Concept# Analytic philosophy

Summary

Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United States, Canada, Australia, New Zealand, and Scandinavia, and continues today. Analytic philosophy is often contrasted with continental philosophy, coined as a catch-all term for other methods, prominent in Europe.
Central figures in this historical development of analytic philosophy are Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Other important figures in its history include the logical positivists (particularly Rudolf Carnap), W. V. O. Quine, and Karl Popper. After the decline of logical positivism, Saul Kripke, David Lewis, and others led a revival in metaphysics. Elizabeth Anscombe, Peter Geach, Anthony Kenny, and others developed an analytic approach to Thomism.
Analytic philosophy is characterized by an emphasis on

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Christina Fragouli, Robert Haas, Xiao-Yu Hu, Vinodh Venkatesan

Replication is a widely used method to protect large- scale data storage systems from data loss when storage nodes fail. It is well known that the placement of replicas of the different data blocks across the nodes affects the time to rebuild. Several systems described in the literature are designed based on the premise that minimizing the rebuild times maximizes the system reliability. Our results however indicate that the reliability is essentially unaffected by the replica placement scheme. We show that, for a replication factor of two, all possible placement schemes have mean times to data loss (MTTDLs) within a factor of two for practical values of the failure rate, storage capacity, and rebuild bandwidth of a storage node. The theoretical results are confirmed by means of event-driven simulation. For higher replication factors, an analytical derivation of MTTDL becomes intractable for a general placement scheme. We therefore use one of the alternate measures of reliability that have been proposed in the literature, namely, the probability of data loss during rebuild in the critical mode of the system. Whereas for a replication factor of two this measure can be directly translated into MTTDL, it is only speculative of the MTTDL behavior for higher replication factors. This measure of reliability is shown to lie within a factor of two for all possible placement schemes and any replication factor. We also show that for any replication factor, the clustered placement scheme has the lowest probability of data loss during rebuild in critical mode among all possible placement schemes, whereas the declustered placement scheme has the highest probability. Simulation results reveal however that these properties do not hold for the corresponding MTTDLs for a replication factor greater than two. This indicates that some alternate measures of reliability may not be appropriate for comparing the MTTDL of different placement schemes.

2010The aim of this thesis is to investigate the mechanisms behind dynamic fragmentation. This phenomenon occurs in a material when a blast or impact loading nucleates multiple cracks, whose propagation and coalescence break the specimen into fragments. Although since the beginning of the last century this topic has been well studied in many fields ranging from engineering to astrophysics, its complexity is still keeping researchers far from a complete understanding of it. Analytical approaches are challenging and sometimes unfeasible, while experiments are limited in scale and are hard to realize due to the extreme rapidity of the phenomenon. In this context, numerical methods constitute a useful tool to provide insights and complement the traditional models. Among the existing techniques, the finite-element method with dynamic insertion of cohesive elements represents an excellent compromise between performance and realistic modeling. The first topic of the thesis is the prediction of residual velocities of fragments. Even in tensile fragmentation, their relative velocity difference leads to impacts, redistributing the kinetic energy in the system. This event is studied in an elementary setup: a quasi-1D ceramic bar is subjected to a constant blast tensile loading until failure. With this simple model, it is possible to identify the link between the elastic waves and the different relative velocities of the fragments, that cause impacts. This aspect highlights the importance of including a realistic reproduction of contact in the numerical models. Another topic is the connection between the shape of a 3D ceramic specimen and its fragmentation patterns, in particular concerning the mass and shape distributions of the fragments. For this purpose extremely large meshes are needed and an optimization of the code is necessary. The best strategy is to extend the algorithms to work in parallel in order to take advantage of the most modern clusters available at EPFL. This accomplishment, together with the analysis and solution of a numerical instability that can affect the method, results in the realization of a powerful numerical tool for large 2D and 3D dynamic fragmentation problems. The last subject treated in this thesis is the influence of eigenstresses on the dynamic fragmentation of glass. The plates made of this material can be thermally treated in order to obtain compression residual stresses along the surfaces, that are balanced by tensile residual stresses in the interior. Therefore the flexural strength is increased but, whenever a crack reaches the tensile region, it becomes unstable and the plate quickly breaks into fragments. In the past, researchers tried to predict both analytically and experimentally the number of fragments as function of the residual stress magnitude and the plate thickness. However the available models are partially inaccurate and in contradiction with each other. Thanks to the parallel implementation of the dynamic insertion of cohesive elements, now also numerical simulations are a valid tool to explore the underlying physics. Their usage permits to easily monitor the evolution of potential, dissipated and kinetic energies over time, highlighting the flaws of the existing analytical approaches as well as providing more information than experiments. A new mathematical expression is proposed to accurately predict the number of fragments in function of the plate thickness for high values of residual stress.

We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by (a) direct sampling of the active work in numerical solutions of the AOUP equations and (b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods (a) and (b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation-dissipation theorem.

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