Data Science: Time Complexity and Inferential Uncertainty (TCIU) Spacekime »

Authors

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 representation and analytical strategies to understand large and complex data. It utilizes information measures, entropy KL divergence, PDEs, Dirac’s bra-ket operators. This fundamentals of data science research project will explore time-complexity and inferential uncertainty in 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.

Mission and Objectives

Defining Characteristics of Big Datasets

Data science

Internet of Things (IoT)

Examples of Driving Motivational Challenges

Neuroimaging-genetics

Census-like Population Studies

4D Nucleome

Climate Change

High-dimensional Data

Scientific Inference and Forecasting

Problems of Time

Definition of Kime

The non-Euclidean kime manifold

Economic Forecasting via Spacekime Analytics

Wavefunctions

Dirac bra-ket notation

Operators

Commutator

Non-Trivial commutator (position/momentum)

Trivial commutator (energy/momentum)

Introduction

Anthropic principle

Minkowski spacetime

Events

Kaluza-Klein Theory

Kime, Kevents and the Spacekime Metric

Problems of Time

Kime-solutions to Time-problems

The Kime-Phase Problem

Common use of Time

Rate of change

Velocity

Newton’s equations of motion

Position (x) and Momentum (p)

Wavefunctions

Schrödinger equation

Wave equation

Lorentz transformation

Euler–Lagrange equation

Wheeler-DeWitt equation

Analogous Kime Extensions

Rate of change

Kime motion equations

Lorentz transformation in space-kime

General properties of the 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

Generalization of Heisenberg's Uncertainty Principle

5D spacekime manifold Waves and the Doppler effect

Wirtinger derivatives

The Copenhagen vs. Spacekime Interpretations

Kime Philosophy

Space-Kime Formalism

Antiparticle in space-kime

The causal structure of space-kime

Kime Applications in Data Science

Observables (Datasets)

Inference Function

Inner Product

Eigenspectra (Eigenvalues and Eigenfunctions)

Fundamental Law of Data Science Inference

Superposition Principle

Terminology

Spacetime IID vs. Spacekime Sampling

Uncertainty in Data Science

Quantum Mechanics Formulation

Statistics Formulation

Decision Science Formulation

Information Theoretic Formulation

Data Science Formulation

The authors are profoundly indebted to all of their mentors, advisors, and collaborators for inspiring the study, guiding the courses of their careers, nurturing their curiosity, and providing constructive and critical feedback. Among these scholars are Gencho Skordev (Sofia University), colleagues ar Burgas Technical University), Kenneth Kuttler (Michigan Tech University, De Witt L. Sumners and Fred Huffer (Florida State University), Jan de Leeuw, Nicolas Christou, and Michael Mega (UCLA), Arthur Toga (USC), Brian Athey, Kathleen Potempa, Janet Larson, Patricia Hurn, Gilbert Omenn, and Eric Michielssen (University of Michigan). Many other colleagues, students, researchers, and fellows have shared their expertise, creativity, valuable time, and critical assessment for generating, validating, and enhancing these open-science resources. Among these are Yufei Yang, Yuming Sun, Lingcong Xu, Simeone Marino, Yi Zhao, Nina Zhou, Alexandr Kalinin, Syed Husain, and many others. In addition, colleagues from the Statistics Online Computational Resource (SOCR) and the Michigan Institute for Data Science (MIDAS) provided encouragement and valuable suggestions. Special thanks to Yongkai Qiu, Yufei Yang, and Zhe Yin for their substantial efforts in developing, packaging, documenting, and validating the TCIU R source code.

The research and development reported in this book was partially supported by the US National Science Foundation (grants 1916425, 1734853, 1636840, 1416953, 0716055 and 1023115), US National Institutes of Health (grants P20 NR015331, U54 EB020406, P50 NS091856, P30 DK089503, R01CA233487, R01MH121079), the Burgas University “Prof. Dr. A. Zlatarov”, and the University of Michigan.


SOCR Resource Visitor number Dinov Email