Fraunhofer Chalmers Research Centre for Industrial Mathematics
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MatematiskmodellavhurglutaminpåverkarfosforyleringavSch9viaTargetofRapamyciniSaccharomyces cerevisiae
No full textTarget of Rapamycin (TOR) är en signalväg i metabolismen hos eukaryota celler som reglerar tillväxt. Syftet med arbetet var att formulera en matematisk modell som kunde återskapa en specifik utsignal för TOR i jästceller, närmare bestämt aktiveringen av kinaset Sch9 som respons på aminosyran glutamin. För att åstadkomma detta översattes ingående reaktioner till matematiska hastighetsuttryck och utifrån dessa formulerades en modell bestående av ordinära differentialekvationer (ODE:er). Vissa antaganden och avgränsningar gjordes vid uppställning av ODE:erna såsom att alla sönderfall var av första ordningen. Samtidigt skrevs ett parameteruppskattningsprogram i MATLAB, med målet att bestämma de okända hastighetskonstanterna i modellerna.
Ett antal olika modeller konstruerades utifrån massverkans lag och testades med varierande resultat. Den tillgängliga mätdatan tillät konstruktion av både större och mindre modeller. Överlag lyckades de mindre modellerna fånga mätdatans utseende relativt bra, men variansen var väldigt stor hos de skattade hastighetskonstanterna. De större modellerna som testades misslyckades med att fånga utseendet hos mätdatan.
Det finns flera möjliga förklaringar till problemen med modellerna. Problemen med variansen kan bero på att de små modellerna innehåller för många okända parametrar och/eller att för lite mätdata fanns tillgänglig. Problemen hos de stora modellerna beror troligen på antagandet som gjordes vid uppställningen av ODE:erna. Även om de stora modellerna misslyckades indikerar resultatet hos de mindre modellerna att dynamiken hos signalvägen TOR är möjlig att modellera. Ytterligare arbete krävs dock innan modellen kan göra förutsägelser om TOR på ett verklighetstroget sätt
Modelling Dynamical Systems Using Neural Ordinary Differential Equations
No full textModelling of dynamical systems is an important problem in many fields of science.
In this thesis we explore a data-driven approach to learn dynamical systems from
data governed by ordinary differential equations using Neural Ordinary Differential
Equations (ODENet). ODENet is a recently introduced family of artificial neural
network architectures that parameterize the derivative of the input data with
a neural network block. The output of the full architecture is computed using any
numerical differential equation solver. We evaluate the modelling capabilities of
ODENet on four datasets synthesized from dynamical systems governed by ordinary
differential equations. We extract a closed-form expression for the derivative
parameterized by ODENet with two different methods: a least squares regression
approach and linear genetic programming. To evaluate ODENet the derivatives
learned by the network were compared to the true ordinary differential equations
used to synthesize the data. We found that ODENet learns a parameterization of
the underlying ordinary differential equation governing the data that is valid in a
region surrounding the training data. From this region a closed-form expression
that was close to the true system could be extracted for both linear and non-linear
ODEs
The thermo-oxidative durability of polyethylene reinforced with wood-based fibres
No full textAccelerated thermo-oxidative ageing of polyethylene reinforced with wood-based cellulose was studied. Materials were prepared by extrusion mixing of un-stabilized and stabilized polyethylene reinforced with 5 and 20 volume % cellulosic content. The materials were extruded into stripes, then aged at 90 °C in circulating air. The ageing of up to 31 days was assessed mainly by oxidation induction time and mechanical properties in tension. The results obtained indicated small effects of the accelerated thermo-oxidative ageing performed for stabilized composites
Predicting annotation difficulty using Monte Carlo dropout
No full textDeveloping products based on machine learning algorithms require relevant and
accurate datasets. In particular when it comes to supervised learning algorithms
whose performance is directly related to the quality and amount of training data.
Within the field of computer vision, classification is a task that require training data
in the form of annotated images. Annotating images is a manual task and I propose
that the annotation difficulty of an image should be interpreted as the likelihood
of someone else annotating an image differently. Knowing in advance which images
are hard to annotate would facilitate the distribution of work between annotators
with varying experience. In this thesis, it is shown that the uncertainty derived from
Monte Carlo dropout resembles the variance of a group of persons annotations of the
same image. This finding indicates that the level of agreement between persons can
be predicted, and thus enable for better distribution of work between annotators.
Furthermore, the finding could also be used to order images during training by
prioritizing harder images higher
