Search references for LOGARITHMICALLY CONCAVE-FUNCTION. Phrases containing LOGARITHMICALLY CONCAVE-FUNCTION
See searches and references containing LOGARITHMICALLY CONCAVE-FUNCTION!LOGARITHMICALLY CONCAVE-FUNCTION
Type of mathematical function
In 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
Logarithmically concave function
Logarithmically_concave_function
Negative of a convex function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to
Concave_function
Real function with secant line between points above the graph itself
like a linear function), while a concave function's graph is shaped like a cap ∩ {\displaystyle \cap } . A twice-differentiable function of a single variable
Convex_function
Function whose composition with the logarithm is convex
0}} is logarithmically convex and non-decreasing, then g ∘ f {\displaystyle g\circ f} is logarithmically convex. A logarithmically convex function f is
Logarithmically convex function
Logarithmically_convex_function
Mathematical function with convex lower level sets
that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in the sense of several complex
Quasiconvex_function
measure, a generalisation of this concept Logarithmically concave function Prékopa, A. (1980). "Logarithmic concave measures and related topics". Stochastic
Logarithmically concave measure
Logarithmically_concave_measure
Type of sequence of numbers
Bibcode:1989NYASA.576..500S. doi:10.1111/j.1749-6632.1989.tb16434.x. Unimodality Logarithmically concave function Logarithmically concave measure v t e
Logarithmically concave sequence
Logarithmically_concave_sequence
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
Mathematical function
chemistry to form basis sets. Gaussian functions arise by composing the exponential function with a concave quadratic function: f ( x ) = exp ( α x 2 + β x
Gaussian_function
Mathematical function
(z)}}.} It is the first of the polygamma functions. This function is strictly increasing and strictly concave on ( 0 , ∞ ) {\displaystyle (0,\infty )}
Digamma_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
x\rightarrow \pm \infty } . A sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point:
Sigmoid_function
Mathematical operation
function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the opposite
Second_derivative
2D graphic with logarithmic scales on both axes
two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k
Log–log_plot
Function related to statistics and probability theory
distributions—notably the exponential family—are only logarithmically concave, and concavity of the objective function plays a key role in the maximization. Given
Likelihood_function
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
Probability distribution
function of the shape parameters α and β. § Moments of logarithmically transformed random variables contains formulas for moments of logarithmically transformed
Beta_distribution
Meromorphic function
the digamma function, ψ ( x ) = ψ ( 0 ) ( x ) {\displaystyle \psi (x)=\psi ^{(0)}(x)} , is strictly monotonic increasing and strictly concave. For m {\displaystyle
Polygamma_function
Probability distribution
the AM–GM inequality and is a consequence of the logarithm being a concave function. In fact, E [ X ] = e μ + 1 2 σ 2 = e μ ⋅ e σ 2 = GM [ X ] ⋅ GVar
Log-normal_distribution
Concept in economics and decision theory
(indirect) utility function for money is a nonlinear function that is bounded and asymmetric about the origin. The utility function is concave in the positive
Utility
Smallest convex set containing a given set
convex hull or lower convex envelope of a function f {\displaystyle f} on a real vector space is the function whose epigraph is the lower convex hull of
Convex_hull
Number of subsets of a given size
previous generating function after the substitution x → x y {\displaystyle x\to xy} . A symmetric exponential bivariate generating function of the binomial
Binomial_coefficient
Functional square root of an exponential
mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f {\displaystyle f} such that f {\displaystyle
Half-exponential_function
Integral inequality
with log-concave distribution. Since the product of two log-concave functions is log-concave, the joint distribution of (X,Y) is also log-concave. Log-concavity
Prékopa–Leindler_inequality
Paradox involving a game with repeated coin flipping
utility function is lower than the power coefficient of the probability weighting function. Intuitively, the utility function must not simply be concave, but
St._Petersburg_paradox
epigraph has an SCB. Let g(t) be a 3-times continuously differentiable concave function on t>0, such that t ⋅ | g ‴ ( t ) | / | g ″ ( t ) | {\displaystyle
Self-concordant_function
Count of the possible partitions of a set
The Bell numbers form a logarithmically convex sequence. Dividing them by the factorials, Bn/n!, gives a logarithmically concave sequence. Several asymptotic
Bell_number
Economical computational problem
ΣP2-complete. However, when the utility function for each player depends only on the actions of a logarithmically small number of other players (that is
Nash_equilibrium_computation
Graph showing survival against age
table. There are three generalized types of survivorship curves: Type I or concave curves are characterized by high age-specific survival probability in early
Survivorship_curve
Mathematical concept
of the entire Pareto front, convex or concave. Definition For a minimization problem with objective functions f 1 , … , f k {\displaystyle f_{1},\dots
Multi-objective_optimization
Logarithm of probabilities, useful for calculations
family—are only logarithmically concave, and concavity of the objective function plays a key role in the maximization of a function such as probability
Log_probability
Probability distribution
{\displaystyle \ell (\alpha )} is strictly concave, by using inequality properties of the polygamma function. Finding the maximum with respect to α by
Gamma_distribution
GL function performs a similar extension to the Leontief production function. A drawback of the GL function is its inability to be globally concave without
Generalized Ozaki cost function
Generalized_Ozaki_cost_function
Thus, a measure being 0-convex is the same thing as it being a logarithmically concave measure. The classes of s-convex measures form a nested increasing
Convex_measure
Quantum
first inequality is saturated, which means that the variance is its own concave roof ( Δ H ) 2 = sup { p k , | Ψ k ⟩ } ∑ k p k ( Δ H ) Ψ k 2 . {\displaystyle
Quantum_Fisher_information
Method of DNA analysis
represented as dashes(-) on a protein/DNA sequence alignment. Unix diff function - computes the minimal difference between two files similarly to plagiarism
Gap_penalty
Exponentially decreasing bounds on tail distributions of random variables
The moment generating function is log-convex, so by a property of the convex conjugate, the Chernoff bound must be log-concave. The Chernoff bound attains
Chernoff_bound
Is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper
Glossary_of_calculus
Method of estimating the parameters of a statistical model, given observations
particular the exponential family – are logarithmically concave. While the domain of the likelihood function—the parameter space—is generally a finite-dimensional
Maximum_likelihood_estimation
Bernoulli and Gabriel Cramer, is that most people have a utility function that is strictly concave, and they aim to maximize their expected utility, rather than
Utility_assessment
Neoclassical economic model
t)=Lu(c)=L_{0}e^{nt}u(c)} The utility function is assumed to be strictly increasing (i.e., there is no bliss point) and concave in c {\displaystyle c} , with
Ramsey–Cass–Koopmans_model
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 [0
Metric_space
Geometric relation between the roots of a polynomial and those of its derivative
For a fourth degree complex polynomial P (quartic function) with four distinct zeros forming a concave quadrilateral, one of the zeros of P lies within
Gauss–Lucas_theorem
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
Theory that attempts to blend economics and ergodic theory
specified by a convex utility function is more risk-seeking than an expected wealth maximizer, and a concave utility function implies greater risk aversion
Ergodicity_economics
Swiss polymath (1728–1777)
angles and the area of hyperbolic triangles. These are triangles drawn on a concave surface, as on a saddle, instead of the usual flat Euclidean surface. Lambert
Johann_Heinrich_Lambert
Chemical kinetics model
Tolman Theorem. The E a ( T ) {\displaystyle E_{a}(T)} function when written as the logarithmic derivative of the rate constants with respect to β = 1
Aquilanti–Mundim deformed Arrhenius model
Aquilanti–Mundim_deformed_Arrhenius_model
Pressure exerted by a vapor in thermodynamic equilibrium
adapted to the fact that vapor pressure is usually increasing and concave as a function of temperature. The basic form of the equation is: log P = A −
Vapor_pressure
Scottish mathematician and astronomer
aberration seen in refracting telescopes. In his design he also placed a concave secondary mirror with an elliptical surface past the focal point of the
James_Gregory_(mathematician)
Number, approximately 1.618
interior angle of 144 ∘ {\displaystyle 144^{\circ }\!} , and darts, concave quadrilaterals with two interior angles of 36 ∘ {\displaystyle 36^{\circ
Golden_ratio
Mathematical and computational problem
more general cost and load functions: Anily, Bramel and Simchi-Levi study a setting where the cost of a bin is a concave function of the number of items in
Bin_packing_problem
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
Statistical test for dose-response trends
linear relationship, which may fail to detect trends that are concave, convex, or step functions. Tukey's trend test provides a robust alternative by using
Tukey's_trend_test
Diagnostic plot of binary classifier ability
However, when adding the recollection component, the zROC curve will be concave up, with a decreased slope. This difference in shape and slope result from
Receiver operating characteristic
Receiver_operating_characteristic
Economical computational problem
utility functions. Concavity: the most general assumption (made by Fisher and Arrow&Debreu) is that the agents' utilities are concave functions, i.e.,
Market equilibrium computation
Market_equilibrium_computation
Regular skew polyhedron Abstract polytope 11-cell 57-cell Convex polygon Concave polygon Constructible polygon Cyclic polygon Equiangular polygon Equilateral
List_of_mathematical_shapes
Extinct genus of cartilaginous fish
Sarcoprion and Ornithoprion. The scales have a cap-shaped base with a concave lower surface. The crowns are conical and covered with serrated, longitudinal
Helicoprion
Property of electrical conductors
1/\left|\mathbf {x} -\mathbf {x} '\right|\ } becomes infinite, leading to a logarithmically divergent integral. This necessitates taking the finite wire radius
Inductance
English polymath (1642–1727)
presented a burning mirror to the Royal Society. It consisted of seven concave glass mirrors, each about one foot in diameter. It is estimated that it
Isaac_Newton
Study of the deformation of solids that touch each other
often a contact between a convex surface (male cylinder or sphere) and a concave surface (female cylinder or sphere: bore or hemispherical cup). Some contact
Contact_mechanics
Mathematical theory for analyzing stock market structure and portfolio behavior
(and it is a non-negative quantity if the generating function G {\displaystyle \mathbb {G} } is concave); and the quantities τ i j μ ( t ) := ∑ ν = 1 n (
Stochastic_portfolio_theory
Movement of solid particles, typically by gravity and fluid entrainment
hillslope. For this reason, the tops of hills generally have a parabolic concave-up profile, which grades into a convex-up profile around valleys. As hillslopes
Sediment_transport
Mathematician (1912–1999)
István Vincze (1992). "Convexity properties of power series with logarithmically S-concave coefficients". Analysis Mathematica. 18 (1): 3–13. doi:10.1007/BF02056656
István_Vincze_(mathematician)
Logarithms are examples of concave functions. Logarithmic identities Several important formulas, sometimes called logarithmic identities or log laws, relate
Glossary_of_engineering:_A–L
All Latin and Greek roots beginning with G
hypocaust cav- hollow Latin cavus cave, cavity, excavation, cavern, cavernous, concave ced-, cess- move, yield, go, surrender Latin cedere, cessus accede, cede
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
Gauge field loop operator
This potential must necessarily be a monotonically increasing and concave function of the quark separation. Since spacelike Wilson loops are not fundamentally
Wilson_loop
Type of antenna
Similar to the Cassegrain design except that the secondary reflector is concave (ellipsoidal) in shape. Aperture efficiency over 70% can be achieved. The
Parabolic_antenna
well that penetrates an aquifer. The amount of draw down diminishes logarithmically with distance from the site of the well, a fact which determines the
Glossary of geography terms (A–M)
Glossary_of_geography_terms_(A–M)
Physics phenomenon
S2CID 118952931. Huang, Yichen (29 July 2010). "Entanglement criteria via concave-function uncertainty relations". Physical Review A. 82 (1) 012335. Bibcode:2010PhRvA
Quantum_entanglement
Noncommutative geometric structure
operators of 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
Singular_trace
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
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
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
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
developed in the 17th century. People have been projecting images using concave mirrors and pin-hole cameras (camera obscura) since Roman times. But glass
List of Dutch inventions and innovations
List_of_Dutch_inventions_and_innovations
LOGARITHMICALLY CONCAVE-FUNCTION
LOGARITHMICALLY CONCAVE-FUNCTION
Boy/Male
Shakespearean German
Much Ado About Nothing' Follower of Don John.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
Boy/Male
German, Shakespearean
Brave Adviser
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a great functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Biblical
Look for pages within Wikipedia that link to this title
If a page was recently created here it may not be visible yet because of a delay in updating the database; wait a few minutes or try the function.
Look for pages within Wikipedia that link to this title
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
LOGARITHMICALLY CONCAVE-FUNCTION
LOGARITHMICALLY CONCAVE-FUNCTION
Female
Hindi/Indian
(करिशà¥à¤®à¤¾) Hindi name KARISHMA means "miracle."
Boy/Male
Hindu
Girl/Female
American, Australian, British, English
White Wave; God is Gracious; Variant of Jenny which is a Diminutive of Jane and Jennifer
Girl/Female
Tamil
Aadhyasri | அதà¯à®¯à®¾à®¸à®°à¯€
First power, The beginning
Surname or Lastname
English
English : variant spelling of Ruston.
Boy/Male
Afghan, American, Arabic, Bangladeshi, Celebrity, Chinese, German, Indian, Malaysian, Muslim, Pashtun, Sindhi
Defender; Supporter; Success; Protector; Granting Victory; Helper
Male
Scottish
Scottish Gaelic name MAOILIOS means "servant of Jesus."Â
Girl/Female
Australian, British, English, French, Irish, Jamaican, Latin
Place Name in France Famous for the Production of Its Cheese; From Brie Region of France; Marshland
Boy/Male
Buddhist, Indian
Great Truth; Boundless Reality
Boy/Male
Tamil
LOGARITHMICALLY CONCAVE-FUNCTION
LOGARITHMICALLY CONCAVE-FUNCTION
LOGARITHMICALLY CONCAVE-FUNCTION
LOGARITHMICALLY CONCAVE-FUNCTION
LOGARITHMICALLY CONCAVE-FUNCTION
n.
The body of cardinals shut up in the conclave for the election of a pope; hence, the body of cardinals.
a.
Concave.
adv.
By the use of logarithms.
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.
Having both ends concave; biconcave; -- said of vertebrae.
n.
Also used adjectively; as, the conacre system or principle.
a.
Slightly concave.
a.
Concave or hollow on both sides; double concave.
p. pr. & vb. n.
of Concave
adv.
Logarithmically.
imp. & p. p.
of Concave
a.
Alt. of Logarithmical
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.
v. t.
To yield or suffer; to surrender; to grant; as, to concede the point in question.
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.
Plane or flat on one side, and concave on the other; as, a plano-concave lens. See Lens.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
v. t.
To make hollow or concave.
a.
Arched; concave.
a.
Concave on both sides; as, biconcave vertebrae.