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matrix theory group theory ring theory field theory lattice theory order theory graph theory combinatorics probability statistics stochastic processes random variables distributions sampling estimation hypothesis testing regression correlation causation inference prediction forecasting projection extrapolation interpolation smoothing filtering signal processing image processing pattern recognition machine learning deep neural networks convolutional recurrent transformer architectures training validation testing deployment monitoring maintenance debugging optimisation hyperparameter tuning gradient descent backpropagation forward pass backward pass loss function accuracy precision recall F1 score ROC curve confusion matrix cross-validation k-fold leave-one-out bootstrap jackknife permutation test t-test ANOVA chi-square Mann-Whitney Wilcoxon Kruskal-Wallis Friedman test post-hoc Bonferroni correction Holm-Bonferroni Benjamini-Hochberg false discovery rate family-wise error rate power analysis sample size effect size Cohen’s d eta squared omega squared partial eta squared generalised eta squared R-squared adjusted R-squared pseudo R-squared AIC BIC deviance information criterion likelihood ratio test Wald test score test Lagrange multiplier test Hausman test Durbin-Watson Breusch-Godfrey White test Breusch-Pagan Goldfeld-Quandt RESET Ramsey specification error test CUSUM CUSUMSQ recursive residuals one-step-ahead forecast errors rolling window expanding window recursive estimation Kalman filter particle filter Markov chain Monte Carlo Metropolis-Hastings Gibbs sampling Hamiltonian Monte Carlo No-U-Turn Sampler variational inference expectation maximisation EM algorithm Baum-Welch forward-backward algorithm Viterbi algorithm dynamic programming Bellman equation value iteration policy iteration Q-learning SARSA temporal difference learning actor-critic methods proximal policy optimisation PPO trust region policy optimisation TRPO deep deterministic policy gradient DDPG twin delayed DDPG TD3 soft actor-critic SAC advantage actor-critic A2C asynchronous advantage actor-critic A3C proximal policy optimisation clipped surrogate objective function constraint violation penalty method augmented Lagrangian primal-dual interior point sequential quadratic programming trust region reflective Newton method conjugate gradient BFGS L-BFGS limited memory quasi-Newton Levenberg-Marquardt Gauss-Newton dogleg method trust region reflective global optimisation simulated annealing genetic algorithm particle swarm optimisation ant colony optimisation differential evolution evolutionary strategies covariance matrix adaptation evolution strategy CMA-ES Bayesian optimisation Gaussian process surrogate acquisition function expected improvement probability improvement upper confidence bound knowledge gradient entropy search predictive entropy search max-value entropy search Thompson sampling multi-armed bandit epsilon-greedy UCB softmax EXP3 adversarial bandits contextual bandits reinforcement learning exploration exploitation trade-off regret bound minimax regret Pareto optimal Nash equilibrium subgame perfect equilibrium Bayesian Nash correlated equilibrium trembling hand perfect sequential rationality commitment credibility signalling screening adverse selection moral hazard principal-agent problem mechanism design auction theory Vickrey sealed bid English Dutch Japanese all-pay lottery contest Tullock rent-seeking tragedy commons public goods free rider problem social dilemma prisoner’s dilemma iterated tit-for-tat grim trigger trigger strategies folk theorem repeated games incomplete information extensive form normal form mixed strategy pure strategy behavioural strategy Kuhn’s theorem perfect recall Harsanyi transformation type space belief updating Bayes rule conditional probability joint distribution marginal distribution copula Archimedean Gaussian Clayton Frank Gumbel Joe survival function hazard function cumulative incidence competing risks cause-specific hazard subdistribution hazard Fine-Gray model Cox proportional hazards accelerated failure time Weibull exponential Gompertz log-logistic log-normal gamma frailty shared frailty random effects robust variance sandwich estimator Huber-White cluster bootstrap block bootstrap moving block stationary bootstrap sieve bootstrap m-out-of-n subsampling double bootstrap triple bootstrap nested bootstrap parametric nonparametric semi-parametric local polynomial kernel Nadaraya-Watson local linear local quadratic bandwidth selection cross-validation plug-in Silverman’s rule-of-thumb Sheather-Jones smoothed cross-validation least squares cross-validation biased unbiased risk estimate SURE Stein unbiased risk estimate wavelet thresholding soft hard adaptive BayesShrink VisuShrink SureShrink translation-invariant cycle spinning undecimated discrete wavelet transform maximal overlap MODWT lifting scheme second generation wavelets packet decomposition best basis search entropy-based complexity measure minimum description length Kolmogorov complexity algorithmic information theory Solomonoff induction universal prior Solomonoff prediction universal intelligence measure AIXI asymptotic convergence rate computable approximation truncation level resource bounded rationality bounded rationality satisficing heuristics availability representativeness anchoring adjustment framing effect loss aversion endowment effect status quo bias confirmation bias hindsight bias optimism bias planning fallacy sunk cost escalation commitment consistency reciprocity social proof authority liking scarcity liking contrast similarity contrast effect halo horn effect primacy recency serial position curve spacing effect testing effect generation effect desirable difficulties interleaving retrieval practice spaced repetition Leitner system SM-2 Anki SuperMemo forgetting curve Ebbinghaus Hermann power law practice learning curve experience curve Wright law Moore law Metcalfe law network effects critical mass tipping point adoption S-curve innovation diffusion Rogers Everett crossing chasm Moore Geoffrey early adopters innovators early majority late majority laggards lead users co-creation crowdsourcing open innovation platform ecosystem multi-sided market chicken egg problem bootstrapping network externalities positive negative feedback loop virtuous vicious cycle flywheel compounding returns compound interest rule doubling time Rule of 72 Albert Einstein allegedly misattributed quote about eighth wonder world power compounding interest bank savings account annual percentage yield APY effective annual rate nominal rate real rate inflation purchasing power parity exchange rate fixed floating peg crawling basket currency board dollarization euroization monetary union fiscal policy austerity stimulus quantitative easing tightening tapering tantrum forward guidance yield curve inversion steepening flattening parallel shift liquidity premium term premium credit spread default probability recovery rate rating agency Moody’s S&P Fitch DBRS Morningstar credit default swap total return swap interest rate swap currency swap swaption cap floor collar straddle strangle butterfly condor iron butterfly iron condor calendar spread vertical spread horizontal spread diagonal spread debit spread credit spread bull bear call put intrinsic extrinsic time value theta decay gamma vega rho delta sensitivity Greeks hedging delta neutral gamma scalping volatility smile skew kurtosis fat tails leptokurtic platykurtic mesokurtic normal Gaussian Cauchy Student t Laplace logistic exponential Weibull Pareto Lomax Burr Type XII generalized extreme value GEV generalized Pareto distribution GPD peaks-over-threshold POT method return level return period extreme value index tail index Hill estimator Pickands estimator moment estimator De Haan Ferreira estimator double bootstrap CI coverage exceedance probability design life annual exceedance probability AEP safety factor partial safety factor load resistance factor design LRFD allowable stress design ASD limit state ultimate serviceability fatigue buckling stability durability fire resistance seismic wind snow live dead thermal moisture chemical biological mechanical electrical acoustic vibration noise attenuation isolation damping natural frequency forced response resonance amplification factor quality factor Q damping ratio zeta critical damping overdamped underdamped critically damped transient steady-state step response impulse response transfer function state-space representation controllability observability Kalman decomposition pole-zero placement root locus Nyquist Bode Nichols chart gain margin phase margin bandwidth crossover frequency rise time settling time overshoot undershoot peak time delay time dead time transport lag first-order second-order higher-order system MIMO SISO decentralized control centralized hierarchical distributed consensus Byzantine fault tolerance Paxos Raft ZAB Chubby ZooKeeper etcd Consul leader election distributed transaction two-phase commit saga pattern eventual consistency strong consistency CAP theorem PACELC theorem BASE basically available soft state eventual consistency ACID atomicity consistency isolation durability MVCC snapshot isolation serializable repeatable read read committed dirty read non-repeatable read phantom read write skew lost update starvation livelock deadlock detection prevention wait-for graph detection algorithm wound-wait wait-die timestamp ordering optimistic concurrency pessimistic locking shared exclusive intent row table page record tuple column field key primary foreign composite unique non-null check default auto-increment identity sequence nextval currval lastval setval serial bigserial smallserial integer bigint smallint tinyint numeric decimal real double precision float char varchar text citext hstore json jsonb xml uuid macaddr inet cidr tsvector tsquery full-text search gin gist brin hash btree spgist GIN GiST BRIN SP-GiST page compression TOAST external storage inline storage null storage main storage extended storage compression ratio dictionary encoding run-length encoding delta encoding bit-packing variable-byte encoding frame-of-reference blocking transform bitmap index skip scan index-only scan heap fetch bitmap heap scan seq scan parallel seq scan parallel index scan parallel aggregate gather merge partition pruning partition-wise join partition-wise aggregate materialized view common table expression recursive CTE lateral join semi anti natural inner outer left right full cross union intersect except all distinct group by having order by asc desc nulls first nulls last limit offset fetch first rows only returning insert update delete truncate alter add drop modify rename constraint primary key foreign references unique check not null deferrable initially deferred immediate cascade restrict no action set null set default match full match partial match simple inherited partition 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fraction decimal percentage proportion ratio rate frequency count sum avg min max stddev variance covariance correlation coefficient pearson spearman kendall tau-biserial point-biserial phi chi-square cramers v contingency table mosaic plot correspondence analysis principal component PCA independent component ICA factor analysis exploratory confirmatory rotation varimax promax oblimin quartimax equamax parsimax geomin CF-EQUAL CF-VAR CF-QUARTIMAX CF-EQUAMAX CF-PARSIMAX target rotation procrustes congruence coefficient Tucker congruence coefficient coefficient of congruence factor score regression Bartlett Anderson Rubin ten Berge Thompson Thurstone centroid principal axes weighted least