DECONVOLUTION AND NETWORK CONSTRUCTION BY SINGLE CELL RNA SEQUENCING DATA

In this dissertation, we develop three novel analytic approaches for scRNA-seq data. In the first project, we aim to utilize scRNA-seq data to efficiently deconvolute bulk RNA-seq data. Deconvolution of bulk RNA-seq data by scRNA-seq data benefits from the high resolution in the characterization of transcriptomic heterogeneity from single-cells while enjoying higher statistical testing power with lower cost provided by bulk samples. Specifically, we propose an ENSEMBLE method SCDC (scRNA-seq DeConvolution), which integrates deconvolution results derived from multiple reference datasets, implicitly addressing the well-known batch effects. SCDC is benchmarked against existing methods and illustrated by the application to a human pancreatic islet dataset and a mouse mammary gland dataset.In the second project, to better understand gene regulatory networks under different but related conditions with single-cell resolution, we propose to construct Joint Gene Networks with scRNA-seq data (JGNsc) using the Gaussian graphical models (GGMs) framework. The sparsity feature of scRNA-seq data hinders the direct application of the popular GGMs. To facilitate the use of GGMs, JGNsc first proposes a hybrid imputation procedure that combines a Bayesian zero-inflated Poisson model with an iterative low-rank matrix completion step to efficiently impute zeros resulted from technical artifacts. JGNsc then transforms the imputed data via a nonparanormal transformation, based on which joint GGMs are constructed. We demonstrate JGNsc and assess its performance using synthetic data and two cancer clinical studies of medulloblastoma and glioblastoma.In the third project, for scRNA-seq data with continuous or ambiguous cell states, we develop a covariance-based change point detection (CPD) procedure to infer the discrete subgroups by utilizing the continuous pseudotime of single-cells. Little research suggests whether and how well the existing multivariate CPD methods work for scRNA-seq data. Hence, popular existing methods are benchmarked and evaluated in the simulation study and are shown to be powered for detecting mean but not covariance changes. To detect covariance changes, we propose the algorithm covcpd, which partitions single-cell samples into homogeneous network groups by utilizing a covariance equality testing statistic. covcpd is evaluated by simulation and is further illustrated through a mouse embryonic dataset and a human embryonic stem-cell dataset.Doctor of Philosoph

Tirer parti de la structure des données incertaines

The management of data uncertainty can lead to intractability, in the case of probabilistic databases, or even undecidability, in the case of open-world reasoning under logical rules. My thesis studies how to mitigate these problems by restricting the structure of uncertain data and rules. My first contribution investigates conditions on probabilistic relational instances that ensure the tractability of query evaluation and lineage computation. I show that these tasks are tractable when we bound the treewidth of instances, for various probabilistic frameworks and provenance representations. Conversely, I show intractability under mild assumptions for any other condition on instances. The second contribution concerns query evaluation on incomplete data under logical rules, and under the finiteness assumption usually made in database theory. I show that this task is decidable for unary inclusion dependencies and functional dependencies. This establishes the first positive result for finite open-world query answering on an arbitrary-arity language featuring both referential constraints and number restrictions.La gestion des données incertaines peut devenir infaisable, dans le cas des bases de données probabilistes, ou même indécidable, dans le cas du raisonnement en monde ouvert sous des contraintes logiques. Cette thèse étudie comment pallier ces problèmes en limitant la structure des données incertaines et des règles. La première contribution présentée s'intéresse aux conditions qui permettent d'assurer la faisabilité de l'évaluation de requêtes et du calcul de lignage sur les instances relationnelles probabilistes. Nous montrons que ces tâches sont faisables, pour diverses représentations de la provenance et des probabilités, quand la largeur d'arbre des instances est bornée. Réciproquement, sous des hypothèses faibles, nous pouvons montrer leur infaisabilité pour toute autre condition imposée sur les instances. La seconde contribution concerne l'évaluation de requêtes sur des données incomplètes et sous des contraintes logiques, sous l'hypothèse de finitude généralement supposée en théorie des bases de données. Nous montrons la décidabilité de cette tâche pour les dépendances d'inclusion unaires et les dépendances fonctionnelles. Ceci constitue le premier résultat positif, sous l'hypothèse de la finitude, pour la réponse aux requêtes en monde ouvert avec un langage d'arité arbitraire qui propose à la fois des contraintes d'intégrité référentielle et des contraintes de cardinalité

Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)

International audienceOriginating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice.This international conference “Algebras, graphs and ordered set” (ALGOS) brings together specialists in the theory of graphs, relational structures and ordered sets, topics that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for mathematicians and computer scientists to meet, to present their latest results, and to discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects.The first edition of ALgebras, Graphs and Ordered Sets (ALGOS 2020) has a particular motivation, namely, an opportunity to honour Maurice Pouzet on his 75th birthday! For this reason, we have particularly welcomed submissions in areas related to Maurice’s many scientific interests:• Lattices and ordered sets• Combinatorics and graph theory• Set theory and theory of relations• Universal algebra and multiple valued logic• Applications: formal calculus, knowledge discovery, biomedical sciences, decision aid and social choice, security, social networks, web semantics..

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Formal approaches to number in Slavic and beyond (Volume 5)

The goal of this collective monograph is to explore the relationship between the cognitive notion of number and various grammatical devices expressing this concept in natural language with a special focus on Slavic. The book aims at investigating different morphosyntactic and semantic categories including plurality and number-marking, individuation and countability, cumulativity, distributivity and collectivity, numerals, numeral modifiers and classifiers, as well as other quantifiers. It gathers 19 contributions tackling the main themes from different theoretical and methodological perspectives in order to contribute to our understanding of cross-linguistic patterns both in Slavic and non-Slavic languages