Numerical Representation Research Articles

Systematic bias in representation of reaction time distribution.

A correct perception of one's own abilities is essential for making appropriate decisions. A well-known bias in probability perception is that rare events are overestimated. Here, we examined whether such a bias also exists for action outcomes using a simple reaction task. In Experiment 1, after completing a set of 30 trials of the simple reaction task, participants were required to judge the probability that they would be able to respond before a given reference time when performing the task next. We assessed the difference between the actual reaction times and the probability judgement and found that the represented probability distribution was more widely distributed than the actual one, suggesting that low-probability events were overestimated and high-probability events were underestimated. Experiment 2 confirmed the presence of such a bias in the representation of both one's own and another's reaction times. In addition, Experiment 3 showed the presence of such a bias regardless of the difference between the representation of another's reaction times and the mere numerical representation. Furthermore, Experiment 4 found the presence of such a bias even when the information regarding actual reaction times was visually shown before the representation. The present results reveal the existence of a highly robust bias in the representation of motor performance, which reflects the ubiquitous bias in probability perception and is difficult to eliminate.

Mathematical modeling of irregularity indices for adriamycin and their statistical analysis for emetic drugs

Anthracyclines exert cytotoxic effects on cancer cells through genotoxicity, inducing damage to their genetic material and impeding their reproductive capacity. The compound possesses a molecular framework consisting of an anthracycline ring system, which confers its pharmacological activity against cancer. Adriamycin is an anthracycline chemotherapeutic agent characterized by a structurally intricate chemical composition. In this article, we computed irregularity indices like the Albertson index, total irregularity index, Randić irregularity index and other degree-based irregularity indices to estimate the biological and chemical properties of Adriamycin. The findings are illustrated through the use of numerical figures and graphical representations. Further, we proposed the relationship between irregularity indices and the physicochemical properties of emetic drugs. We examined that the irregularity indices showed a statistically significant relationship with Molecular Weight, Monoisotopic Mass, Polar Surface Area, Heavy Atom Count, Complexity, Boiling Point, Enthalpy of Vaporization, Flash Point, Molar Refractivity and Polarizability based on the p-value (<0.5). We proposed multiple linear regression models that will be helpful to estimate the physical properties of those drugs that were not calculated. The numerical results and visual representations of our analyses will be helpful in the advancement of knowledge regarding the structure-property correlations of these drugs.

A new Marshall-Olkin lomax distribution with application using failure and insurance data

This study developed a new family of distributions, the Marshall-Olkin generalized distribution. A novel model, the Marshall-Olkin Lomax (NMOL) distribution, was introduced into this family. The NMOL distribution exhibited a variety of density forms, including symmetry, right-skewness, reversed-J shape, upside-down bathtub curves, and scenarios with growing, decreasing, and mixed trends. From a practical perspective, the NMOL model was used to assess the failure and insurance data. Furthermore, a group-acceptance sampling plan (GASP) was developed based on the NMOL distribution, with the median serving as a quality criterion. This analysis also included numerical and graphical representations of the expected shortfalls and values at risk. Simulation studies were conducted to evaluate the effectiveness of the proposed estimation methods, and the findings significantly validated the NMOL model. However, this new distribution family and model has wide-ranging applications in sectors such as engineering, survival analysis, hydrology, and economics.

Heterogeneous Feature Selection Based on Neighborhood Combination Entropy.

Feature selection aims to remove irrelevant or redundant features and thereby remain relevant or informative features so that it is often preferred for alleviating the dimensionality curse, enhancing learning performance, providing better readability and interpretability, and so on. Data that contain numerical and categorical representations are called heterogeneous data, and they exist widely in many real-world applications. Neighborhood rough set (NRS) can effectively deal with heterogeneous data by using neighborhood binary relation, which has been successfully applied to heterogeneous feature selection. In this article, the NRS model as a unified framework is used to design a feature selection method to handle categorical, numerical, and heterogeneous data. First, the concept of neighborhood combination entropy (NCE) is presented. It can reflect the probability of pairs of the neighborhood granules that are probably distinguishable from each other. Then, the conditional neighborhood combination entropy (cNCE) based on NCE is proposed under the condition of considering decision attributes. Moreover, some properties and relationships between cNCE and NCE are derived. Finally, the functions of inner and outer significances are constructed to design a feature selection algorithm based on cNCE (FScNCE). The experimental results show the effectiveness and superiority of the proposed algorithm.

From tomographic imaging to numerical simulations: an open-source workflow for true morphology mesoscale FE meshes

Full-field techniques such as tomography are becoming progressively more central in the study of complex phenomena, in particular where spatiotemporal evolution is crucial, as in moisture transport or crack initiation in porous media. These techniques provide a unique insight in the local process whose quantification allows the improvement of our understanding and of the models describing them. Nevertheless, the model validation can be pushed further by attempting to explicitly represent the heterogeneities and simulate their role in the processes. Once validated, these models can be used to perform “virtual experiments”, and overcome the limitations of the experiments (e.g., sample size and number, fine control of the boundary and initial conditions). This study proposes a connection between tomography images and mesoscale models through a workflow that mainly employs open-source tools. This workflow is illustrated through the digitization of a Portland cement concrete sample, stemming from neutron tomographies and resulting in a numerical finite element mesh. The proposed workflow is flexible, allowing for the conversion of images from various sources, such as x-ray or neutron tomographies, to different numerical representations of the domain, such as finite element meshes or even a discrete domain required by discrete element methods, while preserving real morphologies with an accuracy proportionate to the specific need of the problem. Beside its generalizability, our method also offers automated labelling of the different domains and boundaries in both the volumetric and surface meshes, which is often necessary for assigning material properties and boundary conditions. Finally, the series of image, geometry and mesh processing steps described in this work are made available on a GitHub repository.

Spam analysis and classification of the dynamic message using a vectorizing technique with multi-model machine learning algorithm

Spam analysis and classification of dynamic messages is an essential task in order to combat the ever-increasing volume of unsolicited and malicious emails. One effective approach is to employ a vectorizing technique along with a multi-model machine learning algorithm. This approach involves representing email messages as high-dimensional vectors, capturing various features such as word frequencies, presence of specific keywords, and structural characteristics. By transforming the text into numerical representations, the machine learning algorithm can then learn patterns and make predictions based on these representations. The use of a multi- model algorithm allows for the integration of different classification models, each with its own strengths and weaknesses, to enhance the overall performance. This approach can achieve high accuracy by leveraging diverse learning methods and combining their predictions. Furthermore, the approach is dynamic in nature, meaning that it can adapt to new forms of spam and evolving attack strategies. The key challenge lies in selecting appropriate features and tuning the parameters of the algorithm to ensure optimal performance. The results of this study can contribute to the development of more effective and efficient spam detection systems, helping users to filter out unwanted and potentially harmful messages. Keywords: spam analysis, dynamic messages, classification, vectorizing techniques, multi-model machine learning algorithm, email filtering, unsolicited emails, malicious emails, feature extraction, pattern recognition.

Simultaneously improving accuracy and computational cost under parametric constraints in materials property prediction tasks

Modern data mining techniques using machine learning (ML) and deep learning (DL) algorithms have been shown to excel in the regression-based task of materials property prediction using various materials representations. In an attempt to improve the predictive performance of the deep neural network model, researchers have tried to add more layers as well as develop new architectural components to create sophisticated and deep neural network models that can aid in the training process and improve the predictive ability of the final model. However, usually, these modifications require a lot of computational resources, thereby further increasing the already large model training time, which is often not feasible, thereby limiting usage for most researchers. In this paper, we study and propose a deep neural network framework for regression-based problems comprising of fully connected layers that can work with any numerical vector-based materials representations as model input. We present a novel deep regression neural network, iBRNet, with branched skip connections and multiple schedulers, which can reduce the number of parameters used to construct the model, improve the accuracy, and decrease the training time of the predictive model. We perform the model training using composition-based numerical vectors representing the elemental fractions of the respective materials and compare their performance against other traditional ML and several known DL architectures. Using multiple datasets with varying data sizes for training and testing, We show that the proposed iBRNet models outperform the state-of-the-art ML and DL models for all data sizes. We also show that the branched structure and usage of multiple schedulers lead to fewer parameters and faster model training time with better convergence than other neural networks. Scientific contribution: The combination of multiple callback functions in deep neural networks minimizes training time and maximizes accuracy in a controlled computational environment with parametric constraints for the task of materials property prediction.

Exploring Numerical Competence: Analysis Of Students' Mathematical Representation Skills in PISA Space and Shape Content

This research aims to analyze students' mathematical representation skills in solving PISA Space and Shape content questions, taking into account their numerical ab. Mathematical representation is a key skills in understanding and solving mathematical problems, while numerical skills play a vital role in developing an understanding of concepts and their applications in spatial and shape contexts.The research method employed is a qualitative approach, collecting data from students through written tests and interviews. The research instruments include questions reflecting Space and Shape content from PISA, as well as numerical skills tests.The research findings indicate a significant relationship between students' numerical skills and their skills to represent mathematical problems related to Space and Shape. Students with better numerical skills tend to have better mathematical representation skills. Furthermore, these findings can provide insights for educators and researchers to develop teaching strategies that integrate the development of numerical skills and mathematical representation, there by enhancing the quality of students' mathematical understanding at a global level.

Expected values of sum-based topological indices of random cyclodecane chains

Cyclodecanes, belonging to the class of aliphatic cycloalkanes, comprise non-aromatic carbon-atom rings. Within the 10-membered ring, cyclodecanes exhibit various isomers, characterized by different spatial arrangements of carbon atoms. Serving as model compounds in organic studies, cyclodecanes offer insights into the properties and reactivity of cyclic hydrocarbons. The chemistry of cyclodecane serves as a valuable foundation for understanding the behavior of more complex hydrocarbons. In this paper, we explore the potential probabilities of random cyclodecane chains Dtρ of length t ≥ 3. We derive exact expressions for the expected values of the modified second Zagreb index, inverse index, and second NDe index. A theoretical comparative analysis of these descriptors is provided, accompanied by graphical and numerical representations of the obtained results.

Method of characteristics for transient, planar, cylindrical flows

Cylindrical radiation of individual pulses is studied and strong differences from spherical radiation are highlighted. Prior to this study, the class of available analytical solutions for cylindrical radiation was rather limited. It included (i) a well-known solution for a steady-state, time-harmonic line source and (ii) the solution for a delta-pulse line source. The first of these has no analytical counterpart for individual pulses. By means of the second (actually the Green's function) a more general class of line source solutions can be formulated, but each one is in the form of an integral that has to be evaluated numerically and requires tedious preparation of a singular integrand, making it difficult to achieve perfect accuracy. In the present paper, use is made instead of a particular family of analytically-exact (linear) solutions that has been developed recently. It is used to assess the accuracy of solutions obtained numerically by the method of characteristics (MoC), which is then applied to more general sources than those amenable to analytical treatment. The MoC analysis is specially formulated to reduce the influence of terms involving the reciprocal of the radius (such terms are numerically unmanageable close to the origin). It is found that the qualitative behaviour of waves radiating from the surface of a cylinder of finite radius can depend strongly on the duration of the initiating disturbance and that this can be interpreted in a convolution-like manner. After validation, the numerical method is coupled with a conventional MoC analysis of planar wave propagation and is used to simulate the reflection and radiation of an initially planar wavefront arriving at a flanged duct exit. The numerical representation is one-dimensional in both domains – (x,t) inside the duct and (r,t) outside it. Although its use implies identical behaviour in all radial directions in the external domain, the solution is found to be in close agreement with circumferential-average values from a CFD solution that simulates azimuthal variations as well as radial variations. Whilst being less comprehensive than the CFD simulation, the MoC analysis has the important practical benefit of making highly efficient use of human and computational resources. By comparing the MoC and CFD solutions, it is found that the nominally-cylindrical radiation from the duct approximates closely to radiation from a line source a small distance inside the duct (not at the exit plane). An approximate location of the effective source is quantified.

Evaluation of Machine Learning Methods for Prediction Student Performance

Abstract: Significant findings and useful insights have emerged from the study of using machine learning techniques to predict student performance. used large datasets with a wide variety of demographic, socioeconomic, and academic performance data to conduct in-depth evaluations of several machine learning methods. Our study highlighted the importance of careful data preprocessing, which involves fundamental steps like classifying student performance and doing in-depth exploratory data analysis (EDA). To ensure the validity of our model assessments, we meticulously split the dataset into training and testing subsets. To effectively apply machine learning models, it is necessary to convert categorical data into numerical representations; we did this by using strategic label encoding and one-hot encoding techniques. Metrics on the effectiveness of the recommended machine learning models are presented, with a spotlight on the XG Boost algorithm's remarkable 97% accuracy. The MLP's performance indicators are as follows: 95% accuracy, 98% recall, 95% precision, and 96% F1 score. When compared to these, ADA Boost has a precision of 83%, recall of 90%, F1 score of 86%, and accuracy rate of 81%. XGBoost, on the other hand, claims rates of 98% precision, 98% recall, 98% F1 score, and 97% accuracy, making it stand out from the crowd. Based on these findings, the XG Boost algorithm is the best option among the machine learning models considered for this research.

NLP-based tools for localization of the epileptogenic zone in patients with drug-resistant focal epilepsy

Epilepsy surgery is an option for people with focal onset drug-resistant (DR) seizures but a delayed or incorrect diagnosis of epileptogenic zone (EZ) location limits its efficacy. Seizure semiological manifestations and their chronological appearance contain valuable information on the putative EZ location but their interpretation relies on extensive experience. The aim of our work is to support the localization of EZ in DR patients automatically analyzing the semiological description of seizures contained in video-EEG reports. Our sample is composed of 536 descriptions of seizures extracted from Electronic Medical Records of 122 patients. We devised numerical representations of anamnestic records and seizures descriptions, exploiting Natural Language Processing (NLP) techniques, and used them to feed Machine Learning (ML) models. We performed three binary classification tasks: localizing the EZ in the right or left hemisphere, temporal or extra-temporal, and frontal or posterior regions. Our computational pipeline reached performances above 70% in all tasks. These results show that NLP-based numerical representation combined with ML-based classification models may help in localizing the origin of the seizures relying only on seizures-related semiological text data alone. Accurate early recognition of EZ could enable a more appropriate patient management and a faster access to epilepsy surgery to potential candidates.

An Application of Fuzzy Symbolic Time-Series for Energy Demand Forecasting

In this paper, we present a new fuzzy symbolization technique for energy load forecasting with neural networks, FPLS-Sym. Symbolization techniques transform a numerical time series into a smaller string of symbols, providing a high-level representation of time series by combining segmentation, aggregation and discretization. The dimensional reduction obtained with symbolization can speed up substantially the time required to train neural networks, however, it can also lead to considerable information losses that could lead to a less accurate forecast. FPLS-Sym introduces the use of fuzzy logic in the discretization process, maintaining more information about each segment of the neural network at the expense of requiring more space in memory. Extensive experimentation was made to evaluate FPLS-Sym with various neural-network-based models, including different neural network architectures and activation functions. The evaluation was done with energy demand data from Spain taken from 2009 to 2019. Results show that FPLS-Sym provides better quality metrics than other symbolization techniques and outperforms the use of the standard numerical time series representation in both quality metrics and training time.

Unveiling Efficiency: Investigating Distance Measures in Wastewater Treatment Using Interval-Valued Neutrosophic Fuzzy Soft Set

&#x0D; To reduce the threats that wastewater poses to human health and the environment, water treatment techniques must be improved. The use of a procedure that includes preparation, testing, primary and secondary treatments, filtration, disinfection, and continuous monitoring is therefore required. The objective of this research is to create a hybrid notion that extends the idea of an interval-valued neutrosophic fuzzy soft set (IVNFSS) to an interval-valued neutrosophic fuzzy set. Operations like complement, union, and integration are included in the idea. To improve decision-making accuracy, a quality-assessment distance measure is incorporated, offering a numerical representation of the disparity between various factors. Furthermore, the IVNFSS defines distance measures, which are used in the wastewater treatment process. To monitor water quality, IVNFSS, in conjunction with a distance measure, is a potent instrument whose application extends to water waste treatment procedures. This can completely change the way that water quality management is now done by providing a methodical way to guarantee the security and quality of drinking water.&#x0D;

EFFECT THE PROBLEM-BASED LEARNING MODEL ON ABILITY MULTIPLE REPRESENTATIONS OF XI-GRADE STUDENTS ON ACID-BASED TOPIC

It takes the ability to conceive at three different levels of representation, macroscopic, sub microscopic, and symbolic to comprehend acid-base material. Still, most students are unable to make the connection between the three levels of representation. As a result, instruction that helps students connect various representations in acid-base content is required. The PBL model is one appropriate learning paradigm that can be used. The purpose of this study is to determine whether PBL models and conventional models differ in their capacity to support numerous representations. A quantitative experiment using a quasi-experimental study design is the research methodology employed. A post-test-only control group design is used in this study. The samples of this study were XI MIPA 3 as a control group of 34 students and XI MIPA 4 as an experimental group of 33 students. Simple random sampling was used to get the research samples. A post-test consisting of multiple-choice questions was the instrument utilized. With a reliability score of 0,802 across 20 items, the empirical validation results indicate that all instruments are appropriate for use as research measures. methods for gathering data through tests. Data collection techniques in the form of tests. The data analysis technique in this study is descriptive and inferential statistics with hypothesis testing in the form of the Independent Sample t-Test. With a sig value of 0,000 &lt; 0,05, the results demonstrated that there is a difference in the ability of multiple representations between those taught using the PBL model and those taught using the conventional model.

NeuralBeds: Neural embeddings for efficient DNA data compression and optimized similarity search

The availability of high throughput sequencing tools coupled with the declining costs in the production of DNA sequences has led to the generation of enormous amounts of omics data curated in several databases such as NCBI and EMBL. Identification of similar DNA sequences from these databases is one of the fundamental tasks in bioinformatics. It is essential for discovering homologous sequences in organisms, phylogenetic studies of evolutionary relationships among several biological entities, or detection of pathogens. Improving DNA similarity search is of outmost importance because of the increased complexity of the evergrowing repositories of sequences. Therefore, instead of using the conventional approach of comparing raw sequences, e.g., in fasta format, a numerical representation of the sequences can be used to calculate their similarities and optimize the search process. In this study, we analyzed different approaches for numerical embeddings, including Chaos Game Representation, hashing, and neural networks, and compared them with classical approaches such as principal component analysis. It turned out that neural networks generate embeddings that are able to capture the similarity between DNA sequences as a distance measure and outperform the other approaches on DNA similarity search, significantly.

Primary students’ relational thinking and computation strategies with concrete-to-symbolic representations of subtraction as difference

Children are highly inclined to attend to the properties of numbers, operations and equality when given helpful tools for doing so. Our aim was to investigate early algebraic thinking with the compensation property of equality for subtraction. We provided 22 (9–11-year-old) students with physical blocks for building vertical towers and conducted individual interviews with them as they completed a sequence of 15 tasks involving subtraction as difference using concrete, numeric, and symbolic representations. Relational thinking was evidenced across a range of subtraction calculation skill levels. Those students who could use both indirect addition and take-away strategies flexibly, depending on the size of the numbers involved, were more likely to evidence attention to generality with symbolic equations. The shift to symbolic equations elicited some students’ productive attempts to connect subtraction as difference and subtraction as take way but seemed to hinder others by provoking a return to take away calculations rather than relational thinking strategies.

Numerical representation of topological real algebras

We show that the isomorphism provided by the Gelfand-Mazur theorem for a commutative pre-ordered real Banach algebra A with unit defines a numerical representation which is compatible with the order structure.

Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling the disease, we use the Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, we treat a compartment in the body that contains infectious and non-infectious cells. More precisely, the solvability and Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, we apply the Euler method to develop an approximation solution. It connected with numerous graphical representations of the system using various arbitrary ordering and varying values of the isolation parameters. Here we remark that the multi-step behavior that certain problems exhibit, is one of important issues naturally. This paper introduces the idea of piecewise derivative with the goal of modeling real-world issues that follow multiples processes. With the help of the used approach, we investigate the cancer disease model and its transmission dynamical behavior with crossover effect.

Legal Information Retrieval and Entailment Using Transformer-based Approaches.

The challenge of information overload in the legal domain increases every day. The COLIEE competition has created four challenge tasks that are intended to encourage the development of systems and methods to alleviate some of that pressure: a case law retrieval (Task 1) and entailment (Task 2), and a statute law retrieval (Task 3) and entailment (Task 4). Here we describe our methods for Task 1 and Task 4. In Task 1, we used a sentence-transformer model to create a numeric representation for each case paragraph. We then created a histogram of the similarities between a query case and a candidate case. The histogram is used to build a binary classifier that decides whether a candidate case should be noticed or not. In Task 4, our approach relies on fine-tuning a pre-trained DeBERTa large language model (LLM) trained on SNLI and MultiNLI datasets. Our method for Task 4 was ranked third among eight participating teams in the COLIEE 2023 competition. For Task 4, We also compared the performance of the DeBERTa model with those of a knowledge distillation model and ensemble methods including Random Forest and Voting.