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In the development of vertebrate animals, the functional matrix hypothesis is a phenomenological description of bone growth. It proposes that "the origin
Functional_matrix_hypothesis
American dentist (1923–2006)
June 26, 2006) was an American dentist known for creating the functional matrix hypothesis for growth and development. He was an anatomist and former dean
Melvin_Moss
Conjecture on zeros of the zeta function
Riemann hypothesis (J. E. Littlewood, 1912; see for instance: paragraph 14.25 in Titchmarsh (1986)). The determinant of the order n Redheffer matrix is equal
Riemann_hypothesis
Scientific theories
can act as growth centers, while condylar cartilage can't. The functional matrix hypothesis was popularized by Melvin Moss in 1962. This theory said that
Theories of craniofacial growth
Theories_of_craniofacial_growth
Law stating that bone adapts to mechanical loading
effects of torticollis on craniofacial development in children. Functional matrix hypothesis Iron Shirt, Wushu/Kungfu bone conditioning Osteogenic loading
Wolff's_law
Position that there is no relationship between two phenomena
The null hypothesis (often denoted H 0 {\textstyle H_{0}} ) is the claim in scientific research that the effect being studied does not exist. The null
Null_hypothesis
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
gives a spectral mapping theorem for the polynomial functional calculus: Let A be an n × n matrix with eigenvalues λ1, ..., λn, then for any polynomial
Jordan_normal_form
Method of statistical inference
statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A
Statistical_hypothesis_test
Matrix-valued random variable
associated with a random variable covariance matrix. This matrix calculated in this way becomes the null hypothesis that allows one to find the eigenvalues
Random_matrix
Mathematical conjecture on the Riemann zeta function
In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf about the rate of growth of the Riemann zeta function
Lindelöf_hypothesis
Statistical test
hypotheses that can be represented by a single matrix R. If one wishes to test a non-linear hypothesis of the form: H 0 : c ( θ ) = 0 {\displaystyle H_{0}:c(\theta
Wald_test
Phylum of aquatic animals
needed] In contrast to the model based on functional morphology described earlier, in the Epitheliozoa hypothesis, the ventral and dorsal cell layers of
Placozoa
Concepts from linear algebra
correlation matrix determine the Q-methodologist's judgment of practical significance (which differs from the statistical significance of hypothesis testing;
Eigenvalues_and_eigenvectors
Concept in inferential statistics
statistical hypothesis testing, a result has statistical significance when a result at least as extreme would be very infrequent if the null hypothesis were
Statistical_significance
Extinct genus of dinosaur
hypothesis. Their large body sizes and accommodated intraosseous fat reserves may have been supported by a combination of a dense trabecular matrix and
Huallasaurus
On generating functions from counting points on algebraic varieties over finite fields
prime integers, which obeys a functional equation and (conjecturally) has its zeros restricted by the Riemann hypothesis. The rationality was proved by
Weil_conjectures
Changing between languages during a conversation
morphosyntactic frame of the Matrix Language. The hypotheses are as follows (Myers-Scotton 1993b: 7): The Matrix Language Hypothesis states that those grammatical
Code-switching
Spreading of a disease inside a body
functional status, and cognitive effects. Although metastasis is widely accepted to be the result of the tumor cells migration, there is a hypothesis
Metastasis
Ecological concept
N_{e}=N+{\begin{matrix}{\frac {1}{2}}\end{matrix}}} or more generally, N e = N + D 2 {\displaystyle N_{e}=N+{\begin{matrix}{\frac {D}{2}}\end{matrix}}} where
Effective_population_size
1995 book by Iain Spence
The Sekhmet Hypothesis was first published in book form in 1995 by Iain Spence. It suggested that pop trends of an atavistic nature could be analysed in
The_Sekhmet_Hypothesis
Scientific theory in vertebrate development
The axial twist theory (a.k.a. axial twist hypothesis) is a proposed scientific theory to explain a range of unusual aspects of the body plan of vertebrates
Axial_twist_theory
Mathematical conjecture about the Riemann zeta function
Riemann Hypothesis Volume 2: Analytic Equivalents, Cambridge University Press, p. 192, ISBN 978-1-107-19712-1 Dieudonné, J. (1981), History of Functional Analysis
Hilbert–Pólya_conjecture
Statistical method for handling multiple comparisons
(FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures
False_discovery_rate
Israeli mathematician
Dirichlet L-Functions, Hyper-elliptic Curves and Random Matrix Theory". Geometric and Functional Analysis. 23 (4): 1230–1261. doi:10.1007/s00039-013-0241-8
Zeev_Rudnick
Statistic measuring inter-rater agreement for categorical items
tendency of the raters to give differing ratings. Let O be the C × C confusion matrix, that is, let Oi,j denote the number of items that the first rater placed
Cohen's_kappa
Probability distribution and special case of gamma distribution
distribution is extensively used in hypothesis testing is its relationship to the normal distribution. Many hypothesis tests use a test statistic, such as
Chi-squared_distribution
Function of the observed sample results
In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed,
P-value
Evolutionary theory
explain this occurrence: The essential tRNA hypothesis notes that there have been no documented functional plastid-to-nucleus gene transfers of genes encoding
Symbiogenesis
Computer science metric for string similarity
than 0-based strings. If m is a matrix, m [ i , j ] {\displaystyle m[i,j]} is the ith row and the jth column of the matrix, with the first row having index
Levenshtein_distance
Nucleus in the basal ganglia of the brain
identified two distinct striatal compartments, the matrix, and the striosome (or patch). The matrix is seen to be rich in acetylcholinesterase, while the
Striatum
Procedure for comparing multivariate sample means
n,} where Σ {\textstyle \Sigma } is the covariance matrix. Then we formulate our null hypothesis as H 0 : μ ( 1 ) = μ ( 2 ) = ⋯ = μ ( m ) . {\displaystyle
Multivariate analysis of variance
Multivariate_analysis_of_variance
Multiple ways for multi-joint objects to realize a movement
broad areas: "Western" neurophysiological studies, and "Bernsteinian" functional analysis of movement. The latter has become predominant in motor control
Degrees_of_freedom_problem
Largest absolute value of an operator's eigenvalues
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of
Spectral_radius
Human genetic cluster on chromosome 6
defects in extracellular matrix organization and cell adhesion processes mediated by tenascin-X protein. An "RCCX theory", a hypothesis developed by Sharon
RCCX
Process in bioinformatics that identifies equivalent sites within molecular sequences
the possible functional conservation of specific regions in a sequence. (In the case of nucleotide sequences, the molecular clock hypothesis in its most
Sequence_alignment
mitochondrial protein precursor-processing proteinase, matrix peptidase, matrix processing peptidase, matrix processing proteinase, or MPP). This enzyme catalyses
Mitochondrial processing peptidase
Mitochondrial_processing_peptidase
Statistical linear model
Y, B, and U were column vectors, the matrix equation above would represent multiple linear regression. Hypothesis tests with the general linear model can
General_linear_model
Branch of logic
Y)}{\begin{matrix}FX\\FY\end{matrix}}}\\{\phantom {spacer}}\\&4)\quad {\frac {T(X\supset Y)}{FX|TY}}\quad &&{\frac {F(X\supset Y)}{\begin{matrix
Propositional_logic
niche. The social navigation hypothesis emphasizes that an individual can become tightly ensnared in an overly restrictive matrix of social exchange contracts
Evolutionary approaches to depression
Evolutionary_approaches_to_depression
Domain of life whose cells have nuclei
Multicellularity in some eukaryotes led to cell differentiation and functional specialization, which led to the formation of various organs and tissues
Eukaryote
Statistical property
variance-covariance matrix). However, regarding the general hypothesis testing, as pointed out by Greene, "simply computing a robust covariance matrix for an otherwise
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Growth of fibrous or connective tissue
cells are the functional units of an organ. In contrast, the stromal cells provide the structure of the organ and secrete extracellular matrix as supportive
Desmoplasia
separation of isotopes of uranium necessary to create the atomic bomb. Prout's hypothesis was an early 19th-century attempt to explain the properties of the chemical
History_of_mass_spectrometry
algebra) Sinkhorn's theorem (matrix theory) Specht's theorem (matrix theory) Spectral theorem (linear algebra, functional analysis) Sylvester's determinant
List_of_theorems
Test of normality in frequentist statistics
Sanford Shapiro and Martin Wilk. The Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population
Shapiro–Wilk_test
Australian and American mathematician (born 1975)
Bruijn–Newman constant, the nonpositivity of which is equivalent to the Riemann hypothesis, is nonnegative. In 2020, Tao proved Sendov's conjecture, concerning the
Terence_Tao
Model of cell membranes
mosaic model explains various characteristics regarding the structure of functional cell membranes. According to this biological model, there is a lipid bilayer
Fluid_mosaic_model
Concept in quantum mechanics
show that the quantum hypothesis is invalid for macroscopic systems, and if macroscopic systems do not follow the quantum hypothesis, then as the macroscopic
Adiabatic_theorem
Theory of subatomic structure
the theory is known. In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical
String_theory
Family of distributions that generalize the multivariate normal distribution
the identity-matrix is called a spherical distribution. For spherical distributions, classical results on parameter-estimation and hypothesis-testing hold
Elliptical_distribution
Linguistics concept
account for complementizer-less environments: the CP Hypothesis and the IP Hypothesis. The CP Hypothesis states that finite subordinate clauses that lack
Empty_category
Infinite cardinal number
the aleph number hierarchy, but it follows from ZFC that the continuum hypothesis (CH) is equivalent to the identity 2 ℵ 0 = ℵ 1 {\displaystyle 2^{\aleph
Aleph_number
Relationship between elements of two sets
{\displaystyle X=Y} ) form a matrix semiring (indeed, a matrix semialgebra over the Boolean semiring) where the identity matrix corresponds to the identity
Binary_relation
partially non-nested (also called overlapping). The statistic tests the null hypothesis that the two models are equally close to the true data generating process
Vuong's_closeness_test
Statistical test based on the gradient of the likelihood function
the score—evaluated at the hypothesized parameter value under the null hypothesis. Intuitively, if the restricted estimator is near the maximum of the likelihood
Score_test
Concepts from statistical hypothesis testing
null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the incorrect acceptance of a false null hypothesis. An analysis
Type_I_and_type_II_errors
Resilient and smooth elastic tissue present in animals
but it is much stiffer and much less flexible than muscle or tendon. The matrix of cartilage is made up of glycosaminoglycans, proteoglycans, collagen fibers
Cartilage
Curved, pointed appendage at the end of a digit of a mammal, bird, or reptile
parallel to the direction of growth. The claw grows outward from the nail matrix at the base of the unguis and the subunguis grows thicker while travelling
Claw
Study of collection and analysis of data
model. A hypothesis is proposed for the statistical relationship between the two data sets, an alternative to an idealized null hypothesis of no relationship
Statistics
(on a complex Hilbert space) continuous linear operator
In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H
Normal_operator
Set of related ordination techniques used in information visualization
regarded as the founder of functional data analysis. MDS algorithms fall into a taxonomy, depending on the meaning of the input matrix: It is also known as
Multidimensional_scaling
Technique for shaping training datasets
diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D −
Manifold_regularization
Statistical hypothesis test
column means and S is an m × m sample covariance matrix. For a two-sample multivariate test, the hypothesis is that the mean vectors (μ1, μ2) of two samples
Student's_t-test
Statistical hypothesis test
A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large
Chi-squared_test
Hypothesis in neuroscience
principle that things may or may not conform to, and a process theory or hypothesis about how that principle is realized. Under this distinction, the free
Free_energy_principle
Statistical interpretation with many tests
level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each
Multiple_comparisons_problem
Measure of linear correlation
of −+1⁄2 represents the matrix square root of the inverse of a matrix. The correlation matrix of T will be the identity matrix. If a new data observation
Pearson correlation coefficient
Pearson_correlation_coefficient
Operator encoding information about iterated map
well studied right-shifts include the Jacobi operator and the Hessenberg matrix, both of which generate systems of orthogonal polynomials via a right-shift
Transfer_operator
Clade of birds
to Anseriformes. One hypothesis is that diatrymas and mihirungs are successive sister groups to anseriforms and another hypothesis places mihirungs as
Odontoanserae
Biological term for the interstitial fluid of multicellular organisms
water, forms the matrix of life." This water is related also to the surfaces of proteins, DNA and all living molecules in the matrix. This is a structured
Internal_environment
Statistical method
one may examine both a pattern matrix and a structure matrix. The structure matrix is simply the factor loading matrix as in orthogonal rotation, representing
Factor_analysis
Clade of the first four-limbed vertebrates and their descendants
factor. Water retention was now important, since it was no longer the living matrix, and could be lost easily to the environment. Finally, animals needed new
Tetrapod
Organelle in eukaryotic cells responsible for respiration
include the outer membrane, intermembrane space, inner membrane, cristae, and matrix. In addition to supplying cellular energy, mitochondria are involved in
Mitochondria
Exact statistical hypothesis test
exact statistical hypothesis test. A permutation test involves two or more samples. The (possibly counterfactual) null hypothesis is that all samples
Permutation_test
Outer layer of the cerebrum of the mammalian brain
PMC 4778709. PMID 26359774. Functional columns were first defined in the cortex by Mountcastle (1957), who proposed the columnar hypothesis, which states that
Cerebral_cortex
Property of measure-preserving dynamical systems
in statistical physics, where Ludwig Boltzmann formulated the ergodic hypothesis in connection with the foundations of statistical mechanics. Ergodicity
Ergodicity
Structures of the brain
Perineuronal nets (PNNs) are specialized extracellular matrix structures responsible for synaptic stabilization in the adult brain. PNNs are found around
Perineuronal_net
DNA and protein sequence alignment software package
statistic) derived from a substitution matrix (typically BLOSUM or PAM for amino acids). Although this slows down hypothesis testing considerably, it also makes
FASTA
Type of similarity matrix in computational biology
lethal or that are rejected by natural selection in other ways. A PAM matrix is a matrix where each column and row represents one of the twenty standard amino
Point_accepted_mutation
Method of data analysis
the data's covariance matrix. Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular value decomposition
Principal_component_analysis
Mathematical computing environment
data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation. Maple's capacity
Maple_(software)
Tensor related to gradients
mathematics, the structure tensor, also referred to as the second-moment matrix, is a matrix derived from the gradient of a function. It describes the distribution
Structure_tensor
Correlation of a signal with a time-shifted copy of itself, as a function of shift
autocorrelation matrix is a Hermitian matrix for complex random vectors and a symmetric matrix for real random vectors. The autocorrelation matrix is a positive
Autocorrelation
Unscientific healthcare practices
particular characteristics of a person's illness. A functional medicine practitioner devises a "matrix" from these factors to serve as the basis for treatment
Alternative_medicine
Thought experiment on artificial intelligence
argument is intended to refute a position Searle calls the strong AI hypothesis: "The appropriately programmed computer with the right inputs and outputs
Chinese_room
Mammal reproductive system cell
than MGCs in response to FSH. During expansion CCs also produce a mucified matrix required for ovulation. Cell culture of granulosa cells can be performed
Granulosa_cell
Virus that infects bacteria
the phage genes responsible for coding enzymes that degrade the biofilm matrix, phage structural proteins, and the enzymes responsible for lysis of the
Bacteriophage
Fringe hypothesis
understanding and, by later extension, consciousness derives. Hameroff provided a hypothesis that microtubules would be suitable hosts for quantum behavior. Microtubules
Quantum_mind
Supposition or system of ideas intended to explain something
speculative (which in formal terms is better characterized by the word hypothesis). Scientific theories are distinguished from hypotheses, which are individual
Theory
Folds of throat tissues that help to create n through vocalization
activity. Those results confirm the hypothesis that phonation stimulates stellate cells into producing more extracellular matrix. Furthermore, using a specially
Vocal_cords
Signal processing technique used in radar
cell under the interference only hypothesis, H 0 {\displaystyle H_{0}} . For SMI, the interference covariance matrix for the k t h {\displaystyle k^{th}}
Space-time adaptive processing
Space-time_adaptive_processing
Hungarian and American mathematician and physicist (1903–1957)
the mathematical framework of quantum physics, in the development of functional analysis, and in game theory, introducing or codifying concepts including
John_von_Neumann
Evaluates how likely it is that any difference between data sets arose by chance
statistic are used. It is a p-value test. A simple example is testing the hypothesis that an ordinary six-sided die is "fair" (i. e., all six outcomes are
Pearson's_chi-squared_test
Authorized cyberattack for testing purposes
to remain anonymous. Reporting: Vulnerabilities are classified via risk matrix and documented in a report which contains executive summary, vulnerability
Penetration_test
Set of the elements not in a given subset
ambiguous, as in some contexts (for example, Minkowski set operations in functional analysis) it can be interpreted as the set of all elements b − a , {\displaystyle
Complement_(set_theory)
Any small, fluid-filled, spherical organelle enclosed by a membrane
protein called annexins. Matrix vesicles bud from the plasma membrane at sites of interaction with the extracellular matrix. Thus, matrix vesicles convey to
Vesicle (biology and chemistry)
Vesicle_(biology_and_chemistry)
Second stage of the memory process
between the matrix of multiple traces hypothesis and the neural network model is that while new memory indicates extension of the existing matrix for the
Storage_(memory)
Linear operator equal to its own adjoint
basis, this is equivalent to the condition that the matrix of A {\displaystyle A} is a Hermitian matrix, i.e., equal to its conjugate transpose A ∗ {\displaystyle
Self-adjoint_operator
Mathematically obvious
"nontrivial". The homogeneous matrix equation A x = 0 {\displaystyle A\mathbf {x} =\mathbf {0} } , where A {\displaystyle A} is a fixed matrix, x {\displaystyle \mathbf
Triviality_(mathematics)
Mathematical operation with two operands
readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. A binary function that involves
Binary_operation
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS
FUNCTIONAL MATRIX-HYPOTHESIS