Glosarium Matematika

273 p.; 24 cm

Irreducibility and additivity of set agreement-oriented failure detector classes

Solving agreement problems (such as consensus and $k$-set agreement) in asynchronous distributed systems prone to process failures has been shown to be impossible. To circumvent this impossibility, distributed oracles (also called unreliable failure detectors) have been introduced. A failure detector provides information on failures, and a failure detector class is defined by a set of abstract properties that encapsulate (and hide) synchrony assumptions. Some failure detector classes have been shown to be the weakest to solve some agreement problems (e.g., $\Omega$ is the weakest class of failure detectors that allow solving the;consensus problem in asynchronous systems where a majority of processes do not crash). This paper considers several failure detector classes and focuses on their additivity or their irreducibility. It mainly investigates two families of failure detector classes (denoted $\Diamond {\cal S}_x$ and $\Diamond \phi^y$, $0\leq x,y \leq n$), shows that they can be ``added'' to provide a failure detector of the class $\Omega^z$ (a generalization of $\Omega$). It also characterizes the power of such an ``addition'', namely, $\Diamond {\cal S}_x +\Diamond \phi^y \leadsto \Omega^z \Leftrightarrow x+y+z>t+1$, where $t$ is the maximum number of processes that can crash in a run. As an example, the paper shows that, while $\Diamond {\cal S}_{t}$ allows solving 2-set agreement (and not consensus) and $\Diamond \phi^{1}$ allows solving $t$-set agreement (but not $(t-1)$-set agreement), their ``addition'' allows solving consensus. More generally, the paper studies the failure detector classes $\Diamond {\cal S}_x$, $\Diamond \phi^y$ and $\Omega^z$, and shows whic reductions among these classes are possible and which are not. The paper presents also an $\Omega^k$-based $k$-set set agreement protocol. In that sense, it can be seen as a step toward the characterization of the weakest failure detector class that allows solving the $k$-set agreement problem. \\ Ce rapport étudie la composition de classes de détecteurs de fautes. Il montre aussi que certaines classes ne peuvent être composées pour donner des détecteurs d'une puissance supérieure

Symmetries in Quantum Mechanics

Symmetry and quantum mechanics are two of the most fundamental probes we have of nature. This collection of eleven papers discusses new quantum phenomena in atoms, galaxies, and people (quantum cognition), which is a testimonial to the breadth of the influence of symmetry and quantum mechanics. The book represents an international effort of researchers from educational and research institutions in nine countries, including India, Finland, France, Mexico, Norway, Russia, Spain, Turkey, and the United States. The papers can be divided into four broad categories: Fundamentals of quantum systems, including a new derivation of the uncertainty principle from optimal stochastic control theory, a new model of energy transfer between atoms with no wave function collapse, a new asymmetric optical micro-device with the remarkable property of showing a current with no applied voltage, and a model of quantum cognition to predict the effect of irrelevant information on decision making. 2. Algebraic methods in quantum mechanics, describing an elegant derivation of hydrogen atom Stark effect matrix elements, and a new group theoretical method for the computation of radiative shifts. Teleportation and scattering, including a method to improve the information transfer in teleportation, and the use of permutation symmetry to compute scattering cross sections. Cosmology, including scalar-tensor theory applied to inflation, the characterization of new Levi-Cevita space-times, and a comprehensive analysis of gravitational dispersion forces

PSA 2016

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2016