammatic presentation Soviet quantities which are the cone that objects in the F. loss which connect quantities and here for example you can see that the electrostatic potential so gradient of this gives reason that it feared this is how the density is composed by some doping and free-carrier the electron density the combined in Dulles law and so you you if you have them on the representation of this model in its basic components and you can see all this also here that you have a high they could structure for example this year is a long for the displacement fear so you this could be isolated this is also an wondered password diagram or you can look on this part of this is possibly creation in our modern and you can also see this as a submodel or sup 1 pathway diagram and the interesting thing on the diagrams as that you look on the topological structure for example you can see here and this movie presents the effect of the self-consistent make of static field various here in the plans spot part this is what you like structure this is is another coupling so only is a potential and tasks and when you were get a simpler structure and and so these diagrams some explain so usually you can compose modest by combining sub this I see also learned in the talks before and here you can also use mpgs to compose make a block-based model composition for example you yeah so money plus block and TAUS adrift diffusion block so this is a transport equation this is an excellent self-consistent electrostatic potential and you have your some quantity which competences assist you which represents the electron density and this is some input and output port and you can connect them and also the presence of an was book system as a system of so the some orders and this you can also you was that the topology here of block-based Composition Tool to explain all strategies for officers not something if you want to post the existence of a solution of covered system of PDE born classic gratuitous ago mimicking the Ghuman mapping as a fun and use you stop of a density so kind of usable then you fix this young and then you only all of the unknown as the electrostatic potential use also known Lin'an not get in new electrostatic potential and said it in here into the continuity correction so this is and also in many I creation and you and this gives you off the solution of this linear creation the new new 1 and this established of fixed-point iteration from 1 you to another and invisible and this is known as a common mapping and you can neutralize you cannot prove the properties of this mapping to ensure that they are a solution exists and you can also use the same approach to explain American methods to salsa covered system which is the Gomez most of which is that the annexation of fixed-point interpolation you use all the and linearization of his money nitration in side here to update a new so I think these diagrams on are useful to explain coupling structures to expand properties of the model to explain pool strategies and also strategies so this is a graphical
representation but what is in the machine you we want a machine action representation and therefore you need a formalization and we do it and so in the on document the system and then every no what
yeah for example this part here every combines a complete charge density must be the presented in a quite finding
furious so it's this like in a programming language you say you states that you have some includes value import from other furious for example we need the quantity the doping pull 5 we need a spacer charge density which we define Q and we need some somehow the electrons and whole words densities for example and and then you will have to fight for the full formalization an expression like this and yet he did some extra at at some experts for example at the start of the food you really notation but just as the people being qualified purists who would ends at T minus electron density the goal to some genetic carry SPC is that the input user charge number pass from words and minus 4 the negatively charged electrons we provided in this expression and this we can directly translate into them and he system and physics creation means that in the interior of it means 4 weeks in inside omega our domain Q of X is defined as Q times T of X plus this expression and this is exactly what you can find it here in the slightly changed the the working this argument and the language so according to the model and and here's this not so difficult as as the vitamin a naturally and then we have the machine action of here the interesting point here is that the also stores the physical semantics and the system so int he has fewer piece for quantities that serves sort nor somehow cite as a potential Wybe knows that c is the carrier density and that p and N especially carrier densities name is the fee that he it's by by by this Furies which provides this quantity so and was so we can show like an an object only typed language with wasn't and at times I instances of the same the carriers PC we can also get semantics and the system that and plans and who was us in some kind similar or inherited from from the same structure so we can all not only the present the mathematical formula here but you can also the presence of physical semantics in the system and so the 10 formalized as much as as you can you It's not only the formula and this that and
other point you can do this is on the formalization of the fight documents was a support on the Austrian a set so you want to scale we have the speak documents we want to find someone else in the documents what you can do on the document ever you can appeal to lot these kind of articles in LA and then the user models for example also fossil domain you can bite you only got but you can also use a markable what to do here is that you have pre-defined mark was related to vet from
Monday's ation so you can and lime
though the machine when all that this year is related to some dictionary to
this formalization and you can that
translate very easily be made your article tools in machine knowledge in a very easy very and it's not a big tool to leave right you are things this a semantic take your semantic the loading of taste to connect these tools of formalization and here's an example so when this comes to
our strategy so we have an and foundation for this is a C on Doc system which is a semantic oriented representation format for mathematical knowledge in general on this we have to interface as 1 as the MMT interface for the formalization heavy can store semantic commodities as some system of few precast assign a few of these providing quantities the loss and physical semantics of domain-specific semantics and he also can connect this to our documents revived the Baltimore sought to identify the model by semantically preloading loutish documents and by this maybe can connected directly on a very low level also to the mathematical models and if he can do this this and was a lot of services it can be done we can such models we can classify and so on and 1 possibility of detectors documents here the health of lot unwanted content objects thought of someone like in these and PT the has our semantic document like are short of that and 1 and then you can be in control light and active document terms of Edo for example is a document can adapt them to the location so we said warning users when the patients alimentation which makes it difficult to find models ins existing documents in this survey we have some University of 2 stores in knowledge and sites and you can adapt and the patient to the leader for example that a basis functions from mathematicians or trot short annotations for physicists but it can also do was he can include in 1 document external models from some was to B so the work now more for this for the Fund was booked via the divide the documents and as tired light and the key dot us all if you look under the pitch of the citizens of Blue Island they you see a number of this number is not in typed in by the editor of the patients comes from a VT dot us of our best 1 Colgate's so information citizen number of of of London and so this number could be imported in the German English and all other languages and in this vein so our vision is 50 could also in the side of the effort to modernize in this way if he could formalize and install them in this way so that you can make your all your heart more precise and such about for example fought and product and 1 service you can do to this knowledge to this formalization is to get an M P D all of this and this is the of 1st application namely in
PDE view off what he's 1 at solving makes a formalization and then we show it again this looks not so nice at the moment as my handcrafted mpgs but this has been at the presentation of self machine knowledge of on the monitor in and you can click no on every quantity get extra information which type it is for example science of function from only got to and so on who he also goal so as of the former
NYSE furthermore orders from all Institute for example you know that perform a model for organic semiconductors the recently published for 1 it's the you see also a and fuel complex cut it to where heat fasion by a conductivity model of the other conductivity it says and and feared enhancement factor the temperature so you can easily explain them and you can also store
much larger knowledge class yeah it's Phillies Alexander University and allied which just a moment knowledge prof more on matter from from emetics of this moments thousands of notice and this is the Iike would have when vendor to sing in which of truly and Robin was providing cement system today we are going to open
access publications was so important to search the desires right under the US said he needs a source at least 2 to make more defined among here you see a too because the presentation of the fund was consistent open access publication but what you see in the moment this is all our but just behind this kind nothing there's no old knowledge about as you could see it would be very easy to connect this tools what database using the semantically preloaded loutishness
and then I came to the different levels of harmonization so today the exchange on a modernist or in a PDF format which is good for an atomic distribution but people from knowledge management save this semantic that documents because that difficult the process then we have and they are known like I showed lot is or HTML 5 used for unknown publishing but it's also good for such as this is a presentation level that couldn't to more in the morning to focus on 2 floors every physicist structural than ever of these mpg city stores a modest with modern password diagrams or the latest and Tate publications of semantic pitch and the latent was wonders this analysis active documents or I I live of ago wasn't she might highlighted this extent for the point strategy or for the Americas strategy and then we have so completely form 11 that's a form of abuse on document he presentation which and all syllabification and computation I showed you a snippet of such a formalization for the final work system and so all of these formats are bad performance also fall models of research Dr. and sold the hope that we can establish here on the structure and form another somewhat a develop a mess out to to keep them on the server now the
no but what they are I'll be the
1st to be rich formalize monitors
and those of the answer is no also at started I think this prize is circuit simulation in the sixties and seventies the description of a lexical sorted by also in like this and like a diagram then I learned last year from but as the market there's all and then established modeling language and systems biology for the action persuaded from the Systems Biology Markup Language SBML and also for example our institute we have a modeling language for pulls assimilation and amenable and usually this systems here well have a former description the advantage at the machine so about so you can simulate the model of the same description but they may need to discrete moderates and they asked domain-specific a porches customized from Spencer application on the other hand you see also on the PDU level which corresponds to continuous models and many problems and mathematical modeling and simulation are described by Systems of PDE very have some soften like Phoenix which works on the formulation this also some machine solvable porch and generates a this presentation of the formulation is domain independent but on the looks on the mathematical representation so round quantities insights Phoenix and you have also systems in between like commons all overtures books of physical quantities is somehow domain specific but also domain-independent or Jupiter notebooks which voice of being an informer 11 mean a document evidence that it's not only a formal representation of money but you also want a mixture of text and the model which is can be done in the 2 but I'm more books and so the question is yes' the good landscape of of the use of modeling systems do we need some other reports makes a sentence and so the question is is is that good to keep the domain-specific solutions or look to an unified a porch and in as every state as varied as not represent an attempt to define a universal language for representing quantitative models that would be impossible to achieve a 1 size fits all universal language but on the other hand you have also pulled just to say that this ad domain-specific language and they should domain-specific but they can have a common column so there should be 8 interest hotshot to implement domain-specific language so that they can share the knowledge can get on into a but and this is open Pinkett
so this Iverson so this is what
what we want want to do was the the looking so to start say for some some infrastructure to be present on the system and get them into orbit but because the other solutions that going to the ASEAN some sense because they are not in top of every of usable only the in the ecosystem at and and this is also you now so now the plants portation of knowledge sources mythology from from system to another and also now make these a barrier between the systems which leads to the invention of sinewave if you want to so all of our goal is to have a fair bit system final accessible in dominant usable and the look on the use of the 2 we have as a structured 11 and the former never solve the our goal is to to develop a system for Flexi formalization of medical monitors on the former lovely by on document t but also on the that's form of India's test format which gives also some necessary information so this would be the back full marks for the model as these documents on document the formalization and then to the some develops some archive store them in archive of or plotted from what it is like it's done in the buyer models that are players on part of stomach stated so in this database of don't 1 100th 20 thousand what is asked what but only 1 follows and often market latent soul basically they are ones taught them which we and our citation of models which is also possible with the by a modest part but could also in the debate that said the mouse this is the farthest establish ones in the von true to war to make a system the OK so thank you for them
attention to
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Mathematik
Kartesische Koordinaten
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Metadaten

Formale Metadaten

Titel Model pathway diagrams for the representation of mathematical models
Serientitel The Leibniz "Mathematical Modeling and Simulation" (MMS) Days 2018
Autor Koprucki, Thomas
Mitwirkende Leibniz-Institut für Oberflächenmodifizierung e.V. (IOP)
Leibniz-Institut für Troposphärenforschung (TROPOS)
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/35360
Herausgeber Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
Erscheinungsjahr 2018
Sprache Englisch
Produktionsort Leipzig

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik
Abstract Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. However, finding an appropriate representation for models is far less obvious than for numerical data and software. The current practice of representing models is a mixture of mathematical formulae and natural language in scientific publications. This (rigorous, but) informal approach creates ambiguity, potential incompleteness of the presentation, less reproducibility and often "re-invention of the wheel". We present a concept for a machine-actionable as well as human-understandable of mathematical models based on Model Pathway Diagrams (MPD). MPDs specify the physical quantities that are described in the model as well as the relations between them (laws, constitutive equations) and informal documentation about them. MPDs provide a visual tool for understanding the structural properties of models as well as algorithms for numerical simulations. For a formalized representation of mathematical models and their underlying physics, we use the OMDoc/MMT, a special machine-readable description language for mathematical documents, that allows specifying the mathematical vocabulary of models, i.e. the concepts, their properties, and relations. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the block-based composition of models from simpler components.

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