Mathematics by Yehuda Roth
Defining a hierarchy of spaces, we herein propose a mathematical model to describe a learning pro... more Defining a hierarchy of spaces, we herein propose a mathematical model to describe a learning process based upon fundamental concepts uploaded to higher-rank areas so as to generate more advanced items. We implemented mathematical tools borrowed from quantum mechanics: linear algebraic spaces, the Fock space, and the quantum collapse theory.
Defining a hierarchy of spaces, we herein propose a mathematical model to describe a learning pro... more Defining a hierarchy of spaces, we herein propose a mathematical model to describe a learning process based upon fundamental concepts uploaded to higher-rank areas so as to generate more advanced items. We implemented mathematical tools borrowed from quantum mechanics: linear algebraic spaces, the Fock space, and the quantum collapse theory.
In this paper, we explore a chain of nano-rings connected by optical fibers (see ). When in an ex... more In this paper, we explore a chain of nano-rings connected by optical fibers (see ). When in an excited or a ground state, an electron in each ring dictates a welldefined QCA rule of its ability to absorb or emit a photon. In other words, QCA rules, which are spanned by quantum laws, are carried out by a random process of the creation or annihilation of photons. To test the ability of this system to carry information, it is compared to a reference system defined based on the maximal Shannon entropy. We find that, in contrast to the reference system, the ring system can define exclusive patterns such as separate trajectories. We explore the example of trajectory formation and its reference systems both analytically and numerically to find their Shannon entropy. By introducing a new phenomenological type of state, we suggest an approach for describing QCA systems similar to the one proposed in this study.
Quantum Implementation for Comparing Sets of Data
By simultaneously analyzing sets of data, we propose a quantum implementation for handling a larg... more By simultaneously analyzing sets of data, we propose a quantum implementation for handling a large amount of data. Our research may be useful in big data analysis. 1. Introduction Based on entangled states, quantum computers have the advantage of simultaneously implementing a large number of processes. The coherence of entanglement enables a single operator (logical gate) to be activated simultaneously on all of the states in the superposition [1, 2]. Consequently, to implement a quantum computer, a quantum algorithm has to be implemented. Quantum algorithms were first developed in the early-1990s, such as the Deutsch-Jozsa oracle-algorithm [3], which was followed by Ethan Bernstein and Umesh Vazirani's[4][5] algorithm. In Simon's algorithm,[6] the advantage of a quantum computer is demonstrated with an algorithm that is exponentially faster than any classical algorithm. Meanwhile, Shor's algorithm provides a polynomial complexity, whereas a classical algorithm usually take super-polynomial time (i.e. an algorithm not bounded above by any polynomial) [7]. Grover introduced a search engine algorithm with complexity O √ N that is more efficient then the classical algorithm, which is O (N/2) [8]. The main problem in all of this promising research is the implementation; that is, the ability to built a quantum computer in reasonable terms. In recent years, the digital world has grown very quickly and has become ever more complex. This complexity is associated with the term big data[9], which is a set of data that is so large that it cannot be effectively managed by conventional data management tools [10]. Although it seems that quantum computers are an ideal tool to serve these big data systems, quantum computers are still impracticable to implement. In this paper, we propose a different quantum approach that can simultaneously analyse a large amount of data. Although our process allows many processes to work simultaneously, it is not within the conventional frame of quantum computers.
We present a complete interpretation theory in the following sense: we observe that each measurin... more We present a complete interpretation theory in the following sense: we observe that each measuring device represents a concept set (such as the set of locations) while the measurement activity associates the measured object with an appropriate member from the concepts set. In that sense, the measurement process is the only interpretation of reality. In this article, we deal with the evolution of this interpreting measuring device for a 2-D Hilbert space. It is shown that nonlinear recursive maps give rise to a unique projective operator accompanied with the collapse ability and consequently to a measuring device. Our formalism can be easily interpreted as a single brain signal.
Papers by Yehuda Roth
Springer proceedings in mathematics & statistics, 2024
Heliyon, 2018
We introduce a nonlinear model that defines a complex system possessing diverse mediums shaped by... more We introduce a nonlinear model that defines a complex system possessing diverse mediums shaped by generating functions. Our model is implemented on systems with internal clocks.
Journal of physics, Sep 21, 2015
Coherence and interaction are important concepts in physics. While interaction describes a relati... more Coherence and interaction are important concepts in physics. While interaction describes a relation between individual objects such as forces acting between distinguishable particles, coherent objects exist with the sole purpose of describing a single object. For example, each component of a vector provides us with only partial information. The whole picture is revealed only when the components are coherently related to their generating vector. Another example is a singlet of two spin ½- particles. The true nature of these two coherent particles is described by a spin-less single particle. Apparently it seems that objects can be either coherent or lion-coherent but they cannot be both simultaneously. This is almost true. We show that a system can be described simultaneously as coherent and lion-coherent but an observer can distinguish only one concept at a time.
Quantum theory presents a unique scenario pertaining to collapse processes. A device that measure... more Quantum theory presents a unique scenario pertaining to collapse processes. A device that measures variables incompatible with those being detected collapses randomly into one of the states defined by the measuring device. The distinction that a collapsed output is not an accurate description of reality but rather a random selection from a set of values derived from the measuring device allows us to utilize the collapse process to propose a scheme wherein a machine becomes capable of performing interpreting processes. We present herein a basic schematic of a machine that demonstrates the principle of interpretation relying on the polarization phenomenon of photons. The operation of the device is demonstrated using an ambiguous figure. We believe that building an interpreting device can contribute to the field of AI.
Results in physics, Sep 1, 2019
Some natural phenomena can be measured directly, while others are recognized indirectly by clues.... more Some natural phenomena can be measured directly, while others are recognized indirectly by clues. In this study, we show that the classical laws of mechanics can be reformulated with entangled labeling-states that experience a collapse. As a result, we find indirect evidence of classical particles entangled as spin 1 2-fermions. Through a measurement procedure, these particles collapse to distinguished particles that obey the classical laws.
Frontiers in Computational Neuroscience, Jun 2, 2021
Each neuron in the central nervous system has many dendrites, which provide input information thr... more Each neuron in the central nervous system has many dendrites, which provide input information through impulses. Assuming that a neuron's decision to continue or stop firing is made by rules applied to the dendrites' inputs, we associate neuron activity with a quantum like-cellular automaton (QLCA) concepts. Following a previous study that related the CA description with entangled states, we provide a quantum-like description of neuron activity. After reviewing and presenting the entanglement concept expressed by QLCA terminology, we propose a model that relates quantum-like measurement to consciousness. Then, we present a toy model that reviews the QLCA theory, which is adapted to our terminology. The study also focuses on implementing QLCA formalism to describe a single neuron activity.
In our previous paper, we showed that the so-called quantum entanglement also exists in classical... more In our previous paper, we showed that the so-called quantum entanglement also exists in classical mechanics. The inability to measure this classical entanglement was rationalized with the definition of a classical observer which collapses all entanglement into distinguishable states. It was shown that evidence for this primary coherence is Newton's third law. However, in reformulating a "classical entanglement theory" we assumed the existence of Newton's second law as an operator form where a force operator was introduced through a Hilbert space of force states. In this paper, we derive all related physical quantities and laws from basic quantum principles. We not only define a force operator but also derive the classical mechanic's laws and prove the necessity of entanglement to obtain Newton's third law.
International Journal of Theoretical Physics, Jul 31, 2012
ABSTRACT Quantum measurement requires an observer to prepare a specific measuring device among al... more ABSTRACT Quantum measurement requires an observer to prepare a specific measuring device among alternatives where the prepared basis of states, representing the device, is the way the observer interprets quantum reality into his macroscopic word. We redefine that observer role through a new concept: The observer determination, that is, a selection between the measurement options facing the observer. Unlike the measurement itself that is rationalized as dictated by nature, the observer determination can neither be measured nor proven to be true or false. In this paper we propose a mathematical formalism demonstrating how to define the observer determination. Moreover, we present a scheme showing how the apparently subjective observer determination transform into a measurable quantity.
Journal of Modern Physics, 2013
We propose a new approach in dealing with image recognition. We suggest that recognizing an image... more We propose a new approach in dealing with image recognition. We suggest that recognizing an image is related to the knowledge of a pure quantum state. Since most images are screened through incoherent photons, we introduce a method base on non-linear mapping iterations to regenerate coherence between the image photons.
Results in physics, Mar 1, 2021
In this paper, we explore a chain of nano-rings connected by optical fibers (see Fig. 1). When in... more In this paper, we explore a chain of nano-rings connected by optical fibers (see Fig. 1). When in an excited or a ground state, an electron in each ring dictates a welldefined QCA rule of its ability to absorb or emit a photon. In other words, QCA rules, which are spanned by quantum laws, are carried out by a random process of the creation or annihilation of photons. To test the ability of this system to carry information, it is compared to a reference system defined based on the maximal Shannon entropy. We find that, in contrast to the reference system, the ring system can define exclusive patterns such as separate trajectories. We explore the example of trajectory formation and its reference systems both analytically and numerically to find their Shannon entropy. By introducing a new phenomenological type of state, we suggest an approach for describing QCA systems similar to the one proposed in this study.
Results in physics, 2017
We present four models for describing a 3-D vision. Similar to the mirror scenario, our models al... more We present four models for describing a 3-D vision. Similar to the mirror scenario, our models allow 3-D vision with no need for additional accessories such as stereoscopic glasses or a hologram film. These four models are based on brain interpretation rather than pure objective encryption. We consider the observer ''subjective" selection of a measuring device and the corresponding quantum collapse into one of his selected states, as a tool for interpreting reality in according to the observer concepts. This is the basic concept of our study and it is introduced in the first model. Other models suggests ''soften" versions that might be much easier to implement. Our quantum interpretation approach contribute to the following fields. In technology the proposed models can be implemented into real devices, allowing 3-D vision without additional accessories. Artificial intelligence: In the desire to create a machine that exchange information by using human terminologies, our interpretation approach seems to be appropriate.
Journal of Modern Physics, 2013
We introduce a new approach in dealing with pattern recognition issue. Recognizing a pattern is d... more We introduce a new approach in dealing with pattern recognition issue. Recognizing a pattern is definitely not the exploration of a new discovery but rather the search for already known patterns. In reading for example the same text written in a hand writing, letters can appear in different shapes. Still, the text decoding corresponds with interpreting the large variety of hand writings shapes with fonts. Quantum mechanics also offer a kind of interpretation tool. Although, with the superposition principle it is possible to compose an infinite number of states, yet, an observer by conducting a measurement reduces the number of observed states into the predetermined basis states. Not only that any state collapses into one of the basis states, quantum mechanics also possesses a kind of correction mechanism in a sense that if the measured state is "close enough" to one of the basis states, it will collapse with high probability into this predetermined state. Thus, we can consider the collapse mechanism as a reliable way for the observer to interpret reality into his frame of concepts. Both interpretation ideas, pattern recognition and quantum measurement are integrated in this paper to formulate a quantum pattern recognition measuring procedure.
Defining a hierarchy of spaces, we herein propose a mathematical model to describe a learning pro... more Defining a hierarchy of spaces, we herein propose a mathematical model to describe a learning process based upon fundamental concepts uploaded to higher-rank areas so as to generate more advanced items. We implemented mathematical tools borrowed from quantum mechanics: linear algebraic spaces, the Fock space, and the quantum collapse theory.
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Mathematics by Yehuda Roth
Papers by Yehuda Roth
Today, with the development of artificial intelligence, adding a process where a machine can perform its interpretation can advance this technology.
In this paper, we develop quantum-like algorithms to describe the interpretation process. Although our description is more of a mathematical proposal than a concrete quantum mechanics description, it allows the possibility of planning an actual quantum-based interpreting machine. At the process's core, there is a quantum measurement, where the result represents the event's final interpretation. The randomness accompanying this quantum measurement means that the result (an interpretation) is known only to the observer, who is defined as part of the interpreting machine and is not known to outside observers.
"classical entanglement theory" we assumed the existence of Newton’s second law as an operator form where a force operator was introduced through a Hilbert space of force states. In this paper, we derive all related physical quantities and laws from basic quantum principles. We not only define a force operator but also derive the classical mechanic's laws and prove the necessity of entanglement to obtain Newton’s third law.