Ivo D. Dinov | Milen V. Velev | Contact us |
---|
Review the basics of ODEs/PDEs, the Kaluza-Klein Theory, and the DSPA materials.
Outline:
The SOCR Data Science Fundamentals project explores
new theoretical representations and analytical strategies to
understand large and complex data. It utilizes information
measures, entropy, KL divergence, PDEs, and Dirac’s bra-ket operators.
This fundamentals of data science research project employs
time-complexity and inferential uncertainty for representation, modeling, analysis
and interpretation of large, heterogeneous, multi-source,
multi-scale, incomplete, incongruent, and longitudinal data.
See
The Enigmatic Kime: Time Complexity in Data Science Video, a recording
at the University of Michigan Institute for Data Science (MIDAS)
Seminar Series,
a PDF Slidedeck is available here.
Additional Spacekime talks/presentations are available on the SOCR News page, the Spacekime community site includes a blog, and Spacekime.org website provides more context.
Mission and Objectives
Internet of Things (IoT)
Defining Characteristics of Big Datasets
High-dimensional Data
Scientific Inference and Forecasting
Data science
Artificial Intelligence
Examples of Driving Motivational Challenges
Neuroimaging-genetics
Census-like Population Studies
4D Nucleome
Climate Change
Problems of Time
Definition of Kime and Kime-phases Circular distribution plots
Dirac bra-ket notation
Operators
Commutator
Non-Trivial commutator (position/momentum)
Trivial commutator (energy/momentum)
Wavefunctions and the Fourier Transformation
Fourier Amplitudes and Phases
Phase Equivalence
Amplitude Equivalence
Effects of the Fourier Transform on Phases and Magnitudes
Minkowski spacetime
Events
Coordinate Transformations, Covariance, Contravariance, and Invariance
Kime, Kevents and the Spacekime Metric
Some Problems of Time
Kime-solutions to Time-problems
Common use of Time
Rate of change
Velocity
Newton’s equations of motion
Position (x) and Momentum (p)
Wavefunctions
Schrödinger equation
Lorentz transformation
Euler–Lagrange equation
Wheeler-DeWitt equation
Analogous Kime Extensions
Rate of change
Kime motion equations
Lorentz transformation in spacekime
Properties of the general spacekime transformations
Backwards motion in the two-dimensional kime
Rotations in kime and space hyperplanes
Velocity-addition law
Generalization of the principle of invariance of the speed of light
Heisenberg's Uncertainty Principle
5D spacekime manifold Waves and the Doppler effect
Kime calculus of differentiation and integration
The Copenhagen vs. Spacekime Interpretations
Space-Kime Formalism
Antiparticle in spacekime
The causal structure of spacekime
Reproducing Kernel Hilbert Spaces (RKHS) and Temporal Distribution Dynamics (TDD)
Radon-Nikodym Derivatives, Kimemeasures, and Kime Operator
Kime Applications in Data Science
Kime Philosophy
General Formulation of fMRI inference
Likelihood based inference
Magnitude-only fMRI intensity inference
Complex-valued fMRI time-series inference
Complex-valued Kime-indexed fMRI kintensity inference
Interactive kime-surface parametric plot
Kime-series/kime-surfaces reconstruction, visualization, and predictive analytics
Synergies between the Laplace Transform and Meijer-G Functions
Observables (Datasets)
Inference Function
Inner Product
Eigenspectra (Eigenvalues and Eigenfunctions)
Uncertainty in 5D Spacekime
Fundamental Law of Data Science Inference
Superposition Principle
Terminology
Spacetime IID vs. Spacekime Sampling
Bayesian Formulation of Spacekime Analytics
Uncertainty in Data Science
Quantum Mechanics Formulation
Statistics Formulation
Decision Science Formulation
Information Theoretic Formulation
Data Science Formulation
Kime-Phases Circular distribution plots
Exogenous Feature Time-series analysis
Structured Big Data Analytics Case-Study (UKBB)
Spacekime Analytics of Financial Market and Economics Data and 3D Scene of the longitudinal EU Econometrics Indicators