Assertion level proof planning with compiled strategies

This book presents new techniques that allow the automatic verification and generation of abstract human-style proofs. The core of this approach builds an efficient calculus that works directly by applying definitions, theorems, and axioms, which reduces the size of the underlying proof object by a factor of ten. The calculus is extended by the deep inference paradigm which allows the application of inference rules at arbitrary depth inside logical expressions and provides new proofs that are exponentially shorter and not available in the sequent calculus without cut. In addition, a strategy language for abstract underspecified declarative proof patterns is developed. Together, the complementary methods provide a framework to automate declarative proofs. The benefits of the techniques are illustrated by practical applications.Die vorliegende Arbeit beschäftigt sich damit, das Formalisieren von Beweisen zu vereinfachen, indem Methoden entwickelt werden, um informale Beweise formal zu verifizieren und erzeugen zu können. Dazu wird ein abstrakter Kalkül entwickelt, der direkt auf der Faktenebene arbeitet, welche von Menschen geführten Beweisen relativ nahe kommt. Anhand einer Fallstudie wird gezeigt, dass die abstrakte Beweisführung auf der Fakteneben vorteilhaft für automatische Suchverfahren ist. Zusätzlich wird eine Strategiesprache entwickelt, die es erlaubt, unterspezifizierte Beweismuster innerhalb des Beweisdokumentes zu spezifizieren und Beweisskizzen automatisch zu verfeinern. Fallstudien zeigen, dass komplexe Beweismuster kompakt in der entwickelten Strategiesprache spezifiziert werden können. Zusammen bilden die einander ergänzenden Methoden den Rahmen zur Automatisierung von deklarativen Beweisen auf der Faktenebene, die bisher überwiegend manuell entwickelt werden mussten

Assertion level proof planning with compiled strategies

This book presents new techniques that allow the automatic verification and generation of abstract human-style proofs. The core of this approach builds an efficient calculus that works directly by applying definitions, theorems, and axioms, which reduces the size of the underlying proof object by a factor of ten. The calculus is extended by the deep inference paradigm which allows the application of inference rules at arbitrary depth inside logical expressions and provides new proofs that are exponentially shorter and not available in the sequent calculus without cut. In addition, a strategy language for abstract underspecified declarative proof patterns is developed. Together, the complementary methods provide a framework to automate declarative proofs. The benefits of the techniques are illustrated by practical applications.Die vorliegende Arbeit beschäftigt sich damit, das Formalisieren von Beweisen zu vereinfachen, indem Methoden entwickelt werden, um informale Beweise formal zu verifizieren und erzeugen zu können. Dazu wird ein abstrakter Kalkül entwickelt, der direkt auf der Faktenebene arbeitet, welche von Menschen geführten Beweisen relativ nahe kommt. Anhand einer Fallstudie wird gezeigt, dass die abstrakte Beweisführung auf der Fakteneben vorteilhaft für automatische Suchverfahren ist. Zusätzlich wird eine Strategiesprache entwickelt, die es erlaubt, unterspezifizierte Beweismuster innerhalb des Beweisdokumentes zu spezifizieren und Beweisskizzen automatisch zu verfeinern. Fallstudien zeigen, dass komplexe Beweismuster kompakt in der entwickelten Strategiesprache spezifiziert werden können. Zusammen bilden die einander ergänzenden Methoden den Rahmen zur Automatisierung von deklarativen Beweisen auf der Faktenebene, die bisher überwiegend manuell entwickelt werden mussten

Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry

Wygas M, Oldengott IM, Bödeker D, Schwarz D. Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry. PHYSICAL REVIEW LETTERS. 2018;121(20): 201302.We investigate how a lepton asymmetry impacts the cosmic trajectory in the QCD phase diagram. We study the evolution of chemical potentials during the QCD epoch of the early Universe using susceptibilities from lattice QCD to interpolate between an ideal quark gas and an ideal hadron resonance gas. The lepton asymmetry affects the evolution of all chemical potentials. The standard cosmic trajectory is obtained assuming tiny lepton and baryon asymmetries. For larger lepton asymmetry, the charge chemical potential exceeds the baryon chemical potential before pion annihilation

Recent Developments in Antibody-Based Assays for the Detection of Bacterial Toxins

Considering the urgent demand for rapid and accurate determination of bacterial toxins and the recent promising developments in nanotechnology and microfluidics, this review summarizes new achievements of the past five years. Firstly, bacterial toxins will be categorized according to their antibody binding properties into low and high molecular weight compounds. Secondly, the types of antibodies and new techniques for producing antibodies are discussed, including poly- and mono-clonal antibodies, single-chain variable fragments (scFv), as well as heavy-chain and recombinant antibodies. Thirdly, the use of different nanomaterials, such as gold nanoparticles (AuNPs), magnetic nanoparticles (MNPs), quantum dots (QDs) and carbon nanomaterials (graphene and carbon nanotube), for labeling antibodies and toxins or for readout techniques will be summarized. Fourthly, microscale analysis or minimized devices, for example microfluidics or lab-on-a-chip (LOC), which have attracted increasing attention in combination with immunoassays for the robust detection or point-of-care testing (POCT), will be reviewed. Finally, some new materials and analytical strategies, which might be promising for analyzing toxins in the near future, will be shortly introduced

Accretion in Protoplanetary Disks by Collisional Fusion

The formation of a solar system is believed to have followed a multi-stage process around a protostar. Whipple first noted that planetesimal growth by particle agglomeration is strongly influenced by gas drag; there is a "bottleneck" at the meter scale with such bodies rapidly spiraling into the central star, whereas much smaller or larger particles do not. Thus, successful planetary accretion requires rapid planetesimal growth to km scale. A commonly accepted picture is that for collisional velocities $V_c$ above a certain threshold collisional velocity, ${V_{th}} \sim$ 0.1-10 cm s$^{-1}$, particle agglomeration is not possible; elastic rebound overcomes attractive surface and intermolecular forces. However, if perfect sticking is assumed for all collisions the bottleneck can be overcome by rapid planetesimal growth. While previous work has dealt explicitly with the influences of collisional pressures and the possibility of particle fracture or penetration, the basic role of the phase behavior of matter--phase diagrams, amorphs and polymorphs--has been neglected. Here it is demonstrated that novel aspects of surface phase transitions provide a physical basis for efficient sticking through collisional melting or amphorph-/polymorphization and fusion to extend the collisional velocity range of primary accretion to $\Delta V_c \sim$ 1-100 m s$^{-1}$, which bound both turbulent RMS speeds and the velocity differences between boulder sized and small grains $\sim$ 1-50 m s$^{-1}$. Thus, as inspiraling meter sized bodies collide with smaller particles in this high velocity collisional fusion regime they grow rapidly to km scales and hence settle into stable Keplerian orbits in $\sim$ 10$^5$ years before photoevaporative wind clears the disk of source material.Comment: 11 pages, 7 figures, 1 tabl

The cosmic QCD transition for large lepton flavour asymmetries

We study the impact of large lepton flavour asymmetries on the cosmic QCD transition. Scenarios of unequal lepton flavour asymmetries are observationally almost unconstrained and therefore open up a whole new parameter space in order to study the nature of the cosmic QCD transition. For very large asymmetries, we point out two limitations to our current method, namely the possible formation of a Bose-Einstein condensate of pions and the reliability of the Taylor expansion applied in this work.Comment: 10 pages, 6 figure