An NIP-like Notion in Abstract Elementary Classes

This paper is a contribution to "neo-stability" type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly contains the class of stable AECs. We show that for an AEC $K$ and $\lambda\geq LS(K)$, $K_\lambda$ is NIP if and only if there is a notion of nonforking on it which we call a w*-good frame. On the other hand, the negation of NIP leads to being able to encode subsets

Building models in small cardinals in local abstract elementary classes

There are many results in the literature where superstablity-like independence notions, without any categoricity assumptions, have been used to show the existence of larger models. In this paper we show that stability is enough to construct larger models for small cardinals assuming a mild locality condition for Galois types. $\mathbf{Theorem.}$ Suppose $\lambda<2^{\aleph_0}$. Let $\mathbf{K}$ be an abstract elementary class with $\lambda \geq \operatorname{LS}(\mathbf{K})$. Assume $\mathbf{K}$ has amalgamation in $\lambda$, no maximal model in $\lambda$, and is stable in $\lambda$. If $\mathbf{K}$ is $(<\lambda^+, \lambda)$-local, then $\mathbf{K}$ has a model of cardinality $\lambda^{++}$. The set theoretic assumption that $\lambda<2^{\aleph_0}$ and model theoretic assumption of stability in $\lambda$ can be weaken to the model theoretic assumptions that $|\mathbf{S}^{na}(M)|< 2^{\aleph_0}$ for every $M \in \mathbf{K}_\lambda$ and stability for $\lambda$-algebraic types in $\lambda$. We further use the result just mentioned to provide a positive answer to Grossberg's question for small cardinals assuming a mild locality condition for Galois types and without any stability assumptions. This last result relies on an unproven claim of Shelah (Fact 4.5 of this paper) which we were unable to verify

Revealing the cosmic web dependent halo bias

Halo bias is the one of the key ingredients of the halo models. It was shown at a given redshift to be only dependent, to the first order, on the halo mass. In this study, four types of cosmic web environments: clusters, filaments, sheets and voids are defined within a state of the art high resolution $N$-body simulation. Within those environments, we use both halo-dark matter cross-correlation and halo-halo auto correlation functions to probe the clustering properties of halos. The nature of the halo bias differs strongly among the four different cosmic web environments we describe. With respect to the overall population, halos in clusters have significantly lower biases in the {$10^{11.0}\sim 10^{13.5}h^{-1}\rm M_\odot$} mass range. In other environments however, halos show extremely enhanced biases up to a factor 10 in voids for halos of mass {$\sim 10^{12.0}h^{-1}\rm M_\odot$}. Such a strong cosmic web environment dependence in the halo bias may play an important role in future cosmological and galaxy formation studies. Within this cosmic web framework, the age dependency of halo bias is found to be only significant in clusters and filaments for relatively small halos \la 10^{12.5}\msunh.Comment: 14 pages, 14 figures, ApJ accepte

Omics analysis in Caenorhabditis elegans: pattern inference and interpretation

High-throughput molecular technologies have greatly enhanced our understanding of biological processes by characterizing expression changes of genes (microarray and RNA-Seq data) and proteins (proteomics data), or transcription factor targets and epigenetics states (ChIP-chip and ChIP-Seq data). Among them, transcriptome studies based on microarrays or RNA-Seq have the ability to identify genes involved in the response to environmental change or specific stressors, thereby helping us to infer the underlying biological processes. During my PhD, I mainly focused on transcriptomic data analysis, using in most cases the nematode Caenorhabditis elegans as a model taxon. In particular, I have addressed seven specific projects: i) development of ABSSeq, an improved detection approach of differential gene expression for RNA-Seq data; ii) development of aFold, a method to fully moderate fold-change of RNA-Seq data and to improve gene ranking and visualization; iii) development of WormExp, a knowledge-based approach for interpreting gene sets in C. elegans; iv) exploration of the regulation of the C. elegans immune system using curated data sets from WormExp; v) characterization of putative major effectors (GATA transcription factors) in the C. elegans innate immune system; vi) comparison of the immune response of C. elegans at protein and transcript level. In general, our work facilitates high-throughput data analysis via improving pattern inference and interpretation, which in practice provides new insights into the immune system of C. elegans