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Concept# Large numbers

Summary

Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathematics, cosmology, cryptography, and statistical mechanics. They are typically large positive integers, or more generally, large positive real numbers, but may also be other numbers in other contexts.
Googology is the study of nomenclature and properties of large numbers.
In the everyday world
Scientific notationLogarithmic scaleOrders of magnitude and Names of large numbers
Scientific notation was created to handle the wide range of values that occur in scientific study. 1.0 × 109, for example, means one billion, or a 1 followed by nine zeros: 1 000 000 000. The reciprocal, 1.0 × 10−9, means one billionth, or 0.000 000 001. Writing 109 instead of nine zeros saves readers the effort and hazard of counting a long series of zeros to see how large the number is. In addition to sci

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Names of large numbers

Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but

Order of magnitude

An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representa

Google

Google LLC (ˈɡuːɡəl) is an American multinational technology company focusing on artificial intelligence, online advertising, search engine technology, cloud computing, computer software, quantum co

A high-energy (0.5-3.0 TeV centre of mass) electron-positron Compact Linear Collider (CLIC) is being studied at CERN as a new physics facility. The design study has been optimized for 3 TeV centre-of-mass energy. Intense bunches injected into the main linac must have unprecedentedly small emittances to achieve the design luminosity 1035cm-2s-1 required for the physics experiments. The positron and electron bunch trains will be provided by the CLIC injection complex. This thesis describes an optics design and performance of a positron damping ring developed for producing such ultra-low emittance beam. The linear optics of the CLIC damping ring is optimized by taking into account the combined action of radiation damping, quantum excitation and intrabeam scattering. The required beam emittance is obtained by using a TME (Theoretical Minimum Emittance) lattice with compact arcs and short period wiggler magnets located in dispersion-free regions. The damping ring beam energy is chosen as 2.42 GeV. The lattice features small values of the optical functions, a large number of compact TME cells, and a large number of wiggler magnets. Strong sextupole magnets are needed for the chromatic correction which introduces significant nonlinearities, decreasing the dynamic aperture. The nonlinear optimization of the lattice is described. An appropriate scheme of chromaticity correction is determined that gives reasonable dynamic aperture and zero chromaticity. The nonlinearities induced by the short period wiggler magnets and their influence on the beam dynamics are also studied. In addition, approaches for absorption of synchrotron radiation power produced by the wigglers are discussed. Realistic misalignments of magnets and monitors increase the equilibrium emittance. The sensitivity of the CLIC damping ring to various kinds of alignment errors is studied. Without any correction, fairly small vertical misalignments of the quadrupoles and, in particular, the sextupoles, introduce unacceptable distortions of the closed orbit as well as intolerable spurious vertical dispersion and coupling due to the strong focusing optics of the damping ring. A sophisticated beam-based correction scheme has been developed in order to bring the design target emittances and the dynamic aperture back to the ideal value. The correction using dipolar correctors and several skew quadrupole correctors allows a minimization of the closed-orbit distortion, the cross-talk between vertical and horizontal closed orbits, the residual vertical dispersion and the betatron tune coupling. The small emittance, short bunch length, and high current in the CLIC damping ring could give rise to collective effects which degrade the quality of the extracted beam. A number of possible instabilities and an estimate of their impact on the ring performance are briefly surveyed. The effects considered include fast beam-ion instability, coherent synchrotron radiation, Touschek scattering, intrabeam scattering, resistive-wall wake fields, and electron cloud.

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We present a novel method to trace the propagation of intrusions or malicious code in networked systems. Our solution is aimed at large numbers of loosely managed workstations typical of a research environment as found in CERN. The system tags events which have a potential to become harmful. On a given machine all processes that results from the tagged event are marked with the same tag and the tag is carried on to others machines if a tagged process establishes a connection. Tag creation logs are stored in a central database. When an intrusion is detected at a later time, all machines and processes that may have lost their integrity due to this incident can easily be found. This leads to a quick and effective restoration of the system. Our implementation of the system is designed to incur very little overhead on the machines and integrates easily with many flavors of the Linux operating system on any type of hardware.

2003,

Entry of the facultative intracellular pathogen Brucella into host cells results in the formation of endosomal Brucella-containing vacuoles (eBCVs) that initially traffic along the endocytic pathway. eBCV acidification triggers the expression of a type IV secretion system that translocates bacterial effector proteins into host cells. This interferes with lysosomal fusion of eBCVs and supports their maturation to replicative Brucella-containing vacuoles (rBCVs). Bacteria replicate in rBCVs to large numbers, eventually occupying most of the cytoplasmic volume. As rBCV membranes tightly wrap each individual bacterium, they are constantly being expanded and remodeled during exponential bacterial growth. rBCVs are known to carry endoplasmic reticulum (ER) markers; however, the relationship of the vacuole to the genuine ER has remained elusive. Here, we have reconstructed the 3-dimensional ultrastructure of rBCVs and associated ER by correlative structured illumination microscopy (SIM) and focused ion beam/scanning electron microscopic tomography (FIB/SEM). Studying B. abortus-infected HeLa cells and trophoblasts derived from B. melitensis-infected mice, we demonstrate that rBCVs are complex and interconnected compartments that are continuous with neighboring ER cisternae, thus supporting a model that rBCVs are extensions of genuine ER.

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