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Lattice
Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an ornamental pattern of crossing strips of pastry Companies * Lattice Engines, a technology company specializing in business applications for marketing and sales * Lattice Group, a former British gas transmission business * Lattice Semiconductor, a US-based integrated circuit manufacturer Science, technology, and mathematics Mathematics * Lattice (group), a repeating arrangement of points ** Lattice (discrete subgroup), a discrete subgroup of a topological group whose quotient carries an invariant finite Borel measure ** Lattice (module), a module over a ring which is embedded in a vector space over a field ** Lattice graph, a graph that can be drawn within a repeating arrangement of points ** Lattice-based cryptography, encryption systems based ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Semiconductor
Lattice Semiconductor Corporation is an American semiconductor company specializing in the design and manufacturing of low power, field-programmable gate arrays (FPGAs). Headquartered in the Silicon Forest area of Hillsboro, Oregon, the company also has operations in Shanghai, Manila, and Singapore. Lattice Semiconductor has more than 700 employees and an annual revenue of more than $400 million as of 2019. Founded in 1983, the company went public in 1989 and is traded on the NASDAQ stock exchange under the symbol LSCC. History Founding and early growth Lattice was founded on April 3, 1983, by C. Norman Winningstad, Rahul Sud, and Ray Capece, with investment from Winningstad, Harry Merlo, Tom Moyer, and John Piacentini. Lattice was incorporated in Oregon in 1983 and reincorporated in Delaware in 1985. Co-founder Sud left as president in December 1986, and Winningstad left in 1991 as chairman of the board. Early struggles led to chapter 11 bankruptcy reorganization in July 198 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These ''lattice-like'' structures all admi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (group)
In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point. Closure under addition and subtraction means that a lattice must be a subgroup of the additive group of the points in the space, and the requirements of minimum and maximum distance can be summarized by saying that a lattice is a Delone set. More abstractly, a lattice can be described as a free abelian group of dimension n which spans the vector space \mathbb^n. For any basis of \mathbb^n, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can be formed from a basis in this way. A lattice may be viewed as a regula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Tower
A lattice tower or truss tower is a freestanding vertical framework tower. This construction is widely used in transmission towers carrying high voltage electric power lines, in radio masts and towers (a self-radiating tower or as a support for aerials) and in observation towers. Its advantage is good shear strength at a much lower weight than a tower of solid construction would have as well as lower wind resistance. In structural engineering the term ''lattice tower'' is used for a freestanding structure, while a ''lattice mast'' is a guyed mast supported by guy lines. Lattices of triangular (3-sided) cross-section are most common, particularly in North America. Square (4-sided) lattices are also widely used and are most common in Eurasia. Lattice towers are often designed as either a space frame or a hyperboloid structure. Before 1940, they were used as radio transmission towers especially for short and medium wave. Occasionally lattice towers consisting of wood were utilized. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice-based Cryptography
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions are currently important candidates for post-quantum cryptography. Unlike more widely used and known public-key schemes such as the RSA, Diffie-Hellman or elliptic-curve cryptosystems—which could, theoretically, be defeated using Shor's algorithm on a quantum computer—some lattice-based constructions appear to be resistant to attack by both classical and quantum computers. Furthermore, many lattice-based constructions are considered to be secure under the assumption that certain well-studied computational lattice problems cannot be solved efficiently. History In 1996, Miklós Ajtai introduced the first lattice-based cryptographic construction whose security could be based on the hardness of well-studied lattice problems, and Cynthia Dwork showed that a certain average-cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Engines
Lattice Engines was a technology provider that delivered predictive marketing and sales cloud applications to business-to-business (B2B) companies. The company was privately held and backed by NEA and Sequoia Capital. It was headquartered in San Mateo, CA and has offices in Austin, Boston, New York and Beijing. History The company was founded by Shashi Upadhyay, Kent McCormick and Andrew Schwartz in 2006. As of 2013, Upadhyay served as the company’s CEO, McCormick served as the president and Schwartz served as the chief architect. In 2013, it expanded its suite of predictive applications to marketing with Lattice Predictive Lead Scoring. In 2019, Lattice Engines was acquired by Dun & Bradstreet. Software Lattice offers a suite of predictive, cloud applications for marketing and sales that are powered by the Lattice Data Cloud. The applications analyze data and deliver real-time reports with specific data to its users. Lattice offers a big data analytics platform which provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (discrete Subgroup)
In Lie theory and related areas of mathematics, a lattice in a locally compact group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of R''n'', this amounts to the usual geometric notion of a lattice as a periodic subset of points, and both the algebraic structure of lattices and the geometry of the space of all lattices are relatively well understood. The theory is particularly rich for lattices in semisimple Lie groups or more generally in semisimple algebraic groups over local fields. In particular there is a wealth of rigidity results in this setting, and a celebrated theorem of Grigory Margulis states that in most cases all lattices are obtained as arithmetic groups. Lattices are also well-studied in some other classes of groups, in particular groups associated to Kac–Moody algebras and automorphisms groups of regular trees (the latter are known as ''tree lattices''). Lattices are of inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latticework
__NOTOC__ Latticework is an openwork framework consisting of a criss-crossed pattern of strips of building material, typically wood or metal. The design is created by crossing the strips to form a grid or weave. Latticework may be functional – for example, to allow airflow to or through an area; structural, as a truss in a lattice girder; used to add privacy, as through a lattice screen; purely decorative; or some combination of these. Latticework in stone or wood from the classical period is also called Roman lattice or ''transenna'' (plural ''transenne''). In India, the house of a rich or noble person may be built with a ''baramdah'' or verandah surrounding every level leading to the living area. The upper floors often have balconies overlooking the street that are shielded by latticed screens carved in stone called jalis which keep the area cool and give privacy. Examples File:Amber Fort Screen (6652771501).jpg, Lattice screen at Amber Fort File:Masuleh Window.jpg, La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Model (finance)
In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise, though methods now exist for solving this problem. Equity and commodity derivatives In general the approach is to divid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bravais Lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_3 \mathbf_3, where the ''ni'' are any integers, and a''i'' are ''primitive translation vectors'', or ''primitive vectors'', which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique. A fundamental aspect of any Bravais lattice is that, for any choice of direction, the lattice appears exactly the same from each of the discrete lattice points when looking in that chosen direction. The Bravais lattice concept is used to formally define a ''crystalline arrangement'' and its (finite) frontiers. A crystal is made up of one or more atoms, called the ''basis'' or ''motif'', at each lattice point. The ''basis'' may consist of atoms, mol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Group
Lattice Group plc was a leading British gas transmission business. It was listed on the London Stock Exchange and was a constituent of the FTSE 100 Index. History The Company was established in 2000 when BG Group demerged its UK gas transmission business, formerly known as ''Transco'', and named it ''Lattice Group''.Grid and Lattice form utility supergroup The Telegraph, 22 April 2002 In October 2002 Lattice Group merged with to form ''National Grid Transco''. In July 2005 National Grid Transco was renamed National Grid plc to provide 'a unifying identity across its operations'. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Model (physics)
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model. The exact solution to many of these models (when they are solvable) includes the presence of solitons. Techniques for solving these include the inverse scattering transform and the method of Lax pairs, the Yang–Baxter equation and quantum groups. The solution of these models has given i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
