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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
Method of DNA analysis
of scoring alignments of two or more DNA sequences. When aligning sequences, introducing gaps in the sequences can allow an alignment algorithm to match
Gap_penalty
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
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
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
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
Logarithms are examples of concave functions. Logarithmic identities Several important formulas, sometimes called logarithmic identities or log laws, relate
Glossary_of_engineering:_A–L
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
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
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
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
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
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
Type of non-Euclidean geometry
subject the name hyperbolic geometry to include it in the now rarely used sequence elliptic geometry (spherical geometry), parabolic geometry (Euclidean geometry)
Hyperbolic_geometry
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
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
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
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
scattering, when a charged particle transfers part of its energy to a photon. concave lens condensation point condensed matter physics A branch of physics that
Glossary_of_physics
Extinct genus of marine squamate reptiles
Plesiotylosaurus. The tooth-bearing margin ranges from straight to slightly concave. A small dorsal ridge appears anterior to the first dentary tooth in T
Tylosaurus
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
concave, and they aim to maximize their expected utility, rather than their expected gain. Bernoulli himself assumed that the utility is logarithmic,
Utility_assessment
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
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
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