Computer Algebra with SymbolicC++

18 - Expression Programming Techniques for Formulation of Structural Engineering Systems

Macaulay is a system for computing in algebraic geometry and cummutative algebra; it is capable of a variety of computations which are tedious or impossible to perform by hand. The primitive types in the system are polynomials, matrices, ideals, polynomial rings, modules, maps between rings, and complexes of modules. The system performs algebraic manipulation on objects of these types. The possible manipulations include the computation of standard (Gröbner) bases, modules of syzygies, finite free resolutions, Hilbert polynomials and functions. Using these basic operations, a variety of derived operations are possible, such as projections, ideal intersections, and the computation of coherent sheaf cohomology groups. The algorithm used for constructing standard (Gröbner) bases and syzygies is described in ([Buc76], [Zac78], [Sch80], [Bay82], [BaSt86a]).

An evolutionary-based predictive soft computing model for the prediction of electricity consumption using multi expression programming

Evolutionary Symbolic Models for Predicting Mortar Strength Incorporating Plastic Waste and Supplementary Cementitious Materials for Sustainable Construction

Cementitious composites' performance degrades in extreme conditions, making it more important to enhance its resilience. To further the adaptability of eco-friendly construction, waste materials are increasingly being repurposed. Cementitious composites deteriorate in both direct and indirect ways due to the facilitation of hostile ion transport by water. The effects of using eggshell and glass powder as partial substitutes for cement and sand in mortar on the water-absorption capacity were investigated using machine learning (ML) modeling techniques such as Gene Expression Programming (GEP) and Multi Expression Programming (MEP). To further assess the importance of inputs, sensitivity analysis and interaction research were carried out. The water absorption property of cementitious composites was precisely estimated by the generated ML models. It was noted that the MEP model, with an R2 of 0.90, and the GEP model, with an R2 of 0.88, accurately predicted results. The sensitivity analysis revealed that the absorption capacity of the mortar was most affected by the presence of eggshell powder, sand, and glass powder. GEP and MEP model's significance lies in the fact that they offer one-of-a-kind mathematical formulas that can be applied to the prediction of features in another database. The mathematical models resulting from this study can help scientists and engineers rapidly assess, enhance, and rationalize mixture proportioning. The built models can theoretically compute the water absorption of cement mortar made from eggshell powder and glass powder based on varied input parameters, resulting in cost and time savings.

Geopolymer concrete (GPC) serves as a sustainable substitute for conventional concrete by employing alternative cementitious materials such as fly ash (FA) instead of ordinary Portland cement (OPC), contributing to environmental and durability benefits. To increase the rate of utilization of FA in the construction industry, distinctive characteristics of two machine learning (ML) methods, namely, gene expression programming (GEP) and multi-expression programming (MEP), were utilized in this study to propose precise prediction models for the compressive strength and split tensile strength of GPC comprising FA as a binder. A comprehensive database was collated, which comprised 301 compressive strength and 96 split tensile strength results. Seven distinct input variables were employed for the modeling purpose, i.e., FA, sodium hydroxide, sodium silicate, water, superplasticizer, and fine and coarse aggregates contents. The performance of the developed models was assessed via numerous statistical metrics and absolute error plots. In addition, a parametric analysis of the finalized models was performed to validate the prediction ability and accuracy of the finalized models. The GEP-based prediction models exhibited better performance, accuracy, and generalization capability compared with the MEP-based models in this study. The GEP-based models demonstrated higher correlation coefficients (R) for predicting the compressive and split tensile strengths, with the values of 0.89 and 0.87, respectively, compared with the MEP-based models, which yielded the R values of 0.76 and 0.73, respectively. The mean absolute errors for the GEP- and MEP-based models for predicting the compressive strength were 5.09 MPa and 6.78 MPa, respectively, while those for the split tensile strengths were 0.42 MPa and 0.51 MPa, respectively. The finalized models offered simple mathematical formulations using the GEP and Python code-based formulations from MEP for predicting the compressive and tensile strengths of GPC. The developed models indicated practical application potential in optimizing geopolymer mix designs. This research work contributes to the ongoing efforts in advancing ML applications in the construction industry, highlighting the importance of sustainable materials for the future.

Computation in commutative algebra and algebraic geometry has taken a major step forward in the last decade. This is due to the development of Grobner bases, computer algebra systems which are readily available to researchers, and the great increase in power of computers in this last decade.

This study presents a novel data-driven approach to improving the compressive strength (C-S) of environmentally friendly rubberized mortar that incorporates ingredients that are in line with current sustainability objectives in construction: glass powder, marble powder, and silica fume. Our predictive models were built using state-of-the-art machine learning (ML) approaches, specifically gene expression programming (GEP) and multi-expression programming (MEP), employing a thorough experimental dataset. Thorough evaluations of the models were conducted using important statistical metrics, such as the R 2 coefficient, root mean square error, and mean absolute error. The use of individual conditional expectation plots and partial dependence plots allowed for both individual and average variable effect studies, which were conducted to improve interpretability. Despite the good performance of the GEP model ( R 2 = 0.91), the MEP model proved to be more effective in capturing complicated, nonlinear connections with its superior accuracy and generalization ( R 2 = 0.95). ML has the ability to greatly improve sustainable construction practices by reducing the need for experiments, speeding up the process of mix optimization, and encouraging the creation of cementitious composites that are less harmful to the environment. The findings contribute to the construction sector by integrating digital innovation with material sustainability.

Intelligent prediction modeling for flexural capacity of FRP-strengthened reinforced concrete beams using machine learning algorithms

The author discusses how computer algebra has been used in mathematics teaching at Cornell University. He begins by illustrating some of the commands available in computer algebra software. He reviews the experience at Cornell with MuMath and other computer algebra systems, including MACSYMA, and describes plans for the future. He also discusses student and faculty reactions to the use of computers in this way. He closes with comments about the future of teaching engineering mathematics at Cornell in light of the above experience and new developments in computer technology and computer support for teaching.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In the field of computer algebra, joining separate computer algebra systems with individual strengths into problem solving environments is an important recent research direction. In this paper we describe how we wrapped a specialized computer algebra system, which uses shared-memory parallelism to speed up Grobner basis computations, into a Web component that can be used by other systems. By this component also a new algorithmic development in Grobner basis computations – the use of the Fractal Grobner Walk – was made available to various general purpose computer algebra systems in the form of a single optimized implementation. Previously, all of the important algorithmic improvements to an algorithm had to be reimplemented in the general purpose systems. Our implementation allows access to the Grobner basis computations via ‘intelligent’ graphical user interfaces and via scripting from existing general purpose algebra systems. © 1998 John Wiley & Sons, Ltd.

Computer algebra systems are frequently used for research. In addition, some instructors have based entire advanced courses around these systems. One benefit is that they allow students to become familiar with the methods of calculus by individual experimentation. However, instructors have generally seen computer algebra systems as unsuitable for introductory algebra since the software is capable of doing all the math for the students. That barrier could be overcome if a suitable user interface were developed. Furthermore, embracing computer algebra could make for a completely different type of introductory course that shifts the focus from calculation to problem-solving. Computer algebra systems could also make life easier for math instructors as problem generators for tests and as automatic on-line graders, even of non-multiple choice problems. Computer algebra systems offer many new opportunities for math education.

Transcription and translation are required for consolidation of long-lasting changes in synaptic function and are required for learning and memory. The targets of activity-dependent transcription in neurons have been of great interest. Despite this, the ultimate consequences of an activity-dependent change in programs of gene expression with respect to neural function have been surprisingly elusive. For example, experimental data have not clearly established how gene expression is required for memory-associated events, such as synapse-specific strengthening or changes in the input-output function of the neuron. Many activity-regulated genes are transcriptional factors which themselves modify programs of downstream gene expression, and the short- and long-term consequences of these changes in gene expression remain largely unknown. Although there have been many complementary approaches to experimentally and computationally define the plasticity transcriptome, the specific gene targets that have been identified using different experimental approaches show surprisingly little overlap. The purpose of this review is three-fold: 1) to discuss what is known about activity-dependent transcription during learning, 2) to review efforts to identify genes in the plasticity transcriptome, and 3) to develop a hypothesis about how transcription might be required for information coding at the synaptic and cellular level.

Properties that are needed in a language for programming computer vision tasks are described, and a new object-oriented programming language and data management system approach is suggested. An example from automatic pose estimation is used to illustrate the necessity for the properties in a language system, it is indicated where other languages and data management systems fail to provide these properties, and the type constructors used in the authors' system and features of the language semantics of their system are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Accurately representing and understanding the dynamics driving the global carbon cycle are of strong significance for the study of the Earth System as well as for reliable climate change projections. Model development in the biogeochemistry field traditionally relies on empirical studies and on already established theoretical foundations. With increased data availability, model development in the field of biogeochemistry has started to open more to the use of machine learning approaches for helping to validate and calibrate the existing model formulations. However, the validity of the studied model structures are not often debated. This thesis introduces a novel framework for modelling biogeochemistry fluxes by using symbolic regression approaches to automatically generate interpretable mathematical models. The thesis starts by first illustrating the potential of gene expression programming (GEP) to discover interesting models as mathematical formulas based entirely on real time series data measured at a single monitoring site. The GEP discovered models perform better predictions than already established models in the ecology community. Further, the GEP models have the advantage of being represented as mathematical formulas that can be used similarly to natural laws from the ecology community. Still, the complexity of GEP models makes it difficult to really interpret the described model dynamics. To tackle model complexity GEP is extended with CMA-ES for performing local parameter optimizations in the evolution process. The resulting algorithm is CMAGEP, a novel system that is a GEP and ES hybrid approach capable of delivering more accurate and more compact solutions compared to standard GEP. Generating compact solutions means that CMAGEP discovers mathematical models that can be more easily interpretable, and that can be more easily combined with already established knowledge. CMAGEP is successfully used for modelling various carbon fluxes; first it helps discover non-linear dynamics in the carbon cycle at an Arctic site and produce a very compact solution, and secondly, it reveals interesting and relevant patterns in the underlying processes determining the global terrestrial carbon exchanges. Considering the important results shown in this extensive interdisciplinary study it becomes clear that by introducing the new CMAGEP system, an important contribution was made to the field of symbolic regression by giving deserved attention to the often neglected aspect of interpretability. Furthermore, the application of CMAGEP in a symbolic regression framework to model terrestrial carbon fluxes helped build novel knowledge in the ecology field, giving this approach a significant potential for other future applications.