Addition Subtraction Research Articles

Quantum illumination with noisy probes: Conditional advantages of non-Gaussianity

Entangled states, like the two-mode squeezed vacuum state, are known to give quantum advantage in the illumination protocol, a method to detect a weakly reflecting target submerged in a thermal background. We use non-Gaussian photon-added and -subtracted states, affected by local Gaussian noise on top of the omnipresent thermal noise, as probes in the illumination protocol. Based on the difference between the Chernoff bounds obtained with the coherent state and the non-Gaussian state having equal signal strengths, whose positive values denote quantum advantage in illumination, we highlight the hierarchy among non-Gaussian states, which is compatible with correlations per unit signal strength, although the Gaussian states offer the best performance. Interestingly, such hierarchy is different when comparisons are made using the Chernoff bounds. The entire analysis is performed in the presence of different imperfect apparatus like faulty twin-beam generator, imperfect photon addition (subtraction) as well as with noisy non-Gaussian probe states.

Form perception is a cognitive correlate of the relation between subitizing ability and math performance.

"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation).

Enhancing Additive Restoration of Damaged Polymer Curved Surfaces through Compensated Support Beam Utilization

As additive manufacturing advances, it offers a cost-effective avenue for structurally repairing components. However, a challenge arises in the additive repair of suspended damaged surfaces, primarily due to gravitational forces. This can result in excessive deformation during the repair process, rendering the formation of proper repair impractical and leading to potential failure. In light of this rationale, conventional repair techniques are impractical for extensively damaged surfaces. Thus, this article proposes a novel repair methodology that is tailored to address large-area damage. Moreover, and departing from conventional practices involving the addition and subsequent subtraction of materials for precision machining, the proposed process endeavors to achieve more precise repair outcomes in a single operation. This paper introduces an innovative repair approach employing fused deposition modeling (FDM) to address the complexities associated with the repair of damaged polymer material parts. To mitigate geometric errors in the repaired structural components, beams with minimal deformation are printed using a compensation method. These beams then serve as supports for overlay printing. The paper outlines a methodology by which to determine the distribution of these supporting beams based on the shape of the damaged surface. A beam deformation model is established, and the printing trajectory of the compensated beam is calculated according to this model. Using the deformation model, the calculated deformation trajectories exhibit excellent fitting with the experimentally collected data, with an average difference between the two of less than 0.3 mm, validating the accuracy of the suspended beam deformation model. Based on the statistical findings, the maximum average deformation of the uncompensated sample is approximately 5.20 mm, whereas the maximum deformation of the sampled point after compensation measures around 0.15 mm. Consequently, the maximum deformation of the printed sample post-compensation is mitigated to roughly 3% of its pre-compensation magnitude. The proposed method in this paper was applied to the repair experiment of damaged curved surface components. A comparison was made between the point cloud data of the repaired surface and the ideal model of the component, with the average distance between them serving as the repair error metric. The mean distance between the point clouds of the repaired parts using the proposed repair strategy is 0.197 mm and the intact model surface is noticeably less than the mean distance corresponding to direct repair, at 0.830 mm. The repair error with compensatory support beams was found to be 76% lower than that without compensatory support beams. The surface without compensatory support beams exhibited gaps, while the surface with compensatory support beams appeared dense and complete. Experimental results demonstrate the effectiveness of the proposed method in significantly reducing the geometric errors in the repaired structural parts. The outcomes of the FDM repair method are validated through these experiments, affirming its practical efficacy. It is noteworthy that, although only PLA material was used in this study, the proposed method is general and effective for other polymer materials. This holds the potential to significantly reduce costs for the remanufacturing of widely used polymers.

Simple and reconfigurable photonics-based half adder and half subtracter

A photonics-based digital signal processing structure that has the ability of realising half addition and half subtraction, is presented. It is based on applying the two digital inputs into a dual-polarisation modulator and designing the modulator bias voltages to realise the logical operations. After photodetection, a Sum output and a Carry output for half addition, or a Difference output and a Borrow output for half subtraction, can be generated. Switching between the half addition operation and the half subtraction operation can be achieved by simply changing a digital input amplitude and a modulator bias voltage. The proposed photonics-based digital signal processing structure is theoretically analysed. Using the system parameter setting obtained from the theoretical analysis, half addition and half subtraction operations are experimentally demonstrated.

Calculation of the results of basic arithmetic operations with quaternions defined in the interval form

The goal of the work. Creation of an EXCEL-oriented calculator for determining the results of basic arithmetic operations with quaternions, which are given by hyperbolic interval numbers. The subject of research is the set of quaternions and arithmetic operations defined on this set. Research method: Algorithmic and numerical analysis of procedures for performing basic arithmetic operations with quaternions given by hyperbolic interval numbers. The obtained results. The definition of a quaternion, the coefficients of which are interval numbers, is given. It was obtained the ratios for determining in the interval form the following characteristics: quaternion norm, quaternion modulus, quaternion vector part modulus, quaternion argument, quaternion sign was obtained. It was obtained the ratios for determining in the interval form the following basic arithmetic operations: sum of quaternions, difference of quaternions, multiplication of a constant value by a quaternion, scalar product of quaternions, product of vector parts of quaternions, product of quaternions, vector product of quaternions, left and right division of quaternions. The ratio for calculating the determinants of the second order, the elements of which are defined in the interval form, is obtained. The ratio for the approximate calculation of determinants of arbitrary order, the elements of which are defined in the interval form, is obtained. It is shown that the operations of multiplication (division) of interval numbers and raising them to an integer power are expedient to perform when they have a hyperbolic form. It is advisable to perform the addition (subtraction) operation with interval numbers given in the classic form or in the CENTER-RADIUS system. It is better to use the last form in the case of determining the coefficients of the quaternions based on the results of technological calculations. Screenshots of the formulas for determining the vector product of quaternions are given, provided that the coefficients at their orths are represented by interval numbers.

Can Students’ Misconceptions regarding Decimal Notation be Eliminated with the 5E Model Enriched with Digital Concept Cartoons?

This study eliminates students’ misconceptions about decimal notation with the teaching method implemented according to the 5E model enriched with Digital Concept Cartoons (DCCs). The study was conducted with eight sixth grade students. In this study conducted using the action research method, lesson plans were designed based on the 5E model enriched with DCCs to eliminate misconceptions. The data were collected from Misconception Identification Forms 1 and 2, observation notes, and interviews conducted during the implementation process. Qualitative data analysis techniques were employed to analyze the data. Consequently, it was revealed that most students’ misconceptions about decimal notation decreased with the application of the 5E model enriched with DCCs. After the implementation, it was observed that most of the students’ misconceptions about sorting, place value, addition–subtraction, marking the numbers on the number line, and rounding in decimal notation were largely eliminated. In contrast, it was observed that students’ misconceptions regarding the multiplication/division operations and problems in decimal notation did not decrease.

Shear Strength of Loess in the Yili Region and Corresponding Degradation Mechanisms under Different Cycling Modes

In the Yili region, China, complex environmental conditions induce repeated wet–dry (WD) and freeze–thaw (FT) cycles, deteriorating soil shear strength and producing frequent loess landslides. In this study, we collected soil samples from the Alemale landslide, Yili Prefecture and performed their triaxial shear tests with different numbers of WD, FT, and WD-FT cycles. In addition, we summarized the change mechanisms of loess mechanical properties and its deterioration, in the Yili region, under different cyclic effects. Subsequently, the test results under the three cycling modes were compared and analyzed, the differences in the deterioration effects of different cyclic conditions on loess were discussed in depth, and finally, a multiple linear regression model was established and the weights of single factors under the action of coupled cycles were analyzed. The results show the following: (1) Regardless of the confining pressure values, the principal stress evolution trends in soil samples under different cycling modes were generally consistent, i.e., after an initial increase, peak values were reached, followed by a final decline. (2) Under unconsolidated undrained (UU) conditions, shear strength values of all soil samples tested under the three cycling modes dropped after the first twenty cycles, exhibiting different evolution patterns. (3) Coupled WD-FT cycling most significantly promoted soil shear strength degradation, with less WD cycling effect, and FT cycling had the least significant effect; in all three modes, the first cycle had the highest contribution to this effect. From the perspectives of cohesion, angle of internal friction, and decay of shear strength attenuation, the coupled WD-FT cycling effect on soil shear strength could not be reduced to a simple single-factor addition–subtraction relationship. (4) Weight analysis of soil samples after WD, FT, and WD-FT cycling revealed that WD cycles in the coupled WD-FT cycling mode had the most significant impact on the shear strength attenuation of soil samples (contributing 57%), FT cycles had a medium impact (contributing about 33%), while the effect of the total number of cycles was negligible (about 10%). The research results provide experimental and theoretical bases for subsequent control of loess landslides.

Continuous-variable quantum key distribution based on non-Gaussian operations with on-off detection.

Quantum key distribution (QKD) with continuous variable (CV) is an effective method for achieving the high key rate, but is also limited to a short transmission distance. To overcome this limitation, some solutions have been proposed, including non-Gaussian operations, such as photon addition and photon subtraction using ideal photon source and number-resolving detection. Here we consider the effect of non-Gaussian operation for realistic photon source and ideal on-off photon detection. In the realistic case, it is shown that the performance of CVQKD can not be improved by both photon-subtraction/addition on the right side before the entangled source reaches the channel and photon-subtraction on the left side preceding the entangled source to the sender Alice before performing heterodyne detection, but be enhanced by the photon addition on the left side in a long distance case. These results may provide a useful reference for quantum information with continuous variable.

Axial Cross Attention Meets CNN: Bibranch Fusion Network for Change Detection

In the previous years, vision transformer has demonstrated a global information extraction capability in the field of computer vision that convolutional neural network (CNN) lacks. Due to the lack of inductive bias in vision transformer, it requires a large amount of data to support its training. In the field of remote sensing, it costs a lot to obtain a significant number of high-resolution remote sensing images. Most existing change detection networks based on deep learning rely heavily on the CNN, which cannot effectively utilize the long-distance dependence between pixels for difference discrimination. Therefore, this work aims to use a high-performance vision transformer to conduct change detection research with limited data. A bibranch fusion network based on axial cross attention (ACABFNet) is proposed. The network extracts local and global information of images through the CNN branch and transformer branch, respectively, and then, fuses local and global features by the bidirectional fusion approach. In the upsampling stage, similar feature information and difference feature information of the two branches are explicitly generated by feature addition and feature subtraction. Considering that the self-attention mechanism is not efficient enough for global attention over small datasets, we propose the axial cross attention. First, global attention along the height and width dimensions of images is performed respectively, and then cross attention is used to fuse the global feature information along two dimensions. Compared with the original self-attention, the structure is more graphics processing unit friendly and efficient. Experimental results on three datasets reveal that the ACABFNet outperforms existing change detection algorithms.

GPU implementation of evolving spiking neural P systems

Methods for optimizing and evolving spiking neural P systems (in short, SN P systems) have been previously developed with the use of a genetic algorithm framework. So far, these computations, both evolving and simulating, were done only sequentially. Due to the non-deterministic and parallel nature of SN P systems, it is natural to harness parallel processors in implementing its evolution and simulation. In this work, a parallel framework for the evolution of SN P Systems is presented. This is the result of extending our previous work by implementing it on a CUDA-enabled graphics processing unit and adapting CuSNP design in simulations. Using binary addition and binary subtraction with 3 different categories each as initial SN P systems, the GPU-based evolution runs up to 9x faster with respect to its CPU-based evolution counterparts. Overall, when considering the whole process, the GPU framework is up to 3 times faster than the CPU version.

A mutated addition–subtraction unit to reduce the complexity of FFT

A mutated addition–subtraction unit to reduce the complexity of FFT

Hybrid CV-DV Quantum Communications and Quantum Networks

Quantum information processing (QIP) opens new opportunities for high-performance computing, high-precision sensing, and secure communications. Among various QIP features, the entanglement is a unique one. To take full advantage of quantum resources, it will be necessary to interface quantum systems based on different encodings of information both discrete and continuous. The goal of this paper is to lay the groundwork for the development of a robust and efficient hybrid continuous variable-discrete variable (CV-DV) quantum network, enabling the distribution of a large number of entangled states over hybrid DV-CV multi-hop nodes in an arbitrary topology. The proposed hybrid quantum communication network (QCN) can serve as the backbone for a future quantum Internet, thus providing extensive long-term impacts on the economy and national security through QIP, distributed quantum computing, quantum networking, and distributed quantum sensing. By employing the photon addition and photon subtraction modules we describe how to generate the hybrid DV-CV entangled states and how to implement their teleportation and entanglement swapping through entangling measurements. We then describe how to extend the transmission distance between nodes in hybrid QCN by employing macroscopic light states, noiseless amplification, and reconfigurable quantum LDPC coding. We further describe how to enable quantum networking and distributed quantum computing by employing the deterministic cluster state concept introduced here. Finally, we describe how the proposed hybrid CV-DV states can be used in an entanglement-based hybrid QKD.

Enhancing Mathematical Word Problem Solving Skills: Using Bar Model Visualization Technique

The study purpose is to investigate the effect of Bar Model Visualization Technique on the word problem solving skills of elementary level students in mathematics. Following were the objectives of the study (i) to investigate the effect of Bar Model Visualization Technique on addition word problems-solving skills; (ii) to investigate the effect of Bar Model Visualization Technique on subtraction word problems solving skills; (iii) to investigate the effect of Bar Model Visualization Technique on multiplication word problems solving skills; (iv) to investigate the effect of Bar Model Visualization Technique on division word problems solving skills. The null hypotheses were designed to test the objectives as (i) there is no significant effect of Bar Model Visualization Technique on addition word problem solving skills; (ii) there is no significant effect of Bar Model Visualization Technique on subtraction word problem solving skills; (iii) there is no significant effect of Bar Model Visualization Technique on multiplication word problem solving skills; (iv) there is no significant effect of Bar Model Visualization Technique on division word problem solving skills. The nature of the study was experimental. Pre-test and post-test equivalent group design was used as a tool for data collection in this study. Sample of the study was 40 students (Male & Female) of Government Primary School No.2 Bab-e-Jadeed District Nowshera, Khyber Pakhtunkhwa. The sample students were divided on the basis of pretest scores by applying paired random technique in to experimental group and control group. Data were analyzed by mean, SD and t-test. It was concluded that the concepts of Bar Model Visualization Technique had significant effect on addition word problems and subtraction word problems but it has not significant effect on multiplication word problems neither division word problems. The results of the study show that Bar Model Visualization Technique had significant effect on Mathematical word problem solving skills and also the learner take interest in the subject. It provides alternative method for teacher to teach mathematics subject.

Standard sample evaluation method for noise annoyance suppression from audio injection

Noise control technology based on sound energy reduction uses sound pressure level as an evaluation index, and the addition control technology proposed in recent years uses annoyance as an evaluation index. However, no method has been proposed to link the change in sound pressure level with the change in annoyance. In this paper, three types of transformer substation noise are selected as the target sounds, natural sounds and synthetic sounds are selected as the controllable sound, and the pure tone annoyance and combined noise annoyance evaluation experiments are carried out using the standard sample method, and the curve of the decrease value of annoyance and the equivalent sound pressure level change value is obtained. And the effect of audio injection annoyance control is quantitatively analyzed, aiming to build a bridge between addition control and subtraction control. The research results show the effect of controllable sound on the annoyance of substation noise. This study provides new ideas for quantitative analysis of noise control effects and substation noise control.

Not toeing the number line for simple arithmetic: Two large-n conceptual replications of Mathieu et al. (Cognition, 2016, Experiment 1)

We conducted two conceptual replications of Experiment 1 in Mathieu, Gourjon, Couderc, Thevenot, and Prado (2016, https://doi.org/10.1016/j.cognition.2015.10.002). They tested a sample of 34 French adults on mixed-operation blocks of single-digit addition (4 + 3) and subtraction (4 – 3) with the three problem elements (O1, +/-, O2) presented sequentially. Addition was 34 ms faster if O2 appeared 300 ms after the operation sign and displaced 5° to the right of central fixation, whereas subtraction was 19 ms faster when O2 was displaced to the left. Replication Experiment 1 (n = 74 recruited at the University of Saskatchewan) used the same non-zero addition and subtraction problems and trial event sequence as Mathieu et al., but participants completed blocks of pure addition and pure subtraction followed by the mixed-operation condition used by Mathieu et al. Addition RT showed a 32 ms advantage with O2 shifted rightward relative to leftward but only in mixed-operation blocks. There was no effect of O2 position on subtraction RT. Experiment 2 (n = 74) was the same except mixed-operation blocks occurred before the pure-operation blocks. There was an overall 13 ms advantage with O2 shifted right relative to leftward but no interaction with operation or with mixture (i.e., pure vs mixed operations). Nonetheless, the rightward RT advantage was statistically significant for both addition and subtraction only in mixed-operation blocks. Taken together with the robust effects of mixture in Experiment 1, the results suggest that O2 position effects in this paradigm might reflect task specific demands associated with mixed operations.

Associations between acute exposures to PM2.5 and carbon dioxide indoors and cognitive function in office workers: a multicountry longitudinal prospective observational study

Despite evidence of the air pollution effects on cognitive function, little is known about the acute impact of indoor air pollution on cognitive function among the working-age population. We aimed to understand whether cognitive function was associated with real-time indoor concentrations of particulate matter (PM2.5) and carbon dioxide (CO2). We conducted a prospective observational longitudinal study among 302 office workers in urban commercial buildings located in six countries (China, India, Mexico, Thailand, the United States of America, and the United Kingdom). For 12 months, assessed cognitive function using the Stroop color-word test and addition–subtraction test (ADD) via a mobile research app. We found that higher PM2.5 and lower ventilation rates, as assessed by CO2 concentration, were associated with slower response times and reduced accuracy (fewer correct responses per minute) on the Stroop and ADD for eight out ten test metrics. Each interquartile (IQR) increase in PM2.5 (IQR = 8.8 g m−3) was associated with a 0.82% (95% CI: 0.42, 1.21) increase in Stroop response time, a 6.18% (95% CI: 2.08, 10.3) increase in Stroop interference time, a 0.7% (95% CI: −1.38, −0.01) decrease in Stroop throughput, and a 1.51% (95% CI: −2.65, −0.37) decrease in ADD throughput. For CO2, an IQR increase (IQR = 315 ppm) was associated with a 0.85% (95% CI: 0.32, 1.39) increase in Stroop response time, a 7.88% (95% CI: 2.08, 13.86) increase in Stroop interference time, a 1.32% (95% CI: −2.3, −0.38) decrease in Stroop throughput, and a 1.13% (95% CI: 0.18, 2.11) increase in ADD response time. A sensitivity analysis showed significant association between PM2.5 in four out of five cognitive test performance metrics only at levels above 12 g m−3. Enhanced filtration and higher ventilation rates that exceed current minimum targets are essential public health strategies that may improve employee productivity.

A novel binary operator for designing medical and natural image cryptosystems

Image cryptosystems aim to secure the transmission of images in the presence of adversaries in the network. For ensuring confidentiality, images are encrypted to form unintelligible cipher images, the algorithms of which are much different from those for text data. Most image cryptosystems follow confusion–diffusion or complex architectures, which involves permutation and substitution of pixel values. Often these are done using chaotic maps and involve binary operations such as bitwise XOR, addition–subtraction, DNA operations, etc., each of which has certain limitations. Most of the cryptosystems for medical images proposed in the literature encrypt 8-bit compressed versions of the images rather than the standard 16-bit DICOM version, which results in loss of information. This paper presents a novel binary operation that can be used for all types of image cryptosystems — from DICOM medical to natural images using both conventional and DNA approaches. The use of this operation has been tested on a proposed DNA-based cryptosystem, which has novel steps for encryption to overcome the drawbacks of some existing ones. The cryptosystem has been tested on several images of varying pixel depth and dimensions, and the results obtained meet the standards of a secured image encryption system.

Individual differences in the development of children’s arithmetic fluency from grades 2 to 3.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Non-classicality and Non-Gaussianity of Photons Added and Subtracted Multi-Coherent States

A non classical and non Gaussian states become an essential need in quantum information processing theoretically and experimentally. In the present paper, the non classical and non Gaussian properties of superposed states exposure to photon addition and photon subtraction operations are described. The effect of adding and subtracting photons to multi-coherent state has a great interest in improving the features of the state. Furthermore, the photons added then subtracted multi-coherent states is more efficient than the opposite scenario.

FRACTION CIPHER: A WAY TO ENHANCE STUDENT ABILITY IN ADDITION AND SUBTRACTION FRACTION

Learning the concept of fractions can be one of the most difficult skills to master for primary school students. Fractions are also seen to affect other mathematical knowledge, such as algebra. Researchers have introduced an innovation called Fraction Cipher to help students learn fractions. Fraction Cipher is an innovation in the arena of education that involves learning the Malay language and Mathematics. Design research is used as the research method to solve this problem consisting of three phases: preliminary design, teaching experiment, and retrospective analysis. The instruments used are fraction cipher, fraction test, and observation checklist. The results of the pair's comparative study by controlling the type I error using the Bonferroni method show that the mean values of the mathematical achievement of the experimental group and the control group are significantly different. The results show that Fraction Cipher impacts students to understand and master the concept of fractional addition and fraction subtraction operations. This research also explains the "Sake-Beda" strategy to make it easier for students to solve fractional operation problems. Besides, this study also shows the change in students' attitudes from negative to more positive. Thus, students understand and are more motivated to learn the concept of fractions.