Modeling cell differentiation using dynamical systems on graphs

La cellula vivente è un sistema complesso governato da molti processi che non sono ancora stati compresi: il processo di differenziazione cellulare è uno di questi. La differenziazione cellulare è il processo in cui le cellule di un tipo specifico si riproducono e danno origine a diversi tipi di cellule. La differenziazione cellulare è regolata dai cosiddetti Gene Regulatory Networks (GRN). Un GRN è una raccolta di regolatori molecolari che interagiscono tra loro e con altre sostanze nella cellula per governare i livelli di espressione genica di mRNA e proteine. Kauffman propose per la prima volta nel 1969 di modellare GRN attraverso le cosiddette Random Boolean Networks (RBN). I RBN sono reti in cui ogni nodo può avere solo due possibili valori: 0 o 1, dove ogni nodo rappresenta un gene in GRN che può essere ”on” oppure ”off”. Queste reti possono modellizzare i GRN perchè l’attività di un nodo rappresenta il livello di espressione di un gene nell’intera regolazione. In questo lavoro di tesi ci avvaliamo di un modello matematico per sviluppare e riprodurre una possibile rete di regolazione genica per il processo di differenziazione cellulare

Master Equation per modelli di Lotka-Volterra

Capire i fattori che controllano la dinamica di specie interagenti è un problema fondamentale in ecologia. La natura delle interazioni verso le diverse specie non è sempre compresa a pieno, ma si assume che le varie interazioni tra le specie giochino un ruolo importante nelle proprietà dell'ecosistema. Recenti studi mostrano che l'ipotesi neutrale proposta da Hubbell delle specie non interagenti con una sorgente esterna, permette di spiegare le Abbondanze Relative di Specie (RSA) quando l'ecosistema ha raggiunto una situazione stazionaria. In questo lavoro viene utilizzato il concetto di fitness landscape per introdurre un modello stocastico per analizzare l'evoluzione di un sistema ecologico vicino allo stato di equilibrio. Dopo aver modellizzato un sistema attraverso le equazioni di Lotka-Volterra generalizzate, viene derivata una Master Equation associata a tale modello. I risultati mostrano un possibile approccio per unire la teoria neutrale di Hubbell e le equazioni di Lotka-Volterra

Explanations of Machine Learning Models in Repeated Nested Cross-Validation: An Application in Age Prediction Using Brain Complexity Features

SHAP (Shapley additive explanations) is a framework for explainable AI that makes explanations locally and globally. In this work, we propose a general method to obtain representative SHAP values within a repeated nested cross-validation procedure and separately for the training and test sets of the different cross-validation rounds to assess the real generalization abilities of the explanations. We applied this method to predict individual age using brain complexity features extracted from MRI scans of 159 healthy subjects. In particular, we used four implementations of the fractal dimension (FD) of the cerebral cortex—a measurement of brain complexity. Representative SHAP values highlighted that the most recent implementation of the FD had the highest impact over the others and was among the top-ranking features for predicting age. SHAP rankings were not the same in the training and test sets, but the top-ranking features were consistent. In conclusion, we propose a method—and share all the source code—that allows a rigorous assessment of the SHAP explanations of a trained model in a repeated nested cross-validation setting

Artificial intelligence-based models for reconstructing the critical current and index-value surfaces of HTS tapes

For modelling superconductors, interpolation and analytical formulas are commonly used to consider the relationship between the critical current density and other electromagnetic and physical quantities. However, look-up tables are not available in all modelling and coding environments, and interpolation methods must be manually implemented. Moreover, analytical formulas only approximate real physics of superconductors and, in many cases, lack a high level of accuracy. In this paper, we propose a new approach for addressing this problem involving artificial intelligence (AI) techniques for reconstructing the critical surface of high temperature superconducting (HTS) tapes and predicting their index value known as n-value. Different AI models were proposed and implemented, relying on a public experimental database for electromagnetic specifications of HTS tapes, including artificial neural networks (ANN), eXtreme Gradient Boosting (XGBoost), and kernel ridge regressor (KRR). The ANN model was the most accurate in predicting the critical current of HTS materials, performing goodness of fit very close to 1 and extremely low root mean squared error. The XGBoost model proved to be the fastest method, with training computational times under 1 s; whilst KRR could be used as an alternative solution with intermediate performance

Deep Learning in Neuroimaging: Effect of Data Leakage in Cross-validation Using 2D Convolutional Neural Networks

In recent years, 2D convolutional neural networks (CNNs) have been extensively used to diagnose neurological diseases from magnetic resonance imaging (MRI) data due to their potential to discern subtle and intricate patterns. Despite the high performances reported in numerous studies, developing CNN models with good generalization abilities is still a challenging task due to possible data leakage introduced during cross-validation (CV). In this study, we quantitatively assessed the effect of a data leakage caused by 3D MRI data splitting based on a 2D slice-level using three 2D CNN models to classify patients with Alzheimer’s disease (AD) and Parkinson’s disease (PD). Our experiments showed that slice-level CV erroneously boosted the average slice level accuracy on the test set by 30% on Open Access Series of Imaging Studies (OASIS), 29% on Alzheimer’s Disease Neuroimaging Initiative (ADNI), 48% on Parkinson’s Progression Markers Initiative (PPMI) and 55% on a local de-novo PD Versilia dataset. Further tests on a randomly labeled OASIS-derived dataset produced about 96% of (erroneous) accuracy (slice-level split) and 50% accuracy (subject-level split), as expected from a randomized experiment. Overall, the extent of the effect of an erroneous slice-based CV is severe, especially for small datasets

Fractal dimension of the cortical gray matter outweighs other brain MRI features as a predictor of transition to dementia in patients with mild cognitive impairment and leukoaraiosis

BackgroundThe relative contribution of changes in the cerebral white matter (WM) and cortical gray matter (GM) to the transition to dementia in patients with mild cognitive impairment (MCI) is not yet established. In this longitudinal study, we aimed to analyze MRI features that may predict the transition to dementia in patients with MCI and T2 hyperintensities in the cerebral WM, also known as leukoaraiosis.MethodsSixty-four participants with MCI and moderate to severe leukoaraiosis underwent baseline MRI examinations and annual neuropsychological testing over a 2 year period. The diagnosis of dementia was based on established criteria. We evaluated demographic, neuropsychological, and several MRI features at baseline as predictors of the clinical transition. The MRI features included visually assessed MRI features, such as the number of lacunes, microbleeds, and dilated perivascular spaces, and quantitative MRI features, such as volumes of the cortical GM, hippocampus, T2 hyperintensities, and diffusion indices of the cerebral WM. Additionally, we examined advanced quantitative features such as the fractal dimension (FD) of cortical GM and WM, which represents an index of tissue structural complexity derived from 3D-T1 weighted images. To assess the prediction of transition to dementia, we employed an XGBoost-based machine learning system using SHapley Additive exPlanations (SHAP) values to provide explainability to the machine learning model.ResultsAfter 2 years, 18 (28.1%) participants had transitioned from MCI to dementia. The area under the receiving operator characteristic curve was 0.69 (0.53, 0.85) [mean (90% confidence interval)]. The cortical GM-FD emerged as the top-ranking predictive feature of transition. Furthermore, aggregated quantitative neuroimaging features outperformed visually assessed MRI features in predicting conversion to dementia.DiscussionOur findings confirm the complementary roles of cortical GM and WM changes as underlying factors in the development of dementia in subjects with MCI and leukoaraiosis. FD appears to be a biomarker potentially more sensitive than other brain features