New Constant-Weight Codes from Propagation Rules

This paper proposes some simple propagation rules which give rise to new binary constant-weight codes.Comment: 4 page

Universal Prediction

In this thesis I investigate the theoretical possibility of a universal method of prediction. A prediction method is universal if it is always able to learn from data: if it is always able to extrapolate given data about past observations to maximally successful predictions about future observations. The context of this investigation is the broader philosophical question into the possibility of a formal specification of inductive or scientific reasoning, a question that also relates to modern-day speculation about a fully automatized data-driven science. I investigate, in particular, a proposed definition of a universal prediction method that goes back to Solomonoff (1964) and Levin (1970). This definition marks the birth of the theory of Kolmogorov complexity, and has a direct line to the information-theoretic approach in modern machine learning. Solomonoff's work was inspired by Carnap's program of inductive logic, and the more precise definition due to Levin can be seen as an explicit attempt to escape the diagonal argument that Putnam (1963) famously launched against the feasibility of Carnap's program. The Solomonoff-Levin definition essentially aims at a mixture of all possible prediction algorithms. An alternative interpretation is that the definition formalizes the idea that learning from data is equivalent to compressing data. In this guise, the definition is often presented as an implementation and even as a justification of Occam's razor, the principle that we should look for simple explanations. The conclusions of my investigation are negative. I show that the Solomonoff-Levin definition fails to unite two necessary conditions to count as a universal prediction method, as turns out be entailed by Putnam's original argument after all; and I argue that this indeed shows that no definition can. Moreover, I show that the suggested justification of Occam's razor does not work, and I argue that the relevant notion of simplicity as compressibility is already problematic itself

Universal Prediction

In this dissertation I investigate the theoretical possibility of a universal method of prediction. A prediction method is universal if it is always able to learn what there is to learn from data: if it is always able to extrapolate given data about past observations to maximally successful predictions about future observations. The context of this investigation is the broader philosophical question into the possibility of a formal specification of inductive or scientific reasoning, a question that also touches on modern-day speculation about a fully automatized data-driven science. I investigate, in particular, a specific mathematical definition of a universal prediction method, that goes back to the early days of artificial intelligence and that has a direct line to modern developments in machine learning. This definition essentially aims to combine all possible prediction algorithms. An alternative interpretation is that this definition formalizes the idea that learning from data is equivalent to compressing data. In this guise, the definition is often presented as an implementation and even as a justification of Occam's razor, the principle that we should look for simple explanations. The conclusions of my investigation are negative. I show that the proposed definition cannot be interpreted as a universal prediction method, as turns out to be exposed by a mathematical argument that it was actually intended to overcome. Moreover, I show that the suggested justification of Occam's razor does not work, and I argue that the relevant notion of simplicity as compressibility is problematic itself

Structural insights into the activity regulation of full-length non-structural protein 1 from SARS-CoV-2 and substrate recruitment by the hexameric MecA–ClpC complex

Since the outbreak of the COVID-19 pandemic in December 2019, SARS-CoV-2 has generated awareness for the requirement of novel antiviral drugs that target new proteins. Previous studies have pointed to the pathogenic significance of the non-structural protein 1 (Nsp1), which was proposed to be a major virulence factor due to its dual role in host translation inhibition and viral replication of SARSCoV- 2. The precise mechanisms of these two functions of Nsp1 are still uncovered. Here, I report the backbone chemical-shift assignments and the atomic-resolution NMR structure of full-length Nsp1 from SARS-CoV-2 solved by NMR. I found that Cov-2 Nsp1 consists of a folded N-terminal domain and an unfolded C-terminal region. Previous studies have identified a surface of the folded N-terminal domain of Nsp1 that associates with both host mRNA, in its function as inhibitor of the host protein translation, and the viral 5’-UTR RNA, in its function as promoter of viral protein translation. I found that the acidic C-terminal tail of Nsp1 folds back on this surface and masks the RNA binding site. A recent Cryo-EM study has shown that the end of C-terminal region of Nsp1 interacts with the mRNA entry tunnel on the 40S subunit of the ribosome, thus inhibiting host mRNA entry and promoting its degradation. I propose that the RNA binding site on the Nsp1 N-terminal domain is protected by its C-terminal tail before Nsp1 contacts the ribosome. Upon ribosome binding, the C-terminal tail is displaced, and the RNA binding site is exposed to recruit either host mRNA or the viral 5’ UTR. My findings have consequences for the design of drugs targeting the RNA binding surface of Nsp1, as it demonstrates the need to develop a molecule that can not only recognize this surface with high affinity, but also displace the C-terminal tail to render this surface accessible. In bacteria, the unfoldase ClpC is a member of the conserved Hsp100/Clp family of AAA+ ATPases and is involved in various cellular processes. The functional form of ClpC is an hexameric assembly, which is responsible for controlled unfolding of substrate proteins. The ClpC hexamer can further associate with the protease ClpP to form a complete protein degradation machine. MecA functions as an adaptor protein of ClpC and is necessary to both promote the formation of the functional ClpC hexamer and to recruit specific substrate proteins, such as the transcription factor ComK. Degradation of ComK via MecA-mediated recruitment to the ClpCP complex is part of the regulatory mechanisms of the development of cell competence. The mechanisms of selective substrate recruitment are still unknown, due to the conspicuous conformational dynamics and heterogeneity that characterize this step. To understand how the substrate ComK is recruited to the MecA–ClpC complex, I reconstituted the ComK– MecA–ClpC complex in vitro and applied nuclear magnetic resonance (NMR) spectroscopy and other biophysical techniques, such as multi-angle light scattering. I found that addition of ComK stabilizes the MecA–ClpC complex by forming a homogeneous ternary protein complex, which contains a ClpC hexamer, four MecA and two ComK molecules in the presence of ATP. The structural differences between the MecA–ClpC and the ComK–MecA–ClpC complexes were also monitored by small-angle X-ray scattering datasets, which furthered confirmed the presence of the interaction between ComK and MecA. Seit dem Ausbruch der COVID-19-Pandemie im Dezember 2019 hat SARS-CoV-2 das Bewusstsein für den Bedarf an neuartigen antiviralen Medikamenten geweckt, die neue Proteine abzielen. Frühere Studien haben auf die pathogene Bedeutung des Unstrukturiertenproteins 1 (Nsp1) hingewiesen, das aufgrund seiner doppel Rolle bei der Inhibierung von Translationsprozessen im Wirt, sowie der viralen Replikation von SARSCoV- 2 als wichtiger Virulenzfaktor betrachtet wird. Die genauen Mechanismen dieser beiden Funktionen von Nsp1 sind noch weitesgehnd unerforscht. Ich mittels NMR erhobener Daten die Zuordnungen der chemischen Verschiebung des Rückgrats sowie die atomare NMR-Struktur von Nsp1 in voller Länge aus SARS-CoV-2. Ich fand heraus, dass Cov-2 Nsp1 aus einer gefalteten N-terminalen Domäne und einer ungefalteten C-terminalen Region besteht. Frühere Studien haben einen Oberflächenbereich der gefalteten N-terminalen Domäne von Nsp1 identifiziert, die sowohl mit Wirts-mRNA in ihrer Funktion als Inhibitor der Translation assoziiert, als auch mit der viralen 5'-UTR-RNA in ihrer Funktion als Promotor des viralen Proteins. Ich fand heraus, dass sich der saure C-terminale Emde von Nsp1 auf dieser Oberfläche zurückfaltet und die RNA-Bindungsstelle maskiert. Eine kürzlich durchgeführte Cryo-EM-Studie hat ergeben, dass das Ende der C-terminalen Region von Nsp1 mit dem mRNA-Eintrittstunnel auf der 40S-Untereinheit des Ribosoms interagiert, wodurch der mRNA-Eintritt des Wirts gehemmt und dessen Abbau gefördert wird. Ich schlage vor, dass die RNA-Bindungsstelle auf der N-terminalen Domäne von Nsp1 durch ihr C-terminalen Emde geschützt wird, bevor Nsp1 das Ribosom kontaktiert. Bei der Ribosomenbindung wird der C-terminale Bereich verschoben und die RNA-Bindungsstelle wird freigelegt, um entweder Wirts-mRNA oder die virale 5'-UTR zu rekrutieren. Meine Ergebnisse haben Konsequenzen für das Design von Medikamenten, die auf die RNA-bindende Oberfläche von Nsp1 abzielen, da sie die Notwendigkeit aufzeigen ein Molekül zu entwickeln, welches diese Oberfläche nicht nur mit hoher Affinität erkennen kann, sondern auch das flexible C-terminale Ende verdrängt, um diese Oberfläche zugänglich zu machen. In Bakterien ist die Unfoldase ClpC, ein Mitglied der Hsp100/Clp-Familie von AAA+ ATPasen, und ist an verschiedenen zellulären Prozessen beteiligt. Die funktionelle Form von ClpC folgt einer hexameren Anordnung, die für die kontrollierte Entfaltung von Substratproteinen verantwortlich ist. Das ClpC-Hexamer kann ferner mit der Protease ClpP assoziieren, um eine vollständige Proteinabbaumaschine zu bilden. MecA fungiert als Adapterprotein von ClpC und ist notwendig um sowohl die Bildung des funktionellen ClpCHexamers zu fördern, als auch spezifische Substratproteine wie unter anderem den Transkriptionsfaktor ComK zu rekrutieren. Der Abbau von ComK über MecA-vermittelte Rekrutierung zum ClpCP-Komplex ist Teil der Regulationsmechanismen der Entwicklung von Zellkompetenz. Dies liegt hauptsächlich an der auffällige Konformationsdynamik und Heterogenität des Komplexes, die diesen Schritt charakterisieren. Um zu verstehen, wie das Substrat ComK zum MecA-ClpC-Komplex rekrutiert wird, wurde der ComK-MecA-ClpCKomplex in vitro rekonstituiert und Kernspinresonanz(NMR)-Spektroskopie sowie weitere biophysikalische Techniken wie zum Beispiel Mehrwinkel-Lichtstreuung angewendet. Ich fand heraus, dass die Zugabe von ComK den MecA-ClpC-Komplex durch Bildung eines homogenen ternären Proteinkomplexes stabilisiert, der in Gegenwart von ATP ein ClpC-Hexamer, vier MecA- und zwei ComK-Moleküle enthält. Die strukturellen Unterschiede zwischen den MecA-ClpC- und den ComK-MecA-ClpC-Komplexen wurden auch durch Kleinwinkel-Röntgenstreuungsdatensätze überwacht, die das Vorhandensein der Wechselwirkung zwischen ComK und MecA weiter bestätigten

Combinatorics

Combinatorics is a fundamental mathematical discipline which focuses on the study of discrete objects and their properties. The current workshop brought together researchers from diverse fields such as Extremal and Probabilistic Combinatorics, Discrete Geometry, Graph theory, Combiantorial Optimization and Algebraic Combinatorics for a fruitful interaction. New results, methods and developments and future challenges were discussed. This is a report on the meeting containing abstracts of the presentations and a summary of the problem session

Applied Harmonic Analysis and Data Science (hybrid meeting)

Data science has become a field of major importance for science and technology nowadays and poses a large variety of challenging mathematical questions. The area of applied harmonic analysis has a significant impact on such problems by providing methodologies both for theoretical questions and for a wide range of applications in signal and image processing and machine learning. Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018, this workshop focused on several exciting novel directions such as mathematical theory of deep learning, but also reported progress on long-standing open problems in the field