Integer Operations Research Articles

Quantizing Oriented Object Detection Network via Outlier-Aware Quantization and IoU Approximation

In recent years, a large number of quantization schemes have been proposed for compressing convolutional neural networks (CNN). However, most of them have the following problems: 1) when there are outliers in the weight, post-training quantization cannot obtain the ideal effect, and the accuracy loss is unavoidable; 2) quantizing the non-maximum suppression (NMS) stage of oriented object detection networks is non-trivial so that such networks are difficult to deploy on edge computing devices that only support integer operations. In this letter, we propose the outlier-aware quantization (OAQ) to boost the robustness of the post-training quantization method. Besides, we design a multilayer perceptron network to approximate the intersection-over-union (IoU) of rotated boxes, making the NMS stage can be deployed on integer-arithmetic-only devices. The experiment results demonstrate that our solution outperforms the widely used post-training quantization method. Meanwhile, to the best of our knowledge, this is the first study that focuses on the optimization and quantization of the NMS stage of oriented object detection networks.

Algorithms for Fast Implementation of 4-Point Integer Sine Type Vii Transformswithout Multiplication and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding

The separable directional adaptive integer cosine and sine type VII transforms with 4×4 blocks are proposed for intra prediction in image and video coding. Algorithms for fast implementation of 2D 4-point separable directional integer cosine and sine transforms are developed. These algorithms require 7 times fewer multiplication operations and provide higher compression ratio than the well-known algorithms. Two order-4 integer sine type VII transforms are proposed, and algorithms are developed for fast implementation of 4-point integer sine type VII transforms, which require integer operations only. As compared to the known algorithm, these algorithms can significantly reduce the number of multiplication operations or avoid them at all. These integer sine transforms are very close to discrete sine type VII transform and have a higher compression ratio than the well-known sine transform accepted in standard H.265 does.

PENINGKATKAN PENGUASAAN MEMAHAMI OPERASI BILANGAN BULAT MELALUI TEHNIK PAIKEM THE POWER OF TWO SISWA SMP

This research was aimed to find out the process of activities in an effort to improve mastery of understanding integer operations through the PAIKEM technique The Power Of Two (strength of two peoples) in class VII A Junior High School 3 Kubu. Mastery of understanding integer operations by students in mathematics learning is still low, so that the learning was unpleasant and uninteresting. Therefore, we need a learning technique that is able to improve mastery of understanding by students so that it can also improve learning outcomes. The method used is the method of discussion. Results of this study are indicated by an increase in mastery of understanding integer operating material by students in learning. In the first cycle of meeting 1 obtained 60.25%, and meeting 2 obtained 62.73%. In the second cycle meeting 1 obtained 79.87% and meeting 2 obtained 79.50% with the mastering category.

ANALISIS KESULITAN BELAJAR MAHASISWA PADA MATA KULIAH ALJABAR LINEAR (STUDI KASUS PADA MAHASISWA MANAJEMEN INFORMATIKA AKADEMI MANAJEMEN BELITUNG)

The purpose of this study is to determine the difficulties of students in linear algebra subject. The subject of linear algebra is one of the compulsory subjects in the Informatics Management Study Program. From the last 3 years, in linear algebra subject, students who get below average scores are always there. Difficulties in linear algebra subject need to be analyzed so that it can be known the cause of the difficulties. The study was conducted on informatics management students in 2019/2020. From this study, the causes of difficulties in algebra are 1) the lack of skilled students in integer operations, 2) students didn’t thorough, 3) student logic ability is still lacking to do Elementary Row Operations, 4) students doubt in solving problems.
 

Sources and Possible Causes of Errors and Misconceptions in Operations of Integers

This research investigated students’ sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit errors when solving the problems given in the Error Identification Integer Test (EIIT) were also interviewed to probe their thinking. The different types of errors were categorized according to how they were construed. The sources of errors were found to stem from carelessness, poor basic knowledge such as the inability to multiply and divide even the whole numbers, inability to assimilate concepts of integers since they are used to the schema of whole numbers, and rule mix-up which is also the result of surface understanding. Teachers were questioned about common errors and possible reasons for these errors made by their students. The main cause of errors and misconceptions is superficial understanding, which was most probably due to teachers rushing to complete the extensive syllabus, and consequently, students resorted to memorizing rules because of surface understanding. Teaching episodes were found to lack multiple-representation, creativity, as well as cooperative learning and active learning.

An Energy-Delay Trade-Off in Wireless Visual Sensor Networks Based on Two-Sided Matching

Wireless visual sensor networks (WVSNs) comprise a large number of battery-powered visual sensors with limited processing and transmission capacity in the field of interest. Hence, energy conservation is an important issue in resource-constrained WVSNs. In-network data fusion, clustering networks has been proved to be an effective scheme in reducing energy consumption. However, in most clustering algorithms, clustering may introduce bottlenecks to WVSNs which bring extra delay in the processes of data collection and forwarding. Such delay can be reduced by the design of routing schemes. In this paper, we propose an approach of energy-delay trade-off (EDT) based on two-sided matching theory. First, we determine a balance clustering structure which can balance energy consumption and delay in random-densely-deployed WVSNs. Then, the problem formulation of EDT problem in the balance clustering structure is provided. Moreover, the transformation strategy based on two-sided matching (TS-TSM) is proposed. After the TS-TSM, the EDT problem is transformed into a stable two-sided matching (STSM) problem with single objective function and the computational complexity is reduced. Furthermore, most of floating-point operations in original EDT problem are converted into integer operations which are easy to parallel compute. Finally, an improved deferred-acceptance algorithm (IDAA) is provided to generate a stable matching solution as the EDT scheme. Evaluation results demonstrate that the EDT approach can reduce delay in data aggregation processes and keep the total energy consumption at low levels. Further simulations show that the EDT approach is a fast approach, and it is not inferior to the existing algorithms.

Обучение студентов использованию метода Гаусса для целочисленных матриц при реализации на компьютере

The paper is written on the basis of a part of “Analysis of algorithms” course for students of the Computer science department of the Division of mathematics and mechanics of Saint Petersburg State University. The example of the computer implementation of the Gauss method illustrates the difference between the algebraic complexity (the number of arithmetic operations) of processing integers and the computational complexity which depends on the length of the input data. A formula which specifies the increase in the length of matrix coefficients, along with the implementation the Gauss method, is proved. The problems arising in the processing of large integers associated with “chopping” numbers are shown. To overcome the indicated problems, the possibility of using multi-valued integers is proposed. The upper bounds of the number of steps for processing the multivalued integers is shown to coincide with such bounds for a multi-tape Turing machine.

Integer Alternative for the Region-Adaptive Hierarchical Transform

A recently-introduced coder based on region-adaptive hierarchical transform (RAHT) is being considered as a standard for the compression of point cloud attributes at moving picture experts group. The RAHT coefficients can be encoded in many ways and the transform is based on a series of orthogonal 2 × 2 transform matrices with geometry-dependent floating-point entries. In order to remove computation ambiguity and facilitate deployment, fixed-point operations are often preferred. In this letter, we present an alternative RAHT description that allows for fixed-point implementation of its transform steps. It is based on matrix decompositions akin to lifting steps and a scaling of the quantization steps. Results are presented to show that the new fixed-point transform is, in practical terms, equivalent to the floating-point RAHT. For that we use a reasonable number of precision bits for the integer operations, e.g. 8 b or more.

Perancangan Prototype LKS Materi Operasi Hitung Bilangan Bulat Untuk Peserta Didik Sekolah Dasar

Matematika merupakan ilmu universal yang mendasari perkembangan teknologi modern, mempunyai peranan penting dalam berbagai disiplin ilmu dan memajukan daya pikir manusia. Matematika perlu diberikan kepada semua peserta didik mulai dari sekolah dasar untuk membekali peserta didik dengan kemampuan berpikir logis, analitis, sistematis, kritis, kreatif, dan kemampuan bekerja sama. Tahapan-tahapan aspek yang berurutan dalam matematika yaitu bilangan, geometri dan pengukuran serta pengolahan data. Dari tahapan aspek yang disebutkan terlihat bahwasannya pokok bahasan bilangan merupakan tahapan awal yang harus dikuasai dalam matematika. Bilangan merupakan pokok bahasan dasar yang sangat penting dipahami oleh para peserta didik karena merupakan landasan untuk pokok-pokok bahasan lainnya. Salah satu bagian dari pokok bahasan bilangan ini adalah bilangan bulat. Untuk itu, penelitian ini bertujuan untuk mengembangkan bahan ajar berupa LKS materi operasi hitung bilangan bulat untuk peserta didik sekolah dasar. Penelitian ini merupakan tahap awal dari penelitian pengembangan. Subjek penelitian adalah peserta didik kelas IV SD Negeri 42 Pangkalpinang. Penelitian ini dilakukan tahap preliminary (persiapan) dan tahap formative evaluation ( self evaluation) yang menghasilkan prototipe pertama LKS materi operasi hitung bilangan bulat untuk peserta didik sekolah dasar.

DIAGNOSTIK KESULITAN BELAJAR MATEMATIKA SISWA SEKOLAH DASAR PADA MATERI OPERASI HITUNG BILANGAN BULAT NEGATIF

This study is qualitative research that aims to describe and analyze the students’ learning difficulties in mathematical operations of negative integers. The subjects of the study were two students of 286 SDN 286 Pasaka. Giving test (diagnostic tests) and interviewing were conducted to collect the data. The results of the study show that basically the learning difficulties experienced by the subject IS and subject RV is the same: the lack of understanding of the concept of negative integer operations. Due to the lack of understanding of the concept, the subject is difficult to abstract, generalize and remember the concept or principle of operating negative integer operations. To overcome the learning difficulties experienced by students, the teacher must ensure students have mastered the prerequisite material, design ways of delivering teaching materials with effective communication and pay attention to family circumstances and social conditions of students.Keywords: Characteristics of items, item difficulties, discrimination

A study of the loops control for reconfigurable computing with OpenCL in the LABS local search problem

In this article, we study the steepest descent local search (SDLS) algorithm that is used as the improvement step in the memetic algorithms for the search of low autocorrelation binary sequences (LABS). We address the method of reconfigurable computing, as the algorithm is of the field programmable gate array (FPGA) type as it features the integer operations, bit-wise data representation, regular execution flow, and huge computational complexity. It contains four levels of nested loops, but its direct parallel implementation as a custom processor leads to typical problems because the loops expose a dynamic range and too many iterations. This inhibits a simple parallel data path that is typically produced by the method of the loop unrolling. We have examined the four architectures that mitigate the found obstacles, and we provide the results of their implementation. The solutions take advantages of the loop pipelining, reordering of the loops, and dynamic reconfiguration. The recently available development tool was involved in our study as we have used the OpenCL (OCL) platform for FPGAs to draw practical conclusions. The given proposals are characterized by their performance and capacity for a problem size. Consequently, the speed/size trade-off is highlighted, as an FPGA size is a design constraint. The performance of the FPGA-based solutions is compared to the CPU speed, and the maximum reported speed-up is 750. Readers can further develop and/or use the presented OCL solutions for efficient LABS discovery as we provide the corresponding software repository.

Students’ misconceptions on the algebraic prerequisites concept: causative factors and alternative solutions

Mastery of the concept of number operations is the main prerequisite for understanding the algebraic concepts. The misconception of integer operations is still widely found in students. This research aimed to describe students’ misconceptions on the algebraic prerequisites concept, namely the operation of integers, causative factors and alternative solutions. This research was qualitative descriptive research using diagnostic test methods and interview. Three students who did the most and varied misconceptions were chosen to be the subject of this research. The results showed the misconceptions experienced by the subject occurred in the integer addition, integer subtraction, integer division and multiplication with zero numbers. The factors that cause misconception were wrong intuition and incorrect or incomplete reasoning and alternative solutions were re-explain and cognitive conflict. For further research, other researchers can conduct research on students’ misconceptions on the algebraic prerequisites concept besides number operations.

UPAYA MENINGKATKAN HASIL BELAJAR OPERASI BILANGAN BULAT MELALUI MEDIA KONKRET DI SDN 4 MUARAKUANG

The problem in this study is whether the use and application of concrete media can iprove students' skills in integer operations in class V of Muarakuang 04 Elementary School? The purpose of this study was to determine the improvement of student learning outcomes about integer operations through concrete media. Of the 24 students, there were 17 students who successfully achieved the KKM score. In addition, there are 7 students who have not yet reached KKM. This means that the completeness achieved in Cycle I is 71%. In cycle II, the researcher made a decision to complete the research action and did not need to continue the research at the Cycle III stage due to the fulfillment of 86% KKM. The conclusion of the results of this study is that the application of concrete media can improve learning outcomes about integer operations in Class V students of SDN 4 Muara Kuang

Investigation of free vibration and buckling of Timoshenko nano-beam based on a general form of eringen theory using conformable fractional derivative and Galerkin method

The purpose of this paper is to study the free vibration and buckling of a Timoshenko nano-beam using the general form of the Eringen theory generalized based on the fractional derivatives. In this paper, using the conformable fractional derivative (CFD) definition the generalized form of the Eringen nonlocal theory (ENT) is used to consider the effects of integer and noninteger stress gradients in the constitutive relation and also to consider small-scale effect in the vibration of a Timoshenko nano-beam. The governing equation is solved by the Galerkin method. Free vibration and buckling of a Timoshenko simply supported (S) nano-beam is investigated, and the influence of the fractional and nonlocal parameters is shown on the frequency ratio and buckling ratio. In this sense, the obtained formulation allows for an easier mapping of experimental results on nano-beams. The new theory (fractional parameter) makes the modeling more flexible. The model can conclude all of the integer and non-integer operators and is not limited to the special operators such as ENT. In other words, it allows to use more sophisticated/flexible mathematics to model physical phenomena.

MENINGKATKAN PEMAHAMAN KELAS VII SMP AMALIA PALU DALAM PEMBELAJARAN PENJUMLAHAN DAN PENGURANGAN BILANGAN BULAT PADA PEMBERIAN TUGAS YANG MEMUAT PROBLEM POSING SECARA BERKELOMPOK

The main problem in this study is the low level of understanding of VII grade students of Amalia Palu in integer addition and subtraction material. Some things that cause these problems, including (1) students still have difficulty in solving problems related to the addition and subtraction operations of integers. (2) understanding the concept of addition operations and the reduction of integers is still lacking, this is because students are less active in learning and only receive information from the teacher without reciprocity from students. To improve students' understanding, the researcher applied a summing learning model and integer reduction on assignments that included problem posing in groups. Problem posing learning model that emphasizes constructivist understanding through group work and is heterogeneous. The results of the research carried out obtained student learning outcomes in the first cycle, of the 20 students who took the final test there were 12 students who completed the study with a percentage of classical completeness of 60 %. Student learning outcomes in the second cycle showed that of the 20 students who took the final test it was seen that 19 students who completed learning or classical learning completeness were 95%. In addition, there is also an increase in student activity in learning activities. Based on these results it can be concluded that addition learning and integer reduction in the assignment of tasks that contain problem posing in groups can improve students' understanding.

Learning of Spatial Operations in 1st Grade of Junior High School (MTS. S Nu Paringgonan) Ulu Barumun Padang Lawas District

The background of the problem in this study is that many students are confused and do not understand how to operate integers in a positive form with positive, positive with negative, negative with positive, and negative with negative. The formulation of this research problem is how to learn integer operations in 1st grade class (VII-2), how students behave in learning integer operations in 1st grade class (VII-2), and how student learning outcomes in learning integer operations in 1st grade class (VII-2). The purpose of this study was to find out integer operating learning in 1st grade class VII-2, to find out the attitudes of students in learning integer operations in 1st grade class (VII-2), and to find out student learning outcomes in integer operating learning in 1st grade class (VII-2) MTs. S NU Paringgonan Ulu Barumun District. This research is descriptive qualitative research, namely research intended to investigate the circumstances, conditions or other things that have been mentioned, the results of which are presented in the form of research reports. The data needed are observation, interviews, and documentation. The results of this study are (1) Learning integer operations in 1st grade class (VII-2) that the mathematics teacher in 1st grade class (VII-2) describes integer operations by carrying out preliminary activities, core activities, and closing activities. (2) The attitude of students in learning integer operations in 1st grade class (VII-2) is not good, like many students who pay less attention and respect for the teacher during the learning process. (3) Student learning outcomes reach a value of 50 - 80, namely 30 students who do not complete or 88% and 4 students who complete or 12% with the results of the average value is 60, which is not good.

The design learning of fraction with realistic mathematics education in elementary school

Fractions are one of the mathematics topics that is almost to be a problem for the elementary school. This problem arises because generally, students do not understand the concept of fraction. Fractional operations involve more procedures that must be taken than integer operations, where some of the results of the operation produce numbers that are difficult to understand logically. This research is design research designed to provide an excellent consideration of learning process of fractional operations through allegations built-in framework analysis hypothetical learning trajectory (HLT), which later tested in realistic mathematics education (RME). RME underlies all research design research activities. The results of this study are drawn from local instructional theory in the form of a high consideration of the learning process that provides general answers to a topic being taught. Design research is carried out in three stages, namely preliminary design, teaching experiment consisting of cycle 1 and cycle 2, and the third stage of retrospective analysis. The study involved using a sample of 29 grade V students at Nurul Hasanah elementary school consisting of 4 students in cycle one and 25 students in the second cycle. The results show that the use of circle contexts and bar representations trigger the learning trajectory that students pass through in understanding fraction addition operations. The stages of learning addition operations by HLT are designed, namely: understanding fraction values as part of the whole, comparing two fractions of value, looking for fractions of value, carrying out the same summing operations, and performing the summarized operations not the same.

A novel fractional nonlocal model and its application in buckling analysis of Euler-Bernoulli nanobeam

The present study aims to analyze the buckling behavior of Euler–Bernoulli nanobeam in conjunction with a novel fractional nonlocal model namely conformable fractional nonlocal model. Fractional models are getting more popular among the researchers because of its applicability and fixability to handle many complex physical phenomena which are not possible to model with integer operators. Also, the main advantage of fractional models over integer model is its applicability to handle both the integer and noninteger operators which makes it much more flexible in term of real-world application. In this regards, the nonlocal constitutive relation is developed in conjunction with conformable fractional derivatives and fractional strain energy to analyze the buckling behavior of Euler–Bernoulli Nanobeam. In this study, the Simply Supported-Simply Supported (SS), Clamped-Simply Supported, and Clamped-Clamped boundary conditions are taken into the investigation with the help of the Differential Quadrature Method (DQM). Critical buckling load parameters are computed for the SS, CS, and CC boundary conditions from generalized eigenvalue problem. Graphical, as well as tabular results, are calculated by using MATLAB programmes and effects of various parameters such as fractional parameter, nonlocal parameter, aspect ratio on critical buckling load parameters extensively studied.

Explaining the Concept and Operations of Integer in Primary School Mathematics Teaching: Opposite Model Sample

Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the which is a quantitative model, unlike thermometer, elevator, sea level, or number line, which are directional models. Additionally, it presents solutions to the problem of learning the concept of and operations in integers through models used in teaching integers for primary school 6th grade students. Opposite model is an integer model, which is based on theory and enables the easy learning of the concept of integers and addition and subtraction operations tested with experimental study by [9]. The present research is believed to contribute students' meaningful learning of the concept and operations of integers and alternative thinking through opposite model. The present research discusses the necessity of opposite model, which is to be offered as an alternative mathematical model for teaching the concept of integers and addition-subtraction operations, in light of the findings obtained through literature review.

The Application of Probing Prompting Learning (PPL) Model with Realistic Mathematics Education (RME) Approach to Increase Understanding of Student Mathematics Concepts

Understanding of mathematical concepts is the ability of students to understand facts related to mathematics which can be expressed again in easily understood languages. The problem examined in this study is research on improving mathematical understanding of integer operations through the application of Probing Prompting Learning (PPL) with Realistic Mathematic Education (RME) approach. The method used is observation, documentation, interviews, and test methods, while the data analysis uses the percentage formula of the results of observations and the percentage of completeness of learning outcomes formula. Keyword: probing prompting learning, realistic mathematic education