Gravity Informed

Formulating a universally satisfactory theory of quantum gravity is a long-standing open problem in theoretical physics. Relatively recently, the use of techniques from quantum information has emerged as a powerful tool for analyzing phenomena that lie at the intersection of quantum theory and gravitation. This thesis describes several advances and novel proposals that were made regarding information theoretic aspects of quantum gravity in three broad areas: holography, cosmology, and the black hole information problem. Regarding holography, we first assess the differences between typical holographic states and fully random states. Next, we show that determining Ryu-Takayanagi surfaces in AdS3/CFT2 is computationally easy from a complexity-theoretic standpoint. Finally, we identify precise consistency conditions that constrain the validity of an early tensor network model for the AdS/CFT correspondence that uses the Multiscale Entanglement Renormalization Ansatz (MERA). Regarding cosmology, we propose an alternative interpretation of the MERA as a discretization of de Sitter spacetime. Next, we return to holographic ideas and show that an appropriately-defined Generalized Second Law implies a cosmic no-hair theorem for certain classes of cosmological spacetimes. Finally, we advance an information-theoretic proposal for calculating the signature of a quantum gravity-motivated, fully covariant, natural ultraviolet cutoff in the spectrum of inflationary perturbations. Regarding the black hole information problem, we begin by exhibiting a simple protocol which, under highly specific circumstances, allows one to retrieve a single qubit from a black hole. Next, we propose an operational resolution of the black hole information problem in which observers who enter the black hole could never detect an inconsistency between their experiences and quantum mechanics due to the finite amount of time available before reaching the central singularity. Finally, we discuss a proposal to understand the emergence of an ensemble of definite geometries during the process of black hole evaporation as a decoherence process, as well as its implications for the black hole information problem.</p

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

Ahlfors circle maps and total reality: from Riemann to Rohlin

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known intersection with real algebraic geometry, especially Klein's ortho-symmetric curves via the paradigm of {\it total reality}. This leads to a gallery of pictures quite pleasant to visit of which we have attempted to trace the simplest representatives. This drifted us toward some electrodynamic motions along real circuits of dividing curves perhaps reminiscent of Kepler's planetary motions along ellipses. The ultimate origin of circle maps is of course to be traced back to Riemann's Thesis 1851 as well as his 1857 Nachlass. Apart from an abrupt claim by Teichm\"uller 1941 that everything is to be found in Klein (what we failed to assess on printed evidence), the pivotal contribution belongs to Ahlfors 1950 supplying an existence-proof of circle maps, as well as an analysis of an allied function-theoretic extremal problem. Works by Yamada 1978--2001, Gouma 1998 and Coppens 2011 suggest sharper degree controls than available in Ahlfors' era. Accordingly, our partisan belief is that much remains to be clarified regarding the foundation and optimal control of Ahlfors circle maps. The game of sharp estimation may look narrow-minded "Absch\"atzungsmathematik" alike, yet the philosophical outcome is as usual to contemplate how conformal and algebraic geometry are fighting together for the soul of Riemann surfaces. A second part explores the connection with Hilbert's 16th as envisioned by Rohlin 1978.Comment: 675 pages, 199 figures; extended version of the former text (v.1) by including now Rohlin's theory (v.2