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Type of sequence of numbers
mathematics, a sequence a = (a0, a1, ..., an) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short
Logarithmically concave sequence
Logarithmically_concave_sequence
Type of mathematical function
convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies
Logarithmically concave function
Logarithmically_concave_function
Topics referred to by the same term
Log-concave may refer to: Logarithmically concave function Logarithmically concave measure Logarithmically concave sequence This disambiguation page lists
Log-concave
Real function with secant line between points above the graph itself
{\displaystyle \cup } (or a straight line like a linear function), while a concave function's graph is shaped like a cap ∩ {\displaystyle \cap } . A twice-differentiable
Convex_function
Count of the possible partitions of a set
Bell numbers form a logarithmically convex sequence. Dividing them by the factorials, Bn/n!, gives a logarithmically concave sequence. Several asymptotic
Bell_number
Number, approximately 1.618
sequence and the sequence of Lucas numbers can be used to generate approximate forms of the golden spiral (which is a special form of a logarithmic spiral)
Golden_ratio
Method of DNA analysis
method of scoring alignments of two or more sequences. When aligning sequences, introducing gaps in the sequences can allow an alignment algorithm to match
Gap_penalty
Economical computational problem
generate sequences of feasible joint decisions converging monotonically to a PNE. Concave games (where each player's payoff function is concave in their
Nash_equilibrium_computation
Mathematical operation
The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves
Second_derivative
Paradox involving a game with repeated coin flipping
finite. More importantly, the expected value of the game only grows logarithmically with the resources of the casino. As a result, the expected value of
St._Petersburg_paradox
Probability distribution
can be verified that ℓ ( α ) {\displaystyle \ell (\alpha )} is strictly concave, by using inequality properties of the polygamma function. Finding the
Gamma_distribution
Type of mathematical functions
condition is required, which is called logarithmically convex. A Reinhardt domain D is called logarithmically convex if the image λ ( D ∗ ) {\displaystyle
Function of several complex variables
Function_of_several_complex_variables
Mathematical function
polygamma functions. This function is strictly increasing and strictly concave on ( 0 , ∞ ) {\displaystyle (0,\infty )} , and it asymptotically behaves
Digamma_function
triangulorum (1620). concave function Is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex
Glossary_of_calculus
Number of subsets of a given size
a sequence of k distinct objects, retaining the order of selection, from a set of n objects. The denominator counts the number of distinct sequences that
Binomial_coefficient
Hungarian mathematician (1929-2016)
constrained stochastic optimization problems. He introduced the concept of logarithmic concave measures and provided several fundamental theorems on logconcavity
András_Prékopa
Theory that attempts to blend economics and ergodic theory
function is more risk-seeking than an expected wealth maximizer, and a concave utility function implies greater risk aversion. Comparing (2) to (1), we
Ergodicity_economics
Foundational principle in quantum physics
_{k}p_{k}L(\varrho _{k})\right]^{2},} where on the right-hand side there is a concave roof over the decompositions of the density matrix. The improved relation
Uncertainty_principle
Mathematical space with a notion of distance
found many applications. Given a metric space (X, d) and an increasing concave function f : [ 0 , ∞ ) → [ 0 , ∞ ) {\displaystyle f\colon [0,\infty )\to
Metric_space
Noncommutative geometric structure
the form Mf where f is an essentially bounded function, the sequence ⟨Sen, en⟩ logarithmically converges and ∫ S = lim n → ∞ ∑ k = 0 n 1 1 + k ⟨ S e k ,
Singular_trace
concave, and they aim to maximize their expected utility, rather than their expected gain. Bernoulli himself assumed that the utility is logarithmic,
Utility_assessment
Method of estimating the parameters of a statistical model, given observations
probability distributions – in particular the exponential family – are logarithmically concave. While the domain of the likelihood function—the parameter space—is
Maximum_likelihood_estimation
Hydrocarbon composed of multiple aromatic rings
organic-rich sediments. Aqueous solubility of PAHs decreases approximately logarithmically as molecular mass increases. Two-ringed PAHs, and to a lesser extent
Polycyclic aromatic hydrocarbon
Polycyclic_aromatic_hydrocarbon
Mathematical and computational problem
Anily, Bramel and Simchi-Levi study a setting where the cost of a bin is a concave function of the number of items in the bin. The objective is to minimize
Bin_packing_problem
Extinct genus of marine squamate reptiles
Plesiotylosaurus. The ventral margin of the dentary ranges from straight to slightly concave. A small dorsal ridge appears anterior to the first dentary tooth in mature
Tylosaurus
Logarithms are examples of concave functions. Logarithmic identities Several important formulas, sometimes called logarithmic identities or log laws, relate
Glossary_of_engineering:_A–L
Function related to statistics and probability theory
probability distributions—notably the exponential family—are only logarithmically concave, and concavity of the objective function plays a key role in the
Likelihood_function
U V W X Y Z See also References External links watch glass A circular, concave piece of glass commonly used in chemistry laboratories as a working surface
Glossary_of_chemistry_terms
Threshold of percolation theory models
For the monodisperse particle systems, the percolation thresholds of concave-shaped superdisks are obtained as seen in For binary dispersions of disks
Percolation_threshold
if it satisfies the following properties: 1. Barrier property: on any sequence of points in C that converges to a boundary point of C, f converges to
Self-concordant_function
LOGARITHMICALLY CONCAVE-SEQUENCE
LOGARITHMICALLY CONCAVE-SEQUENCE
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Sequence
Boy/Male
German, Shakespearean
Brave Adviser
Boy/Male
Indian, Sanskrit
Order; Sequence
Boy/Male
Shakespearean German
Much Ado About Nothing' Follower of Don John.
Boy/Male
Indian, Sikh
Music; In-sequence
Surname or Lastname
English
English : from a medieval male personal name (from Latin Hilarius, a derivative of hilaris ‘cheerful’, ‘glad’, from Greek hilaros ‘propitious’, ‘joyful’). The Latin name was chosen by many early Christians to express their joy and hope of salvation, and was borne by several saints, including a 4th-century bishop of Poitiers noted for his vigorous resistance to the Arian heresy, and a 5th-century bishop of Arles. Largely due to veneration of the first of these, the name became popular in France in the forms Hilari and Hilaire, and was brought to England by the Norman conquerors.English : from the much rarer female personal name Eulalie (from Latin Eulalia, from Greek eulalos ‘eloquent’, literally well-speaking, chosen by early Christians as a reference to the gift of tongues), likewise introduced into England by the Normans. A St. Eulalia was crucified at Barcelona in the reign of the Emperor Diocletian and became the patron of that city. In England the name underwent dissimilation of the sequence -l-l- to -l-r- and the unfamiliar initial vowel was also mutilated, so that eventually the name was considered as no more than a feminine form of Hilary (of which the initial aspirate was in any case variable).
Girl/Female
Tamil
Anuloma | அநà¯à®²à¯‹à®®à®¾
Sequence
LOGARITHMICALLY CONCAVE-SEQUENCE
LOGARITHMICALLY CONCAVE-SEQUENCE
Girl/Female
Hindu, Indian, Sikh
One who Feels Shy
Boy/Male
Tamil
Boy/Male
Dutch, Finnish, German
Ever Ruler
Girl/Female
Hindu
Smile
Biblical
guide or he directs,
Boy/Male
Hindu
Female
English
Anglicized form of Irish Gaelic SÃne, SHEENAGH means "God is gracious."
Boy/Male
Hindu, Indian, Marathi
Causing Happiness
Girl/Female
Biblical
Blotting or wiping out, smiting.
Girl/Female
Muslim/Islamic
The mixture of the smell of the petals of Rose and Sundal
LOGARITHMICALLY CONCAVE-SEQUENCE
LOGARITHMICALLY CONCAVE-SEQUENCE
LOGARITHMICALLY CONCAVE-SEQUENCE
LOGARITHMICALLY CONCAVE-SEQUENCE
LOGARITHMICALLY CONCAVE-SEQUENCE
a.
Arched; concave.
a.
Slightly concave.
a.
Convex on one side, and concave on the other. The curves of the convex and concave sides may be alike or may be different. See Meniscus.
a.
Having both ends concave; biconcave; -- said of vertebrae.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
v. t.
To make hollow or concave.
adv.
By the use of logarithms.
adv.
Logarithmically.
n.
The body of cardinals shut up in the conclave for the election of a pope; hence, the body of cardinals.
a.
Concave on both sides; as, biconcave vertebrae.
p. pr. & vb. n.
of Concave
v. t.
To yield or suffer; to surrender; to grant; as, to concede the point in question.
a.
Congenitally united; growing from one base, or united at their bases; united into one body; as, connate leaves or athers. See Illust. of Connate-perfoliate.
n.
Also used adjectively; as, the conacre system or principle.
a.
Alt. of Logarithmical
a.
Plane or flat on one side, and concave on the other; as, a plano-concave lens. See Lens.
a.
Hollow and curved or rounded; vaulted; -- said of the interior of a curved surface or line, as of the curve of the of the inner surface of an eggshell, in opposition to convex; as, a concave mirror; the concave arch of the sky.
a.
Concave or hollow on both sides; double concave.
imp. & p. p.
of Concave
a.
Concave.