Deep Learning-based reduced order models for PDEs : multi-fidelity strategies for transfer learning

LAUREA MAGISTRALEI modelli di ordine ridotto basati su tecniche di Deep Learning (Deep Learning-based Reduced Order Models, DL-ROM) sono metodi che sfruttano tecniche di Machine Learning per approssimare in maniera efficiente la mappa parametro-soluzione associata a Equazioni a Derivate Parziali (EDP) parametriche. Attraverso l’impiego di Deep Neural Networks e di un insieme di snapshots della EDP, dopo una fase di allenamento offline i DL-ROM permettono una valutazione online computazionalmente efficiente della soluzione della EDP per ogni nuovo valore dei parametri. Grazie ad un rigoroso setting teorico, le capacità di approssimazione dei DL-ROM e la complessità, in termini di architettura, delle reti che li compongono sono state di recente investigate. Questa tesi estende tali risulti al caso di EDP parametrizzate da un oggetto infinito dimensionale come un campo stocastico, confermando la stima ottenuta attraverso esperimenti numerici. Inoltre, questo lavoro sviluppa diverse strategie, tutte basate sul concetto di Transfer Learning, per ridurre l’onere computazionale della fase di costruzione offline dei DL-ROM. Specificatamente, presentiamo un algoritmo di allenamento multi-livello, che sfrutta l’utilizzo di soluzioni a bassa risoluzione come snapshots, e DL-ROM Ibridi, che possono acquisire da altri DL-ROM più semplici una rappresentazione interna della varietà delle soluzioni per poi arricchirla di ulteriori dettagli attraverso un opportuno ri-allenamento. Entrambe le strategie proposte sono corredate di un’analisi dei costi computazionali che permette di valutarne l’efficacia su dei problemi modello associati a EDP ellittiche. Infine, i DL-ROM Ibridi sono stati impiegati nella soluzione di un problema di stima di parametri in ambito Bayesiano, attraverso la versione rivisitata di un algoritmo Markov-Chain Monte-Carlo, nel contesto della Uncertainty Quantification per le EDP.Deep Learning-based Reduced Order Models (DL-ROMs) are a recently developed framework for the efficient approximation of the parameter-to-solution map associated to parametric Partial Differential Equations (PDEs) exploiting Machine Learning techniques. Taking advantage of a set of PDEs snapshots and deep neural networks, after an offline training DL-ROMs enable the inexpensive online evaluation of the PDE solution for any new parameter instance. Thanks to a rigorous theoretical setting, approximation capabilities of DL-ROMs and network architecture complexity have been recently investigated. This thesis extends these results to the case of PDE parameterized by infinite dimensional objects like random fields, confirming the error estimates with numerical experiments. Moreover, this work presents several strategies, all based on the concept of Transfer Learning, to alleviate the computational burden of the DL-ROM offline stage. In particular, we designed a multi-level training algorithm, that takes advantage of snapshots at lower resolution, and a Hybrid DL-ROM, that inherits the internal representation of the solution manifold from a simpler DL-ROM and enhances it with further details through a suitable re-training. Both these strategies have been assessed on a set of model problems involving linear elliptic PDEs. Finally, Hybrid DL-ROMs have been exploited to solve a Bayesian inverse problem for parameter estimation by means of a revisited Monte-Carlo Markov-Chain algorithm in the framework of Uncertainty Quantification of PDEs

Increased tRNA modification and gene-specific codon usage regulate cell cycle progression during the DNA damage response

S-phase and DNA damage promote increased ribonucleotide reductase (RNR) activity. Translation of RNR1 has been linked to the wobble uridine modifying enzyme tRNA methyltransferase 9 (Trm9). We predicted that changes in tRNA modification would translationally regulate RNR1 after DNA damage to promote cell cycle progression. In support, we demonstrate that the Trm9-dependent tRNA modification 5-methoxycarbonylmethyluridine (mcm⁵U) is increased in hydroxyurea (HU)-induced S-phase cells, relative to G₁ and G₂, and that mcm⁵U is one of 16 tRNA modifications whose levels oscillate during the cell cycle. Codon-reporter data matches the mcm⁵U increase to Trm9 and the efficient translation of AGA codons and RNR1. Further, we show that in trm9Δ cells reduced Rnr1 protein levels cause delayed transition into S-phase after damage. Codon re-engineering of RNR1 increased the number of trm9Δ cells that have transitioned into S-phase 1 h after DNA damage and that have increased Rnr1 protein levels, similar to that of wild-type cells expressing native RNR1. Our data supports a model in which codon usage and tRNA modification are regulatory components of the DNA damage response, with both playing vital roles in cell cycle progression.National Institute of Environmental Health Sciences (R01 ES015037)National Institute of Environmental Health Sciences (R01 ES017010)National Institute of Environmental Health Sciences (P30 ES002109)Massachusetts Institute of Technology (Westaway Fund)Singapore-MIT Alliance for Research and Technolog

PENGARUH PENERAPAN MODEL PLANNING MONITORING EVALUATING (PME) TERHADAP KEMAMPUAN PEMECAHAN MASALAH MATEMATIS DITINJAU DARI SELF EFFICACY SISWA SMA DI PEKANBARU

ABSTRAK Fraulin Nalvira, (2023): Pengaruh Penerapan Model Planning Monitoring Evaluating (PME) Terhadap Kemampuan Pemecahan Masalah Matematis Ditinjau Dari Self Efficacy Siswa SMA Di Pekanbaru Penelitian ini dilatarbelakangi oleh adanya fakta di lapangan yang menunjukkan bahwa masih rendahnya kemampuan pemecahan masalah matematis siswa. Adapun tujuan dari penelitian ini ialah untuk mengetahui terdapat atau tidaknya pengaruh penerapan model Planning Monitoring Evaluating terhadap kemampuan pemecahan masalah matematis jika ditinjau dari self efficacy siswa. Jenis penelitian ini adalah penelitian kuantitatif dengan desain penelitian yaitu factorial experiment. Adapun populasi dalam penelitian ini adalah kelas X SMA Negeri 15 Pekanbaru tahun ajaran 2022/2023. Sampel pada penelitian ini yaitu kelas X.C sebagai kelas eksperimen dan kelas X.D sebagai kelas kontrol yang dipilih menggunakan teknik cluster random sampling. Teknik pengumpulan data yang digunakan dalam penelitian ini ialah tes, angket, observasi dan dokumentasi. Instrumen pengumpulan data yang digunakan berupa soal tes kemampuan pemecahan masalah matematis, angket self efficacy, lembar observasi guru dan lembar kendali keterlaksanaan (LKK) PME. Analisis data yang digunakan yaitu uji anova dua arah. Berdasarkan hasil analisisnya didapati kesimpulan bahwa: 1) Terdapat perbedaan kemampuan pemecahan masalah matematis siswa yang belajar menggunakan model pembelajaran PME dengan siswa yang belajar menggunakan pembelajaran langsung, 2) Terdapat perbedaan kemampuan pemecahan masalah matematis antara siswa yang memiliki self efficacy tinggi, sedang dan rendah, 3) Tidak terdapat interaksi antara model pembelajaran dan self efficacy terhadap kemampuan pemecahan masalah matematis siswa. Dengan demikian, secara umum dapat disimpulkan bahwa penerapan model pembelajaran Planning Monitoring Evaluating (PME) berpengaruh terhadap kemampuan pemecahan masalah matematis ditinjau dari self efficacy siswa di SMA Negeri 15 Pekanbaru Kata Kunci: Model Planning Monitoring Evaluating (PME), Kemampuan Pemecahan Masalah Matematis, Self Efficac

Timing is everything: The link between chromosomal mobility and homologous recombination

Chromosomes are very dynamic structures that are constantly undergoing physical changes necessary for cell survival. Studies in yeast and metazoans have shown that chromosomal loci exhibit large-scale changes in mobility in response to DNA double-strand breaks (DSBs). If left unrepaired, DSBs can lead to disease and even cell death. One of the predominant cellular pathways utilized to repair DSBs is homologous recombination (HR). DSB repair via HR requires a homologous DNA template to recover the missing genetic information lost at the break site. Our lab proposes that increased chromosome mobility (ICM) facilitates recombination by helping a broken chromosome successfully find its homolog. In support of this view, ICM is under the genetic control of the HR machinery and requires activation of the DNA damage checkpoint response. However, there is currently no consensus on the precise functional role of ICM in HR. In Chapter 1, I describe in detail the known steps of DSB repair via the HR pathway, and discuss some of the important advancements made in the field of cell biology that has helped shape our understanding of HR. I highlight the use of in vivo cell imaging and fluorescently labeled DNA repair proteins during the study of HR. Additionally, I discuss some of the first studies that examined chromosome dynamics within the nucleus in live cells. Lastly, I describe the phenomenon of increased chromosome mobility and expand upon why it needs to be studied further. In Chapter 2, I present in detail our method for measuring the pairing of DNA loci during HR at a site-specific DSB in Saccharomyces cerevisiae. This method utilizes live cell imaging and a chromosome tagging system in diploid yeast to visualize homologous chromosomes during HR-mediated repair. Using this method, we demonstrate that in wild type (WT) cells, homologous chromosomes come together, repair and then move apart after repair is complete. Importantly, the kinetics we observe in the pairing of homologous chromosomes match the kinetics of site-specific DSB formation and the subsequent gene conversion of that site. In Chapter 3, I describe our study that elucidates the relationship between ICM and multiple HR steps. We find a tight temporal correlation between the recruitment of the recombination proteins, ICM, the physical pairing of homologous loci, and gene conversion. Importantly, we can shift the timing of ICM by altering the initiation of DNA end resection - an early step in the HR process. Our data highlight the importance of DNA end resection as a vital precursor to ICM and demonstrate a strong temporal linkage between ICM and HR. Taken together our data support the claim that ICM is essential to HR and mechanistically involved in the process of DNA repair. In Chapter 4, we explore chromosome mobility in response to different forms of DNA damage such as spontaneous DSBs, collapsed replication forks, and ionizing radiation (IR). We find that spontaneous DSBs and collapsed replication forks do not induce a change in chromosome mobility. However, exposure to ionizing radiation results in a robust increase in global chromosome mobility that is dependent on activation of the DNA damage checkpoint. Overall, these findings demonstrate how ICM is tightly regulated and highly dependent on the circumstances surrounding the formation of the DSB. Lastly, in Chapter 5, I summarize all of my findings and discuss how they relate to one another with respect to the linkage between ICM and HR. I also provide a perspective on future experiments needed to advance the field.

On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental role, as they provide an extremely flexible tool for reducing the dimensionality of a given problem by leveraging on the nonlinear capabilities of neural networks. Indeed, starting from this paradigm, several successful approaches have already been developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs). Nevertheless, when it comes to stochastic problems parameterized by random fields, the current understanding of DL-ROMs is mostly based on empirical evidence: in fact, their theoretical analysis is currently limited to the case of PDEs depending on a finite number of (deterministic) parameters. The purpose of this work is to extend the existing literature by providing some theoretical insights about the use of DL-ROMs in the presence of stochasticity generated by random fields. In particular, we derive explicit error bounds that can guide domain practitioners when choosing the latent dimension of deep autoencoders. We evaluate the practical usefulness of our theory by means of numerical experiments, showing how our analysis can significantly impact the performance of DL-ROMs

On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental role, as they provide an extremely flexible tool for reducing the dimensionality of a given problem by leveraging on the nonlinear capabilities of neural networks. Indeed, starting from this paradigm, several successful approaches have already been developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs). Nevertheless, when it comes to stochastic problems parameterized by random fields, the current understanding of DL-ROMs is mostly based on empirical evidence: in fact, their theoretical analysis is currently limited to the case of PDEs depending on a finite number of (deterministic) parameters. The purpose of this work is to extend the existing literature by providing some theoretical insights about the use of DL-ROMs in the presence of stochasticity generated by random fields. In particular, we derive explicit error bounds that can guide domain practitioners when choosing the latent dimension of deep autoencoders. We evaluate the practical usefulness of our theory by means of numerical experiments, showing how our analysis can significantly impact the performance of DL-ROMs

Analysis of travelling waves associated with the modelling of aerosolised skin grafts

A previous model developed by the authors investigates the growth patterns of keratinocyte cell colonies after they have been applied to a burn site using a spray technique. In this paper, we investigate a simplified one-dimensional version of the model. This model yields travelling wave solutions and we analyse the behaviour of the travelling waves. Approximations for the rate of healing and maximum values for both the active healing and the healed cell densities are obtained

Eye-Tracking online: a new lie detection technique

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Practical guideline for international nursing students - how to take a Pap-smear test

The purpose of this project was to produce good quality, evidence-based learning material. This project was meant to enable the students to acquire the necessary skills, which can then be applied in their future career. The objective of this thesis was a recommendation by Satakunnan Ammattikorkeakoulu (SAMK), to create learning material tailored for the international Nursing students of SAMK on how to take a Pap-smear test. The educational material created was then provided in the format of a PowerPoint presentation. This thesis provided an easy step by step procedure on how to take a Pap-smear test according to the Finnish guidelines. The instruction provided along with the images and the PowerPoint presentation, was made according to the key points found on adult learning. As the audience whom this is directed at, are categorized as adults. The authors of this thesis used the hybrid method to plan and implement each step. The hybrid method was more suitable for this project as it would allow small changes. First, literature review was conducted in order to gather evidence-based material on the topic including the actual guidelines on how to take a Pap-smear test applied in the local hospitals and healthcare centers. Secondly the authors focused on the learning needs and features of their client and the target group. Thirdly the authors make a working schedule considering the limitations given by a student being abroad for the academic year and the Covid-19 pandemic. As a result of the above-mentioned limitations, a delay in concluding the project was experimented and it was needed to adjust the final product from a video into a PowerPoint presentation. However, the authors believed that criteria of quality and ethics have been fulfilled. The final PowerPoint presentation has been positively evaluated by the representatives of SAMK. The original product can be used by the teachers as an educational material for the international students