Catgories of projects are

From Feb 2013 through Dec 2018, as Principal Investigator (PI) of several National Science Foundation (NSF.gov) Extreme Science and Engineering Discovery Environment (XSEDE) supercomputer-resource grants, I developed ideas published in several papers. For more information about XSEDE see https://www.xsede.org .

The grants used these resources for applications of computational physics, based on some projects related to those I have worked on previously.

Work performed under a project, "Electroencephalographic field influence on calcium momentum waves" utilized an initial grant spanning 20 Feb 2013 - 19 Aug 2014 passed peer review for a second research grant spanning 1 Jul 2014 - 30 Jun 2015. On 20 Nov 2014 a request to double the current resources passed another round of review and was granted. In June 2015 another Renewal Request passed peer review, extending this grant through June 2016.

The grant, "Quantum path-integral qPATHTREE and qPATHINT algorithms", through 30 Jun 2017 (extended through Dec 2017) shifted focus from computational neuroscience to broader contexts across computational physics, e.g., quantum financial options (more info below).

The paper below, https://www.ingber.com/path17_qpathint.pdf , was the core of a successful renewal grant for Jan-Dec 2018.

The 2016-2017 grant developed complex-number versions of PATHTREE and
PATHINT:

L. Ingber, C. Chen, R.P. Mondescu, D. Muzzall, and M. Renedo, "Probability tree
algorithm for general diffusion processes," Physical Review E 64 (5),
056702-056707 (2001). https://www.ingber.com/path01_pathtree.pdf

L. Ingber, "High-resolution path-integral development of financial options,"
Physica A 283 (3-4), 529-558 (2000). https://www.ingber.com/markets00_highres.pdf

Several other papers in my archive have used these codes.

A paper has shown the strengths and weaknesses of qPATHTREE and qPATHINT:

L. Ingber, "Path-integral quantum PATHTREE and PATHINT algorithms,"
International Journal of Innovative Research in Information Security 3 (5),
1-15 (2016). https://www.ingber.com/path16_quantum_path.pdf

Since this 2016 paper, qPATHINT has been properly baselined to PATHINT using
the same input and stochastic models, and applied to neuroscience and finance
problems:

L. Ingber, "Evolution of regenerative Ca-ion wave-packet in neuronal-firing
fields: Quantum path-integral with serial shocks," International Journal of
Innovative Research in Information Security 4 (2), 14-22 (2017). [ URL https://www.ingber.com/path17_quantum_pathint_shocks.pdf
]

L. Ingber, ``Options on quantum money: Quantum path-integral with serial
shocks,'' International Journal of Innovative Research in Information Security
4 (2), 7-13 (2017). [ URL https://www.ingber.com/path17_quantum_options_shocks.pdf
]

L. Ingber, "Quantum Path-Integral qPATHINT Algorithm," The Open Cybernetics
Systemics Journal 11, 3-18 (2017). [ URL https://www.ingber.com/path17_qpathint.pdf
]

qPATHTREE and qPATHTREE will provide researchers in several disciplines, in contexts utilizing path-integrals in many applied physics contexts, including problems in physics, neuroscience and blockchain derivatives, with a new fast numerical C-coded algorithm to perform path integrals of complex-number systems using the standard GCC compiler.

PATHTREE and PATHINT already have provided such algorithms for real-number
systems in several projects detailed at

https://www.ingber.com/#PATH-INTEGRAL
.

PATHINT and PATHTREE have been used to develop systems in neuroscience,
financial markets and combat analysis, as reported in several papers at

https://www.ingber.com/#NEOCORTEX

https://www.ingber.com/#MARKETS

https://www.ingber.com/#COMBAT
.

These papers deal with discretization issues that have been addressed in
several contexts, including theoretical physics as reported in several papers
at

https://www.ingber.com/#NUCLEAR
.

A related sub-project is to implement the N-dimensional code in PATHINT into PATHTREE.

See Lecture Plates: Quantum Variables in Finance and Neuroscience

https://l.ingber.com/lect2108

This project calculates synchronous quantum systems and macroscopic systems with well-defined interactions.

This project was mapped out in several publications, recently in L. Ingber, ``Quantum calcium-ion interactions with EEG,'' Sci 1 (7), 1-21 (2018). [ URL https://www.ingber.com/smni18_quantumCaEEG.pdf and https://doi.org/10.3390/sci1010020 ] which was performed with the help of XSEDE.org supercomputer resources from Feb 2013 through Dec 2018. The Abstract is given below, and that Conclusion is the starting point of this project.

This project would use quantum computing in one or both contexts:

(a) to perform the optimization of the cost/objective function over the space
of parameters defined by the SMNI model with EEG data as input.

(b) to propagate the Ca2+ wave function between EEG epochs in lock-step with
the changing magnetic vector potential defined by highly synchronous neuronal
firings.

Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options.

In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach.

Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales.

The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models.

This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

Thanks.

Lester Ingber

[email protected]

Lester

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