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Semiring arising in tropical analysis
In mathematics, in the field of tropical analysis, the log-semiring is the semiring structure on the logarithmic scale, obtained by considering the extended
Log_semiring
Semiring with minimum and addition replacing addition and multiplication
In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing
Tropical_semiring
Mathematical function, inverse of an exponential function
and form a semiring, called the probability semiring; this is in fact a semifield. The logarithm then takes multiplication to addition (log multiplication)
Logarithm
Algebraic ring that need not have additive negative elements
semiring called the trivial semiring. This triviality can be characterized via 0 = 1 {\displaystyle 0=1} and so when speaking of nontrivial semirings
Semiring
Smooth approximation to the maximum function
family. In tropical analysis, this is the sum in the log semiring. Logarithmic mean Log semiring Smooth maximum Softmax function Zhang, Aston; Lipton
LogSumExp
Measurement scale based on orders of magnitude
Napier Level (logarithmic quantity) Log–log plot Logarithm Logarithmic mean Log semiring Preferred number Semi-log plot Order of magnitude Entropy Entropy
Logarithmic_scale
relates log semiring to the min-plus semiring. lim T → 0 − T log ( e − s T + e − t T ) = m i n { s , t } {\displaystyle \lim _{T\rightarrow 0}-T\log(e^{-{\frac
List of logarithmic identities
List_of_logarithmic_identities
Semiring defined over probabilities
The Viterbi semiring is a commutative semiring defined over the set of probabilities (typically the interval [ 0 , 1 ] {\displaystyle [0,1]} ) with addition
Viterbi_semiring
Algebraic structure
extended by an absorbing 0, forming the probability semiring, which is isomorphic to the log semiring. Rational functions of the form f /g, where f and
Semifield
Skeletonized version of algebraic geometry
semiring. This is defined in two ways, depending on max or min convention. The min tropical semiring T {\displaystyle \mathbb {T} } is the semiring T
Tropical_geometry
Smooth approximation of one-hot arg max
arg min, corresponding to using the log semiring instead of the max-plus semiring (respectively min-plus semiring), and recovering the arg max or arg
Softmax_function
Finite state machine with two tapes (input, output)
the set of weights to form a semiring. Two typical semirings used in practice are the log semiring and tropical semiring: nondeterministic automata may
Finite-state_transducer
Real numbers with + and - infinity added
Extended complex plane Extended natural numbers Improper integral Infinity Log semiring Series (mathematics) Projectively extended real line Computer representations
Extended_real_number_line
Difference of two numbers divided by the logarithm of their quotient
case of the Stolarsky mean. Logarithmic mean temperature difference Log semiring Citations B. C. Carlson (1966). "Some inequalities for hypergeometric
Logarithmic_mean
Subset of real numbers that are greater than zero
{\displaystyle \mathbb {R} _{\geq 0}} has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice
Positive_real_numbers
functions Log canonical singularity Log-likelihood ratio Log-log graph Log-normal distribution Log-periodic antenna Log semiring Log structure Log-Weibull
Index_of_logarithm_articles
Generalization of means
\exp(x)\ ,} then the f mean is the mean in the log semiring, which is a constant-shifted version of the LogSumExp (LSE) function (which is the logarithmic
Quasi-arithmetic_mean
Probabilistic logic programming language
instead. aProbLog generalizes ProbLog by allowing any commutative semiring instead of just probabilities. ProbFOIL: given a set of ProbLog facts as a probabilistic
ProbLog
Recursive algorithm for matrix multiplication
large matrices, with a better asymptotic complexity ( O ( n log 2 7 ) {\displaystyle O(n^{\log _{2}7})} versus O ( n 3 ) {\displaystyle O(n^{3})} ), although
Strassen_algorithm
Computational problem of graph theory
approach to these is to consider the two operations to be those of a semiring. Semiring multiplication is done along the path, and the addition is between
Shortest_path_problem
Infinite sum that is considered independently from any notion of convergence
Magnus ring over R. Given an alphabet Σ {\displaystyle \Sigma } and a semiring S {\displaystyle S} . The formal power series over S {\displaystyle S}
Formal_power_series
Mathematical operation in linear algebra
requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications
Matrix_multiplication
Design pattern in functional programming to build generic types
near-semiring, and some additive monads do qualify as such. However, not all additive monads meet the distributive laws of even a near-semiring. In Haskell
Monad (functional programming)
Monad_(functional_programming)
Function in algebra
addition form a semiring, called the min tropical semiring, and a valuation v is almost a semiring homomorphism from K to the tropical semiring, except that
Valuation_(algebra)
Algorithm in graph theory
a regular expression, with the difference being the use of a min-plus semiring. The modern formulation of the algorithm as three nested for-loops was
Floyd–Warshall_algorithm
Algebraic structure with a binary operation
magma (M, •) to (N, ∗). proof: log x y = log x + log y 2 . {\displaystyle \log {\sqrt {xy}}\ =\ {\frac {\log x+\log y}{2}}.} Note that these commutative
Magma_(algebra)
Mathematical model of computation
problem to graphs with edges weighted by the elements of an (arbitrary) semiring.[jargon] An example of an accepting state appears in Fig. 5: a deterministic
Finite-state_machine
Formal language that can be expressed using a regular expression
generalization, this time in the context of a formal power series over a semiring. This approach gives rise to weighted rational expressions and weighted
Regular_language
Algebraic expansion of powers of a binomial
is valid more generally for two elements x and y in a ring, or even a semiring, provided that xy = yx. For example, it holds for two n × n matrices, provided
Binomial_theorem
Study of numbers that are not solutions of polynomials with rational coefficients
lower bound for the quantity | β 1 log α 1 + β 2 log α 2 | {\displaystyle |\beta _{1}\log \alpha _{1}+\beta _{2}\log \alpha _{2}|\,} where all four unknowns
Transcendental_number_theory
Abstract machine model in computer science
automaton A is unambiguous, then the set of weight does not need to be a semiring, instead it suffices to consider a monoid. Indeed, there is at most one
Unambiguous_finite_automaton
Infinite sequence of numbers satisfying a linear equation
over the unary alphabet Σ = { a } {\displaystyle \Sigma =\{a\}} over the semiring ( R , + , × ) {\displaystyle (\mathbb {R} ,+,\times )} (which is in fact
Constant-recursive_sequence
Branch of number theory
R r 1 + r 2 L ( x ) = ( log | x | v ) v {\displaystyle {\begin{cases}L:K^{\times }\to \mathbf {R} ^{r_{1}+r_{2}}\\L(x)=(\log |x|_{v})_{v}\end{cases}}}
Algebraic_number_theory
protracta (Butler, 1874) Pseudacraea poggei (Dewitz, 1879) Pseudacraea semire (Cramer, 1779) Pseudacraea warburgi Aurivillius, 1892 Neptis agouale agouale
List of butterflies of the Democratic Republic of the Congo
List_of_butterflies_of_the_Democratic_Republic_of_the_Congo
LOG SEMIRING
LOG SEMIRING
Male
English
English unisex short form of French Louis and Louise, both LOU means "famous warrior."Â
Boy/Male
French, German, Polish
Long
Boy/Male
Hindu
Lord Buddha
Boy/Male
Biblical
Roof, covering.
Surname or Lastname
English and French
English and French : nickname for a tall person, from Old English lang, long, Old French long ‘long’, ‘tall’ (equivalent to Latin longus).Irish (Ulster (Armagh) and Munster) : reduced Anglicized form of Gaelic Ó Longáin (see Langan).Chinese : from the name of an official treasurer called Long, who lived during the reign of the model emperor Shun (2257–2205 bc). his descendants adopted this name as their surname. Additionally, a branch of the Liu clan (see Lau 1), descendants of Liu Lei, who supposedly had the ability to handle dragons, was granted the name Yu-Long (meaning roughly ‘resistor of dragons’) by the Xia emperor Kong Jia (1879–1849 bc). Some descendants later simplified Yu-Long to Long and adopted it as their surname.Chinese : there are two sources for this name. One was a place in the state of Lu in Shandong province during the Spring and Autumn period (722–481 bc). The other source is the Xiongnu nationality, a non-Han Chinese people.Chinese : variant of Lang.Cambodian : unexplained.
Surname or Lastname
English and Scottish
English and Scottish : topographic name for someone who lived near a tumulus, mound or hill, Middle English lowe, from Old English hlÄw (see Law 2).Scottish and English : nickname for a short man, from Middle English lah, lowe (Old Norse lágr; the word was adopted first into the northern dialects of Middle English, where Scandinavian influence was strong, and then spread south, with regular alteration of the vowel quality).English and Scottish (of Norman origin) : nickname for a violent or dangerous person, from Anglo-Norman French lou, leu ‘wolf’ (Latin lupus). Wolves were relatively common in Britain at the time when most surnames were formed, as there still existed large tracts of uncleared forest.Scottish : from a pet form of Lawrence. Compare Lowry 1.Americanized spelling of Jewish Lowe.
Male
English
Anglicized form of Hebrew Gowg, GOG means "mountain." In the bible, this is the name of a son of Shemaiah and the name of the prophetic prince of the land of Magog. In British legend, God and Magog are the names of two giant guardians of London. Geoffrey of Monmouth states that Gogmagog was one giant who was slain by the Cornish hero Corin.
Boy/Male
Arthurian Legend Biblical Hebrew
Name of a king.
Male
French
French form of Latin Eligius, ÉLOI means "to choose."
Male
French
 French form of Latin Eligius, ÉLOY means "to choose."
Biblical
the multitude of Gog
Male
Greek
(Λώτ) Greek form of Hebrew Lowt, LOT means "covering, veil." In the bible, this is the name of a nephew of Abraham and father of Moab.
Girl/Female
Spanish
Diminutive of Dolores: Sorrow. From Maria de los Dolores (the Virgin Mary, or Mary of the...
Boy/Male
Welsh
light'.
Girl/Female
Teutonic American Latin
Famous in war.
Boy/Male
French American
Famous warrior, from the Old German 'Chlodovech'. Eighteen kings of France have borne this name,...
Male
English
 English short form of Spanish Alonso, LON means "noble and ready." Compare with another form of Lon.
Female
Spanish
Spanish form of Greek Lois, possibly LOÃDA means "agreeable."
Boy/Male
Hindu
Universe
Girl/Female
Biblical
The multitude of Gog.
LOG SEMIRING
LOG SEMIRING
Boy/Male
Hindu
Boy/Male
Tamil
Bharddwaj | பாரà¯à®¤à¯à®¤à¯à®µà®¾à®œ
A Lucky bird, A sage
Girl/Female
Muslim
Companion of prophet Muhammad
Boy/Male
Tamil
Intelligence
Girl/Female
Danish, German, Polish, Swedish
Conqueror; Victorious; Victory
Boy/Male
Tamil
Belonging to a good clan, Good birth
Boy/Male
Hindu
Opinion
Girl/Female
Tamil
Inexhaustible, Limitless
Girl/Female
Hindu, Indian
Beads Ornament of an Ear
Female
Croatian
, from the forest.
LOG SEMIRING
LOG SEMIRING
LOG SEMIRING
LOG SEMIRING
LOG SEMIRING
n.
Hence: The record of the rate of ship's speed or of her daily progress; also, the full nautical record of a ship's cruise or voyage; a log slate; a log book.
v. t.
To enter in a ship's log book; as, to log the miles run.
superl.
Moderate; not intense; not inflammatory; as, low heat; a low temperature; a low fever.
n.
That which resembles a leg in form or use; especially, any long and slender support on which any object rests; as, the leg of a table; the leg of a pair of compasses or dividers.
adv.
With a low voice or sound; not loudly; gently; as, to speak low.
adv.
At a point of duration far distant, either prior or posterior; as, not long before; not long after; long before the foundation of Rome; long after the Conquest.
v. t.
To pasture cattle on the fog, or aftergrass, of; to eat off the fog from.
n.
A part of the log. See Log-chip, and 2d Log, n., 2.
a.
Last; long-delayed; -- obsolete, except in the phrase lag end.
superl.
Drawn out or extended in time; continued through a considerable tine, or to a great length; as, a long series of events; a long debate; a long drama; a long history; a long book.
superl.
Depressed in the scale of sounds; grave; as, a low pitch; a low note.
v. i.
To engage in the business of cutting or transporting logs for timber; to get out logs.
n.
A thin, flat piece of board in the form of a quadrant of a circle attached to the log line; -- called also log-ship. See 2d Log, n., 2.
n.
A fellow; -- used humorously or contemptuously; as, a sly dog; a lazy dog.
superl.
Not loud; as, a low voice; a low sound.
superl.
Deficient in vital energy; feeble; weak; as, a low pulse; made low by sickness.
superl.
Wanting strength or animation; depressed; dejected; as, low spirits; low in spirits.
superl.
Mean; vulgar; base; dishonorable; as, a person of low mind; a low trick or stratagem.
superl.
Not rising to the usual height; as, a man of low stature; a low fence.
v. t.
To cause to jog; to drive at a jog, as a horse. See Jog, v. i.