General Transformation Research Articles

Reconfigurable unitary transformations of optical beam arrays

Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However, until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85 ± 0.03. This high-fidelity suggests that MPLCs are a useful tool for implementing the unitary transformations that comprise quantum and classical information processing.

Quaternion and Biquaternion Representations of Proper and Improper Transformations in Non-Cartesian Reference Systems

Quaternion and biquaternion symmetry transformations have been applied to non-Cartesian reference systems of direct and reciprocal crystal lattices. The transformations performed directly in the sets of crystal reference axes simplify the calculations, eliminate the need for orthogonalization, permit the use of crystallographic vectors for defining the directions of rotations and perform the computations directly in the crystal coordinates. The applications of the general quaternion transformations are envisioned for physical, chemical, crystallographic and engineering applications. The general quaternion multiplication rules for any symmetry-unrestricted lattices have been derived for the triclinic crystallographic system and have been applied to the biquaternion representations of all point-group symmetry elements, including the crystallographic hexagonal system. Cayley multiplication matrices for point-groups, based on the biquaternion symbols of proper and improper symmetry elements, have been exemplified.

Flow of temporal network properties under local aggregation and time shuffling: a tool for characterizing, comparing and classifying temporal networks

Abstract Although many tools have been developed and employed to characterize temporal networks (TNs), the issue of how to compare them remains largely open. It depends indeed on what features are considered as relevant, and on the way the differences in these features are quantified. In this paper, we propose to characterize TNs through their behavior under general transformations that are local in time: (i) a local time shuffling, which destroys correlations at time scales smaller than a given scale b, while preserving large time scales, and (ii) a local temporal aggregation on time windows of length n. By varying b and n, we obtain a flow of TNs, and flows of observable values, which encode the phenomenology of the TN on multiple time scales. We use a symbolic approach to summarize these flows into labels (strings of characters) describing their trends. These labels can then be used to compare TNs, validate models, or identify groups of networks with similar labels. Our procedure can be applied to any TN and with an arbitrary set of observables, and we illustrate it on an ensemble of data sets describing face-to-face interactions in various contexts, including both empirical and synthetic data.

Families of exact similaritons with flexible modulations in N-coupled homogeneous and inhomogeneous systems

In this paper, a family of exact solutions to N-coupled nonlinear Schrödinger (N-CNLS) equations including bright and dark solitons, Akhmediev breathers, Kuznetsov-Ma breathers, and rogue waves are derived with the aid of a generic nonlinear wave assumption. As an application of the solutions, we present a scheme to realize amplitude coding in an identical waveguide system. Furthermore, by a general self-similar transformation method, exact controllable similaritons of N-coupled inhomogeneous NLS (N-CINLS) equations are constructed under relaxed compatibility conditions. Flexible modulations of similaritons are investigated in a typical inhomogeneous system. Based on the general self-similar transformation, we further study various and novel modulations of composite similariton of 2-CINLS regimes. The various similaritons presented here may be expected to find application in the control and transmission of nonlinear waves in realizable complex systems including those based on optical fibers and Bose-Einstein condensates.

General Double-sided Orthogonal Split Quadratic Phase Clifford-Fourier Transform

General Double-sided Orthogonal Split Quadratic Phase Clifford-Fourier Transform

A universal application of the general integral transform: New technique for the analysis of nonlinear oscillator systems

The wide applicability of a nonlinear oscillator is the main reason why it has gained so much attention from mathematicians and scientists, while it is difficult to be solved both numerically and theoretically. Variational iteration method is one of the numerical approaches which are used to investigate these nonlinear systems. In this paper, we present a nonlinear oscillator arising in a micro-electromechanical system as an example and derive its analytical solution by He’s frequency formula method and variational iteration method coupled with a new general integral transformation. The Lagrange multiplier is formulated and the new iterative format for the correction functional of the variational iteration method is given by the general integral transformation. The approximate nonlinear frequencies are achieved by this new technique and compared with the numerical ones obtained by the Runge–Kutta method. The new general integral transformation has the same essential qualities as those for Laplace and Fourier transform, and it becomes a promising tool to nonlinear problems when coupled with the variational iteration method.

Deprotective Lossen rearrangement: a direct and general transformation of Nms-amides to unsymmetrical ureas.

Ureas stand out as potent pharmacophores in drug development, rendering them a prime focus for synthesis. Herein, we present an appealing entry point for urea synthesis from protected amines (Nms-amides) and relying on a Lossen-type rearrangement process as an elegant example of deprotective functionalisation. The method developed exhibits an exceptionally broad tolerance towards various protected amines, encompassing numerous drug derivatives, and delivers high reaction yields.

Conformal symmetry in quantum gravity

We study the problem of how to derive conformal symmetry in the framework of quantum gravity. We start with a generic gravitational theory which is invariant under both the general coordinate transformation (GCT) and Weyl transformation (or equivalently, local scale transformation), and then construct its BRST formalism by fixing the gauge symmetries by the extended de Donder gauge and scalar gauge conditions. These gauge-fixing conditions are invariant under global GL(4) and global scale transformations. The gauge-fixed and BRST invariant quantum action possesses a huge Poincaré-like IOSp(10|10) global symmetry, from which we can construct an extended conformal symmetry in a flat Minkowski background in the sense that the Lorentz symmetry is replaced with the GL(4) symmetry. Moreover, we construct the conventional conformal symmetry out of this extended symmetry. With a flat Minkowski background ⟨gμν⟩=ημν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle g_{\\mu \ u } \\rangle = \\eta _{\\mu \ u }$$\\end{document} and a non-zero scalar field ⟨ϕ⟩≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\phi \\rangle \ e 0$$\\end{document}, the GL(4) and global scale symmetries are spontaneously broken to the Lorentz symmetry, thereby proving that the graviton and the dilaton are respectively the corresponding Nambu–Goldstone bosons, and therefore they must be exactly massless at nonperturbative level. One of remarkable aspects in our findings is that in quantum gravity, a derivation of conformal symmetry does not depend on a classical action, and its generators are built from only the gauge-fixing and the FP ghost actions. Finally, we address a generalized Zumino theorem in quantum gravity.

Application of the New General Integral Transform for Newton’s Law of Cooling

Application of the New General Integral Transform for Newton’s Law of Cooling

Handling Growth and Decay Problems by the New General Integral Transform

Handling Growth and Decay Problems by the New General Integral Transform

DETERMINING THE LEVEL OF DIGITAL COMPETENCE OF A UNIVERSITY FOREIGN LANGUAGE TEACHER

Background. The relevance of the article is due to the tasks of digitalization of education and the focus on the development of all types of digital activities of a university teacher and is determined by the state policy of the Russian Federation in the field of digital transformation of society in general and digital transformation of education in particular. The article examines the conditions of education that are changing in connection with digitalization, and defines digital competence. The purpose of the article is to determine the level of digital competence of a modern university foreign language teacher and take this competence into account in the educational process. Materials and methods. The material of the work was the scientific works of domestic and foreign authors on the topic of research, legislative acts, electronic resources, materials of web conferences, etc. The research methods were interviewing, methods of description, observation and analysis. As a result of the conducted research, the levels of digital competence of foreign language teachers (basic, high, advanced) were identified and the level of digital competence of foreign language teachers in scientific and educational activities of Samara State University of Economics (SGEU) was determined; the skills and abilities of the selected levels were described; possible digital services for use in writing scientific papers, textbooks were highlighted and content creation, as well as for classroom work and distance learning; pedagogical options for using digital technologies both in education and in scientific research of a modern teacher are proposed.

Applications of The Double General Rangaig Integral Transform in Integro-Differential Equations

Applications of The Double General Rangaig Integral Transform in Integro-Differential Equations

Transformer-CNN for small image object detection

Object recognition in computer vision technology has been a popular research field in recent years. Although the detection success rate of regular objects has achieved impressive results, small object detection (SOD) is still a challenging issue. In the Microsoft Common Objects in Context (MS COCO) public dataset, the detection rate of small objects is typically half that of regular-sized objects. The main reason is that small objects are often affected by multi-layer convolution and pooling, leading to insufficient details to distinguish them from the background or similar objects, resulting in poor recognition rates or even no results. This paper presents a network architecture, Transformer-CNN, that combines a self-attention mechanism-based transformer and a convolutional neural network (CNN) to improve the recognition rate of SOD. It captures global information through a transformer and uses the translation invariance and translation equivalence of CNN to maximize the retention of global and local features while improving the reliability and robustness of SOD. Our experiments show that the proposed model improves the small object recognition rate by 2∼5 % than the general transformer architectures.

Utilizing Large Language Models to Illustrate Constraints for Construction Planning

Effective construction project planning relies on addressing constraints related to materials, labor, equipment, and others. Planning meetings are typical venues for stakeholders to identify, communicate, and remove constraints. However, a critical gap exists in lacking an automated approach to identify, classify, analyze, and track constraint discussions during onsite planning meetings. Therefore, this research aims to 1. develop a natural language processing model to classify constraints in meeting discussions; 2. uncover the discussion patterns of managers and foremen regarding various constraints; and 3. extract the root causes for constraints, evaluate their impacts, and prepare managers to develop practical solutions for constraint removal. This research collected meeting transcripts from 94 onsite planning meetings of a building project, spanning 263,836 words. Next, this research leveraged a general pretrained transformer (GPT) to segment discussion dialogs into topics. A Bidirectional Encoder Representations from Transformers (BERT)-based model was developed to categorize constraint types for each topic. The constraint patterns among meeting attendees were assessed. Furthermore, a GPT-based tool was devised to track root causes, impacts, and solutions for various constraints. Test results revealed an 8.8% improvement in constraint classification accuracy compared with the traditional classification model. An occupational characteristic in constraint discussion was observed in that the management team tended to balance their focus on various constraints, while foremen concentrated on more practical issues. This research contributes to the body of knowledge by leveraging language models to analyze construction planning meetings. The findings facilitate project managers in establishing constraint logs for diagnosing and prognosticating planning issues.

Resurgence of Refined Topological Strings and Dual Partition Functions

We study the resurgent structure of the refined topological string partition function on a non-compact Calabi-Yau threefold, at large orders in the string coupling constant $g_s$ and fixed refinement parameter $\mathsf{b}$. For $\mathsf{b}\neq 1$, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by $\mathsf{b}$ and $1/\mathsf{b}$. We show that the corresponding Stokes automorphism is expressed in terms of a generalization of the non-compact quantum dilogarithm, and we conjecture that the Stokes constants are determined by the refined Donaldson-Thomas invariants counting spin-$j$ BPS states. This jump in the refined topological string partition function is a special case (unit five-brane charge) of a more general transformation property of wave functions on quantum twisted tori introduced in earlier work by two of the authors. We show that this property follows from the transformation of a suitable refined dual partition function across BPS rays, defined by extending the Moyal star product to the realm of contact geometry.

Quantum modeling simulates nutrient effect of bioplastic polyhydroxyalkanoate (PHA) production in Pseudomonas putida

Polyhydroxyalkanoates (PHAs) could be used to make sustainable, biodegradable plastics. However, the precise and accurate mechanistic modeling of PHA biosynthesis, especially medium-chain-length PHA (mcl-PHA), for yield improvement remains a challenge to biology. PHA biosynthesis is typically triggered by nitrogen limitation and tends to peak at an optimal carbon-to-nitrogen (C/N) ratio. Specifically, simulation of the underlying dynamic regulation mechanisms for PHA bioprocess is a bottleneck owing to surfeit model complexity and current modeling philosophies for uncertainty. To address this issue, we proposed a quantum-like decision-making model to encode gene expression and regulation events as hidden layers by the general transformation of a density matrix, which uses the interference of probability amplitudes to provide an empirical-level description for PHA biosynthesis. We implemented our framework modeling the biosynthesis of mcl-PHA in Pseudomonas putida with respect to external C/N ratios, showing its optimization production at maximum PHA production of 13.81% cell dry mass (CDM) at the C/N ratio of 40:1. The results also suggest the degree of P. putida’s preference in channeling carbon towards PHA production as part of the bacterium’s adaptative behavior to nutrient stress using quantum formalism. Generic parameters (kD, kN and theta θ) obtained based on such quantum formulation, representing P. putida’s PHA biosynthesis with respect to external C/N ratios, was discussed. This work offers a new perspective on the use of quantum theory for PHA production, demonstrating its application potential for other bioprocesses.

The Challenges of Conflict Transformation, Peacebuilding and Education Towards Intractable Conflicts: The Youth Involvement in North-Kivu Province, Democratic Republic of Congo

Peacebuilding and transformation are essential in creating a peaceful environment, in responding to conflicts and in promoting good relationships for social harmony. This paper establishes the challenges to transformation and peacebuilding in dealing with conflicts and violence among young people as it explores the strategies for conflict transformation and peacebuilding in North Kivu province. It looks at how these tools can help the youths and the communities to break away from violence and work towards peace. The study is based on the systems theory in general and confict transformation in particular how to train young generations to get out of conflicts and violence in order to preapre a bright future. Thus, the paper triangulates the systems theory, transformation, peacebuilding and the intergroup contact. From the participatory action research design, the paper provides resources in the struggle against intractable conflicts and subsequent violence for peacemaking. The paper establishes ubuntu as a starting point for conflict transformation, peacebuilding and in restoring peace and peaceful cohabitation among the youth in Eastern Democratic Republic of Congo.

Bilayer graphene in periodic and quasiperiodic magnetic superlattices

Starting from the effective Hamiltonian arising from the tight-binding model, we study the behaviour of low-lying excitations for bilayer graphene placed in periodic external magnetic fields by using irreducible second-order supersymmetry transformations. The coupled system of equations describing these excitations is reduced to a pair of periodic Schrödinger Hamiltonians intertwined by a second-order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create non-singular Schrödinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated with quasiperiodic magnetic superlattices. Applications in quantum metamaterials stem from the ability to engineer and control such bound states which could lead to a fast development of the subject in the near future.

Linguistic Harmonization: Dissecting Alfiyah Ibn Malik with Chomsky's Transformational Generative Theory

This study is motivated by the need to update and deepen the understanding of Alfiyah Ibnu Malik through a modern linguistic perspective, given the complexity of the 1,002 stanzas that are difficult for students with a weak language foundation to comprehend, and the existing gap in the literature regarding the application of Transformational Generative Theory (TGT) in Arabic grammar, which can help elucidate language structure and enhance understanding and interest in learning. This research aims to examine Alfiyah Ibnu Malik using the modern linguistic approach of Transformational Generative Theory (TGT). The research method applied is library research with a descriptive qualitative approach. The findings indicate that Transformational Generative Theory has specific characteristics in linguistic studies, including deep and surface structures, the concepts of competence and performance, as well as specific and general transformations. Additionally, TGT includes a universal grammar that can be applied to Alfiyah Ibnu Malik. The application of TGT to Alfiyah Ibnu Malik reveals that specific transformations occur in various aspects of Arabic grammar, including optional and obligatory deletion, optional substitution, optional replacement, optional expansion, optional addition, and optional and obligatory permutation.

THE LANGUAGE OF PEACE AND WAR: UKRAINIAN FANDOM ON THE WAY TO SELF-IDENTIFICATION

The article discusses the peculiarities of the functioning of Ukrainian fantasy fandom as well as its transformations related to two main aspects: 1) from “the old” fandom to the new one and 2) from the ordinary forms of existence during the peaceful times to existence during the wartime after Russian full-scale invasion in Ukraine in February 2022.The article indicates the general transformation of the scholarly research of the fandom in the Western academic context. It is possible to present it as the flow from an “ethnographic” or external interpretation of the fandom as a part of the mass culture that depends on the specifics of the popular culture production, to the “internal” or integrated descriptions of the fandom functioning as a separated sphere of social activity.The article argues that there are two stages of the existence of Ukrainian fantasy-related fandom. “The old” fandom emerged in the pre-computer era and was based on the Soviet fandom, which influenced its peculiarities. For instance, there are such aspects as statelessness, the absence of national representation (and the dominance of Russo-centrism as the common cultural platform), the importance of direct interpersonal contacts, distancing from contact with authorities, and the tendency to reduce the presence of the fandom in the shared urban space.Unlike “the old” fandom, “the new” one is developing under the influence of new communicational technologies, which erases the barriers to entering the fandom for new members, enlarges the zones of potential contacts, eliminates geographic and territorial barriers, etc. Moreover, “the new” fandom is more integrated into the urban space and is more available for communications. For the Ukrainian fandom, the transition from “the old” fandom to the “new one” means focusing on domestic cultural issues as the fandom becomes Ukraine-centric.Russian military aggression against Ukraine, from annexing Crimea in 2014 to the full-scale invasion in 2022, became the inner catalyst for the development and transformation of the Ukrainian fandom. The external existential threat led to the transformation of the practices, implemented by the fandom and to the rise of the Ukrainian popular culture, which is closely related to the fandom. During the full-scale invasion, the Ukrainian fandom, preserving its core responsibilities (communication and social activity around popular culture functioning), spreads its new topical responsibilities: apart from the domestic volunteer work, which unites the majority of Ukrainian communities, it includes the educational activity, gaining subjectivity during international communication with the foreign fandom of Europe and the USA, charitable activity, etc.