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STATISTICAL ANALYSIS OF ECOLOGICAL DIVERSITY
abundance estimation
abundances
average rarity index
design-based inference
diversity
diversity index
encounter sampling
field study
information theory
intrinsic diversity ordering
intrinsic diversity profile
model-based inference
relative abundances
simple random sampling
species richness estimation
species-abundance curve
taxocene
DESCRIPTIVE MEASURES OF ECOLOGICAL DIVERSITY
concentration
diversity
equitability
evenness
heterogeneity
homogeneity
inequality
SAMPLING DESIGNS FOR MONITORING ECOLOGICAL DIVERSITY
area sampling.
diversity index estimation
environmental sampling
sampling design
species abundance estimation
unit sampling
INFERENCE ON ECOLOGICAL DIVERSITY
abundance vector estimation
Bayesian diversity index estimation
broken-stick distribution
diversity index estimation
geometric distribution
jackknife
logarithmic series distribution
lognormal series distribution
negative binomial distribution
Poisson distribution
simple random sampling
species-abundance curve model
THE INVENTORY AND ESTIMATION OF PLANT SPECIES RICHNESS
biodiversity
bootstrap
estimation
jackknife
species richness
SPATIAL STATISTICS
geostatistics
isotropy
kriging
lattice data
spatial point patterns
stationarity
GEOSTATISTICS: PAST, PRESENT AND FUTURE
Distribution-free techniques
Kriging
Likelihood-based analyses
Spatial Correlation
Spatial Prediction
Variogram
Bayesian Methodology
SPATIAL DESIGN
covariogram estimation
entropy sampling
optimum design
random field
space-filling
STATISTICAL ANALYSIS OF SPATIAL COUNT DATA
epidemiology
hierarchical models
Markov random fields
spatial quadrats
disease mapping
SPATIAL DISEASE MAPPING
bayesian methods
epidemiology
geostatistics
hierarchical models
random effects
small area estimation
spatial point process
statistics
MULTIVARIATE DATA ANALYSIS
covariance models
discriminant analysis
elliptically contoured distributions
factor analysis.
linear models
multiple regression
multivariate analysis of variance
multivariate normal distribution
parameter estimation
partial correlation
principal components
quadratic forms
tests of hypotheses
Multivariate statistical inference
THE ANALYSIS OF PUTATIVE SOURCES OF HEALTH HAZARD
epidemiology
hazard, risk
health
pollution
putative source
statistical modeling
SPATIO-TEMPORAL METHODS IN CLIMATOLOGY
canonical correlation
data assimilation
empirical orthogonal function
principal oscillation pattern
RANK TESTS FOR INDEPENDENCE AND RANDOMNESS
correlation
independence
locally most powerful rank tests.
randomness
ties
trend
Rank
AREA PRECIPITATION MEASUREMENT
area rainfall estimate
cokriging
kalman filter
kriging
radar meteorology
WATER-QUALITY MONITORING OF RIVERS
chemistry
concentration
loadings
network design
rivers
STOCHASTIC MODELING IN LIFE SUPPORT SYSTEMS
atmospheric science
bayesian
carcinogenesis
cause-effect associations
decision making
environmental pollution
epidemiology
epistemic
epistemology
genetics
geographical information systems
human exposure
knowledge integration
maximum entropy
modeling
modern geostatistics
natural laws
non-bayesian
physical geometry
population indicators
quantum evolution
random fields
risk assessment
sampling design
space/time scales
spatiotemporal mapping
stochastic
subsurface contamination
toxicokinetics
ECONOMIC ASPECTS OF MONITORING ENVIRONMENTAL FACTORS: A COST-BENEFIT APPROACH
environmental resources
evaluation
instruments
policies
regulation.
standards
Cost and benefit
TREND ANALYSIS FOR ENVIRONMENTAL FACTORS: TIME EFFECTS ON NITROUS OXIDE (N2O) LEVELS AT MACE HEAD, IRELAND
change in variability.
estimation
likelihood ratio test
nitrous oxide
trend analysis
Change-point
MODERN BIOMETRY
agriculture
biodiversity
biology
data analysis
design
ecology
health
mathematics
medicine
sampling
statistics
DATA COLLECTION AND ANALYSIS IN BIOMETRICS
case-control studies
clinical trials
data collection
experimental design
longitudinal studies
repeated measures
species abundance
split plots
survey sampling
time series
THE DESIGN OF EXPERIMENTS
components
design issues
factorial designs
random and fixed effects
repeated measures designs
split-plot designs
SAMPLE SURVEYS
cluster sampling
designed experiments
nonresponse
observational data
probability sampling
rare populations
stratified sampling
RESPONSE ADAPTIVE RANDOMIZATION IN CLINICAL TRIALS
branching processes
hellinger distance
likelihood
play-the-winner
polya urns
randomized play-the-winner
TIME SERIES MODELS
autocorrelation
autoregressive
bilinear spatial
estimation
exponential
gaussian
linear
moving average
seasonal
ESTIMATING SPECIES ABUNDANCE
adaptive sampling
calibration study
capture-recapture
edge bias
expansion estimator
line transect sampling
nearest neighbour distance
quadrat sampling
removal method
transect line
trapping web
t-square sampling
unstocked quadrats
wandering quarter method
STATISTICAL METHODOLOGY IN BIOMETRY
categorical data
hierarchical data
linear regression
survival analysis
Statistical models
LINEAR REGRESSION MODELS
diagnostics
estimation
inference
multiple regression
simple linear regression
GENERALIZED LINEAR MODELING
generalized estimating equations
quasi-likelihood
random component
systematic component
Exponential family
CATEGORICAL DATA ANALYSIS
bernoulli experiment
chi-squared test
clustered categorical data
confounding
conti-ngency table
likelihood ratio test
logistic regression
log-linear model
multinomial regression
poisson regression
proportion
SURVIVAL ANALYSIS
average hazard rate
average survival time
censoring
cox proportional hazards model
extended cox model
failure
goodness-of-fit test
hazard function
hazard ratio
heavyside function
kaplan-meier method
likelihood ratio test
log-log survival curves
log-rank test
ordered failure times
stratified cox model
survival analysis
survival function
wald test
wilcoxon test
MULTIVARIATE AND MULTIDIMENSIONAL ANALYSIS
canonical correlation
dimensionality reduction
discriminant analysis
factor analysis
multivariate normal distribution
multivariate regression
principal component
variables relationships
REPEATED MEASURES AND MULTILEVEL MODELING
conditional model
generalized estimating equations
generalized linear mixed model
linear mixed model
longitudinal data
marginal model
non-linear mixed model
random effect
Covariance model
META-ANALYSIS
clinical trials
fixed effects models
heterogeneity
interaction
random effects models
stratification
Meta-analysis
COMPUTATION AND BIOMETRY
biometry
computer language
computing
database
document preparation
expert system
markup system
statistical analysis
statistical package
study design
STATISTICAL GRAPHICS
added variable plot
autocorrelation function
boxplot
brushing display
chernoff faces
cluster analysis
coplot
grand tour
histogram
influence
kaplan-meier (product-limit) estimator
lowess
multidimensional scaling
multivariate analysis
outliers
partial autocorrelation function
partial residual plot
plotting symbols
principal components analysis
projection pursuit
quantile-quantile (qq) plots
regression diagnostics
residuals
sabl decomposition
scatterplot
scatterplot matrix
scatterplot smoothing
survival analysis
survival curve
time series analysis
transformations
trellis display
variogram.
COMPUTER-INTENSIVE STATISTICAL METHODS
Classification tree
Monte Carlo
Neural network
Smoothing
Bootstrap
STATISTICAL COMPUTING
biometry
computer language
computing
database
document preparation
expert system
markup system
statistical analysis
statistical package
SPATIAL STATISTICAL MODELING IN BIOLOGY
Cokriging
Convolution
Generalized linear mixed model
Generalized linear model
GIS
GLMM
Hierarchical
Kriging
LMM
Markov chain Monte Carlo
Markov random fields
Maximum likelihood
MCMC
Mixed model
Poisson
REML
Spectral
Variogram
Bayesian
BIOSTATISTICAL METHODS AND RESEARCH DESIGNS
Cohort study
Cross-Sectional Study
Generalized linear model
Longitudinal data
Statistical inference
Statistical model
Study design
Survival analysis
Case-control study
EPIDEMIOLOGY METHODS
Case-control design
Cohort design
Disease Development
Measurement error
Missing data
Observational Studies
Odds ratio
Randomization
Relative Risk
Attributable risk
COMMUNICABLE DISEASES AND DATA ANALYSIS
basic reproductive number
infectious
secondary attack rate
vaccines
Transmission probability
NUTRITIONAL EPIDEMIOLOGY
chronic disease
confounding
dietary assessment
energy balance
measurement error
nutrient consumption
research strategies
study design
STATISTICAL METHODS IN LABORATORY AND BASIC SCIENCE RESEARCH
Comparative genomic hybridization
Gene expression microarrays
Luria Delbrück fluctuation test
Modeling
Molecular biology
Probability
Randomization
Statistics
STATISTICAL METHODS FOR TOXICOLOGY
animal bioassay
carcinogencity
developmental toxicology
dose-response
generalized estimating equations
litter effect
quasi-likelihood methods
reproductive toxicity
risk assessment
SELECTED TOPICS IN BIOMETRY
designed experiments
multivariate analysis
spatial analysis
statistical analysis
STATISTICAL METHODOLOGY IN AGRICULTURE AND HORTICULTURE
analysis of deviance
analysis of variance (anova)
experimental design
generalised linear model (glm)
on-farm experimentation
precision agriculture
regression
restricted maximum likelihood (reml)
spatial data
variability
STATISTICAL METHODOLOGY IN FORESTRY
basal area
biomass
breast height
dbh (diameter at breast height)
forest growth and yield models
forest inventory, taper models
site quality
stand density
STATISTICAL ECOLOGY AND ENVIRONMENTAL STATISTICS
biodiversity measurement and comparison
change detection
diversity profiles
echelon analysis
ecological sampling
ecometrics
environmental indicators and their integration
environmental monitoring and assessment
environmental statistics
environmetrics
hierarchical classified map simulation model
hierarchical markov transition matrix models
landscape ecology
landscape fragmentation profiles
multiscale assessment
multispectral environmental change detection
observational economy
risk assessment
statistical ecology
POPULATION GENETICS
evolution
genetic drift
genetic variation
mathematical models
molecular biology
mutation
natural selection
neutral theory
population structure
STATISTICAL GENETICS
breeding
genetic markers
heritability
inbreeding
linkage
mapping
quantitative genetics
quantitative trait locus
relatedness
selection
BIOINFORMATICS: PAST, PRESENT AND FUTURE
bio-grids
biological sequence analysis
comparative genomics
design and analysis of microarray experiments
evolutionary models
federated data integration
functional genomics
gene expression analysis
hidden Markov models
microarray data
phylogenetic reconstruction
proteomics
sequence alignment
systems biology
Bioinformatics
A VIEW OF MATHEMATICS
Abelian category
cohomology
cross ratio
index formula
line element
motives
non-commutative geometry
non-Euclidean geometry
positivity
projective geometry
quantum field theory
renormalization
Riemannian geometry
standard model
symmetry
topos
trace
Space
MATHEMATICS THROUGH MILLENIA
abstraction in mathematics.
applications of mathematics
mathematicians
mathematics in various civilizations
History of mathematics
MATHEMATICS ALIVE AND IN ACTION
impact of mathematics on society.
mathematical modeling in the sciences
mathematics and the arts
mathematics in industry
pure and applied mathematics
Mathematical work
ALGEBRA
Abelian category
Abelian sheaf
additive category
additive functor
algebraic statistics
Buchberger’s criterion
complex
degree shift
derived category
derived functor
direct image
distinguished triangle
division
elimination
Groebner basis
homological algebra
homotopic
injective resolution
integer programming
leading term
lexicographic order
mapping cone
monomial order
poset
projective resolution
quasi-isomorphism
remainder
spectral sequence
equivalence relation
MATRICES, VECTORS, DETERMINANT AND LINEAR ALGEBRA
Cramer’s rule
determinant
eigenvalue
Jordan canonical form
linear equation
linear map
symmetric matrix
vector space
matrix
GROUPS AND APPLICATIONS
group action
homomorphism
quotient group
representation
symmetry
transformation
group
RINGS AND MODULES
completion
homomorphism
integral
localization
module
Noetherian
residue ring
ring
FIELDS AND ALGEBRAIC EQUATIONS
cyclotomic
field
finite field
Galois theory
ruler and compass construction
solvability
algebraic equation
NUMBER THEORY AND APPLICATIONS
Caesar’s cipher
Chinese remainder theorem
class field theory
complex multiplication
cyclotomic fields
discrete logarithm problem
Euclidean algorithm
figure numbers
fundamental theorem of arithmetic
Kronecker’s dream in his youth
Kronecker-Weber theorem
mathematical induction
Pell’s Equations
prime number theorem
prime numbers
public key cryptology
Pythagorean triples
quadratic reciprocity law
Riemann hypothesis
well-ordered structure
ALGEBRAIC GEOMETRY AND APPLICATIONS
affine
algebraic curve
algebraic surface
algebraic variety
alteration
birational
complete
complete linear system
complex analytic space
discrete valuation ring
divisor
error-correcting code
function field
Hilbert’s Nullstellensatz
Jacobian matrix
local homomorphism
local ring
maximal ideal space
Mori’s Minimal Model Program
morphism
Noether’s normalization theorem
nonsingular
normal
product
projective
proper
resolution
Riemann-Roch theorem
scheme
separated
sheaf
singular
stalk
valuation ring
Zariski tangent space
algebraic set
BASIC NOTIONS OF GEOMETRY AND EUCLIDEAN GEOMETRY
circle
conic section
crystallography
ellipse
Euclidean space
Euclidean vector space
hyperbola
inverse square central force
isometry
parabola
regular polyhedron
space group
symmetry group
symmorphic space group
Transformation group
triangle
Metric space
AFFINE GEOMETRY, PROJECTIVE GEOMETRY, AND NON-EUCLIDEAN GEOMETRY
affine transformation
collinearity
conic
cross ratio
non-euclidean geometry
parallelism
perspective
projective geometry
projective transformation
Affine geometry
DIFFERENTIAL GEOMETRY
connection
curvature
curvature tensor
differential form
Gauss-Bonnet theorem
Gaussian curvature
geodesic
harmonic map
Laplacian
manifold
mean curvature
minimal surface
Riemannian metric
surface
tangent space
tensor field
torsion
vector bundle
vector field
curve
TOPOLOGY
cohomology group
compactness
connectedness
continuity
convergence
Euler-Poincaré characteristic number
homeomorphism
homology group
homotopy
homotopy group
homotopy type
intersection numbers
knot theory.
linking numbers
metric space
Morse theory
open sets
Poincaré conjecture
Poincaré duality theorem
Poincaré-Hopf theorem
simplicial complex
neighborhood
COMPLEX ANALYTIC GEOMETRY
analytic variety
Chern class
complex manifold
de Rham and Dolbeault theorems
divisor
Grothendieck residue
Poincaré and Kodaira-Serre dualities
Riemann-Roch theorem
sheaf cohomology
vector bundle
holomorphic function
DIFFERENTIAL AND INTEGRAL CALCULUS
cauchy sequence
continuity
convergence
definite integral
derivative
-function
graph of a function
higher order derivative
iterated integral
leibnitz rule
limit
maximum
minimum
multiple integral
partial derivative
real numbers
riemann integral
taylor’s formula
total differential
COMPLEX ANALYSIS
analytic continuation
analytic function
analytic function of several complex variables
argument principle
associated convergence radii
cauchy’s integral theorem
cauchy-hadamard theorem
cauchy-riemann differential equation
complex number
complex plane
de moivre theorem
differentiability
domain of holomorphic
essential singularity
holomorphic function
laurent series
meromorphic function
morera’s theorem
natural boundary
picard theorem
pluriharmonic function
point at infinity
pole
power series
pseudoconvexity
radius of convergence
regular function
residue
riemann sphere
riemann surface
rouche’s theorem
singularity (of an analytic function)
stereographic projection
MEASURE AND PROBABILITY
algebra (field)
almost sure convergence
black-scholes formula
borel-cantelli lemma
bounded convergence
brownian motion
central limit theorem
characteristic function
conditional expectation
conditional probability
convergence in law
convergence in probability
ergodic theorem
fatou’s lemma
feller process
feynman-kac formula
gaussian process
haar measure
increasing process
infinitely divisible distribution
itô process
law of large numbers
lebesgue integral
lévy measure
lévy process
markov chain
markov process
martingale
measurable function
measure
measure-preserving transformation
moment generating function
normal (gaussian) distribution
poisson distribution
probability
probability space
product measure
queuing process
radon measure
radon-nikodym
random walk
recurrent
signed measure
stable law
stationary process
stochastic differential equation
stochastic integral
stopping time
tchebychev inequality
transient
transition probability
FUNCTIONAL ANALYSIS AND FUNCTION SPACES
banach algebras
banach spaces
bounded linear functionals
bounded linear operators
dual spaces
function spaces
functional analysis
hilbert spaces
locally convex spaces
spectra
strong convergence
topological vector spaces
weak convergence weak* convergence
NUMERICAL ANALYSIS AND COMPUTATION
accuracy
condition number
eigenvalues
error analysis
linear systems of equations
norms
singular values and software packages
stable algorithm
stable problems
vector spaces
INFINITE ANALYSIS
affine lie algebra
conformal field theory
exactly solvable models
free bosons
free fermions
quantum affine algebra
soliton equation
the ising model
the sine-gordon model
the XXZ model
vertex operator
FOURIER ANALYSIS AND INTEGRAL TRANSFORMS
approximate identity
conjugate function
convergence
convolution
cost of computation
dirichlet kernel
dirichlet series
divergence
fast Fourier transform
fejér kernel Finite Fourier transform
fourier series
fourier transform
fourier transform on a group
gauss-Weierstrass kernel
gibb’s phenomenon
hankel transform
hardy space
harmonic function in the unit disk
integral transform
inversion formula
laplace transform
lebesgue space
locally compact Abelian group
mellin transform
multiresolution analysis
nontangential limit
orthogonal function
orthogonal polynomial
partial sum
poisson integral
poisson kernel
power-of-2 FFT
real Hardy space
summability
summability kernel
test for convergence
wavelet
wavelet transform
OPERATOR THEORY AND OPERATOR ALGEBRA
AFD factors
C*-algebra, type I C*-algebra
compact operator
dilation
free probability
hilbert space
invariant subspace
jones index
K-theory
linear operator
modular theory
nuclear C*-algebra
operator monotone function
polar decomposition
purely infinite C*-algebra
spectral decomposition
spectrum
toeplitz operator
unilateral shift
von Neumann algebra
FORMAL LOGIC
analytical hierarchy
arithmetical hierarchy
Axiom of Choice
axiomatizable theory
cardinal arithmetic
Church-Turing Thesis
complete theory
computable function
conjunctive normal form
consistent theory
countable (enumerable) set
decidable relation
Deduction Theorem
diagonal argument
disjunctive normal form
elementary equivalence
equinumerous
First Order Logic
formal sentence
formal syntax
formal theorem
Formalism
General Comprehension Principle
Generalized Continuum Hypothesis
Gödel Completeness Theorem
Gödel Incompleteness Theorem
Gödel Second Incompleteness Theorem
grounded set
inconsistent theory
Intuitionism
Kuratowski operation
logical axiom
logical consequence
logical truth
Logicism
mathematical logic
metatheorem
Model Theory
Modus Ponens
non-standard model
numeralwise expressibility
ordinal arithmetic
ordinal recursion
partial function
Peano Arithmetic
prenex normal form
primitive recursive function
Principle of Extensionality
programming language
proof by induction
Proof Theory
proofs-as-types
propositional connective
quantifier
Realism
recursive definition
recursive function
recursive program
Russell paradox
satisfaction relation
Scott-continuous
Second Order Language
semantics
set theory
symbolic computation
Tarski Truth Conditions
tautology
transfinite induction
transfinite recursion
Turing machine
Typed ? -Calculus
uncountable set
undecidable relation
unsolvable problem
wellorder
Zermelo-Fraenkel Set Theory.
algorithm
MODEL THEORY
admissible set
approximate satisfaction
axiom
cardinality quantifier
categorical theory
cell decomposition
compactness theorem
complete theory
definable set
diagram
Ehrenfeucht-Fraïssé game
elementary chain
elementary diagram
elementary embedding
elementary equivalence
elementary type
elimination of imaginaries
elimination of quantifiers
existentially closed
first order logic
forking
Hanf number
independence
indiscernible
infinitary logic
Löwenheim-Skolem theorem
many-sorted logic
model
model-complete
Morley rank
neocompact
nonstandard hull
o-minimal
omitting types
positive bounded
positive formula
prime structure
probability logic
quantifier
realizing types
resplendent model
saturated model
Scott height
simple theory
stable theory
strongly minimal
theory
topological logic
ultrafilter
ultrapower
ultraproduct.
adapted probability logic
PROOF THEORY AND CONSTRUCTIVE MATHEMATICS
almost negative formula
axiom of open data
bar induction
Bishop's constructive mathematics
Brouwer-Heyting-Kolmogorov interpretation
choice sequence
Church-Kleene ordinal
Church's thesis
constructive recursive mathematics
constructivism
continuity axioms
contraction
cut elimination
disjunction property
elimination rule
explicit definability property
finitism
Gentzen sequent
Glivenko theorem
Gödel-Gentzen translation
Heyting arithmetic
Hilbert's program
Hilbert-type system
I-completeness
introduction rule
intuitionism
intuitionistic arithmetic
intuitionistic logic
inversion lemma
Kreisel-Lacombe-Shoenfield-Tsejtin theorem
Kripke forcing
Kripke semantics
lawless sequence
Markov's principle
Markov's rule
natural deduction
negative formula
normalization
order type
ordinal notation
predicativism
proof theory
proof-theoretic ordinal
realizability
semi-formal system
singular cover
Specker sequence
Tait calculus
topological semantics
truth-complexity
typed lambda-calculus
weakening.
Algebraical semantics
COMPUTABILITY AND COMPLEXITY
Bounded Quantifier Theorem
Chinese Remainder Theorem
Church-Turing thesis
complexity measure
computable function
computable set
creative set
Diophantine set
Enumeration Theorem
Fibonacci number
halting problem
Hilberts 10th Problem
maximal set
m-complete set
MRDP theorem
NP-complete problem
oracle
P = NP problem
partially computable function
polynomial-time computability
priority method
productions
r.e. degree
r.e. set
recursive function
recursive set
recursively enumerable set
simple set
true arithmetic
Turing degree
universal Diophantine equation
unsolvable problem
word problems.
arithmetical hierarchy
SET THEORY
Axiom of Choice
Axiom of Infinity
Borel determinacy
cardinal number
closed unbounded set
Cohen real
Cohen's forcing method
consistency strength
constructible set
Continuum Hypothesis
countable set
Covering lemma
cumulative hierarchy of sets
descriptive set theory
diamond sequence
elementary embedding
fine structure theory
Fodor’s lemma
forcing conditions
generic absoluteness
generic extension
generic filter
inner model
iterated ultrapower
large cardinal hypothesis
Lebesgue measure
Levy collapse
Levy hierarchy
Martin's Axiom
Martin's Maximum
measurable cardinal
ordinal number
Powerset Axiom
projective determinacy
random real
Reflection Principle
regular cardinal
relative consistency
set theory
singular cardinal
stationary set
super-compact cardinal
Suslin tree
Suslin's Hypothesis
transfinite induction
transitive model
transitive set
ultrafilter
wellfounded relation
wellorder
Woodin cardinal
Zermelo-Fraenkel Set Theory.
Aronszajn tree
LOGIC AND COMPUTER SCIENCE
Armstrong’s axioms
complete problem
complexity class
computable function
computational complexity
conjunctive query
constraints
data complexity
database
database query language
database system
database theory
Datalog
decidable problem
decision problem
definable query
descriptive complexity
deterministic Turing machine
domain-independent formula
Ehren-feucht-Fra?ssé game
existential second-order logic
expression complexity
finite model theory
finite-variable logics
first-order logic
functional dependency
inductive definition
infinitary logic
intractable problem
least fixed-point logic
logarithmic space
many-one reduction
mathematical logic
model checking problem
model theory
NL
non-deterministic logarithmic space
non-deterministic polynomial time
non-deterministic Turing machine
NP
NP-complete
partial fixed-point logic
pebble games
polynomial hierarchy
polynomial space
polynomial time
preservation theorem
preservation under extensions
propositional logic
PSPACE
query
recursive function
recursively enumerable
relational algebra
relational databases
satisfaction relation
satisfiability problem
satisfiable formula
second-order logic
solvable problem
SQL
structured query language
superkey
tautology
tractable problem
Turing machine
undecidable problem
unsolvable problem
zero-one law.
algorithm
MODAL LOGIC AND ITS APPLICATIONS
counterpart theory
decidability
deontic logic
dynamic programming logic
epistemic logic
extension
intension
intutionistic logic
Kripke
Lewis
modal logic
multi-modal logic
necessity
possibility
possible world
predicate
proposition
provability interpretation
quantifier
quantifying in
relevance logic
semantics
tense logic
completeness
A BASIC EXAMPLE OF NONLINEAR EQUATIONS: THE NAVIER-STOKES EQUATIONS
Boltzmann equations
hierarchies.
Navier-Stokes equations
scaling
shock-waves
singularities
stability
turbulence
Wave equation
CALCULUS OF VARIATIONS, PARTIAL DIFFERENTIAL EQUATIONS, AND GEOMETRY
bubbles
compactness
conformal invariance
curvature
curvature driven interfaces
interfaces
minimal surfaces
parameterization
phase transitions
Minimization
LINEAR DIFFERENTIAL EQUATIONS
cauchy-kowalewsky theorem
cauchy-riemann equations
derivatives
differential equations
distributions
heat equation
laplace equation
partial differential equations
schrödinger equation
wave equation
DIFFERENTIAL EQUATIONS AND SYMPLECTIC GEOMETRY
canonical relations
caustics
cotangent bundle
Fourier integral operators
Hamiltonian systems
Hamilton-Jacobi theory
Lagrange manifolds
Maslov theory
oscillatory integrals
propagation of singularties.
reduced phase space
symplectic form
Lagrangian mechanics
FROM THE ATOMIC HYPOTHESIS TO MICROLOCAL ANALYSIS
caustics
laplace equation
microlocal analysis
propagation
rays and bicharacteristics
schrödinger equation
symplectic geometry
variational calculus
wave equation
DISCRETE MATHEMATICS
algorithm
discrete convex function
discrete mathematics
dulmage-Mendelsohn decomposition
euler square
graph
latin square
matching
matroid
optimization
GRAPH THEORY
coloring
connectivity
cycles
directed graphs
graphs
paths
planarity
COMBINATORICS
codes
combinatorics
discrete Geometry
hypergraph
matroid
partition Theory
set Theory
COMPUTATIONAL COMPLEXITY
{deterministic, randomized, nondeterministic, circuit}computation model
{time, space, circuit size, circuit depth}complexity measure
combinatorial lower bound
completeness
complexity class
derandomization
inclusion by simulation
monotone circuit complexity
one-way function
pseudo random bit generator
reducibility
separation by diagonalization
OPTIMIZATION
approximation algorithms
branch-and-bound
branch-and-cut
combinatorial optimization
discrete optimization
genetic algorithms
integer polyhedron
integer programming
local search
metaheuristics
network flows
simulated annealing
tabu search
total unimodularity
PROBABILITY AND STATISTICS
bayesian statistics
confidence estimates
conventional statistics
data quality
data science
descriptive statistics
estimation
fuzziness
imprecise data
probability
probability distributions
randomness
statistical hypotheses
statistical tests
statistics
statistics and non-precise data
stochastic processes
stochastic quantity
stochastics
uncertainty
PROBABILITY THEORY
annuities
average man
axiomatization
chance mechanisms
classical ruin problem
dam theory
demography
design and analysis of experiments
duration of play
fishery
forestry
gambling
games
insurance
law of large numbers
least squares
matching problem
mathematical expectation
needle problem
problem of points
reliability theory
spatial statistics
ST. petersburg paradox
ST. petersburg school
stochastic hydrology
stochastic process
theory of errors
time series
weather modification
wildlife sampling
wind
MATHEMATICAL FOUNDATIONS AND INTERPRETATIONS OF PROBABILITY
kolmogorov triplet
probability space
RANDOM VARIABLES AND THEIR DISTRIBUTIONS
conditional probability distribution.
distribution function
independence
probability distribution
random variable
LIMIT THEOREMS OF PROBABILITY THEORY
central limit theorem
law of iterated logarithm
laws of large numbers
limit distributions of extremes
local limit theorems
modes of convergence
normal limit distribution
poisson limit distribution
probabilities of large deviation
sequences of random variables
sums of random variables
ALTERNATIVE PROBABILISTIC SYSTEMS
ambiguity
imprecise probabilities
interval-probability.
interval-valued probability
uncertainty
STOCHASTIC PROCESSES AND RANDOM FIELDS
correlation theory
covariance function
empirical process
fractal
gaussian process
gaussian random field
gibbs random field
independent increment process
invariance principle
markov process
martingale
mean value function
phase transition
point process
random field
renewal process
self-similar process
stochastic differential equation
stochastic process
strictly stationary process
wide-sense stationary process
CONSTRUCTION OF RANDOM FUNCTIONS AND PATH PROPERTIES
brownian motion
poisson process
stochastic process
MARKOV PROCESSES
birth and death process
diffusion process
feller process
galton-Watson process
infinitesimal generator
infinitesimal operator
markov chain
markov process
markov property
random walk
recurrence
stopping times
strong Markov property
transience
transition matrix
transition operator
STOCHASTIC CALCULUS
brownian motion
ito formula
ito integral
stieltjes integral
tanaka formula
STOCHASTIC DIFFERENTIAL EQUATIONS
existence
stochastic differential equation
stochastic integral equation
unicity
STATIONARY PROCESSES
correlation function
linear regularity
linear singularity
mean square error prediction
regularity
singularity
spectral density
spectral function
spectral process
stationary process
strict sense stationary process
weak sense stationary process
ERGODIC PROPERTIES OF STATIONARY, MARKOV, AND REGENERATIVE PROCESSES
Markov processes
regenerative processes
semi Markov processes
stationary processes
Ergodic theorems
HOMOGENEOUS RANDOM FIELDS AND THEIR EVALUATION
correlation function
covariance function
empirical orthogonal functions
generalized spherical functions
helicity
homogeneity in the large sense
isotropy
longitudinal and transversal components of a homogenous vector random field
random field
solenoidal and potential random vector fields
stochastic ito integral
PROBABILISTIC MODELS AND METHODS
brownian motion
central limit theorem
diffusion process
expectation
expected utility principle
fair game
independent increment
ito's formula
law of large numbers
markov process
martingale
normal distribution
poisson process
random variable
risk
simulation
stochastic differential equation
stochastic processes
STATISTICAL SIMULATION AND NUMERICAL PROCEDURES
Acceptance-rejection method
Accepting probability
Bootstrap method
Composition method
Gibbs sampler
Inverse method
Linear congruential generators
Markov Chain Monte Carlo (MCMC) method
Metropolis-Hastings algorithm
Monte Carlo method
Monte Carlo procedure
Primary estimator
Random number generators
Random variates
Ratio-of-uniform method
Secondary estimator
Simulated annealing
Random numbers
INSURANCE MATHEMATICS
credibility
insurance
life
non-life
premium
reinsurance
reserve
ruin
stop loss
MATHEMATICAL MODELS IN FINANCE
arbitrage
black-Scholes price
bond
brownian motion
change of measure
equivalent martingale measure
financial derivative
future
girsanov transformation
interest rate
it stochastic calculus
martingale
option
securitization of risks
value at Risk (VaR)
RELIABILITY AND MAINTAINABILITY
availability
failure rate
lifetime
maintainability
mean time to failure
network
reliability
INVENTORIES, WATER STORAGE AND QUEUES
(s, S) inventory model
base stock inventory model
closed and open networks
input
interarrival times
its extension to continuous time
loss and delay systems
markovian networks
markovian switching
morans dam model
newsvendor problem
periodic and continuous inspection
queue discipline
queue length, (Q, r) model
service mechanism
service times
shortfall
solberg model
switching probabilities
traffic equations
traffic intensity
workload
INFORMATION THEORY AND COMMUNICATION
(information) source
(information) transmission
(transmission) channel
alphabet
capacity
channel coding
cryptology
data compression
data processing
digital signature
discrete memoryless source
entropy
error-correcting codes
error-detecting codes
fidelity criterion
hashing
internet
measures of information
memoryless channel
modulation
multi-port systems
multi-user communication
networks
noise
public key cryptography
quantization
rate-distortion theory
redundancy
reliable communication
shannon theory
source coding
white Gaussian noise
FOUNDATIONS OF STATISTICS
a-priori distribution
a-priori information
bayes risk
bayes strategy
conditional probability
data
decision
ensembles flous
estimation
fuzzy data
fuzzy probability
information
likelihood
loss
measurement
minimax strategy
philosophical foundations
probability
random sample
risk function
sample
sampling
sampling distributions
sensitivity
statistical inference
statistical population
sufficiency
testing
uncertainty
utility
PRELIMINARY DATA ANALYSIS
data sets (uni-, bi-, multivariate)
data transformations
exploratory data analysis (EDA)
graphical representations
mean
measures of location
measures of spread
outliers
probability plots
quantiles. regression
variance
Box-plots
STATISTICAL INFERENCE
bayesian statistics
classical statistics
confidence regions
data
data quality
estimation
fuzziness
likelihood function
nonparametric models
parametric models
semiparametric models
standard statistics
statistical decisions
stochastic models
sufficiency
testing
STATISTICAL PARAMETER ESTIMATION
confidence interval
confidence set
consistency
coverage probability
estimator
likelihood function
loss function
maximum likelihood
mean squared error
parameters
point estimator
risk function
sufficient statistic
unbiasedness
variance bound
STATISTICAL TESTING OF HYPOTHESES
acceptance region
bayesian approach
binomial distribution
chi-squared distribution
chi-squared test
composite hypothesis
consistency
critical function
critical region
critical value
error of the first kind
error of the second kind
exponential family
fuzzy data
goodness-of-fit test
hypothesis
kolmogorov test
likelihood-ratio test
minimax approach
neyman structure
neyman-Pearson Lemme
non-parametric hypothesis
non-randomized test
normal approximation
parametric hypothesis
poisson distribution
power function
power of test
randomized test
sample space
sign test
significance level
simple hypothesis
size of test
statistical hypothesis
statistical testing hypotheses
sufficient statistic
test
unbiased Test
uniformly most powerful test
ROBUST STATISTICS
breakdown value
multivariate location and scatter
outlier detection.
robust estimation
robust regression
BAYESIAN STATISTICS
amount of Information
axiomatics
bayes Estimator
bayes Factor
bayes Theorem
credible Region
decision Theory
degree of Belief
exchangeability
foundations of Statistics
hierarchical Models
hypothesis Testing
interval Estimation
intrinsic Discrepancy
likelihood Principle
lindleys Paradox
logarithmic Divergence
maximum Entropy
model Choice
model Criticism
noninformative Priors
nuisance Parameters
objectivity
point Estimation
posterior Distribution
predictive Distribution
prior Choice
prior Distribution
probability Assessment
probability model
probability Theory
reference Distributions
representation Theorem
scientific Reporting
sensitivity Analysis
steinss Paradox
sufficiency
STATISTICAL INFERENCE WITH IMPRECISE DATA
Classical statistics
Data quality
Fuzzy information
Fuzzy numbers
Fuzzy probability
Imprecise data
Imprecision
Standard statistics
Statistical estimation
Statistics
Bayesian statistics
APPLIED STATISTICS
bayesian methods
control
data acquisition
data reduction
estimation
experimental design
exploratory analysis
graphs
inference
likelihood
models
probability
random variable
randomization
replication
sample space
tables
CORRELATION ANALYSIS
canonical correlation.
multiple correlation
multivariate normal distribution
partial correlation
random vector
simple correlation
REGRESSION ANALYSIS
gau-Markov theorem.
least squares estimates
linear models
regression models
ANALYSIS OF VARIANCE AND ANALYSIS OF COVARIANCE
analysis of covariance.
higher way layouts
least squares method
mixed models
models with fixed effects
models with random effects
one-way layout
partitioning a sum of squares
Analysis of variance
SAMPLE METHOD AND QUALITY CONTROL
control chart
economic evaluation
inspection
intervention
lot quality
operating characteristic function
prevention
process quality
product quality
sampling plan
statistical evaluation
TIME SERIES ANALYSIS
basic interpolation polynomial
basin of attraction
boundary conditions
characteristic equation
chebyshev (uniform) approximation
chebyshev polynomial
chebyshev theorem
difference quotients
double-sweep method
euler scheme
fibonacci numbers
fixed point
fourier transform
fractal structure
generalized Lagrange polynomial
green function
hausdorff dimension
hoin scheme
interpolational polynomial (Lagrange form and Newton form)
jacobi matrix
julia set
lebesgue constant
local spline (Ryabenkii spline)
logistic equation
lotka Volterra equation
maunders butterfly
method of least squares
neutral case
newton method
periodical points
points of alternance
rational spline
runge Kutta methods
schoenberg spline
spline of degree with the defect
stable point
super-convergence
th order finite-difference ordinary equation
three-diagonal matrix with diagonal dominance
wavelet
weakened Newton method
weierstrass theorem
windrose
STATISTICAL EXPERIMENTS AND OPTIMAL DESIGN
concentration ellipsoid
distribution of estimators
entropy
experiment design
information matrix
least squares
linear statistical model
nonlinear regression
optimality criterion
MATHEMATICAL MODELS OF LIFE SUPPORT SYSTEMS
Agriculture Sciences Models
Biomathematical Models
Climatic System
Data Assimilation
Ecosystem
Energy Sciences Models
Food Sciences Models
Geophysical Hydrodynamics
Global Processes Models.
Hydrodynamics
Mathematical Models of Atmosphere
Water Sciences Models
World ocean
Mathematical Model
INTRODUCTION TO MATHEMATICAL MODELING
Classification of Computational Experiments
Computational Algorithms
Mathematical Models
Software.
Computational Experiment
Mathematical Modeling
MATHEMATICAL MODELING OF LIFE SUPPORT SYSTEMS: CLASSIFICATION OF MODELS
applied mathematical models
approximation models
deterministic models
discrete models
distributed models
ill-posed models
imitation models
Markov processes
nonlinear models
point models
probabilistic models
superposition principle
Mathematical modeling
MATHEMATICAL MODELS IN WATER SCIENCES
climatic system
data assimilation
ecosystem
general circulation
geophysical hydrodynamics
hydrodynamics
mathematical model
numerical simulation
ocean waves
world Ocean
MATHEMATICAL MODELS OF CIRCULATION IN OCEANS AND SEAS
Adjoint Model
Data Assimilation
Marine Dynamics
Numerical Modeling
Ocean General Circulation
Primitive Equations
Shallow-Water Equations
Solvability of Sea Dynamics Problems
Mathematical Model
MATHEMATICAL MODELS FOR WATER RESOURCES MANAGEMENT
decision making
general circulation model
mathematical model
optimization
pollution
system analysis models
wastewater
water quality
water resources system
MATHEMATICAL MODELS OF PLASMA PHYSICS
adjoint Model
data Assimilation
marine Dynamics
mathematical Model
numerical Modeling
ocean General Circulation
primitive Equations
shallow-Water Equations
solvability of Sea Dynamics Problems
MATHEMATICAL MODELS AND SIMULATION IN ENVIRONMENT
aerosol
coagulation
condensation
environment
gaseous pollutants
modeling
nucleation
photochemistry
thermo-hydrodynamics
turbulent diffusion
MATHEMATICAL MODELS FOR PREDICTION OF CLIMATE
attractor
climate
climate system
dimension
dynamic system
energy
modeling
stability
stochasticity.
MATHEMATICAL MODELING IN METEOROLOGY AND WEATHER FORECASTING
adiabatic process
anticyclone
atmospheric boundary layer
atmospheric front
atmospheric turbulence
baroclinic flow
barotropic flow
cloud cluster
coriolis force
cyclone
geophysical fluid dynamics
geophysical turbulence
geostrophic balance
geostrophic wind
global models
hydrostatic approximation
interaction of tropical cyclones with ocean
limited-area models
mesoscale atmospheric processes
meteorological variables
multiple interactions of tropical cyclones
nested grids
parameterization of physical processes
primitive equations
quasi-geostrophic approximation
steering current
synthetic observations (bogus vortex)
tropical cyclone development (evolution)
tropical cyclone genesis (formation)
tropical cyclone landfall
tropical cyclone motion (tracks)
vorticity
weather forecasting.
weather-creating atmospheric mechanisms
ENVIRONMENTAL POLLUTION AND DEGRADATION MODELS
adsorption
bioaccumulation
degradation
deposition
diffusion
gaseous pollutants
modeling, environment
photolysis
FOOD PRODUCTION AND AGRICULTURAL MODELS: BASIC PRINCIPLES OF DEVELOPMENT
climate
crop yield
experiment planning
forecast
mathematical model
production process
soil
system
Agroecosystem
MATHEMATICAL MODELS OF SOIL IRRIGATION AND SALTING
Drainage
Evapotranspiration
Forecast
Simulation models.
Soil Salting
Underground Hydrodynamics
Underground water
Irrigation
DETERMINISTIC MODELS OF PLANT ENVIRONMENT
agroecosystem
energy-mass exchange
evapotranspiration
hydrometeorological regime
plant environment
plant productivity
simulation
MATHEMATICAL MODELS OF AGRICULTURAL SUPPLY
decision making
fertilizer distribution
livestock rations
optimization
precision agriculture.
simplex method
sown areas
Economic-mathematical models
MATHEMATICAL MODELS IN BIOPHYSICS
age structure
biochemical reactions
biological systems
cell cycles
cell regulation
glycolysis
interaction of species
mathematical modeling
metabolism control
molecular dynamics
morphogenesis
nerve conductivity
oscillations
photosynthesis
population dynamics
selection
spatio-temporal organization
trigger systems
POPULATION MODELS
age-Structure
competition
continuous Population Models
discrete population Models
distributed Mathematical Models
evolution Models
harvesting
interacting Populations
mathematical Models
population ecology
population Models
preyPredator Models
renewable Resources
selection
stability
theoretical Population Genetics
PATTERN FORMATION AND NEURAL MODELS
autowaves
autowaves in the cerebrum structures
mathematical models of morphogenesis
mechanochemical autowaves
neurocomputers
neuron-like systems
self-organization
Open distributed systems
MATHEMATICAL MODELS IN IMMUNOLOGY
adaptation
cellular and humoral immunity
clonal selection
effectiveness.
energy cost
immune defense
immune network
infectious diseases
lymphocyte circulation
mathematical modeling
MATHEMATICAL MODELING IN MEDICINE
automatic control
blood circulation
hierarchic systems
respiratory system
homeostasis
MATHEMATICAL MODELS AND CONTROL OF CATASTROPHIC PROCESSES
bifurcation
control systems
discriminants
dynamical systems
smooth mappings
Singularity
MODELS AND METHODS OF ACTUARIAL MATHEMATICS
"ruin" probability
actuarial mathematics
claim
collective risk model
estimations
factorization model
individual risk model
insurance
premium
risk
Last Update: 20 April 2008
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