Symbolic Expressions Research Articles

Inka Unku: Imperial or provincial? State-local relations.

Standardized Inka tunics, or unku, were created under the auspices of the state as symbolic expressions of its expansionist power. To ensure these textiles acquired the status of effective insignias of power and territorial control, the Inka established and imposed technical and stylistic canons for their production (techne) by means of highly-skilled state weavers. In the provinces, social groups that came under imperial rule, local expert weaving agents adopted the conventions of the state and included meaningful symbolic elements of the idiosyncrasies, traditions, and experiential knowledge of the local community (metis). We therefore propose that this was not a unidirectional process and that the Caleta Vitor Inka unku (hereon referred to as the CV unku), presented here, reflects a syncretism promoted by local weavers. In terms of methods, we have developed a decoding tool for the unku, with the aim of distinguishing state from local hallmarks, thereby revealing the syncretic complexity of these iconic tunics. This methodological tool is based on a series of standard analytical parameters and attributes linked to morphological, technological, and stylistic features, which we applied to the CV unku. Unlike others, this unku does come from a looted tomb but was scientifically excavated in a cemetery located in the Caleta Vitor Bay in northern Chile. By deconstructing the CV unku we determined the steps in the chaîne opératoire at which local technical and stylistic elements were incorporated, thus affecting or transforming, in part, its emblematic imperial imagery. This study also marks a step forward in our understanding of a syncretic landscape that combines the state worldview and organized production system (imperial Inka) with craft-production practices that were rooted in provincial and local communities (provincial Inka).

Classification of Faults Operation of a Robotic Manipulator Using Symbolic Classifier

In autonomous manufacturing lines, it is very important to detect the faulty operation of robot manipulators to prevent potential damage. In this paper, the application of a genetic programming algorithm (symbolic classifier) with a random selection of hyperparameter values and trained using a 5-fold cross-validation process is proposed to determine expressions for fault detection during robotic manipulator operation, using a dataset that was made publicly available by the original researchers. The original dataset was reduced to a binary dataset (fault vs. normal operation); however, due to the class imbalance random oversampling, and SMOTE methods were applied. The quality of best symbolic expressions (SEs) was based on the highest mean values of accuracy (ACC¯), area under receiving operating characteristics curve (AUC¯), Precision¯, Recall¯, and F1−Score¯. The best results were obtained on the SMOTE dataset with ACC¯, AUC¯, Precision¯, Recall¯, and F1−Score¯ equal to 0.99, 0.99, 0.992, 0.9893, and 0.99, respectively. Finally, the best set of mathematical equations obtained using the GPSC algorithm was evaluated on the initial dataset where the mean values of ACC¯, AUC¯, Precision¯, Recall¯, and F1−Score¯ are equal to 0.9978, 0.998, 1.0, 0.997, and 0.998, respectively. The investigation showed that using the described procedure, symbolically expressed models of a high classification performance are obtained for the purpose of detecting faults in the operation of robotic manipulators.

Thermodynamically consistent stochastic models for active transmembrane transport processes.

Simulating the full transport cycle of an active transporter driven an ionic electrochemical transmembrane gradient with atomistic detail has been challenging because full cycle completions occur on typical time scales ranging from milliseconds to seconds, out of reach of typical molecular dynamic (MD) simulations. Instead, multiscaling approaches have been developed that break the cycle into elementary steps for which kinetic and equilibrium parameters can be obtained from MD. These parameters are combined in a stochastic kinetic model whose master equation is solved under varying external conditions such as ion concentrations and membrane potential. We developed two improvements for this well-known approach: (1) We introduce the multibind algorithm to derive thermodynamically consistent state free energies and rates from input free energy differences and rates; without such a step, a kinetic model is not guaranteed to obey the laws of thermodynamics and may produce nonsensical results. We also show how the resulting model can be used for parameter inference of microscopic parameters from macroscopic experimental measurements. (2) As an alternative to the numerical solution of the steady state problem, one can exactly solve it using Hill's diagrammatic approach. Our Kinetic Diagram Analysis (KDA) implementation of Hill's method yields symbolic rational expressions for arbitrary kinetic graphs that can be analytically manipulated and directly evaluated. We demonstrate the kinetic graph multiscale approach for sodium/proton antiporters.

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier–Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models.

Drive System Inverter Modeling Using Symbolic Regression

For accurate and efficient control performance of electrical drives, precise values of phase voltages are required. In order to achieve control of the electric drive, the development of mathematical models of the system and its parts is often approached. Data-driven modeling using artificial intelligence can often be unprofitable due to the large amount of computing resources required. To overcome this problem, the idea is to investigate if a genetic programming–symbolic regressor (GPSR) algorithm could be used to obtain simple symbolic expressions which could estimate the mean phase voltages (black-box inverter model) and duty cycles (black-box compensation scheme) with high accuracy using a publicly available dataset. To obtain the best symbolic expressions using GPSR, a random hyperparameter search method and 5-fold cross-validation were developed. The best symbolic expressions were chosen based on their estimation performance, which was measured using the coefficient of determination (R2), mean absolute error (MAE), and root mean squared error (RMSE). The best symbolic expressions for the estimation of mean phase voltages achieved R2, MAE, and RMSE values of 0.999, 2.5, and 2.8, respectively. The best symbolic expressions for the estimation of duty cycles achieved R2, MAE, and RMSE values of 0.9999, 0.0027, and 0.003, respectively. The originality of this work lies in the application of the GPSR algorithm, which, based on a mathematical equation it generates, can estimate the value of mean phase voltages and duty cycles in a three-phase inverter. Using the obtained model, it is possible to estimate the given aforementioned values. Such high-performing estimation represents an opportunity to replace expensive online equipment with a cheaper, more precise, and faster approach, such as a GPSR-based model. The presented procedure shows that the symbolic expression for the accurate estimation of mean phase voltages and duty cycles can be obtained using the GPSR algorithm.

Analytical formulas for calculating the electrical characteristics of multiparameter arbitrary configurational homogenous ladder networks

SummaryMost electrical systems are represented as ladder networks made up of resistances, inductances and capacitances. Electrical characteristics of these networks, such as voltages, currents and equivalent impedance, are difficult to compute because they require solving multiple differential‐algebraic equations. Further, circuit simulator‐based modelling is a time‐consuming and tedious process for simulating large networks with multiparameters present in various configuration. This paper presents generalised analytical formulae for computing the electrical properties of any multiparameter arbitrary section homogenous ladder network that can be reduced to series and shunt impedances. Circuit principles, chain matrix decomposition and linear transformation are used to derive the symbolic expressions. Simply plugging the values of the series and shunt impedances, as well as the number of sections, into the derived expression yields the impedance. Thereafter, the calculated impedances can be used to calculate the nodal voltages and mesh currents. Simulation results of a six‐section homogeneous ladder network are presented and compared with those of other existing techniques to validate the derived expressions. The derived expressions eliminate the need for recursive relations, complex integro‐differential equations, large state‐space matrices and simulator‐based circuit modelling, which are all clearly advantageous.

Student Understanding of the Sign of Negative Definite Integrals in Mathematics and Physics

In a study of student understanding of negative definite integrals at two institutions, we administered a written survey and follow-up clinical interviews at one institution and found that “backward integrals”, where the integral was taken from right to left on the x-axis, were the most difficult for students to interpret. We then conducted additional interviews focused on backward integrals at a second institution. Our analysis uses the concept image framework and a recent categorical framework for mathematical sense making. We found that students were most successful using the Fundamental Theorem of Calculus to determine the sign of an integral when a symbolic expression was provided. When considering a definite integral in a graphical context, students often had difficulty if they viewed the integral as a spatial area, stating that area must always be positive. Some students were able to conceptualize Delta x or dx as a difference or change and thus a signed quantity; when these students were able to view the area as a sum of smaller pieces, they were more successful in justifying a negative backward integral. Students who used amounts or similar images often had difficulty making sense of the negative sign. Even more progress was made when students either invoked or were asked explicitly about a specific physical context to be represented by the backward integral, other than spatial area. The context provided a meaning to the difference represented by Delta x or dx and thus to the sign of that difference and the definite integral.

A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge

Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED), which integrates scientific discipline wisdom in a scientist-in-the-loop approach, with state-of-the-art symbolic regression (SR) methods. SciMED combines a wrapper selection method, that is based on a genetic algorithm, with automatic machine learning and two levels of SR methods. We test SciMED on five configurations of a settling sphere, with and without aerodynamic non-linear drag force, and with excessive noise in the measurements. We show that SciMED is sufficiently robust to discover the correct physically meaningful symbolic expressions from the data, and demonstrate how the integration of domain knowledge enhances its performance. Our results indicate better performance on these tasks than the state-of-the-art SR software packages , even in cases where no knowledge is integrated. Moreover, we demonstrate how SciMED can alert the user about possible missing features, unlike the majority of current SR systems.

Classification of Wall Following Robot Movements Using Genetic Programming Symbolic Classifier

The navigation of mobile robots throughout the surrounding environment without collisions is one of the mandatory behaviors in the field of mobile robotics. The movement of the robot through its surrounding environment is achieved using sensors and a control system. The application of artificial intelligence could potentially predict the possible movement of a mobile robot if a robot encounters potential obstacles. The data used in this paper is obtained from a wall-following robot that navigates through the room following the wall in a clockwise direction with the use of 24 ultrasound sensors. The idea of this paper is to apply genetic programming symbolic classifier (GPSC) with random hyperparameter search and 5-fold cross-validation to investigate if these methods could classify the movement in the correct category (move forward, slight right turn, sharp right turn, and slight left turn) with high accuracy. Since the original dataset is imbalanced, oversampling methods (ADASYN, SMOTE, and BorderlineSMOTE) were applied to achieve the balance between class samples. These over-sampled dataset variations were used to train the GPSC algorithm with a random hyperparameter search and 5-fold cross-validation. The mean and standard deviation of accuracy (ACC), the area under the receiver operating characteristic (AUC), precision, recall, and F1−score values were used to measure the classification performance of the obtained symbolic expressions. The investigation showed that the best symbolic expressions were obtained on a dataset balanced with the BorderlineSMOTE method with ACC¯±SD(ACC), AUC¯macro±SD(AUC), Precision¯macro±SD(Precision), Recall¯macro±SD(Recall), and F1−score¯macro±SD(F1−score) equal to 0.975×1.81×10−3, 0.997±6.37×10−4, 0.975±1.82×10−3, 0.976±1.59×10−3, and 0.9785±1.74×10−3, respectively. The final test was to use the set of best symbolic expressions and apply them to the original dataset. In this case the ACC¯±SD(ACC), AUC¯±SD(AUC), Precision¯±SD(Precision), Recall¯±SD(Recall), and F1−score¯±SD(F1−Score) are equal to 0.956±0.05, 0.9536±0.057, 0.9507±0.0275, 0.9809±0.01, 0.9698±0.00725, respectively. The results of the investigation showed that this simple, non-linearly separable classification task could be solved using the GPSC algorithm with high accuracy.

Symbolism In Mohsin Naqvi's Poetry

Symbolic language is a basic requirement for poetry. Therefore, we can say that in every era, poets have worked with symbolic language and will continue to do so. In such a way that every metaphor is a symbol. For he denotes something beyond himself more than the basic meaning he has formulatedSymbolism is one such way of representation. In instead of directly mentioning emotions and thoughts, these concepts are described through indirect factors. For poets with symbolic thinking, describing the feelings of the inner world rather than the outside world is the basic basis of poetry. Therefore, he considered symbolic expression to be the first in both form and style. The thinking presented topics such as dreams, misery, the mysteriousness of thought, disorder, madness, and nervous tension as symbols. This article deals Symbolism in Mohsin Naqvi's Poetry

Reclaiming Métis Identity: Implications for Art Therapy Research and Practice (Réappropriation de l’identité Métis : implications pour la recherche et la pratique en art-thérapie)

This paper presents a brief historical context of the issue of Métis identity, discussion of a proposed theoretical framework, analysis of recent literature, and a critical review of the role of art therapy when serving and advocating for Métis people. The following questions are a proposal for consideration when working with Métis people, from a feminist and symbolic interactionist (humanist) point of view: (1) Which life experiences, on a family, community, social, and cultural level have influenced and contributed to your identity as a Métis person? (2) How would you share your identity through symbolic and creative expression? and (3) What would have made a difference in claiming your Métis identity in your formative years, presently, and what do you hope for our future generation?

Dissipation minimization of two-stage amplifier using deep learning

Designing electrical circuits and devices is usually based on expertise in electronics and the thorough use of numerical software tools. This procedure can be time-consuming, and the designer has only one solution. This paper introduces a new approach focused on new concept design and optimization of specific circuits using symbolic expressions. The primary amplifier circuit, realized by a deep learning module, changes the value to reduce power dissipation. The control signal of the deep learning module is output from an amplifier that depends on the statistics of the input signal value.

Primordial feeling of possession in development.

Boyer's minimalist model of human ownership psychology overlooks important cues that children provide in their development leading them from pre-conceptual to conceptual (symbolic) expressions of the basic feeling experience of control over things, qua ownership in the most basic psychological sense. Appeal for innate core knowledge and evolutionary logic blows out the light of this rich and unique ontogenetic progression.

Two Faces of Urbanization in the Muslim East: Tehran in the Second Half of the 19th Сentury — 1930s.

In this study the authors examine the main stages of evolution and social characteristics of the capital cities in the Muslim East on the example of Tehran, which over the course of a century has made its way from the medieval Shah's residence to the capital of a modern country. This period in the history of Iran was marked by a gradual modernization of state and society, associated with the personalities of Naser al-Din Shah Qajar and the new ruler Reza Shah Pahlavi, who managed to offer a radical way to transform the country basing on a new ideological doctrine, the symbolic expression of which was his renovated capital. The image of Tehran is reconstructed on the basis of urban planning outlines of the 1920s — 1930s, a wide range of narrative sources, mainly diaries of the Iranian rulers themselves and European diplomats and travelers, and information from Persian literary works.

Frame Modeling of The Linguocultural Concept “Religion”

The article analyzes the concept “religion” as a unit of knowledge that allows verbally expressing the national and cultural specificity of the language, and also defines this concept as a category of universal human values. The difference between the concept and the concept is indicated, where the concept is formed against the background of experience, as well as on the cognition and logical understanding of reality, and the concepts are designated as real phenomena contained in the general symbolic expression and lexical definitions of objects. The concept is presented in the form of an extensive formation that reflects the general nature of the surrounding reality, which contains the characteristics and values of society. The aim of the work is to analyze the manifestation at the contextual level of the linguocultural concept “religion / religion” in English and Russian. To consider the concept, frame modeling was used as the most universal model that helps to reveal the essence of the concept under consideration. According to this analysis, it was indicated that the structure of the concept is multifaceted and includes several meaningful frames.

The Development of RBL-STEM Learning Materials in Improving Students’ Generalization Thinking Skills to Solve Local Vertex Irregular Reflexive Coloring Problem

Generalization is the process of drawing general or simple conclusions about a problem. The stages of mathematical generalization consist of four stages, namely perception of generality, expression of generality, symbolic expression of generality, and manipulation of generality . There needs to be a learning model that can improve students’ generalization thinking skills, one of which is by using the Research Based Learning (RBL) model. The Research Based Learning (RBL) model is also supported by the STEM (Science, Technology, Engineering, and Mathematics) approach to make it easier for students to develop generalization thinking skills. In this study, there searchers developed a material using the Research Based Learning (RBL) model and the STEM (Science, Technology, Engineering, and Mathematics) approach, with the aim of improving students’ generalization skills. The results of developing research-based learning materials in with the STEM approach after testing the materials in and analyzing them, it can be concluded that the materials in meet the valid, practical, and effective criteria.

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Символика лояльности к власти Тевтонского ордена у пруссов в XIII—XIV веках

Formation of the State of Teutonic Order in Prussia in the XIIIth—XIVth centuries based beside military oppression on the relations with local population supported by the incorporation of them in the system of condition landholding. These relations implied, from the one hand, the representation by the Order its own status as a collective ruler, and from the other hand, symbolic expression of the loyalty of Old Prussians in various spheres of social communication: language, onomastic, objects of material culture. Definition of the ways to express loyalty that is the purpose of the article allows to characterize the comprehension of Old Prussians their own status in new political conditions. For this purpose by the using of the old comparative-historical, typological and diachronous-synchronous methods were re­sear­ched both written sources and funds from the Old Prussian necropolis. It allows to define that Old Prus­sians expressed their loyalty by the reception of Middle High German language, Chris­tian names and symbols and sign of Teutonic order. Being included in the culture of Old Prussians these elements co-existed with traditional names, language and principle of heathen fu­ne­ral rite. The resulting co-existence of the symbols different by their character became one of the basis for the relations between Old Prussians and Teutonic order that provided stable de­velopment of the State until 1525.

An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials

Zernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open: firstly, there is a lack of sufficient mathematical formulas of the ZCP for optics designers; secondly the formulas for inter-conversion of Noll's single index and Born-Wolf's double indices of ZCP are neither uniquely determinate nor satisfactory. An automatic method for generating symbolic expressions for ZCP is proposed based on five essential factors: the new theorems for converting the single/double indices of the ZCP, the robust and effective numeric algorithms for computing key parameters of ZCP, the symbolic algorithms for generating mathematical expressions of ZCP, and meta-programming \& \LaTeX{} programming for generating the table of ZCP. The theorems, method, algorithms and system architecture proposed are beneficial to both optics design process, optics software, computer-output typesetting in publishing industry as well as STEM education.

Jewish Toronto’: street naming policies and practices in the north of Metropolitan Toronto

This article deals with street naming policies and practices with regard to the Jewish urban community in the north of Metropolitan Toronto, Canada. It highlights the linguistic landscape as a cultural and symbolic expression of a Jewish-Israeli minority group in Vaughan, a city in North Toronto. The Jewish nomenclature is also examined viewing Toronto’s multicultural- cum-pragmatic street naming policies. While such a display of Jewish toponymy is almost non-existent in Toronto itself, the creation of ‘Jewish Toronto’ in the north of the metropole is the product of both ‘Jewish’ and ‘Canadian-Torontonian’ factors. This article analyzes these two factors and their related characteristics in terms of demography, sociopolitical approach, religiocultural identity, economy, and municipal by-laws. It concludes that the development of a Jewish toponymic culture as an ethnic-minority culture in the public domain of northern Metropolitan Toronto is a result of a bipartite process. This process has been enabled by the aspirations of the minority group, on the one hand, and the flexibility and tolerance inherent in the multicultural policies of the majority group/ government, on the other.