Symbol

Summary

A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication (and data processing) is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas, or visual s and are used to convey other ideas and beliefs. For example, a red octagon is a common symbol for "STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerals are symbols for numbers; letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The academic study of symbols is semiotics. In cartography, an organized collection of symbols forms a legend for a map. Etymology The word symbol derives from the late Middle French masculine noun symbole, which appear

Official source

https://en.wikipedia.org/wiki/Symbol

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We discuss a set of topics that are important for the understanding of modern data science but that are typically not taught in an introductory ML course. In particular we discuss fundamental ideas and techniques that come from probability, information theory as well as signal processing.

We introduce formal verification as an approach for developing highly reliable systems. Formal verification finds proofs that computer systems work under all relevant scenarios. We will learn how to use formal verification tools and explain the theory and the practice behind them.

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Method of detecting anomalous behaviour in a computer network

Pedro Bados, Boi Faltings

Method of detecting anomalous behaviour in a computer network comprising the steps of - monitoring network traffic flowing in a computer network system, - authenticating users to which network packets of the network traffic are associated, - extracting parameters associated to the network packets for each user, said parameters including at least the type (T) of network services, - forming symbols based on a combination of one or more of said parameters, and - modelling and analysing individual user behaviour based on sequences of occurrence of said symbols (S).

2005

Bin Packing via Discrepancy of Permutations

Friedrich Eisenbrand, Doemoetoer Palvoelgyi, Thomas Rothvoss

A well-studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxation for this problem into an integral solution that requires at most O(log n) additional bins. The three-permutations-problem of Beck is the following. Given any three permutations on n symbols, color the symbols red and blue, such that in any interval of any of those permutations, the number of red and blue symbols is roughly the same. The necessary difference is called the discrepancy. We establish a surprising connection between bin packing and Beck's problem: The additive integrality gap of the 3-partition linear programming relaxation can be bounded by the discrepancy of three permutations. This connection yields an alternative method to establish an O(log n) bound on the additive integrality gap of the 3-partition. Conversely, making use of a recent example of three permutations, for which a discrepancy of Omega(log n) is necessary, we prove the following: The O(log(2) n) upper bound on the additive gap for bin packing with arbitrary item sizes cannot be improved by any technique that is based on rounding up items. This lower bound holds for a large class of algorithms including the Karmarkar-Karp procedure.

Association for Computing Machinery2013

Bin Packing via Discrepancy of Permutations

Friedrich Eisenbrand, Doemoetoer Palvoelgyi, Thomas Rothvoss

A well studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxation for this problem into an integral solution that requires at most O(log n) additional bins. The three-permutations-conjecture of Beck is the following. Given any 3 permutations on n symbols, one can color the symbols red and blue, such that in any interval of any of those permutations, the number of red and blue symbols differs only by a constant. Beck's conjecture is well known in the field of discrepancy theory. We establish a surprising connection between bin packing and Beck's conjecture: If the latter holds true, then the additive integrality gap of the 3-partition linear programming relaxation is bounded by a constant.

Siam, 3600 Univ City Science Center, Philadelphia, Pa 19104-2688 Usa2011