Mathematical Symmetry Research Articles

Hidden dual mathematical symmetry in the genetic code

We describe the genetic code in terms of numbers that help us to find several dual symmetries. Our formulation can even be rewritten regarding the up-down and right-left dual concepts. We argue that our work may bring many topological tools to studying the DNA molecule, including the Grassmann-Plücker coordinates, which are important in mathematical and physical contexts.

Internally Disclosed Sets of a Real Space

There is no single set in a real space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which a real number axis is defined at the new level, namely, at the level of real space allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of a real space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.

Mathematical Symmetry and Psychological Benefits of the Hare Krishna Mantra: A Comprehensive Analysis

Mathematical Symmetry and Psychological Benefits of the Hare Krishna Mantra: A Comprehensive Analysis

The intersections of indigenous religion, Christianity, and Islam in mathematical symmetry

Pupils have always presented their mathematical thought through their religions. However, teachers gloss over these relationships. In this study, I explored the philosophy behind religious intersections among Indigenous, Christian, and Islamic pupils interacting in one class. Standing on narrative phenomenological design, mathematics representations, practices, and applications were the three congruences developed by the principle of saturation from the pupils’ lived experiences. I also formed focus group discussions that comprised a class of 40 pupils. I made 10 groups, and each group was composed of 10 participants that cut across the three religions. The responses were recorded, transcribed, coded, and analyzed. The results showed that the three religions shared many similar mathematical thoughts. However, one, three, four, five, and ten featured more than the other numbers. This implies that the philosophy of religious values in mathematical practice must anchor on the three objects permeating all three major religions.Pupils have always presented their mathematical thought through their religions. However, teachers gloss over these relationships. In this study, I explored the philosophy behind religious intersections among Indigenous, Christian, and Islamic pupils interacting in one class. Standing on narrative phenomenological design, mathematics representations, practices, and applications were the three congruences developed by the principle of saturation from the pupils’ lived experiences. I also formed focus group discussions that comprised a class of 40 pupils. I made 10 groups, and each group was composed of 10 participants that cut across the three religions. The responses were recorded, transcribed, coded, and analyzed. The results showed that the three religions shared many similar mathematical thoughts. However, one, three, four, five, and ten featured more than the other numbers. This implies that the philosophy of religious values in mathematical practice must anchor on the three objects permeating all three major religions.

Пифагорейский аргумент разумного замысла вселенной и его критика. Статья 2: Пифагорейская стратегия физики

Since the time of Galileo and Newton, physics has been engineered as a mathematical discipline, seeking its axioms, laws of nature, by means of specially organized experiments. The motivation of specifi cally this mode of cognizing nature was explored in the fi rst paper of this series, in which Christian Platonism and the Pythagorean crede of the founding fathers of modernity’s physics were discussed. The present article aims to lay out the cognitive strategy of physics as revealed by refl ecting upon its seminal discoveries. One central inquiry concerning physics is how exactly it has mined its axioms. Merely pointing to experimentation is insuffi cient. Experiments are conceived and executed as verifi cation of an already-formulated hypothesis, without which it would be indeterminate what should be observed and what there is to do with those observations. A hypothesis for a law is not derived from an experiment; on the contrary, it defi nes the experiment in order to be rigorously scrutinized by it. The objective of this article is to demonstrate on facts that the strategy for hypothesizing physical laws has invariably emanated from the same wellspring as the originating metaphysical credo. This Pythagorean strategy is founded on the belief in mathematical elegance, high precision, and the universality of the sought-after axioms of matter. The quest for hypotheses went along the pathways of universal mathematical symmetries, equivalencies, invariances, correspondences, and analogies–complex enough to account for a plethora of relevant phenomena, yet simple enough to facilitate scientifi c discovery. We are not the fi rst to propound this Pythagorean understanding of physics. This concept, as well as the term ‘Pythagorean strategy,’ was a quarter-century ago formulated and developed by the American-Israeli philosopher Mark Steiner (1942–2020) in his monograph, “The Applicability of Mathematics as a Philosophical Problem.” The present article serves as a free contemplation in the footsteps of that brilliant and still largely unparalleled tome.

Fully Regular Sets of an Imaginary Space

There is no single set in an imaginary space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which appears an imaginary number axis strictly defifined at the level of imaginary space, allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of an imaginary space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.

The second law of infodynamics and its implications for the simulated universe hypothesis

The simulation hypothesis is a philosophical theory, in which the entire universe and our objective reality are just simulated constructs. Despite the lack of evidence, this idea is gaining traction in scientific circles as well as in the entertainment industry. Recent scientific developments in the field of information physics, such as the publication of the mass-energy-information equivalence principle, appear to support this possibility. In particular, the 2022 discovery of the second law of information dynamics (infodynamics) facilitates new and interesting research tools at the intersection between physics and information. In this article, we re-examine the second law of infodynamics and its applicability to digital information, genetic information, atomic physics, mathematical symmetries, and cosmology, and we provide scientific evidence that appears to underpin the simulated universe hypothesis.

Математика и физическая реальность: тема отсутствия «трансцендентального означаемого» в языке современной фундаментальной науки

Introduction. It is argued that today the expansion of mathematics into the field of physical reality is not being performed in line with the classical paradigm, but in line with the linguistic turn of non-classical philosophy. Theoretical analysis. Such aspect of nature’s “non-fittability” into the conceptual network of mathematics as the problem of asymmetry is explored. It is stated that the world, constructed according to the logic of ideal mathematical symmetries, passes into a state called unmanifested in Hinduism. In the same direction the concept of J. Baudrillard is considered, where the structures of ideal reversibility are supposed to be the most radical way to destroy what exists and the symbol of nothingness. Accordingly, ideal mathematical symmetry describes states that cannot exist as a physical reality. The settlement of “dense” reality in the mathematical language of theoretical physics is seen in irrational, transcendent and imaginary numbers, in which the ideal reversibility of mathematical operations is violated. Conclusion. The search for “supersymmetry” is regarded as a variation of general language problems. Ideal symmetry in mathematics, “supersymmetry” in fundamental physics, like any “transcendental signified”, can only exist “under the sign of strikeout”. Variations on the theme of differance are revealed here. A generating source of difference, according to J. Derrida, is always on the other side of the language.

ETHNOMATHEMATICS OF 100-PILLARS LIMAS HOUSE AND ITS INTEGRATION IN MATHEMATICS LEARNING FOR JUNIOR HIGH SCHOOL

The purpose of this study is to explore ethnomathematicss elements in 100-Pillars Limas House and integrate it into mathematic learning. This research use ethnographic approach. The data are collected through interviews, observation, documentation, and test. The data obtained from observations and interviews are carried out by data analysis with the stages of data reduction, data display and verification. While the data obtained from the test will be analyzed by accumulating the test results of students who reach the KKM and then looking at the completeness of student learning outcomes. The results of this study indicate that: (1) there are several mathematical concepts, namely geometry and symmetry used in the construction of the 100-pillars Limas house structure and the philosophy that underlies each of the parts contained in the house. 2) its integration in learning mathematics is conducted to contextualize abstract mathematical objects so that the student will be easier to understanding mathematical concepts while introducing cultural elements to students. The learning outcomes of students after implementing ethnomathematicss-based learning shows that there are 88% of students who finished the integration of ethnomathematicss into mathematic learning in effective category.

Symmetry and Symmetry Breaking in Science and Arts

In this review article, symmetry and symmetry breaking are considered as complementary principles in science and arts. It starts with symmetry and symmetry breaking in early world views of nature and art. Then, symmetries are definied as fundamental structures of mathematics. Mathematical models of symmetry and symmetry breaking are used to explain the emergence of space-time and matter in modern physics. Even molecular structures in chemistry are distinguished by mathematical symmetries. Their elegance and beauty seem to realize aesthetical categories in nature. In biological evolution, the question arises how symmetry breaking (e.g. molcular chirality) can be explained. In modern arts, symmetry and symmetry breaking are „hidden“ structures which can be found in music, painting, and architecture. In a philosophical outlook, symmetry and symmetry breaking are highlighted as regulative guiding ideas of research.

Symmetry and symmetry breaking in science and arts

In this review article, symmetry and symmetry breaking are considered as complementary principles in science and arts. It starts with symmetry and symmetry breaking in early world views of nature and art. Then, symmetries are definied as fundamental structures of mathematics. Mathematical models of symmetry and symmetry breaking are used to explain the emergence of space-time and matter in modern physics. Even molecular structures in chemistry are distinguished by mathematical symmetries. Their elegance and beauty seem to realize aesthetical categories in nature. In biological evolution, the question arises how symmetry breaking (e.g. molcular chirality) can be explained. In modern arts, symmetry and symmetry breaking are "hidden" structures which can be found in music, painting, and architecture. In a philosophical outlook, symmetry and symmetry breaking are highlighted as regulative guiding ideas of research. _______________________________________________________________________________________________________________________________________________________ This article is an extended version and English translation of my article "Symmetrie und Symmetriebrechung. Von der Urmaterie zu Kunst und Leben,“ in: Schriftenreihe der Heisenberg-Gesellschaft: Quanten 2 (ed. Konrad Kleinknecht), S. Hirzel Verlag, 9-59. An abridged version was presented in the EASA Colloquium Science meets Art (https://www.youtube.com/watch?v=nIUVNEQ7AR8 )

Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics

One of the key tools in an organization’s performance management is the goal tree, which is used for solving both direct and inverse problems. This research deals with goal setting based on a model of the future by presenting the goal and subgoal in the form of concrete quantitative and qualitative characteristics and stepwise formation of factors. A stepwise solution to a factor generation problem is considered on the basis of mathematical symmetry. This paper displays an algorithm for solving hierarchical inverse problems with constraints, which is based on recursively traversing the vertices that constitute the separate characteristics. Iterative methods, modified for the case of nonlinear models and the calculation of constraints, were used to generate solutions to the subproblems. To realize the algorithm, the object-oriented architecture, which simplifies the creation and modification of software, was elaborated. Computational experiments with five types of models were conducted, and the solution to a problem related to fast-food restaurant profit generation was reviewed. The metrics of remoteness from set values and t-statistics were calculated for the purpose of testing the received results, and solutions to the subproblems, with the help of a mathematical package using optimization models and a method of inverse calculations, were also provided. The results of computational experiments speak to the compliance of the received results with set constraints and the solution of separate subproblems with the usage of the mathematical package. The cases with the highest solution accuracy reached are specified.

Editorial of Special Issue “Application of Mathematical Modelling and Symmetry in Neuroscience”

The first article is “Spectral Clustering Reveals Different Profiles of Central Sensitization in Women with Carpal Tunnel Syndrome (CTS)” [...]

The relationship between Education area, Architecture and Environment

Human needs to be protected from nature and shelter in natural space conditions. Therefore, people need an environment to sustain their lives. Environment; It is divided into two as natural and artificial. The natural environment is the environment in which people and other creatures maintain their relationships and interact with each other. What is done by people who do not form spontaneously is called Artificial Environment. An art branch that designs civil structures to meet people's housing needs is called architecture. But not every design is architecture. In order for a building to be accepted as an architectural product, it is essential to apply the mathematical symmetry called golden ratio throughout the building. The aim of this research is to find the effects of environmental arrangements on the aesthetic, emotional and behavioral outputs of individuals in educational spaces. The importance of this aim is to find the relationship between environment, architecture and education. As a result of the survey conducted in the findings, which locations are liked most are presented in the data analysis. The questionnaire was asked 5 different photographs of the participants in 3 different question titles. As a result of the percentages taken, the participants mostly chose places that are intertwined with nature.
 Keywords: Education, environment, architecture, nature.

Fast Treetops Counting Using Mathematical Image Symmetry, Segmentation, and Fast k-Means Classification Algorithms

Forests are important because they contribute to biodiversity, regulation of carbon dioxide, protection of hydrographic basins, wood production. This article presents a methodology for fast and effective counting of treetops using the mathematical symmetry of the grayscale image. For the treetop counting, the unsupervised k-means classification Algorithm was used with two groups or centroids: treetop and not-treetop. By using these groups and the mathematical symmetry of the image, a fast k-means classification Algorithm is generated. To solve the problem of treetop overlapping and perform a more accurate counting, the watershed Algorithm was used. This methodology has a mean treetop count accuracy of 98.3% with a confidence level of 99% in the interval (97.31, 99.7). Aerial images of the coniferous forest of Alcudia, Mallorca, Spain were used. Forests attenuate climatic changes originated by global warming. Drastic climatic changes cause catastrophes to humanity. This research would help the automatic, massive and recurring counting of treetops with the aim of obtaining forest inventories in order to take care of forests.

Symmetries in Dynamic Models of Biological Systems: Mathematical Foundations and Implications

Symmetries are ubiquitous in nature. Almost all organisms have some kind of “symmetry”, meaning that their shape does not change under some geometric transformation. This geometrical concept of symmetry is intuitive and easy to recognize. On the other hand, the behavior of many biological systems over time can be described with ordinary differential equations. These dynamic models may also possess “symmetries”, meaning that the time courses of some variables remain invariant under certain transformations. Unlike the previously mentioned symmetries, the ones present in dynamic models are not geometric, but infinitesimal transformations. These mathematical symmetries can be related to certain features of the system’s dynamic behavior, such as robustness or adaptation capabilities. However, they can also arise from questionable modeling choices, which may lead to non-identifiability and non-observability. This paper provides an overview of the types of symmetries that appear in dynamic models, the mathematical tools available for their analyses, the ways in which they are related to system properties, and the implications for biological modeling.

Visual Features and Their Own Optical Flow.

Symmetries, invariances and conservation equations have always been an invaluable guide in Science to model natural phenomena through simple yet effective relations. For instance, in computer vision, translation equivariance is typically a built-in property of neural architectures that are used to solve visual tasks; networks with computational layers implementing such a property are known as Convolutional Neural Networks (CNNs). This kind of mathematical symmetry, as well as many others that have been recently studied, are typically generated by some underlying group of transformations (translations in the case of CNNs, rotations, etc.) and are particularly suitable to process highly structured data such as molecules or chemical compounds which are known to possess those specific symmetries. When dealing with video streams, common built-in equivariances are able to handle only a small fraction of the broad spectrum of transformations encoded in the visual stimulus and, therefore, the corresponding neural architectures have to resort to a huge amount of supervision in order to achieve good generalization capabilities. In the paper we formulate a theory on the development of visual features that is based on the idea that movement itself provides trajectories on which to impose consistency. We introduce the principle of Material Point Invariance which states that each visual feature is invariant with respect to the associated optical flow, so that features and corresponding velocities are an indissoluble pair. Then, we discuss the interaction of features and velocities and show that certain motion invariance traits could be regarded as a generalization of the classical concept of affordance. These analyses of feature-velocity interactions and their invariance properties leads to a visual field theory which expresses the dynamical constraints of motion coherence and might lead to discover the joint evolution of the visual features along with the associated optical flows.

Data transfer in the mathematical broken symmetry group model

The article shows a mathematical description of data transfer using a directed graph, as well as an algorithm for data transport in a network based on the multiplication tables of substitutions – elements of the broken symmetry group. It was analyzed how many steps are necessary when data transmission in systems with alternate sending of data packets. Using multiplication tables of substitutions the possibility of calculating the graph trees with nested nodes was demonstrated, including PQ-trees. The article provides examples of models for collecting information in two main network nodes, as well as networks with a more complex topology, for example the tree with its “rootstock”.

One-particle and two-particle visibilities in bipartite entangled Gaussian states

Complementarity between one- and two-particle visibility in discrete systems can be extended to bipartite quantum-entangled Gaussian states. The meaning of the two-particle visibility originally defined by Jaeger, Horne, Shimony, and Vaidman with the use of an indirect method that first corrects the two-particle probability distribution by adding and subtracting other distributions with varying degree of entanglement, however, deserves further analysis. Furthermore, the origin of complementarity between one-particle visibility and two-particle visibility is somewhat elusive and it is not entirely clear what is the best way to associate particular two-particle quantum observables with the two-particle visibility. Here, we develop a direct method for quantifying the two-particle visibility based on measurement of a pair of two-particle observables that are compatible with the measured pair of single-particle observables. For each of the two-particle observables the corresponding visibility is computed, after which the absolute difference of the latter pair of visibilities is considered as a redefinition of the two-particle visibility. Our approach reveals a mathematical symmetry as it treats the two pairs of one-particle or two-particle observables on equal footing by formally identifying all four observable distributions as rotated marginal distributions of the original two-particle probability distribution. The complementarity relation between one-particle visibility and two-particle visibility obtained with the direct method is exact in the limit of infinite Gaussian precision where the entangled Gaussian state approaches an ideal EPR state. The presented results demonstrate the theoretical utility of rotated marginal distributions for elucidating the nature of two-particle visibility and provide tools for the development of quantum applications employing continuous variables.

Improving FM Radar Dynamic Range Using Target Phase Noise Cancellation

A method for improving the dynamic range of frequency-modulated continuous-wave (FMCW) radar systems is presented. Bright echo signals detected with FMCW radars can carry strong phase noise sidelobes, especially for radars at W-band and higher frequencies where extremely quiet local oscillators do not exist or are not practical. These sidelobes can hide targets that would otherwise be detectable by the radar. Owing to the mathematical symmetry of phase noise with respect to a dominant carrier tone, the phase noise on the negative-frequency side of a bright echo can be used in post-processing to coherently cancel the corresponding phase noise on the positive-frequency side, revealing the presence of any weak target on the positive-frequency side. We show experimentally how this procedure improves the dynamic range of an airborne 167 GHz cloud radar by up to 18 dB, albeit with a detection sensitivity penalty of about 3 dB.