Search

This paper defines a convertible nonconvex function (CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions, and proposes algorithms for solving the unconstrained optimization problems with decomposable CN functions. First, to illustrate the fact that some nonconvex functions, nonsmooth or discon)tinuous, are actually weak uniform CN functions, examples are given. The operational properties of CN functions are proved, including addition, subtraction, multiplication, division, and compound operations. Second, optimization conditions of the global optimal solution to the unconstrained optimization with weak uniform CN function are proved. Based on the unconstrained optimization problem with decomposable CN functions, a decomposable algorithm is proposed by its augmented Lagrangian penalty function and its convergence is proved. Numerical results demonstrate that an approximate global optimal solution to unconstrained optimization with CN function may be obtained by the decomposable algorithm. The decomposable algorithm can effectively reduce the scale in solving the unconstrained optimization problem with decomposable CN function. This paper provides a new idea for solving unconstrained nonconvex optimization problems. [ABSTRACT FROM AUTHOR]

The paper aims at answering the following question, in the scalar as well in the vector case: What do the famous Aitken's $\Delta ^{2}$ and Wynn's $\varepsilon $-algorithm exactly do with the terms of the input sequence? Inspecting the rules of these algorithms from a geometric point of view leads to change the question into another one: By what kind of geometric object can the parallel (or harmonic) sum be represented? Thus, the paper begins with geometric considerations on the parallel addition and the parallel subtraction of vectors, including equivalent definition, and properties derived from the new point of view. It is shown how the parallel sum of vectors is related to the Bézier parabola controlled by these vectors and to their interpolating equiangular spiral. In the second part, observing that Aitken's $\Delta ^{2}$ and Wynn's $\varepsilon $-algorithm may be defined through hybrid sums, mixing standard and parallel sums, the consequences are drawn regarding the way one can define and analyze these algorithms. New explanatory rules are derived for the $\varepsilon $-algorithm, providing a better understanding of its basic step and of its cross-rule. [ABSTRACT FROM AUTHOR]

In order to solve the problem of large error of delay estimation in low SNR environment, a new delay estimation method based on cross power spectral frequency domain weighting and spectrum subtraction is proposed. Through theoretical analysis and MATLAB simulation, among the four common weighting functions, it is proved that the cross-power spectral phase weighting method has a good sharpening effect on the peak value of the cross-correlation function, and it is verified that the improved spectral subtraction method generally has a good noise reduction effect under different SNR environments. Finally, the joint simulation results of the whole algorithm show that the combination of spectrum subtraction and crosspower spectrum phase method can effectively sharpen the peak value of cross-correlation function and improve the accuracy of time delay estimation in the low SNR environment. The results of this paper can provide useful help for sound source localization in complex environments. [ABSTRACT FROM AUTHOR]

The d-MP is a special state vector such that the maximal flow is d in the related network and any state vector less than d-MP is not a d-MP. The d-MP is one of the major tools in evaluating the reliability of a multistate flow network. The d-MPs for all d problem is to search for all d-MPs for all possible d. Decision-makers may use them to choose the best d under given scenarios. Current algorithms for addressing this problem are all based on the addition of 1-MPs and (d − 1)-MPs to generate d-MP combinations, and then detect and remove d-MP combinations with infeasible states, redundant states, and/or duplications. A new algorithm based on the subtraction of (d + 1)-MPs and 1-MPs to obtain d-MP combinations is proposed in this paper to overcome the above three obstacles in current algorithms. The time complexity and demonstration of the proposed algorithm are also analyzed and provided using examples. An experiment is conducted to compare the performance of the proposed subtraction-based algorithm with that of the best known addition-based algorithm. [ABSTRACT FROM AUTHOR]

Background subtraction is the classical approach to differentiate moving objects in a scene from the static background when the camera is fixed. If the fixed camera assumption does not hold, a frame registration step is followed by the background subtraction. However, this registration step cannot perfectly compensate camera motion, thus errors like translations of pixels from their true registered position occur. In this paper, we overcome these errors with a simple, but effective background subtraction algorithm that combines Temporal and Spatio-Temporal approaches. The former models the temporal intensity distribution of each individual pixel. The latter classifies foreground and background pixels, taking into account the intensity distribution of each pixels' neighborhood. The experimental results show that our algorithm outperforms the state-of-the-art systems in the presence of jitter, in spite of its simplicity. [ABSTRACT FROM AUTHOR]

In this work, we present a novel approach for resolving a fuzzy single-objective function with fuzzy constraints. The algorithm of the method is based on the null set concept and is focused on minimizing cases. With the null set concept, two partial subtraction orders for fuzzy numbers have been defined, namely simple subtraction and the Hukuhara difference. That allows us to define, respectively, optimal solutions and H-optimal solutions. First, the initial optimization problem is transformed into a deterministic, nonlinear, bi-objective optimization problem. Then, Karush Kuhn Tucker’s (KKT) optimality conditions are applied to find deterministic optimal solutions. Finally, a few fuzzy algebraic operations are employed to transform deterministic optimal solutions into fuzzy optimal solutions for the initial solutions. In order to demonstrate the effectiveness of the approach, we have dealt with eleven test problems from the literature. Our method has been compared to those of other methods, and our method is at least the best in each instance. [ABSTRACT FROM AUTHOR]

The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach. [ABSTRACT FROM AUTHOR]

In this paper, a new simplified iterative division algorithm for modular numbers that is optimized on the basis of the Chinese remainder theorem (CRT) with fractions is developed. It requires less computational resources than the CRT with integers and mixed radix number systems (MRNS). The main idea of the algorithm is (a) to transform the residual representation of the dividend and divisor into a weighted fixed-point code and (b) to find the higher power of 2 in the divisor written in a residue number system (RNS). This information is acquired using the CRT with fractions: higher power is defined by the number of zeros standing before the first significant digit. All intermediate calculations of the algorithm involve the operations of right shift and subtraction, which explains its good performance. Due to the abovementioned techniques, the algorithm has higher speed and consumes less computational resources, thereby being more appropriate for the multidigit division of modular numbers than the algorithms described earlier. The new algorithm suggested in this paper has O (log2Q) iterations, where Q is the quotient. For multidigit numbers, its modular division complexity is Q(N), where N denotes the number of bits in a certain fraction required to restore the number by remainders. Since the number N is written in a weighed system, the subtraction-based comparison runs very fast. Hence, this algorithm might be the best currently available. [ABSTRACT FROM AUTHOR]

This paper proposes a robust method to detect and extract silhouettes of foreground objects from a video sequence of a static camera based on the improved background subtraction technique. The proposed method analyses statistically the pixel history as time series observations. The proposed method presents a robust technique to detect motions based on kernel density estimation. Two consecutive stages of the k-means clustering algorithm are utilized to identify the most reliable background regions and decrease the detection of false positives. Pixel and object based updating mechanism for the background model is presented to cope with challenges like gradual and sudden illumination changes, ghost appearance, non-stationary background objects, and moving objects that remain stable for more than the half of the training period. Experimental results show the efficiency and the robustness of the proposed method to detect and extract the silhouettes of moving objects in outdoor and indoor environments compared with conventional methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a new method for utilising phase information by complementing it with traditional magnitude-only spectral subtraction speech enhancement through complex spectrum subtraction (CSS). The proposed approach has the following advantages over traditional magnitude-only spectral subtraction: (a) it introduces complementary information to the enhancement algorithm; (b) it reduces the total number of algorithmic parameters; and (c) is designed for improving clean speech magnitude spectra and is therefore suitable for both automatic speech recognition (ASR) and speech perception applications. Oracle-based ASR experiments verify this approach, showing an average of 20% relative word accuracy improvements when accurate estimates of the phase spectrum are available. Based on sinusoidal analysis and assuming stationarity between observations (which is shown to be better approximated as the frame rate is increased), this paper also proposes a novel method for acquiring the phase information called Phase Estimation via Delay Projection (PEDEP). Further oracle ASR experiments validate the potential for the proposed PEDEP technique in ideal conditions. Realistic implementation of CSS with PEDEP shows performance comparable to state of the art spectral subtraction techniques in a range of 15–20dB signal-to-noise ratio environments. These results clearly demonstrate the potential for using phase spectra in spectral subtractive enhancement applications, and at the same time highlight the need for deriving more accurate phase estimates in a wider range of noise conditions. [Copyright &y& Elsevier]

Motion detection is a challenging problem in video sequel with complex background. Different background subtraction techniques are introduced to detect moving objects from video sequel, but none of these has been adequate to address the complex nature of the dynamic scene in real-surveillance task. So a simple and efficient vector-based method is proposed to address real-surveillance challenges. In this paper, the concept of linear dependence of vectors is used to build background models corresponding to each pixel. Consecutively, linear independence is used to detect moving object from incoming video sequel. The proposed method is spatio-temporal based background subtraction method, as it uses spatial and temporal information for constructing background model. The background models are updated using an adaptive update rate with region diffusion to produce efficient results in the dynamic background. The benchmark datasets taken from complex scenario are experimented using the proposed algorithm and the generated results are compared with recent background subtraction methods. The presented method attains better performance in terms of qualitative and quantitative results. [ABSTRACT FROM AUTHOR]

This paper first presents a study on the classical BCD adders from which a carry-chain type adder is redesigned to fit within the Xilinx FPGA's platforms. Some new concepts are presented to compute the P and G functions for carry-chain optimization purposes. Several alternative designs are presented. Then, attention is given to FPGA implementations of add/subtract algorithms for 10's complement BCD numbers. Carry-chain type circuits have been designed on 4-input LUTs (Virtex-4, Spartan-3) and 6-input LUTs (Virtex-5) Xilinx FPGA platforms. All designs are presented with the corresponding time performance and area consumption figures. Results have been compared to straight implementations of a decimal ripple-carry adder and an FPGA 2's complement binary adder-subtractor using the dedicated carry logic, both carried out on the same platform. Better time delays have been registered for decimal numbers within the same range of operands. [ABSTRACT FROM AUTHOR]

An important problem in the realization of floating-point subtraction is the identification of the position of the first nonzero digit in a radix-represented number, since the significand usually is to be represented left-normalized in the part of the word(s) allocated for representing its value. There are well known log-time algorithms for determining this position for numbers in nonredundant representations, which may also be applied to suitably (linear-time) transformed redundant representations. However, due to the redundancy in the latter case, the position thus determined may need a correction by one. When determination of the shift amount is to be performed in parallel with conversion to nonredundant representation (the subtraction), it must be performed on the redundant representation. This is also the case when the significand is to be retained in a redundant representation until the final rounding. This paper presents an improved algorithm for determining the need for a correction of the normalization shift amount, which can be run in parallel with the algorithm finding the "approximate" position. [ABSTRACT FROM AUTHOR]

Moving cast shadows are a major concern for foreground detection algorithms. The processing of foreground images in surveillance applications typically requires that such shadows be identified and removed from the detected foreground. This paper presents a novel pixel-based statistical approach to model moving cast shadows of nonuniform and varying intensity. This approach uses the Gaussian mixture model (GMM) learning ability to build statistical models describing moving cast shadows on surfaces. This statistical modeling can deal with scenes with complex and time-varying illumination, including light saturated areas, and prevent false detection in regions where shadows cannot be detected. The proposed approach can be used with pixel-based descriptions of shadowed surfaces found in the literature. It significantly reduces their false detection rate without increasing the missed detection rate. Results obtained with different scene types and shadow models show the robustness of the approach. [ABSTRACT FROM AUTHOR]

in this paper, we propose hardware algorithms for computing exponentials and logarithms utilizing the redundant binary representation for internal computation. The algorithms proposed in this paper are improved versions of modified STL methods which were improved by Specker and by Chen and are known as methods suited for the dedicated circuits for computing exponentials and logarithms. The algorithms by Specker and by Chen compute exponentials and logarithms by repeating a simple procedure composed of an additional subtraction, a shift and a table look-up. in the proposed algorithms, by using the redundant binary representation, each digit at which is an element of {0, 1, -1} for the internal computation, we eliminate carry (borrow) propagation from addition (subtraction) and improve the speed of computation. Using the traditional methods, because of carry (borrow) propagation addition (subtraction), combinational circuits for computing n-bit exponentials and logarithms require at least a computation time proportional to n log n and the number of elements proportional to n² . Using the proposed algorithms, the computation time is improved to be proportional to n, and the number of elements is proportional to n² using traditional methods. [ABSTRACT FROM AUTHOR]

With the latest developments in deep neural networks, the convolutional neural network (CNN) has made considerable progress in the area of foreground detection. However, the top-rank background subtraction algorithms for foreground detection still have many shortcomings. It is challenging to extract the true foreground against complex background. To tackle the bottleneck, we propose a hybrid loss-assisted U-Net framework for foreground detection. A proposed deep learning model integrates transfer learning and hybrid loss for better feature representation and faster model convergence. The core idea is to incorporate reference background image and change detection mask in the learning network. Furthermore, we empirically investigate the potential of hybrid loss over single loss function. The advantages of two significant loss functions are combined to tackle the class imbalance problem in foreground detection. The proposed technique demonstrates its effectiveness on standard datasets and performs better than the top-rank methods in challenging environment. Moreover, experiments on unseen videos also confirm the efficacy of proposed method. [ABSTRACT FROM AUTHOR]

Velocity measurement by an incremental encoder is an important issue for advanced motion control applications such as robotics. In this paper, we deal with a kind of MT-type velocity estimation method. Though the conventional MT method is well known and has been well proven in practice, it requires execution of an arithmetic division operation that prevents an efficient implementation on low-cost FPGA-based control platforms. Thus, we propose a divisionless MT-type algorithm, which can provide a similar performance in velocity estimation accuracy as the conventional method, but requiring significantly less FPGA resources, since it implements only simple arithmetic operations such as addition, subtraction, and multiplication, that can be implemented more easily on the processing hardware. Furthermore, the algorithm is fast in execution, thus, it provides the output in only a few clock cycles. Though the proposed algorithm can be described in a recursive form, the stability of the estimation process is not jeopardized, although it is an important issue in this case. Hence, the algorithm is introduced in a form which assures stability in a wide speed range. We show the implementation of the algorithm on the experimental FPGA platform. The experimental results validated the proposed divisionless MT-type algorithm fully for accurate velocity estimation. [ABSTRACT FROM AUTHOR]

Motion detection methods are widely integrated in modern intelligent video surveillance systems. Many of these methods use background subtraction techniques to separate the foreground objects from the background. Temporal averaging is one of the most commonly used and simple method for background subtraction. In this paper we propose new version of the original Temporal averaging algorithm. The speed of updating the background model has been modified to be adaptive and determined by pixel difference. Another approach with simultaneously adaptive threshold and background update speed is also proposed. Our goal is increasing the F-measure of the method by making the algorithm more versatile for different scene scenarios. Experimental results are shown and analyzed. The quality parameters of the original method and the proposed method are compared. [ABSTRACT FROM AUTHOR]

• We propose a novel regularized TWSVM called ITWSVM for indefinite kernel. • We introduce a smooth quadratic hinge loss function and a maximum margin regularization term to ITWSVM. • We theoretically analyze the nature of ITWSVM and expand ITWSVM to indefinite kernels and multi-class classification. • We introduce difference of convex functions (DC) to solve the non-convex problem in indefinite kernel settings and further propose ITWSVM-DC. • Extensive experiments demonstrate that ITWSVM-DC is a robust and prominent algorithm and can perform excellently in different situations. Twin support vector machine (TWSVM) is an efficient algorithm for binary classification. However, the lack of the structural risk minimization principle restrains the generalization of TWSVM and the guarantee of convex optimization constraints TWSVM to only use positive semi-definite kernels (PSD). In this paper, we propose a novel TWSVM for indefinite kernel called indefinite twin support vector machine with difference of convex functions programming (ITWSVM-DC). The indefinite TWSVM (ITWSVM) leverages a maximum margin regularization term to improve the generalization of TWSVM and a smooth quadratic hinge loss function to make the model continuously differentiable. The representer theorem is applied to the ITWSVM and the convexity of the ITWSVM is analyzed. In order to address the non-convex optimization problem when the kernel is indefinite, a difference of convex functions (DC) is used to decompose the non-convex objective function into the subtraction of two convex functions and a line search method is applied in the DC algorithm to accelerate the convergence rate. A theoretical analysis illustrates that ITWSVM-DC can converge to a local optimum and extensive experiments on indefinite and positive semi-definite kernels show the superiority of ITWSVM-DC. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel algorithm for mobile-object segmentation from static background scenes, which is both robust and accurate under most of the common problems found in motion segmentation. In our first contribution, a case analysis of motion segmentation errors is presented taking into account the inaccuracies associated with different cues, namely colour, edge and intensity. Our second contribution is an hybrid architecture which copes with the main issues observed in the case analysis by fusing the knowledge from the aforementioned three cues and a temporal difference algorithm. On one hand, we enhance the colour and edge models to solve not only global and local illumination changes (i.e. shadows and highlights) but also the camouflage in intensity. In addition, local information is also exploited to solve the camouflage in chroma. On the other hand, the intensity cue is applied when colour and edge cues are not available because their values are beyond the dynamic range. Additionally, temporal difference scheme is included to segment motion where those three cues cannot be reliably computed, for example in those background regions not visible during the training period. Lastly, our approach is extended for handling ghost detection. The proposed method obtains very accurate and robust motion segmentation results in multiple indoor and outdoor scenarios, while outperforming the most-referred state-of-art approaches. [Copyright &y& Elsevier]

Abstract: Fast robust background subtraction under sudden lighting changes is a challenging problem in many applications. In this paper, we propose a real-time approach, which combines the Eigenbackground and Statistical Illumination method to address this issue. The first algorithm is used to reconstruct the background frame, while the latter improves the foreground segmentation. In addition, we introduce an online spatial likelihood model by detecting reliable background pixels. Extensive quantitative experiments illustrate our approach consistently achieves significantly higher precision at high recall rates, compared to several state-of-the-art illumination invariant background subtraction methods. [Copyright &y& Elsevier]

The article discusses the influence of gender differences of elementary school children in preferring and using strategies to solve multidigit addition and subtraction story problems. Two research studies are presented revealing that children using invented strategies likely possess advance understanding than those using standard algorithms. It is noted that more boys use invented strategies than girls, and children's reasons in choosing strategies relate to accuracy, speed and ease of use.

Abstract: In background subtraction, it is challenging to detect foreground objects in the presence of dynamic background motions. The paper proposes two new algorithms to this problem by improving the codebook model with the incorporation of the spatial and temporal context of each pixel. The spatial context involves the local spatial dependency between neighboring pixels, and the temporal context involves the preceding detection result. Only the spatial context is incorporated into the first algorithm which makes the background representation more compact than the standard codebook. The second algorithm explicitly models the spatio-temporal context with a Markov random field model, thus achieving more accurate foreground detection. Extensive experiments on several dynamic scenes are conducted to compare the two proposed algorithms with each other and with the standard codebook algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents a new scalable hardware implementing modular multiplication. A high radix Montgomery multiplication algorithm without final subtraction is used to perform this operation. An alternative proof for the final Montgomery multiplication by 1, removing the condition on the modulus, is given. This hardware fits in any chip area and is able to work with any size of modulus. Unlike other scalable designs only one cell is used. This cell contains standard and well optimized digit multiplier and adder. Time–area trade-offs are also available before hardware synthesis for differents sizes of internal data path. The pipeline architecture of the multiplier component increases the clock frequency and the throughput. Time–area trade-offs are analyzed in order to make the best choice for given time and area constraints. This architecture seems to provide a better time–area compromise than previous scalable hardware. [Copyright &y& Elsevier]

The Generalized Subtraction Correction Algorithm (GSCA) improves upon the Modified Subtraction method for determining duct-leakage-to-outside using only a blower door. GSCA utilizes attic pressure both to calculate a generalized Subtraction Correction Factor and to properly identify and assign the correct pressure difference between the ducts and attic responsible for the calculated duct-leakage flow. This paper also describes the normal procedures that enhance the accuracy of data collection and the subsequent tests on the resulting information for validating the applicability of GSCA to an individual home. GSCA collects associated pressure-coupling data and enhances the reliability of house-leakiness results. [ABSTRACT FROM AUTHOR]

Outlines when a fraction computer should be used to supplement other fraction manipulatives most effectively. Significance of fraction addition and subtraction; Use of the fraction computer for addition; Application of paper-and-pencil algorithm.

Featured Application: We provide a non-intrusive tool for the detection of adjacent and non-adjacent bar breakage from the acoustic noise radiated by a motor. It can be included as a smart application in a transportable device. We apply power spectral analysis based on covariance function and spectral subtraction to detect adjacent and non-adjacent bar breakages. We obtain a spectral pattern when the signal presents one or various broken bars, independent of the relative position of the bar breakages. The proposed algorithm gives satisfactory results for detectability compared to some previous research. Additionally, we also present illustrations of faults and signal to noise in the noise-reduction stage. [ABSTRACT FROM AUTHOR]

This observational study used data from 270 second‐grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm, (b) invented, (c) mixed, and (d) unclassified. We used two‐level hierarchical linear regression to investigate the association between students' strategy use and their performance on a standardized test in mathematics. Results indicated that students in the mixed strategy groups had significantly higher mathematics achievement than those in the standard algorithm and the unclassified groups. [ABSTRACT FROM AUTHOR]

The method of Semantic Background Subtraction (SBS), which combines semantic segmentation and background subtraction, has recently emerged for the task of segmenting moving objects in video sequences. While SBS has been shown to improve background subtraction, a major difficulty is that it combines two streams generated at different frame rates. This results in SBS operating at the slowest frame rate of the two streams, usually being the one of the semantic segmentation algorithm. We present a method, referred to as "Asynchronous Semantic Background Subtraction" (ASBS), able to combine a semantic segmentation algorithm with any background subtraction algorithm asynchronously. It achieves performances close to that of SBS while operating at the fastest possible frame rate, being the one of the background subtraction algorithm. Our method consists in analyzing the temporal evolution of pixel features to possibly replicate the decisions previously enforced by semantics when no semantic information is computed. We showcase ASBS with several background subtraction algorithms and also add a feedback mechanism that feeds the background model of the background subtraction algorithm to upgrade its updating strategy and, consequently, enhance the decision. Experiments show that we systematically improve the performance, even when the semantic stream has a much slower frame rate than the frame rate of the background subtraction algorithm. In addition, we establish that, with the help of ASBS, a real-time background subtraction algorithm, such as ViBe, stays real time and competes with some of the best non-real-time unsupervised background subtraction algorithms such as SuBSENSE. [ABSTRACT FROM AUTHOR]

This paper presents a study of some basic blocks needed in the design of floating-point summation algorithms. In particular, in radix-2 floating-point arithmetic, we show that among the set of the algorithms with no comparisons performing only floating-point additions/subtractions, the 2Sum algorithm introduced by Knuth is minimal, both in terms of number of operations and depth of the dependency graph. We investigate the possible use of another algorithm, Dekker's Fast2Sum algorithm, in radix-10 arithmetic. We give methods for computing, in radix 10, the floating-point number nearest the average value of two floating-point numbers. We also prove that under reasonable conditions, an algorithm performing only round-to-nearest additions/subtractions cannot compute the round-to-nearest sum of at least three floating-point numbers. Starting from an algorithm due to Boldo and Melquiond, we also present new results about the computation of the correctly-rounded sum of three floating-point numbers. For a few of our algorithms, we assume new operations defined by the recent IEEE 754-2008 Standard are available. [ABSTRACT FROM AUTHOR]

Due to its high spectrum efficiency, 64‐amplitude phase‐shift keying (64‐APSK) is one of the primary technologies used in deep space communications and digital video broadcasting through satellite‐second generation. However, 64‐APSK suffers from considerable computational complexity because of the de‐mapping method that it employs. In this study, a low‐complexity de‐mapping method for (4 + 12 + 20 + 28) 64‐APSK is proposed in which we take full advantage of the symmetric characteristics of each symbol mapping. Moreover, we map the detected symbol to the first quadrant and then divide the region in this first quadrant into several partitions to simplify the formula. Theoretical analysis shows that the proposed method requires no operation of exponents and logarithms and involves only multiplication, addition, subtraction, and judgment. Simulation results validate that the time consumption is dramatically decreased with limited degradation of bit error rate performance. [ABSTRACT FROM AUTHOR]

Although students' invented strategies typically prove to be meaningful and effective in improving the students' mathematical understanding, much remains unexplored in the current literature. This study examined, through a teaching-scenario task, the nature of 80 preservice teachers' reasoning and responses to students' informal and formal strategies for whole number subtraction. This study also examined challenges reported by preservice teachers attempting to connect students' informal strategies to a traditional method. The broader implications of this study for the international community are discussed, and recommendations for teacher education programs are presented in accordance with the findings of the study. [ABSTRACT FROM AUTHOR]

This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two no-choice conditions. In the choice condition, children could apply their preferential strategy on each item; in the no-choice conditions, they had to solve all items with mental computation and the standard algorithm, respectively. Results revealed that children of all achievement levels applied the standard algorithm remarkably frequently and efficiently, even on subtractions that were intended to evoke mental computation. Moreover, children did not fit their strategy choices to the numerical characteristics of the items, but high and above-average achieving children based their strategy choices on their individual mastery of the different strategies. We discuss the theoretical, methodological, and instructional implications of these results. [ABSTRACT FROM AUTHOR]

This study analysed children's use of mental computation strategies and standard written algorithms in the domain of multi-digit addition and subtraction, using the choice/no-choice method. Twenty-one Flemish fourth-graders (MAge=9y10m) solved problem-items that either stimulated the use of mental computation strategies or a standard written algorithm, in one choice and two no-choice conditions. In the choice condition, children could use their preferred strategy on each item. In the two no-choice conditions, they had to solve all items with, respectively, a mental computation strategy (no-choice mental condition) and the standard written algorithm (no-choice written condition). The results revealed that children tended to use the written algorithm on multi-digit sums, even on sums that evoke a mental computation strategy. Moreover, they also used the standard written algorithms with high efficiency and flexibility on sums that elicit a mental computation strategy. We discuss the theoretical, instructional and methodological implications of these results. [ABSTRACT FROM AUTHOR]

Subtraction can be understood by two basic models-taking away (ta) and determining the difference (dd)-and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics learning processes, the article highlights some exemplary steps in which the inverse relation is discussed in light of the two models, namely mental subtraction, the standard algorithms for subtraction, negative numbers and manipulations for solving algebraic equations. For each step, the article presents educational considerations for fostering a flexible use of the two models as well as of the inverse relation between subtraction and addition. In each section, a mathe-didactical analysis is conducted, empirical results from literature as well as from our own case studies are presented and consequences for teaching are sketched. [ABSTRACT FROM AUTHOR]

This work presents two algorithms based on a finite-difference method to calculate the integer ηth root y of an integer number x. The algorithm ηRA uses only additions and subtractions to calculate y. The algorithm is extremely simple and takes time [image omitted] and space O(η) to calculate the ηth root. The algorithm FηRA divides x in group of digits to calculate y; it has a temporal and spatial complexity of [image omitted] and O(η2), respectively. The set of operations of FηRA also includes multiplications and divisions. The algorithms were compared theoretically and empirically against binary search and a numerical method that calculate y. Results show that ηRA has a good performance when the quotient (log 2x)/η is small, and FηRA presents a fair performance when η is small in comparison with log 2x. An additional contribution is a short addition chain for the sequence {1η, 2η, ..., yη} produced by ηRA. [ABSTRACT FROM AUTHOR]

Research literature is reviewed, identifying a need to design instruction to support multi-digit mental computation and critiquing conventional place value instruction. A distinctive instructional domain is proposed, called conceptual place value (CPV) - incrementing and decrementing numbers by units of ones, tens and hundreds. A design research study is reported, focusing on refining the instructional design for CPV with low-attaining 3rd and 4th graders. Two cases of extensive instruction in CPV are described, drawn from 10-week, 1-on-1 teaching cycles of 29 and 32 25-minute lessons. Three key features of instruction that appear to support the two students' learning of CPV are identified: advancing the level of tasks over the lessons, micro-adjusting tasks within lessons and the linking of number words, numerals and quantity. Three dimensions for advancing the level of tasks are identified: extending the range of numbers, making increments and decrements more complex and progressively distancing materials. [ABSTRACT FROM AUTHOR]

In this work, a new approach to background subtraction based on independent component analysis is presented. This approach assumes that background and foreground information are mixed in a given sequence of images. Then, foreground and background components are identified, if their probability density functions are separable from a mixed space. Afterwards, the components estimation process consists in calculating an unmixed matrix. The estimation of an unmixed matrix is based on a fast ICA algorithm, which is estimated as a Newton-Raphson maximization approach. Next, the motion components are represented by the mid-significant eigenvalues from the unmixed matrix. Finally, the results show the approach capabilities to detect efficiently motion in outdoors and indoors scenarios. The results show that the approach is robust to luminance conditions changes at scene. [ABSTRACT FROM AUTHOR]

Abstract  We examine the problem of integer representation in a nearly minimal number of bits so that the increment and the decrement (and indeed the addition and the subtraction) operations can be performed using few bit inspections and fewer bit changes. The model of computation we considered is the bit probe model, where the complexity measure counts only the bitwise accesses to the data structure. We present several efficient data structures to represent integer that use a logarithmic number of bit inspections and a constant number of bit changes per operation. The most space-efficient data structure uses only one extra bit. We also present an extension to our data structure to support efficient addition and subtraction, where the larger value is replaced by the result, while retaining the same asymptotic bounds for the increment and the decrement operations. [ABSTRACT FROM AUTHOR]

We obtain lower bounds on the cost of computing various arithmetic functions and deciding various arithmetic relations from specified primitives. This includes lower bounds for computing the greatest common divisor and deciding coprimeness of two integers, from primitives like addition, subtraction, division with remainder and multiplication. Some of our results are in terms of recursive programs, but they generalize directly to most (plausibly all) algorithms from the specified primitives. Our methods involve some elementary number theory as well as the development of some basic notions and facts about recursive algorithms. [ABSTRACT FROM AUTHOR]

A new method for the assessment of the atrial fibrillatory wave (AFW) from the ECG is presented. This methodology is suitable for signals registered from Holter systems, where the reduced number of leads is insufficient to exploit the spatial information of the ECG. The temporal dependence of the bio-electrical activity were exploited using principal component analysis. The main features of ventricular and atrial activity were extracted, and several basis signals for each subspace were determined. Hence, the estimated (AFW) are reconstructed exclusively from the basis signals that formed the atrial subspace. Its main advantage with respect to adaptive template subtraction techniques was its robustness to variations in the QRST morphology, which thus minimised QRST residua. The proposed approach was first validated using a database of simulated recordings with known atrial activity content. The estimated AFW was compared with the original AFW, obtaining correlation indices of 0.774 +/- 0.106. The suitability of this methodology for real recordings was also proven, though its application to a set of paroxysmal AF ECGs. In all cases, it was possible to detect the main frequency peak, which was between 4.6 Hz and 6.9 Hz for the patients under study. [ABSTRACT FROM AUTHOR]