Seminaria

Mass spectrometry (MS) is one of the most important technologies for study of proteins. MS experiments generate massive amounts of complex data which require advanced pre-processing and careful statistical analysis. In bottom-up approach to MS, peptides - smaller segments of proteins - enter the mass spectrometer and thus measurements are made on a peptide level. Because of this, one of the problems in protein quantification based on MS is the presence of peptides that can be assigned to multiple proteins. Such peptides are referred to as shared or degenerate peptides. Since it is not obvious how to assign the abundance of shared peptides to proteins, they are often discarded from the analysis. This leads to a loss of a substantial amount of data. In this talk, I will first present the basics of Mass Spectrometry data analysis. Then, I will review existing methods for handling shared peptides. I will finish with a summary of our progress on improving methodology of protein quantification with shared peptides and related statistical challenges. The talk is based on an ongoing collaboration with Tomasz Burzykowski (Hasselt University) and Jurgen Claesen (Belgian Nuclear Research Centre).

Let $T$ be a complete, model complete o-minimal theory extending the theory $\mathrm{RCF}$ (in some language $L$). We study derivations $\delta$ on models $M \models T$. We introduce the notion of a $T$-derivation: a derivation which is compatible with the $L(\varnothing)$-definable $\mathcal{C}^1$-functions on $M$.
The theory of $T$-models with a $T$-derivation has a model completion $\mathrm{T \delta G}$. The derivation in models $(M, \delta) \models \mathrm{T \delta G}$ behaves “generically,” it is wildly discontinuous, and its kernel is a dense elementary $L$-substructure of $M$.
If $T = \mathrm{RCF}$, then $\mathrm{T \delta G}$ is the theory of closed ordered differential fields ($\mathrm{CODF}$) as introduced by Michael Singer. We are able to recover many of the known facts about $\mathrm{CODF}$ in our setting.
Among other things, $\mathrm{T \delta G}$ has $T$ as its open core, and $\mathrm{T \delta G}$ is distal.
We also examine the case of finitely many commuting $T$-derivations.
Joint work with Elliot Kaplan.

The notion of inverse limits was generalized by Ingram and Mahavier to multivalued settings. We investigate topological properties that are preserved by those generalized inverse limits. We have +theorems about local connectedness, trivial shape, arc-likeness, tree-likeness, dimension etc. The talk is illustrated by many examples.