[3] **viXra:1611.0352 [pdf]**
*submitted on 2016-11-26 05:11:34*

**Authors:** Robert Deloin

**Comments:** 16 Pages.

Collatz' conjecture (stated in 1937 by Collatz and also named Thwaites conjecture, or Syracuse, 3n+1 or oneness problem) can be described as follows:
Take any positive whole number N. If N is even, divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat this process to the result over
and over again. Collatz' conjecture is the supposition that for any positive integer N, the sequence will invariably reach the value 1.
The main contribution of this paper is to present a new approach to Collatz' conjecture. The key idea of this new approach is to clearly differentiate
the role of the division by two and the role of what we will name here the jump: a = 3n + 1.
With this approach, the proof of the conjecture is given as well as generalizations for jumps of the form qn + r and for jumps being polynomials
of degree m >1.

**Category:** Data Structures and Algorithms

[2] **viXra:1611.0328 [pdf]**
*submitted on 2016-11-24 06:35:11*

**Authors:** George Rajna

**Comments:** 22 Pages.

EPFL scientists have developed a new perovskite material with unique properties that can be used to build next-generation hard drives. [16] Scientists have fabricated a superlattice of single-atom magnets on graphene with a density of 115 terabits per square inch, suggesting that the configuration could lead to next-generation storage media. [15] Now a researcher and his team at Tyndall National Institute in Cork have made a 'quantum leap' by developing a technical step that could enable the use of quantum computers sooner than expected. [14] A method to produce significant amounts of semiconducting nanoparticles for light-emitting displays, sensors, solar panels and biomedical applications has gained momentum with a demonstration by researchers at the Department of Energy's Oak Ridge National Laboratory. [13] A source of single photons that meets three important criteria for use in quantum-information systems has been unveiled in China by an international team of physicists. Based on a quantum dot, the device is an efficient source of photons that emerge as solo particles that are indistinguishable from each other. The researchers are now trying to use the source to create a quantum computer based on "boson sampling". [11] With the help of a semiconductor quantum dot, physicists at the University of Basel have developed a new type of light source that emits single photons. For the first time, the researchers have managed to create a stream of identical photons. [10] Optical photons would be ideal carriers to transfer quantum information over large distances. Researchers envisage a network where information is processed in certain nodes and transferred between them via photons. [9] While physicists are continually looking for ways to unify the theory of relativity, which describes large-scale phenomena, with quantum theory, which describes small-scale phenomena, computer scientists are searching for technologies to build the quantum computer using Quantum Information. In August 2013, the achievement of "fully deterministic" quantum teleportation, using a hybrid technique, was reported. On 29 May 2014, scientists announced a reliable way of transferring data by quantum teleportation. Quantum teleportation of data had been done before but with highly unreliable methods. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to build the Quantum Computer with the help of Quantum Information.

**Category:** Data Structures and Algorithms

[1] **viXra:1611.0088 [pdf]**
*submitted on 2016-11-07 07:25:12*

**Authors:** George Rajna

**Comments:** 29 Pages.

Dynamic programming is a technique that can yield relatively efficient solutions to computational problems in economics, genomic analysis, and other fields. But adapting it to computer chips with multiple "cores," or processing units, requires a level of programming expertise that few economists and biologists have. [16] Researchers at Lancaster University's Data Science Institute have developed a software system that can for the first time rapidly self-assemble into the most efficient form without needing humans to tell it what to do. [15] Physicists have shown that quantum effects have the potential to significantly improve a variety of interactive learning tasks in machine learning. [14] A Chinese team of physicists have trained a quantum computer to recognise handwritten characters, the first demonstration of " quantum artificial intelligence ". Physicists have long claimed that quantum computers have the potential to dramatically outperform the most powerful conventional processors. The secret sauce at work here is the strange quantum phenomenon of superposition, where a quantum object can exist in two states at the same time. [13] One of biology's biggest mysteries-how a sliced up flatworm can regenerate into new organisms-has been solved independently by a computer. The discovery marks the first time that a computer has come up with a new scientific theory without direct human help. [12] A team of researchers working at the University of California (and one from Stony Brook University) has for the first time created a neural-network chip that was built using just memristors. In their paper published in the journal Nature, the team describes how they built their chip and what capabilities it has. [11] A team of researchers used a promising new material to build more functional memristors, bringing us closer to brain-like computing. Both academic and industrial laboratories are working to develop computers that operate more like the human brain. Instead of operating like a conventional, digital system, these new devices could potentially function more like a network of neurons. [10] Cambridge Quantum Computing Limited (CQCL) has built a new Fastest Operating System aimed at running the futuristic superfast quantum computers. [9] IBM scientists today unveiled two critical advances towards the realization of a practical quantum computer. For the first time, they showed the ability to detect and measure both kinds of quantum errors simultaneously, as well as demonstrated a new, square quantum bit circuit design that is the only physical architecture that could successfully scale to larger dimensions. [8] Physicists at the Universities of Bonn and Cambridge have succeeded in linking two completely different quantum systems to one another. In doing so, they have taken an important step forward on the way to a quantum computer. To accomplish their feat the researchers used a method that seems to function as well in the quantum world as it does for us people: teamwork. The results have now been published in the "Physical Review Letters". [7] While physicists are continually looking for ways to unify the theory of relativity, which describes large-scale phenomena, with quantum theory, which describes small-scale phenomena, computer scientists are searching for technologies to build the quantum computer. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to build the Quantum Computer.

**Category:** Data Structures and Algorithms