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This thesis presents research which spans three conference papers and one manuscript which has not yet been submitted for peer review.
The topic of 1 is the inherent complexity of maintaining perfect height in B-trees. We consider the setting in which a B-tree of optimal height contains n = (1−ϵ)N elements where N is the number of elements in full B-tree of the same height (the capacity of the tree). We show that the rebalancing cost when updating the tree—while maintaining optimal height—depends on ϵ. Specifically, our analysis gives a lower bound for the rebalancing cost of Ω(1/(ϵB)). We then describe a rebalancing algorithm which has an amortized rebalancing cost with an almost matching upper bound of O(1/(ϵB)⋅log²(min{1/ϵ,B})). We additionally describe a scheme utilizing this algorithm which, given a rebalancing budget f(n), maintains optimal height for decreasing ϵ until the cost exceeds the
budget at which time it maintains optimal height plus one. Given a rebalancing budget of Θ(logn), this scheme maintains optimal height for all but a vanishing fraction of sizes in the intervals between tree capacities.
Manuscript 2 presents empirical analysis of practical randomized external-memory algorithms for computing the connected components of graphs. The best known theoretical results for this problem are essentially all derived from results for minimum spanning tree algorithms. In the realm of randomized external-memory MST algorithms, the best asymptotic result has I/O-complexity O(sort(|E|)) in expectation while an empirically studied practical algorithm has a bound of O(sort(|E|)⋅log(|V|/M)). We implement and evaluate an algorithm for connected components with expected I/O-complexity O(sort(|E|))—a simplification of the MST
algorithm with this asymptotic cost, we show that this approach may also yield good results in practice.
In paper 3, we present a novel approach to simulating large-scale population protocol models. Naive simulation of N interactions of a population protocol with n agents and m states requires Θ(nlogm) bits of memory and Θ(N) time. For
very large n, this is prohibitive both in memory consumption and time, as interesting protocols will typically require N > n interactions for convergence. We describe a histogram-based simulation framework which requires Θ(mlogn) bits of memory instead—an improvement as it is typically the case that
n ≫ m. We analyze, implement, and compare a number of different data structures to perform correct agent sampling in this regime. For this purpose, we develop dynamic alias tables which allow sampling an interaction in expected amortized
constant time. We then show how to use sampling techniques to process agent interactions in batches, giving a simulation approach which uses subconstant time per interaction under reasonable assumptions.
With paper 4, we introduce the new model of fragile complexity for comparison-based algorithms. Within this model, we analyze classical comparison-based problems such as finding the minimum value of a set, selection (or finding the median), and sorting. We prove a number of lower and upper bounds and in particular, we give a number of randomized results which describe trade-offs not achievable by deterministic algorithms.
The deubiquitinase USP32 regulates non-proteolytic ubiquitination in the endosomal-lysosomal system
(2021)
The regulation of essential cellular processes requires tightly controlled and directed transport of proteins and membranes. The highly dynamic endosomal and lysosomal system forms the key network for exchange and trafficking of molecules with its early endosomes, recycling endosomes, late endosomes, lysosomes, and additionally autophagosomes.
In this system, the small GTPase Rab7 has an essential role at the late endosomal stage regulating vesicle transport, tethering, and fusion, and retromer mediated receptor recycling back to the trans-Golgi network (TGN). Thus, Rab7 is also important for autophagosomes and lysosomes.
Lysosomes do not only represent the end point of the degradation pathway with several feeder pathways. But these organelles are also a dynamic signaling hub for a variety of metabolic processes. The ever-important regulator of cellular biosynthetic pathways mTORC1 dynamically associates with lysosomes where it is activated. mTORC1 activation is a complex multi-step process where a series of signaling events converge in dependence of amino acid levels thereby enabling interactions between the lysosomal v-ATPase, Ragulator complex (consisting of LAMTOR1-5), and Rag GTPases.
Ubiquitin signals are involved in almost all cellular processes. With this, their regulatory mechanism is also described for the endosomal-lysosomal system as well as mTORC1 signaling. Deubiquitinases (DUBs) release conjugated ubiquitin from proteins and thereby maintain the dynamic state of the cellular ubiquitinome.
The ubiquitin-specific protease 32 (USP32) is a poorly characterized DUB with only emerging cellular function. However, its predicted domain structure includes two unique domains within the entire DUB family. It has been linked to the development of breast cancer and small cell lung cancer. Furthermore, overexpressed GFP-USP32 was localized at the TGN, and a global mass spectrometry-based DUB interactome study suggested an interaction with the retromer complex. Based on these data, USP32 was a very interesting candidate to study its cellular function in this PhD project.
To investigate the function without disease background, a polyclonal USP32 knockout (USP32KO) RPE1 cell line was generated using the CRISPR/Cas9 technology. First experiments revealed different protein expression levels in various cell lines, and a subcellular localization of USP32 at membranes of the Golgi and lysosomal compartments. In a subsequent SILAC-based ubiquitinome analysis potential substrates of USP32 were identified. Interestingly, various proteins of the endosomal-lysosomal system were detected with enriched non-proteolytic ubiquitination upon USP32 depletion.
The further characterization of Rab7 as USP32 substrate confirmed the USP32-sensitive ubiquitination of Rab7 at lysine (K) residues 191 and 194. The ubiquitination in USP32KO cells did not change the subcellular localization of Rab7, but enhanced the interaction with the effector protein RILP. This implied that Rab7 was either more active or RILP had higher affinity to ubiquitinated Rab7. The subsequent results verified this theory. The retromer mediated recycling of CI-M6PR back to the TGN was faster or more efficient in USP32-depleted cells.
Accompanying this, levels of hydrolases were enriched in lysosomes isolated from USP32KO cells. Notably, USP32 had no direct effect on expression level or assembly of the retromer complex itself.
The observed lysosomal phenotypes connected another identified substrate to the function of USP32 in the endosomal-lysosomal system: LAMTOR1. LAMTOR1 is a component of the Ragulator complex and thus involved in the activation of mTORC1 at the lysosomal surface. Similar as for Rab7, the first experiments to characterize LAMTOR1 as USP32 substrate confirmed the USP32-sensitive ubiquitination at K20 independent of amino acid availability. However, ubiquitination of LAMTOR1 decreased its lysosomal localization in untreated and amino acid starved USP32KO cells. The following label-free interactome study detected a reduced interaction of LAMTOR1 and subunits of the lysosomal v-ATPase upon loss of USP32. This resulted in a shifted subcellular localization of mTOR (subunit of mTORC1) away from lysosomes. Furthermore, direct substrates of mTORC1 were less or slower re-phosphorylated after long amino acid starvation and re-activation of mTORC1 in USP32KO cells indicating a reduced mTORC1 activity.
Both USP32-dependent regulations of Rab7 and LAMTOR1/Ragulator converged in enhanced autophagic processes analyzed by increased LC3 levels upon amino acid starvation and USP32 depletion.
In summary, the presented thesis described the diverse role of USP32 in the endosomal and lysosomal system, and contributes to the understanding of novel ubiquitin signals in this context.
Recent advances in natural language processing have contributed to the development of market sentiment measures through text content analysis in news providers and social media. The effectiveness of these sentiment variables depends on the imple- mented techniques and the type of source on which they are based. In this paper, we investigate the impact of the release of public financial news on the S&P 500. Using automatic labeling techniques based on either stock index returns or dictionaries, we apply a classification problem based on long short-term memory neural networks to extract alternative proxies of investor sentiment. Our findings provide evidence that there exists an impact of those sentiments in the market on a 20-minute time frame. We find that dictionary-based sentiment provides meaningful results with respect to those based on stock index returns, which partly fails in the mapping process between news and financial returns.