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Property of having a unique mode or maximum value
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of
Unimodality
Value that appears most often in a set of data
continuous distribution is called multimodal (as opposed to unimodal). In symmetric unimodal distributions, such as the normal distribution, the mean (if
Mode_(statistics)
Probability distribution with more than one mode
(perfect unimodality). It is defined as A = U ( 1 − S − 1 K − 1 ) {\displaystyle A=U\left(1-{\frac {S-1}{K-1}}\right)} where U is the unimodality of the
Multimodal_distribution
Numbers parameterizing ways to partition a set
{\displaystyle n} , { n k } {\displaystyle \left\{{n \atop k}\right\}} is unimodal, that is, the sequence increases and then decreases. The maximum is attained
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Unimodal thresholding is an algorithm for automatic image threshold selection in image processing. Most threshold selection algorithms assume that the
Unimodal_thresholding
Middle quantile of a data set or probability distribution
well-defined mean, such as the Cauchy distribution: The median of a symmetric unimodal distribution coincides with the mode. The median of a symmetric distribution
Median
Intelligence in machines
Hussain, Amir (September 2017). "A review of affective computing: From unimodal analysis to multimodal fusion". Information Fusion. 37: 98–125. Bibcode:2017InfFu
Artificial_intelligence
Mathematical function with convex lower level sets
to a point and increases from that point on is quasiconvex (compare unimodality). The floor function x ↦ ⌊ x ⌋ {\displaystyle x\mapsto \lfloor x\rfloor
Quasiconvex_function
Place where passengers and cargo are exchanged
of these. For private transport by car, the parking lot functions as an unimodal hub. Historically, an interchange service in the scheduled passenger air
Transport_hub
Mathematical theorem first conjectured by Ronald Read
Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph
Read's_conjecture
Graphical representation of the distribution of numerical data
"symmetric", "skewed left" or "right", "unimodal", "bimodal" or "multimodal".[citation needed] Symmetric, unimodal Skewed right Skewed left Bimodal Multimodal
Histogram
Algorithm for finding the extrema of a unimodal function
technique in computer science for finding the minimum or maximum of a unimodal function. Assume we are looking for a maximum of f ( x ) {\displaystyle
Ternary_search
Perception that only seems real
hallucinations are the perception of erogenous or orgasmic stimuli. They may be unimodal or multimodal in nature and frequently involve sensation in the genital
Hallucination
Number taken as representative of a list of numbers
mean is infinite (+∞ or −∞), while for others the mean is undefined. For unimodal distributions the following bounds are known and are sharp: | θ − μ | σ
Average
Rule in statistics
desired[citation needed]. Chebyshev's inequality removes the assumption of unimodality at the price of a higher multiplier (about 4.5 for 95% confidence)[citation
Rule_of_three_(statistics)
Probabilistic inequality
Chebyshev's inequality, concerns distance from the mean without requiring unimodality Concentration inequality – a summary of tail-bounds on random variables
Gauss's_inequality
Statistical quantity
Gastwirth estimated the asymptotic variance of n−1/2D. If the distribution is unimodal and symmetric about 0, the asymptotic variance lies between 1/4 and 1.
Nonparametric_skew
Description of continuous random distribution
Geometric visualisation of the mode, median and mean of an arbitrary unimodal probability density function.
Probability_density_function
Personal rapid transit system concept
by the inventor Douglas Malewicki in 1990 and was under development by Unimodal Inc. A prototype of the skyTran vehicle and a section of track have been
SkyTran
American mathematician (born 1983)
during his PhD studies, Huh proved the Read–Hoggar conjecture, about the unimodality of coefficients of chromatic polynomials in graph theory, which had been
June_Huh
sampled data, a derivation of the above to test for non-uniformity (as unimodal clustering) of a set of points on a circle (e.g. compass directions), sometimes
Rayleigh_test
bound nearly all (i.e. 95%) of the values of a process output. Without unimodality Chebyshev's inequality would give a looser bound of 1/9 = 0.11111...
Vysochanskij–Petunin inequality
Vysochanskij–Petunin_inequality
samples points randomly, using a uniform distribution on the box. For a unimodal function, the probability of reducing the objective function decreases
Luus–Jaakola
Psychedelic drug
psychedelic drugs LSD and psilocybin reduce the hierarchical differentiation of unimodal and transmodal cortex". NeuroImage. 256 119220. bioRxiv 10.1101/2020.05
LSD
doubling is infinite. This dimension is the same for any differentiable and unimodal function. log 3 2 {\displaystyle \log _{3}2} 0.6309 Cantor set Built
List of fractals by Hausdorff dimension
List_of_fractals_by_Hausdorff_dimension
Measure of the asymmetry of random variables
The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly
Skewness
Part of the cerebral cortex
into unimodal and heteromodal (or polymodal) areas, which process either a single sensory modality or multiple modalities, respectively. Unimodal association
Association_cortex
Fourth standardized moment in statistics
one moves outward from the origin (has fat tails). Several well-known, unimodal, and symmetric distributions from different parametric families are compared
Kurtosis
Geographical measurement
crust. On other planets within this solar system, elevations are typically unimodal, owing to the lack of plate tectonics on those bodies.[citation needed]
Hypsometry
Mathematical measure invariant under linear isometries
measures in addition to the measure being isotropic. A unimodal measure (or isotropic unimodal measure) is any isotropic measure μ ( d z ) = μ 0 ( | z
Isotropic_measure
Probability distribution
\operatorname {Gamma} (\alpha ,\beta )} ). The full width at half maximum of a unimodal probability distribution is the difference between the two values of the
Gamma_distribution
On when a function on convex body K does not decrease if K is translated inwards
and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative function f over an n-dimensional convex body K does not decrease
Anderson's_theorem
Metrics related to human characteristics
fingerprints. While unimodal biometric systems are limited by the integrity of their identifier, it is unlikely that several unimodal systems will suffer
Biometrics
Physiological capacity
another is perceived. Multimodal perception is qualitatively different from unimodal perception. There has been a growing body of evidence since the mid-1990s
Sense
Range of genetic disorders which cause a person to appear to grow older faster
older individuals. They affect only one tissue and can be classified as unimodal progeroid syndromes. Segmental progeria, which is more frequently associated
Progeroid_syndromes
Technique for finding an extremum of a function
or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum
Golden-section_search
Canadian computer scientist (1944–2019)
problem, polygon triangulation, the largest empty circle problem, unimodality (unimodal function), and others. Other interests included meander (art), compass
Godfried_Toussaint
Bound on probability of a random variable being far from its mean
from the mode of a unimodal distribution, to deviation from the mean, or more generally, any center. If X {\displaystyle X} is a unimodal distribution with
Chebyshev's_inequality
German polymath and scholar (1777–1855)
first paper he proved Gauss's inequality (a Chebyshev-type inequality) for unimodal distributions, and stated without proof another inequality for moments
Carl_Friedrich_Gauss
Shorthand used in statistics
cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within three-sigma is at least
68–95–99.7_rule
Type of probability distribution
x_{0}} about which the symmetry occurs. If a symmetric distribution is unimodal, the mode coincides with the median and mean. All odd central moments of
Symmetric probability distribution
Symmetric_probability_distribution
Romantic attraction to individuals of particular age ranges
Sexual behavior, Seto defined chronophilias as lying in a continuous, unimodal distribution of age preferences, ranging from nepiophilia to gerontophilia
Chronophilia
Probability distribution
same time the mode, the median and the mean of the distribution. It is unimodal: its first derivative is positive for x < μ , {\textstyle x<\mu ,} negative
Normal_distribution
List of Greek and Latin roots in English starting with the letter M
supermodel, trimodal, trimodality, ultramodern, ultramodernity, unimodal, unimodality, unimodular, unimodularity mol- grind Latin mola, molere, molitus
List of Greek and Latin roots in English/M
List_of_Greek_and_Latin_roots_in_English/M
Hill of loose sand built by aeolian processes or the flow of water
These dunes form under winds that blow consistently from one direction (unimodal winds). They form separate crescents when the sand supply is comparatively
Dune
Technique for proving sets have equal size
degrees" – by Gilles Schaeffer. "Kathy O'Hara's Constructive Proof of the Unimodality of the Gaussian Polynomials" – by Doron Zeilberger. "Partition Bijections
Bijective_proof
Israeli mathematician
Zeilberger, Doron (1989). "Kathy O'Hara's constructive proof of the unimodality of the Gaussian polynomials". Amer. Math. Monthly. 96 (7): 590–602. doi:10
Doron_Zeilberger
supermodel, trimodal, trimodality, ultramodern, ultramodernity, unimodal, unimodality, unimodular, unimodularity mol- grind Latin mola, molere, molitus
List of Greek and Latin roots in English/H–O
List_of_Greek_and_Latin_roots_in_English/H–O
decreasing, and this trend seems to be accelerating. Income distribution is now unimodal, with most people living in middle-income countries. In the 2000s, a study
World_economy
Order-preserving mathematical function
\left(X\leq x\right)} is a monotonically increasing function. A function is unimodal if it is monotonically increasing up to some point (the mode) and then
Monotonic_function
Any algorithm which solves the search problem
Kiefer devised Fibonacci search which can be used to find the maximum of a unimodal function and has many other applications in computer science. There are
Search_algorithm
American mathematician
Abelian Groups. She subsequently published some of this research as "A unimodality result in the enumeration of subgroups of a finite abelian group" (Proc
Lynne_Butler
Type of Solar System object
"Reopening the TNOs Color Controversy: Centaurs Bimodality and TNOs Unimodality". Astronomy and Astrophysics. 410 (3): L29–L32. arXiv:astro-ph/0309428
Centaur (small Solar System body)
Centaur_(small_Solar_System_body)
Solar system objects beyond Neptune
"Reopening the TNOs Color Controversy: Centaurs Bimodality and TNOs Unimodality". Astronomy and Astrophysics. 410 (3): L29–L32. arXiv:astro-ph/0309428
Trans-Neptunian_object
"Thyroid Volume in Hypothyroidism due to Autoimmune Disease Follows a Unimodal Distribution: Evidence against Primary Thyroid Atrophy and Autoimmune Thyroiditis
List_of_autoimmune_diseases
Natural number
"Sequence A001523 (Number of stacks, or planar partitions of n; also weakly unimodal compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
1000_(number)
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
Logarithmically concave sequence
Logarithmically_concave_sequence
Type of numerical analysis
L_{2}} fit with its least squares criterion. Another generalisation is to unimodal regressions, i.e. to fits with a non-decreasing segment followed by a non-increasing
Isotonic_regression
Australian-American statistician (born 1937)
ISSN 0162-1459. Hartigan, J. A.; Hartigan, P. M. (1985). "The Dip Test of Unimodality". The Annals of Statistics. 13 (1). doi:10.1214/aos/1176346577. ISSN 0090-5364
John_A._Hartigan
Integrative theory of therapy
CD004492.pub4. PMID 21069681. Noël, Yvonnick (June 1999). "Recovering unimodal latent patterns of change by unfolding analysis: application to smoking
Transtheoretical_model
Speech comprehension region in the dominant hemisphere of the hominid brain
borders. Some researchers associate Wernicke's area primarily with the unimodal auditory association cortex located just anterior to primary auditory cortex
Wernicke's_area
Generating polynomial of the number of ways to place non-attacking rooks on a chessboard
number of non-attacking placements of k rooks in B: these numbers are unimodal, i.e., they increase to a maximum and then decrease. This follows (by a
Rook_polynomial
New technologies actively in development
systems Deployed at various airports and federal security checkpoints Unimodal facial recognition scanners Nanoelectromechanical systems Research and
List_of_emerging_technologies
Brazilian mathematician
Strien). He proved the global hyperbolicity of renormalization for Cr unimodal maps (co-authored with Alberto Pinto and Edson de Faria). He was a recipient
Welington_de_Melo
ordination technique that determines axes from the response data as a unimodal combination of measured predictors. CCA is commonly used in ecology in
Canonical correspondence analysis
Canonical_correspondence_analysis
have properties such as infinite divisibility, power law tails, and unimodality. The most well-known discrete stable distribution is the special case
Discrete-stable_distribution
Species of rodent
relative humidity have negative effects. The daily activity of maras is unimodal in winter and bimodal in other seasons. Their preferred temperature is
Patagonian_mara
Intermodal freight transport system
ASTM D 5728 Standard Practice for Securement of Cargo in Intermodal and Unimodal Surface Transport "Container Dimensions and Capacity". Export 911. Archived
Containerization
Romanian-American mathematician
in Mathematics. Simion's thesis research concerned the concavity and unimodality of certain combinatorially defined sequences, and included what Richard
Rodica_Simion
Statistical model for a binary dependent variable
Both the logistic and normal distributions are symmetric with a basic unimodal, "bell curve" shape. The only difference is that the logistic distribution
Logistic_regression
Quality measure of a statistical method
simple distribution, such as the normal distribution (which is symmetric, unimodal, and has thin tails) may not be robust to contamination by outliers, and
Efficiency_(statistics)
Standardized reusable metal crate for transporting goods
D5728-00 Standard Practices for Securement of Cargo in Intermodal and Unimodal Surface Transport ISO 668:2013 Series 1 freight containers – Classification
Intermodal_container
Family of statistical methods based on sampling of available data
coefficients. It is not consistent for the sample median. In the case of a unimodal variate the ratio of the jackknife variance to the sample variance tends
Resampling_(statistics)
Type of data
differences in processing (e.g., text vs. image). A system is designated unimodal if it has only one modality implemented, and multimodal if it has more
Modality (human–computer interaction)
Modality_(human–computer_interaction)
Mathematical function having a characteristic "bell"-shaped curve
asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at small x. Hence, the integral of a bell-shaped function is typically
Bell-shaped_function
Continuous probability distribution
exponent equals 1. The exponentiated Weibull distribution accommodates unimodal, bathtub shaped and monotone failure rates. The Weibull distribution is
Weibull_distribution
Foundational principle in quantum physics
than one period. Other examples include highly bimodal distributions, or unimodal distributions with divergent variance. A solution that overcomes these
Uncertainty_principle
Centaur
"Reopening the TNOs color controversy: Centaurs bimodality and TNOs unimodality". Astronomy and Astrophysics. 410 (3): L29–L32. arXiv:astro-ph/0309428
(342842)_2008_YB3
Sound to color synesthesia
between unimodal auditory and visual regions in the brain, or they may reflect feedback pathways from multimodal audiovisual regions to unimodal visual
Chromesthesia
Venus has a topography reflecting its single, strong crustal plate, with a unimodal elevation distribution (over 90% of the surface lies within an elevation
Surface_features_of_Venus
Approximation for factorials
Now the function t ↦ 1 + t − e t {\displaystyle t\mapsto 1+t-e^{t}} is unimodal, with maximum value zero. Locally around zero, it looks like − t 2 2 {\textstyle
Stirling's_approximation
Dynamical system
spatial chaos phenomena and are popular in neural models. Weak coupling unimodal maps are characterized by their stable periodic points and are used by
Coupled_map_lattice
Wrapped probability distribution
Directional Data. Academic Press.[page needed] J. Copas (1975). "On the unimodality of the likelihood function for the Cauchy distribution". Biometrika.
Wrapped_Cauchy_distribution
Simple polynomial map exhibiting chaotic behavior
the interval [0, 1] to [0, 1] and satisfy the following property, called unimodal . f ( 0 ) = f ( 1 ) = 0 {\displaystyle f(0)=f(1)=0} . The map is differentiable
Logistic_map
Securing of cargo for transportation
ASTM D5728 Standard Practices for Securement of Cargo in Intermodal and Unimodal Surface Transport EN 12195-1:2010 en - Load restraining on road vehicles
Load_securing
Uniformly most powerful test Unimodal distribution – redirects to Unimodal function (has some stats context) Unimodality Unit (statistics) Unit of observation
List_of_statistics_articles
Function used as a performance test problem for optimization algorithms
While Ackley gives the function as an example of "fine-textured broadly unimodal space" his thesis does not actually use the function as a test. On an d
Ackley_function
Type of probability distribution
unlike other commonly used circular distributions, it is not symmetric nor unimodal. Circular mean Circular uniform distribution von Mises distribution Dodge
Circular_distribution
Rate of generation of biomass in an ecosystem
believe that the relationship between species diversity and productivity is unimodal within an ecosystem. A 1999 study on grassland ecosystems in Europe, for
Productivity_(ecology)
Science of extracting information from chemical systems by data-driven means
application of additional constraints is common, such as non-negativity, unimodality, or known interrelationships between the individual components (e.g.
Chemometrics
Dysfunction in one's ability to comprehend and respond to multiple sensory stimuli
in the Pacinian corpuscles receptor pathways, and other alterations in unimodal and multisensory processing have been detected in autism populations. People
Sensory_processing_disorder
Probabilistic optimization technique and metaheuristic
algorithm (RRA) is a meta-heuristic optimization algorithm for solving unimodal and multimodal problems inspired by the runners and roots of plants in
Simulated_annealing
Developmental or acquired neurological disorders
understanding of the relative contributions of perceptual and non-sensory, unimodal and supramodal factors to performance on psychoacoustic tests may well
Auditory_processing_disorder
technique for finding the extremum (minimum or maximum) of a continuous unimodal function by successively fitting parabolas (polynomials of degree two)
Successive parabolic interpolation
Successive_parabolic_interpolation
Tool to assess control of a manufacturing process
The finer result of the Vysochanskii–Petunin inequality, that for any unimodal probability distribution, the probability of an outcome greater than k
Control_chart
Natural number
sphenic number, a strobogrammatic number, and a nontotient. There are 986 unimodal compositions of 14 where the maximal part appears once. 987 = 3 × 7 × 47
900_(number)
Type of mathematical function
ISBN 0-471-99545-2. MR 0489333. Dharmadhikari, Sudhakar; Joag-Dev, Kumar (1988). Unimodality, convexity, and applications. Probability and Mathematical Statistics
Logarithmically concave function
Logarithmically_concave_function
Algorithm for pseudo-random number sampling
decreasing probability distribution. It can also be applied to symmetric unimodal distributions, such as the normal distribution, by choosing a value from
Ziggurat_algorithm
Period with less precipitation than normal
the Nile basin (Ethiopia, Sudan), the rainfall is characterized by an unimodal cycle with a wet season from July to September. The rest of the region
Drought
Biological process that adjusts the strength of connections between neurons in the brain
(whisker somatosensory map), for example, synapses initially exhibit a unimodal timing rule, essentially all correlated activity results in potentiation
Spike-timing-dependent plasticity
Spike-timing-dependent_plasticity
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