[4] **viXra:1809.0601 [pdf]**
*submitted on 2018-09-30 07:15:47*

**Authors:** Yuly Shipilevsky

**Comments:** 6 Pages.

We introduce and suggest to research a special class of optimization problems,
wherein an objective function is a real-valued complex variables function
and constraints comprising complex-valued complex variables functions.

**Category:** Data Structures and Algorithms

[3] **viXra:1809.0324 [pdf]**
*submitted on 2018-09-15 08:18:55*

**Authors:** George Rajna

**Comments:** 46 Pages.

Workflow management systems allow users to prepare, produce and analyze scientific processes to help simplify complex simulations. [27] Now, a team of A*STAR researchers and colleagues has developed a detector that can successfully pick out where human actions will occur in videos, in almost real-time. [26] A team of researchers affiliated with several institutions in Germany and the U.S. has developed a deep learning algorithm that can be used for motion capture of animals of any kind. [25] In 2016, when we inaugurated our new IBM Research lab in Johannesburg, we took on this challenge and are reporting our first promising results at Health Day at the KDD Data Science Conference in London this month. [24] The research group took advantage of a system at SLAC's Stanford Synchrotron Radiation Lightsource (SSRL) that combines machine learning—a form of artificial intelligence where computer algorithms glean knowledge from enormous amounts of data—with experiments that quickly make and screen hundreds of sample materials at a time. [23] Researchers at the UCLA Samueli School of Engineering have demonstrated that deep learning, a powerful form of artificial intelligence, can discern and enhance microscopic details in photos taken by smartphones. [22] Such are the big questions behind one of the new projects underway at the MIT-IBM Watson AI Laboratory, a collaboration for research on the frontiers of artificial intelligence. [21] The possibility of cognitive nuclear-spin processing came to Fisher in part through studies performed in the 1980s that reported a remarkable lithium isotope dependence on the behavior of mother rats. [20] And as will be presented today at the 25th annual meeting of the Cognitive Neuroscience Society (CNS), cognitive neuroscientists increasingly are using those emerging artificial networks to enhance their understanding of one of the most elusive intelligence systems, the human brain. [19] U.S. Army Research Laboratory scientists have discovered a way to leverage emerging brain-like computer architectures for an age-old number-theoretic problem known as integer factorization. [18]

**Category:** Data Structures and Algorithms

[2] **viXra:1809.0204 [pdf]**
*submitted on 2018-09-10 17:59:12*

**Authors:** Yuly Shipilevsky

**Comments:** 20 Pages.

We develop two different polynomial-time integer factorization algorithms.
We reduce integer factorization problem to equivalent problem of minimizing
a quadratic polynomial with integer coefficients over the integer points
in a quadratically constrained two-dimensional region.
Next, we reduce those minimization problem to the polynomial-time minimizing
a quadratic polynomial with integer coefficients over the integer
points in a special two-dimensional rational polyhedron.
Next, we reduce integer factorization problem to the problem of enumeration
of vertices of integer hull of a special two-dimensional rational polyhedron,
solvable in time polynomial by Hartmann's algorithm.
Finally, as we show that there exists an NP-hard minimization problem,
equivalent to the original minimization problem, we conclude that P = NP.

**Category:** Data Structures and Algorithms

[1] **viXra:1809.0070 [pdf]**
*submitted on 2018-09-05 07:47:16*

**Authors:** Shravan Mohan

**Comments:** 10 Pages.

This preliminary note presents a heuristic for determining rank constrained solutions to
linear matrix equations (LME). The method proposed here is based on minimizing a non-
convex quadratic functional, which will hence-forth be termed as the Low-Rank-Functional
(LRF). Although this method lacks a formal proof/comprehensive analysis, for example in
terms of a probabilistic guarantee for converging to a solution, the proposed idea is intuitive
and has been seen to perform well in simulations. To that end, many numerical examples are
provided to corroborate the idea.

**Category:** Data Structures and Algorithms