How to tidy up the jungle of mathematical models? A prerequisite for sustainable research software

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How to tidy up the jungle of mathematical models? A prerequisite for sustainable research software
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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 extend the corresponding scientific software as research data. Both have their origin in mathematical models. A holistic approach to research data in MMS should cover all three aspects: models, software, and data. Yet it is unclear, whether a suitable management of the mathematical knowledge related to models is possible and how it would look like. In this talk, we outline an approach to address this problem based on a flexiformal representation of the mathematical knowledge in publications and research software. We will discuss how this can improve the sustainability of research obtained by mathematical modeling and numerical simulations.
Software Confidence interval Self-organization Event horizon
Logical constant Stochastic Orientation (vector space) Mathematical analysis Subset Form (programming)
Mixture model Message passing Software Code Multiplication sign Mathematical analysis Modulare Programmierung Cartesian coordinate system
Scripting language Software Software developer Core dump Mereology Information privacy
Arithmetic mean Bridging (networking) Forcing (mathematics) Computer simulation Computer Mereology
Mathematics Different (Kate Ryan album) Mereology Theory
Predictability Type theory Statistics Core dump Integer Musical ensemble Office suite Resultant Social class
Software Video game Open set Distance Condition number
Word Vapor barrier Natural number Mathematical model Formal language
Vapor barrier Computer simulation Code Mathematical model Field (computer science)
Software Scientific modelling Blog Conic section Computer simulation Quicksort Binary file Field (computer science) Number
Information Computer file Software Causality Set (mathematics) output Inverse element Parameter (computer programming) Resultant
Service (economics) Multiplication sign 1 (number) Set (mathematics) Function (mathematics) Mereology Mathematical model Field (computer science) Fluid statics Digital rights management Software Causality Integrated development environment output Website Monster group Task (computing)
Goodness of fit Word Group action Computer file Software Software developer Event horizon Computing platform
Software Physical law Mathematical model
Point (geometry) Information Lattice (order) Mathematical model
Category of being Type theory Digital rights management State of matter Personal digital assistant Multiplication sign Expert system Quicksort Mathematical model Mathematical model
Process (computing) Observational study Personal digital assistant Mathematical model
Mixture model Information Water vapor Iteration Form (programming) Physical system Probability density function
Digital rights management Mathematics Well-formed formula Virtual machine Vapor Semantics (computer science) Field (computer science) Form (programming)
Mixture model Well-formed formula Different (Kate Ryan album) Virtual machine Representation (politics) Flow separation Mathematical model Formal language
Multiplication sign Weight Moment (mathematics) Displacement Mapping Insertion loss Mathematical model Semantics (computer science) Revision control Population density Hierarchy Electric field Diagram Traffic reporting Physical system
Complex (psychology) Presentation of a group Context awareness State of matter Displacement Mapping Graph (mathematics) Virtual machine Mereology Semantics (computer science) Message passing Nonlinear system Bounded variation Physical system
Domain name Purchasing Functional (mathematics) Concentric Multiplication sign Source code Displacement Mapping Virtual machine Insertion loss Food energy Number Formal language Vector potential Limit of a function Typprüfung
Medical imaging Presentation of a group Functional (mathematics) Observational study Displacement Mapping Formal grammar Quicksort Bounded variation Vector potential
Estimator Group action Personal digital assistant Markup language Virtual machine Set (mathematics) Computer simulation Line (geometry) Object (grammar) Mathematical model Semantics (computer science) Formal language
Mathematics Presentation of a group Estimator Diagram
Group action Virtual machine Energy level System call
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Point (geometry) Service (economics) Decision theory Network topology 1 (number) Iteration Task (computing)
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Geometry Presentation of a group Polygon mesh Software Quicksort Computer
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Point (geometry) Zirkulation <Strömungsmechanik> Software View (database)
but I think it wasn't so that is the end of the fangs organisers of this event is then nice confidence for inviting me and presenting my idea also to these topic of sustainable research software and
usually on basically that as of the search of which also developed a lot of stuff there but in the last 2 years and I the about be so what is the subset of all of our presents few and so we developed some constants and get in contact with which I call houses forms of University of Allen and yeah I present on the sides of his joint work which esthetic reasons
and so advise has Institute of our mission is to get the all-important oriented Applied Analysis and Stochastics and this means of which
aims starting of modern and not an analysis of the trations this as a master search developing American message code and also performing applications and doing this practice be developed in the last 20 years uh Mum on 16 software packages which we which is on long-term software and you have also optic edges In all put for you but um and and so this is 1 of our it points to the times the mixture presides to other disciplines Orton's free the software so it's very important for us I'm involved the visitors from a cogent and the US yeah conducted
this is 1 part and I use some of these stories and come to the end for this reason the core software development is an important topic at the US and also the Institute all decided to develop a policy software policy
on software development policy which states which soft every year for like this publication oriented this obvious more scripts we discussed yesterday and the of his long-term software like these packages can be defined whole in these development and guidelines to this the and a lot of things I learned and in particular this today I found also in his personal privacy sold
what is my driving force the
messenger the talk before the about this part of the team of science idea the that a different meaning so we have experience if you'll be this was in the past and now we have the things that also got exploration of computational outside of the family as mental making money and simulation which bridges this approach
between theory and practice and this is very successful to and M. M.
S. connects different disciplines because it's it's a common technique it's interdisciplinarity itself so you do have the for example the 2 disciplines and and by since there always things are expressed by mathematics in some kind the mathematics this evening lost on of evanescent and it's basically an interdisciplinarity part and so successfully
and end of that he's in office integer of the school common quarters and you often shares the same methods for ensemble statistics is can be used in different disciplines but also proven by that you have the same for the phenomenon for example of what class in the Michael studied in biochip but as the same phenomenon which types of the result or the or the prediction so
desires of reasons why this interdisciplinary core them and
this also due to genetic softer somehow for example the learned yesterday about the our community and also the supplies and community so this distance synergies to make this efficient and also on on the phenomenon that we have that the conditions of their life open fall for the of the of commercial software which connects
us but but this is few in practice
we have introduced can often the situation of the given up their own MMS words independently and we have language barriers between disciplines and this leads often to the invention of severe not on your modeling side but also on the south side and this also stated
as 1 problem of interdisciplinary science but by nature that's an
interdisciplinary science make must break down barriers between fields to build a common ground and I mathematical modeling and simulation codes such as the common cold
OK so because domestic techniques become so popular in my fear uh overtures opted for the
modeling and simulation of optoelectronic devices alone it the number of publications going because they have a lot of available software and native people use these techniques but often this is fairly difficult to sort of they they make that also the events in in in in and and now the bins are reasoning and for most of the the big players in this field you often key co-organizers not community which
is 1 of the largest conferences and this creates on international 1 of what's in this blog posts that looking better to pose and 60 I just be nice that my union Lord of piety was increased almost 80 John at papers mainly in the field of automatic conic device simulation by the number of such
paper submissions to Pope John is the certainly would news but a paper quality is often insufficient unfortunately I have to propose projecting of most of the papers after a detailed assessment of essential mistakes and so this inspired him to give some recommendations like guidelines is it could possibly information but an inverse of eta exactly to reproduce the results by using the same software input file from the parameters a set of increasing number of jobless not accept what even you find such supplemented documents now
and so this is what the had before on 1 hand these techniques are enabling but on the other hand I'm just it's also to other producibility causes
and sold in this sense of what he mentioned so stage of software stage data of 1 on such this and reproducibility causes to say see this is a crisis of the management of the more the such data are so um
alone because in this field so if there is producing of food they have certain classic today doesn't America data input output and perform a task uh um be discussed how to cite the software discussed importance of software and also for the data set of static models it is are launched and open doctor is emerging the emergence of a services like Dr. site which assigns the use of our time software he accepted trade uh there's a radar is emerging as a technology to manage the entire environment you have to put large deposits ones on the software side the part aboard SW monster yesterday it happens in between
and also uh we could use a good quality of software is the mission of autumn leuciscus file as a scientist of another talk before and also platforms are the launch tools and sustains the development of these open so search words um bottles of was
11 action know the event yesterday has has its aims thought that unknown looking on software to a to look on this parts but on and so I
think this is the important step in this direction but in my opinion as as as impractical and MMS is that you cannot understand software and data which also related
mathematical models so know In this thing is this effect of the law uh and and and and this is not mentioned in this discussion of the of producibility causes so I don't
see it as a subclass he sold this as if the had last going on the same point namely all the search 2 types of
people by rumor such his eyes on the sides of our model they time it and so there and so this
concept uh basic concepts you have to do that the um we could that presented at last year it's from the info grown in Rome meeting
and the ICMS the which leads to tools more publications that the states about us of our opinion and that it's important to include models and to this discussion and in particular this publication and I the initiate this time ultimately into which sense of mathematical models uh the such data category in contact emission who has a with an expert in middle-aged and knowledge management and so the the get and contact and kites tool to this is the only sort of saying yes we we have to do this but we don't know how to be a nice this and them by this
quantity the types so the state of case
study and the case study of our own for these process to convert of mathematical models came directly from my fear was that this self-imposed problem in
this paper the we make our discussion on the he tetration that's also some the Working morsels of N and S but some people said OK this is to simpler than and so the
selected isolated some part of of my basic research and these are the basic iterations of the system I don't want to explain in in detail I only want to say this is typically they use light arms and water so in a mixture of naturally text and form last and even when and a PDF document this is the baby % information pay parcel documentations in but if you want to
do the same as for software and
for for data we with some digital vagal handed to in machine it's a vapor this and this now comes to the field of mathematical knowledge management so um the odd things to and if you see these formula so if I look on the following if I see him
was he sought some semantics in the form of maybe you are not the because you're not going to work the situations so in our
brains severe artifice modestly of a cognitive representation of his contacts in our minds this gets played by working with this model and the communicate between each other as in in a mixture of native language and formulas but how we can bring this knowledge of if representation into the machine and the tightest
this fish different approaches the
end at the moment have uh favor some reports which is called model parsley diagrams here only to see for the former of Fund was talk system such a diagram of which basically consists of connecting quantities but um the like here is the is the charge density is composed of the doping 5 and so who in and a ton density by loss on the uh on displacement is the net electric use electric field times the permittivity who and so on so this had did you what about this very so we have some natural eventually expresses so deserves underlying semantics in the system and so here's a
simpler version of the so called you need all of Russian and you can see even that this has some hierarchy so you have you could put out some MPEG 4 hours
of displacement here you have an NPD for the nonlinear pass occasion and this then this coupled to an amputee also transport complex and so by this state you get that a lot of semantics and tools of the system by working the knowledge graphs but this is only some the perfect the presentation that makes it can be used can be presented in the machine and they
are alone me the apparent that the system and it a bit and if they had the look only on on the use of part of the percentage variation and then the user system which is quite common to use to formally describe the continent medical context here you see
some uh snapshot from the energy source code for example which describes the of of of permittivity loss of we introduce a quantity permittivity which is the number of the of the dielectric permittivity purchase was then at times the epsilon there's a long the we can formalize the quantities for example the electrostatic potential as a function from the domain tool to your values so but we can express a loss for example here the displacement in this formal language and also to concentration of the gospel or can be expressed in some niche where they and and this can be checked if everything is compact and the in in a in a in a former destruction the so but this is not
very practical a tool to work this is what's in machine can check and type-checker evening um the next
step is the In this formalization step is to use sort of say semantic only and have a presentation of the semantic knowledge which 1 possibility is from the soul must documents formant over may you get sort of some more not nice of you on on this knowledge in the image for example you just say OK it's I ascetical static potential as a function from 2 are different spatial variation of selected study potential uh it it includes device geology and device and so on the
influence of the displacement
in the next step in this because the 5 documents and we want to align them on all shoulders knowledge uh in connectivist to this mission actionable knowledge and 1 way to do this possibility is estimation of this as semantic markup for cases is a lot of sets of you revise our documents so in the In mathematical modeling and simulation and and soul you or you can also and and lines of definitions funds on North tool to
use as a definitions and then you can provide your doctor escort uh in this thing that you use here some articles usually do you this on your own but these markers are directly connected to this mathematical model so at the end of the machine also how this is connected to these objects he defined in the formal language and so this
is called semantic the loading of slotted documents and by having this change
starting from informant mathematical what it's like the on presentation we can formulate an amendment to the generates the on off presentation from the mn TV can generate these modern parsley diagrams automatically not but I wanted it this estimation for vitamin our documents and the then our documents on mortgages or documentation has our semantic be ordered and this leads to the notion selected documents so on
the 1 hand here in the energy level of the has these machine actionable knowledge by the of also semantic documents which side the hour of how they are related to these data the
and good example for these calls that they developed as a 1st so
this is an NP give you all 4 of these MNT only got knowledge
in in in this part of the machine and you can see a snapshot of
these 1st designed it looks very similar to what love what I sketched before us started form but this is not generated forms of knowledge and the sheet so what could be
future services based on this knowledge of 1 point as they are the many variants of of writing this iterations 1 point is here using monte trees and so this is the the CATH like but some people only will want you can insert everything and when you get back to the decisions so Mr. this this coolest ones and task that
I flattened all past a single iteration so all of the 1 they
as tools to to generate these possible the variance by by flattening of the modern passing their comes
and bonding was important thing is that in different parts of communities they use different notations so you'll see that 1 um Tober connotations of this same occasion basically for me as an expert I can add this but it makes
me also difficult to read the literature I I need to pass to look to check how this corresponds into my setting and and vise versa so this is also a barrier in communication even working on the same model and the semantic previewed in could be if they choose to work on that so a step further and in having different node and generating different notations for the same model
the and so this this this
ideas but what what is today we are going to be to the open to all want to open access publications and here you see also the fund was book system in such a nexus publication nicely can operate in HTML 5 but at the moment you can see here this is only the knowledge so there is no semantics here but as you see we have the technology to me to have these online publications of on the publications and by the system i for which we could if that's not a big step to to get also the matter make and land as to the mathematical knowledge and to connect this to use the services and benefits well much clearer and to to do this discovers
things and this brings me to further services based on user mathematical knowledge management from which are active documents which can adapt to the audience for some variables as functions for the mitogens there as soon as far physicists in document implement effective means to get to 4 iterations or simplified experience integration to compute the idea was this is an example of know to be included you eyes from all what is the opposite of these mortgage find us and model identification a composition model effectively that could be part of any and these are could applies the
fair principles I learned yesterday findable excessive and and usable work on mortgage and pay to tidy up so John of mathematical model for the present literature and hopefully to lead to better papers by on and states now I come back to the
software so I started to these tiny beta software and moderates
on this is sort of say basically containers and practice but it's more
difficult than what this this a continuous the presentation you often have to discretize them to serve the computer the software consists of API is the coated surface and and the documentation also often diffuse the oxygen you have yet cost and the same applies for data you have only 2 quantities geometry and mesh and so on so what I think important
is if you want not to link them as contain us that we need to put semantics into these
connections as as the word use of in the 1st taught and I
presented some ideas what could be the poachers for this part yeah so this is he's an empty on talks about system and PDC true to bring semantics of intermediate tool in mathematical models and the discretization and sperm now for the other part I think it's open and if he could get all you get us so this would be from your digital research environment for on special service which should not done by a single Institute but more
by infrastructure institutions and
now I come to my summary and our clock that produces ability of it's in MMSE which is my future of of research in the in the final the precise information on mathematical models so software to solve and and some data 4 4 forms of special cases so I presented empty OMDoc as of the end model pass idea comes as if they were to machine-actionable and human
understandable and possibility to manage this mathematical not it's involved in mathematical models and to carry out this is this case study on the fund was book system and content and the continue in this direction and now I want to formulate the two-hop poses uses the be discussed also unmetered out 1st off the oposite them I would say moderate parsley diagrams but also some kind of made up about half of scientific software and data data safe because they have and I some kind to some kind of semantics In the integration of mathematical knowledge management the signs of the courts have to formalize size documentations and
also the he was the development and testing of new software development could benefit from some from doing so because you
directly see holds a a modest online choose a software and how how spirit and and this could In the future the 2 this is my point of view what is important for sustainable sulfur in the
future and I the clauses the the war came on open science I would more so to science because not everyone wants to all this data and the salsa optimizes circulation excess and transport of scientific knowledge and
so this is our our ideas to this and also offers eyes in available as people and and our we so thank you for the attention of fj


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