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
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
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
PATHINT and PATHTREE have been used to develop systems in neuroscience, financial markets and combat analysis, as reported in several papers at
These papers deal with discretization issues that have been addressed in several contexts, including theoretical physics as reported in several papers at
A related sub-project is to implement the N-dimensional code in PATHINT into PATHTREE.
See Lecture Plates: Quantum Variables in Finance and Neuroscience
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