Symbolic Manipulation Research Articles

There is more to algebra than meets the eye: the case of blindness

Abstract Research literature about visually impaired students’ approach to mathematics is still very scarce, especially in the case of algebra, even though mathematical content is becoming increasingly accessible thanks to assistive technologies. This paper presents a case study aimed at describing a blind subject’s process of algebraic symbol manipulation while solving equations supported by assistive technology. In particular, we analyze how a subject with blindness manifests their structure sense within algebraic instrumented activity mediated by programming languages (such as LaTeX). The epistemic and pragmatic mediations of the programming language are described in terms of the developed utilization schemes. The results show how hearing can replace the eye in developing algebraic structure sense. Data analysis reveals that the system of screen reader, speech synthesis, and programming language has interesting potentialities in the development of structure sense for subjects with blindness, but, taking an inclusive perspective, we discuss how these potentialities can be applied more generally in mathematics education.

The disencapsulated mind: A premotor theory of human imagination.

Our premodern ancestors had perceptual, motoric, and cognitive functional domains that were modularly encapsulated. Some of these came to interact through a new type of cross-modular binding in our species. This allowed previously domain-dedicated, encapsulated motoric and sensory operators to operate on operands for which they had not evolved. Such operators could at times operate nonvolitionally, while at other times they could be governed volitionally. In particular, motoric operations that derive from the same circuits that compute hand motions for object manipulation could now be retooled for virtual manipulation in a mental workspace in the absence of any physical hand or other effector movements. I hypothesize that the creativity of human imagination and mental models is rooted in premotor simulation of sequential manipulations of objects and symbols in the mental workspace, in analogy with the premotor theory of attention, which argues that attention evolved from "internalized" eye movement circuitry. Overall, operator "disencapsulation" led to a bifurcation of consciousness in humans: a concrete form centered on perception of the body in the physical world and an abstract form focused on explanatory mental models. One of the consequences of these new abilities was the advent of psychotic disorders that do not exist in species possessed solely of the concrete type of consciousness. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Symbolic Manipulation Planning with Discovered Object and Relational Predicates

Symbolic Manipulation Planning with Discovered Object and Relational Predicates

Causal representation learning through higher-level information extraction

The large gap between the generalization level of state-of-the-art machine learning and human learning systems calls for the development of artificial intelligence (AI) models that are truly inspired by human cognition. In tasks related to image analysis, searching for pixel-level regularities has reached a power of information extraction still far from what humans capture with image-based observations. This leads to poor generalization when even small shifts occur at the level of the observations. We explore a perspective on this problem that is directed to learning the generative process with causality-related foundations, using models capable of combining symbolic manipulation, probabilistic reasoning, and pattern recognition abilities. We briefly review and explore connections of research from machine learning, cognitive science, and related fields of human behavior to support our perspective for the direction to more robust and human-like artificial learning systems.

Superposition and Interaction Dynamics of Complexitons, Breathers, and Rogue Waves in a Landau–Ginzburg–Higgs Model for Drift Cyclotron Waves in Superconductors

This article implements the Hirota bilinear (HB) transformation technique to the Landau–Ginzburg–Higgs (LGH) model to explore the nonlinear evolution behavior of the equation, which describes drift cyclotron waves in superconductivity. Utilizing the Cole–Hopf transform, the HB equation is derived, and symbolic manipulation combined with various auxiliary functions (AFs) are employed to uncover a diverse set of analytical solutions. The study reveals novel results, including multi-wave complexitons, breather waves, rogue waves, periodic lump solutions, and their interaction phenomena. Additionally, a range of traveling wave solutions, such as dark, bright, periodic waves, and kink soliton solutions, are developed using an efficient expansion technique. The nonlinear dynamics of these solutions are illustrated through 3D and contour maps, accompanied by detailed explanations of their physical characteristics.

Expressive Epistemic Injustice: Definition, Measurement, and Deliberative Cure

Epistemic injustice means that knowledge relevant to collective decisions gets discounted, thus inflicting harm on disadvantaged groups. The most familiar kinds (established by Fricker 2007) are testimonial (dismissing arguments because of the social characteristics of the speaker) and hermeneutical (lack of collective interpretive resources to make sense of oppression). We develop the idea of expressive epistemic justice, which exists when social forces induce a systematic failure for an individual or group’s values and beliefs to be reflected in what the individual or group expresses as its wants. Expressive epistemic injustice can persist even if testimonial and hermeneutic injustice were to be eliminated. The degree of failure can be quantified, enabling us in an empirical analysis of multiple cases to locate the source of expressive epistemic injustice in the conditions of discourse in a public sphere awash in symbolic manipulations by relatively powerful actors. We then show how citizen deliberation can remedy expressive epistemic justice. Our analysis adds to existing epistemic arguments for deliberative democracy, for it shows that deliberation increases the likelihood that collective decisions will respond to the values and beliefs that define these decisions as good to begin with.

Commutator technique for the heat kernel of minimal higher derivative operators

We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic 2Mth order, F(∇)=(−□)M+⋯, in the background field formalism of gauge theories and quantum gravity. This technique represents the conversion of the recently suggested Fourier integral method of generalized exponential functions [A. O. Barvinsky and W. Wachowski, Heat kernel expansion for higher order minimal and nonminimal operators, ] into the commutator algebra of special differential operators, which allows one to express expansion coefficients for F(∇) in terms of the Schwinger-DeWitt coefficients of a minimal second-order operator H(∇). This procedure is based on special functorial properties of the formalism including the Mellin-Barnes representation of the complex operator power HM(∇) and naturally leads to the origin of generalized exponential functions without directly appealing to the Fourier integral method. The algorithm is essentially more straightforward than the Fourier method and consists of three steps ready for a computer codification by symbolic manipulation programs. They begin with the decomposition of the operator into a power of some minimal second-order operator H(∇) and its lower derivative perturbation part W(∇), F(∇)=HM(∇)+W(∇), followed by considering their multiple nested commutators. The second step is the construction of special local differential operators—the perturbation theory in powers of the lower derivative part W(∇). The final step is the so-called procedure of their “Syngification,” consisting of a special modification of the covariant derivative monomials in these operators by the Synge world function σ(x,x′) with their subsequent action on the Hadamard-Minakshisundaram-DeWitt coefficients of H(∇). Published by the American Physical Society 2024

Demystifying Jung's "Archetypes" with Embodied Cognition.

Since he first proposed it, Carl Jung's "archetype" theory has faced resistance from a pervasive but seldom examined set of underlying Cartesian assumptions embedded in mainstream psychology. This paradigm assumed a physical universe (and hence body) free of psyche that coincided with an essentially disembodied mind largely concerned with abstract symbol manipulation. This situation led archetype theory to remain largely within insulated psychoanalytic circles for decades. Since the 1980s, however, cognitive psychology has increasingly become embodied from a variety of standpoints. This article shows how the results of embodied cognition and spontaneous thought "demystify" many of the attributes Jung described in his archetype theory, making archetype theory not only more comprehensible but clinically applicable. Combining approaches suggests new avenues of inquiry for experimental research and enriches the psychoanalytic perspective.

The Instrumentalization of Cultural Heritage in Ceausescu’s Romania

This article analyzes the heritagisation policies and the instrumentalization of cultural heritage by Ceausescu's regime for political purposes. I argue that Ceausescu’s political regime was neopatrimonial, a system where rules took place within the framework of legal bureaucracy of a modern state in which formal structures and rules did exist, although in practice, the separation of the private and public sphere was not always observed. This system was characterized by insecurity about the behavior and role of state institutions, but primarily the actions of the supreme leader that were erratic and unpredictable. In this regime, the rural cultural heritage was used for political-ideological purposes, in close connection with the cult of the personality of the supreme leader. In this context, the heritigisation of folk creations such as folk plays did not mean the preservation of these rural cultural forms under threat in a society undergoing major economic and social transformations that imperiled traditional community life. Instead, it was a form of symbolic political manipulation used to acquire political legitimacy. Received: 17 January 2024 / Accepted: 29 May 2024 / Published: 02 July 2024

Unlocking Synergy: Leveraging SysML and Modelica with Bi‐Directional Transformation and Simulation Integration Standards

AbstractBoth the SysML and Modelica standards are used in the field of Systems Engineering (SE) to model systems from different perspectives, on different abstraction levels. SysML is strong when modeling systems on a functional level because it provides different views. With the capabilities of other simulation specifications, the engineers can simulate the system architecture. On the other hand, an open standard, such as Modelica is a key enabler for representing multi‐physical systems described by differential, algebraic, and discrete equations. With the symbolic manipulation, the dynamics of the systems are represented in state space form, and solved by the numerical integration methods fixed or variable step. However, it is clear that the connection between systems engineering and system simulation, with their respective domain knowledge of the actual equipment in their system, is missing. By seeing these complementary values, the authors demonstrate language interaction to integrate SysML and Modelica to achieve complimentary values through bi‐directional transformation and simulation.

Tinned: A symbolic library for response theory and high-order derivatives.

A symbolic C++ library-Tinned-has been developed for symbolic differentiation and manipulation in response theory. By recognizing different key building blocks in the density matrix-based (Thorvaldsen et al., J. Chem. Phys. 2008, 129, 214108) and coupled-cluster response theories, we have implemented their corresponding C++ symbolic classes, including but not limited to one- and two-electron operators, exchange-correlation energy and potential, and coupled-cluster operator. Formulas of response theory can be well expressed in terms of the symbolic classes in the library Tinned. Their high-order perturbation-strength derivatives can be straightforwardly computed and extracted afterwards for numerical evaluation. The library Tinned will greatly facilitate the development work of response theory and may lead to a unified framework for response theory at different levels of electronic structure theory.

Teaching Algebra to High School Students Using Desmos Graphing Calculator

Many high school students find algebra difficult because it requires comprehending abstract concepts, performing symbol and sign manipulation, and solving multi-step problems. Graphing calculators can visualize algebraic expressions and equations, and make learning more interactive. We conducted an experiment in which Desmos online graphing calculator was used to augment the algebra lessons of tenth-standard students. The students were taught about polynomials, linear and quadratic equations, and arithmetic progressions during an intervention period lasting seven weeks. We found that properly integrating the graphing calculator with classroom sessions and homework helped the students to perform better in the post-test and also retain the concepts. The students found the graphing calculator to be easy to use and helpful in learning, which increased their interest in algebra and encouraged them to practice algebra regularly.

Analytic method for finding stationary solutions to generalized nonlinear Schrödinger equations

Analytic method for finding stationary solutions to generalized nonlinear Schrödinger equations

Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning

Large Language Models (LLM) exhibit zero-shot mathematical reasoning capacity as a behavior emergent with scale, commonly manifesting as chain-of-thoughts (CoT) reasoning. However, multiple empirical findings suggest that this prowess is exclusive to LLMs that have exorbitant sizes (beyond 50 billion parameters). Meanwhile, educational neuroscientists suggest that symbolic algebraic manipulation be introduced around the same time as arithmetic word problems so as to modularize language-to-formulation, symbolic manipulation of the formulation, and endgame arithmetic. In this paper, we start with the hypothesis that much smaller LMs, which are weak at multi-step reasoning, can achieve reasonable arithmetic reasoning if arithmetic word problems are posed as a formalize-then-solve task. In our architecture, which we call SyReLM, the LM serves the role of a translator to map natural language arithmetic questions into a formal language (FL) description. A symbolic solver then evaluates the FL expression to obtain the answer. A small frozen LM, equipped with an efficient low-rank adapter, is capable of generating FL expressions that incorporate natural language descriptions of the arithmetic problem (e.g., variable names and their purposes, formal expressions combining variables, etc.). We adopt policy-gradient reinforcement learning to train the adapted LM, informed by the non-differentiable symbolic solver. This marks a sharp departure from the recent development in tool-augmented LLMs, in which the external tools (e.g., calculator, Web search, etc.) are essentially detached from the learning phase of the LM. SyReLM shows massive improvements (e.g., +30.65 absolute point improvement in accuracy on the SVAMP dataset using GPT-J 6B model) over base LMs, while keeping our testbed easy to diagnose and interpret, and within the reach of most researchers.

Ідеологема «русского міра» та її реалізація в медіа Української православної церкви 2022–2024 рр.

The article examines specific communication technologies that can be classified as manipulative, using materials from the online publication “Orthodox Life” as a case study. This publication is one of the official organs of the UOC, and its topics, ideas, and concepts are disseminated through various information channels, influencing different audience groups. The authors of the article argue that several manipulative techniques are employed in this publication – myth-making technology, manipulation of certain ideals and values, spiritual and symbolic manipulation, emphasis on emotional aspects of readership, among others – to promote the ideology of the “Russian world.” The attributes of this ideological concept include the Russian language, media attempts to create a common historical and cultural space between Ukraine and the Russian Federation, Orthodoxy, loyalty to the Russian Federation, hostility towards Europe and the USA, and a negative attitude towards representatives of other religions. The article also highlights the use of the “spiral of silence” technique, popular in this and other UOC MP publications. Key events of 2022-2024, namely the war of the Russian Federation against Ukraine, are silenced in the analyzed media, and materials conceal the aggression of the Russian Federation and the role of the Russian Orthodox Church, which has declared murders and terror a “holy war.” Instead of informing the audience, low-content publications create so-called information noise, aiming to distract the audience from real issues. Through manipulative technologies, the myth of the “Russian world” is constructed in “Orthodox Life” as the dominant ideology for the people of Ukraine. The study of manipulative technologies used in UOC media is crucial for effective information warfare and countering the ideology of the Russian Federation, which is propagated through the Russian Orthodox Church and its affiliates. Keywords: information war, manipulative technologies, “Russian world,” religious organizations.

The Guru of Abuse: Analysing Cultural Distortions in Anuradha Roy s Sleeping on Jupiter

This research paper delves into the intricate relationship between culture as a tool of oppression and liberation, focusing on the experiences of child abuse within the context of Anuradha Roy’s Sleeping on Jupiter (2015). The study investigates how the abuse perpetuated against the orphaned girls reflects distortions of cultural norms and traditions, thereby revealing the potential for culture to be used as an instrument of oppression. The central figure in this narrative, Guruji, manipulates religious notions of the guru-disciple relationship, exploiting his claimed status as the girls’ new “God” to mask his exploitation. Through a comprehensive analysis of the novel, this study reveals the dichotomous role of religious and cultural elements. The paper argues that while religion can be harnessed for both oppression and liberation, its enduring symbols and narratives form the foundation for survivors to reclaim their agency and cultural heritage. On one hand, the guru’s invocations of worship and devotion underscore the manipulation of cultural symbols to enable abuse and control. On the other hand, the paper explores how the orphaned girls find solace by reengaging with Hindu mythological narrative traditions through storytelling. The study demonstrates that the tales from the Ramayana provide solace from the guru’s falsehoods. Ultimately, the paper contributes to a deeper understanding of the intricate interaction between cultural forces, gender dynamics, and the potential for empowerment within the framework of religious traditions, as depicted in the novel.

REVISITING THE THEORETICAL FOUNDATIONS OF ETHNOMODELLING

By including mathematical activities from outside of the school environment, the process of modelling shows us that mathematics is more than the manipulation of mathematical symbols, procedures, and practices. The application of ethnomathematical techniques along with the tools of modelling allows us to see a holistic reality to mathematics. From this perspective, one pedagogical approach that connects the cultural features of mathematics with its school/academic aspects is named ethnomodelling, which is a process of translation and elaboration of problems and questions taken from systems that are part of the reality of the members of any cultural group. In this article we offer an alternative goal for educational research, which is the acquisition of both emic (local) and etic (global) approaches for the implementation of ethnomodelling in the classrooms. We also discuss a third approach on ethnomodelling, which is the dialogical (glocal) approach, which combines both emic and etic approach bases. Finally, we define ethnomodelling as the study of mathematical phenomena within a culture because it is a social construct and is culturally bound, which adds the cultural characteristics of mathematics into the modelling process.

Enhancing Symbolic Manipulation through Pairing Primitive Recursive String Functions and Interplay with Generalized Pairing PRSF

In earlier studies, the notion of generalized primitive recursive string functions has been presented, and their connections with abstract paring-based primitive recursive string functions have been investigated. Our study is centered around establishing a fundamental theorem that states a connection between these two distinct sorts of functions. The theorem specifically establishes that the universal definition of every generalized pairing primitive recursive string function is contingent upon its correspondence with a conventional(abstract) pairing primitive recursive string function. This article introduces innovative concept of Pairing Primitive Recursive String Functions (P-PRSF) for manipulating and interacting with word pairs. Based on the principles of primitive recursion and pairing functions, P-PRSF enables the extraction, transformation, and combination of word components. The proposed theorems validate the effectiveness of P-PRSF in capturing relationships within word pairs. Moreover, the interplay between P-PRSF and Generalized Pairing PRSF (GP-PRSF) extends the concept to involve more intricate interactions.

Automatic extension of a symbolic mobile manipulation skill set

Automatic extension of a symbolic mobile manipulation skill set

Graphical User Interface for Design, Analysis, Validation, and Reporting of Continuous-Time Systems Using Wolfram Language

A graphical user interface presented is intended for fast design, symbolic analysis, accurate simulation, exact verification, and test report preparation. It helps to skip the gap between theory and practice in electrical engineering because the numeric analysis is usually approximate, and the power of symbolic systems has insufficient speed even, for simple engineering problems. The software is written using a computer algebra system that is free on small computers. The mathematical representation of the system can be obtained automatically from the schematic description. Further automated symbolic manipulations are possible according to the user’s aspirations.