Showing papers on "Division (mathematics) published in 2017"

Self-learning Monte Carlo method

Abstract: United States. Department of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering. (award DE-SC0010526)

Automatic Search of Bit-Based Division Property for ARX Ciphers and Word-Based Division Property

Abstract: Division property is a generalized integral property proposed by Todo at Eurocrypt 2015. Previous tools for automatic searching are mainly based on the Mixed Integer Linear Programming (MILP) method and trace the division property propagation at the bit level. In this paper, we propose automatic tools to detect ARX ciphers’ division property at the bit level and some specific ciphers’ division property at the word level.

Pseudo Time-Slice Construction Using a Variable Moving Window k Nearest Neighbor Rule for Sequential Uneven Phase Division and Batch Process Monitoring

Abstract: Multiphase characteristics and uneven-length batch duration have been two critical issues to be addressed for batch process monitoring. To handle these issues, a variable moving window-k nearest neighbor (VMW-kNN) based local modeling, irregular phase division, and monitoring strategy is proposed for uneven batch processes in the present paper. First, a pseudo time-slice is constructed for each sample by searching samples that are closely similar to the concerned sample in which the variable moving window (VMW) strategy is adopted to vary the searching range and the k nearest neighbor (kNN) rule is used to find the similar samples. Second, a novel automatic sequential phase division procedure is proposed by similarity evaluation for local models derived from pseudo time-slices to get different irregular phases and ensure their time sequence. Third, the affiliation of each new sample is real-time judged to determine the proper phase model and fault status can be distinguished from phase shift event. The pr...

A region division based diversity maintaining approach for many-objective optimization

Abstract: Evolutionary algorithms have been used to solve a variety of many-objective optimization problems, where these problems contain more than three conflicting objectives. Most existing evolutionary algorithms have shown to perform well on many-objective optimization problems with regular Pareto optimal fronts, their performance, however, will often considerably deteriorate on those whose Pareto optimal fronts are irregular, e.g., discontinuous, degenerated and convex. To address this issue, in this paper, we propose a region division based many-objective optimization evolutionary algorithm, termed RdEA, where a region division approach is suggested to maintain diversity of population for many-objective optimization (especially for problems with irregular Pareto fronts). In the proposed region division based diversity maintaining approach, the geometric information of Pareto optimal fronts is taken into account by using the non-dominated solutions found at each generation, which helps to solve the problems with irregular Pareto optimal fronts better. The proposed RdEA is compared with five state-of-the-art many-objective evolutionary algorithms on 16 test problems from two test suites DTLZ and WFG and a real-world optimization problem. Experimental results on these problems demonstrate that the competitiveness of the proposed algorithm in solving many-objective optimization problems, especially for those with irregular Pareto optimal fronts.

Parametric Loop Division for 3D Localization in Wireless Sensor Networks.

Abstract: Localization in Wireless Sensor Networks (WSNs) has been an active topic for more than two decades. A variety of algorithms were proposed to improve the localization accuracy. However, they are either limited to two-dimensional (2D) space, or require specific sensor deployment for proper operations. In this paper, we proposed a three-dimensional (3D) localization scheme for WSNs based on the well-known parametric Loop division (PLD) algorithm. The proposed scheme localizes a sensor node in a region bounded by a network of anchor nodes. By iteratively shrinking that region towards its center point, the proposed scheme provides better localization accuracy as compared to existing schemes. Furthermore, it is cost-effective and independent of environmental irregularity. We provide an analytical framework for the proposed scheme and find its lower bound accuracy. Simulation results shows that the proposed algorithm provides an average localization accuracy of 0.89 m with a standard deviation of 1.2 m.

Topological Phases Protected by Point Group Symmetry

Abstract: United States. Dept. of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering (Grant DE-SC0010526)

Relevant parameters in models of cell division control.

Abstract: A recent burst of dynamic single-cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different models were used to propose specific mechanisms, but the links between them are poorly explored. The lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with simple physical analogues. By perturbative expansion around the mean initial size (or interdivision time), we show how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulations, the available data are described precisely by the first-order approximation of this expansion, i.e., by a "linear response" regime for the correction of size fluctuations. Hence, a single dimensionless parameter defines the strength and action of the division control against cell-to-cell variability (quantified by a single "noise" parameter). However, the same strength of linear response may emerge from several mechanisms, which are distinguished only by higher-order terms in the perturbative expansion. Our analytical estimate of the sample size needed to distinguish between second-order effects shows that this value is close to but larger than the values of the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

Self-learning quantum Monte Carlo method in interacting fermion systems

Abstract: United States. Dept. of Energy. Division of Materials Sciences and Engineering (DE-SC0010526)

Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth

Abstract: Quantum circuits for basic mathematical functions such as division are required to implement scientific computing algorithms on quantum computers. In this work, we propose two designs for quantum integer division. The designs are based on quantum Clifford+T gates and are optimized for T-count and T-depth. Quantum circuits that are based on Clifford+T gates can be made fault tolerant in nature but the T gate is very costly to implement. As a result, reducing T-count and T-depth have become important optimization goals. Existing quantum hardware is limited in terms of number of available qubits. Thus, ancillary qubits are a circuit overhead that needs to be kept to a minimum. We propose two quantum integer division circuits. The first quantum integer division circuit is based on the non-restoring division algorithm. The proposed non-restoring division circuit is optimized for total quantum hardware (T-count and T-depth) cost but requires 2* n + 1 ancillary qubits. We also propose a quantum integer division circuit based on the restoring division algorithm. The proposed restoring division circuit is optimized for total qubits. The design requires only n ancillary qubits but will need more quantum hardware than the non-restoring division circuit. Both proposed quantum circuits are based on (i) a new quantum conditional addition circuit, (ii) a new quantum adder-subtractor and (iii) a new quantum subtraction circuit. Further, both designs are compared and shown to be superior to existing work in terms of T-count and T-depth. The proposed quantum non-restoring integer division circuit has a 96% improvement in terms of T-count and a 93% improvement in terms of T-depth compared to existing work. The proposed quantum restoring integer division circuit has a 91% improvement in terms of T-count and a 86% improvement in terms of T-count compared to the existing work.

Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic

Abstract: We analyze several classical basic building blocks of double-word arithmetic (frequently called “double-double arithmetic” in the literature): the addition of a double-word number and a floating-point number, the addition of two double-word numbers, the multiplication of a double-word number by a floating-point number, the multiplication of two double-word numbers, the division of a double-word number by a floating-point number, and the division of two double-word numbers. For multiplication and division we get better relative error bounds than the ones previously published. For addition of two double-word numbers, we show that the previously published bound was incorrect, and we provide a new relative error bound. We introduce new algorithms for division. We also give examples that illustrate the tightness of our bounds.

Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division

Abstract: When children learn about fractions, their prior knowledge of whole numbers often interferes, resulting in a whole number bias. However, many fraction concepts are generalizations of analogous whole number concepts; for example, fraction division and whole number division share a similar conceptual structure. Drawing on past studies of analogical transfer, we hypothesize that children’s whole number division knowledge will support their understanding of fraction division when their relevant prior knowledge is activated immediately before engaging with fraction division. Children in 5th and 6th grade modeled fraction division with physical objects after modeling a series of addition, subtraction, multiplication, and division problems with whole number operands and fraction operands. In one condition, problems were blocked by operation, such that children modeled fraction problems immediately after analogous whole number problems (e.g., fraction division problems followed whole number division problems). In another condition, problems were blocked by number type, such that children modeled all four arithmetic operations with whole numbers in the first block, and then operations with fractions in the second block. Children who solved whole number division problems immediately before fraction division problems were significantly better at modeling the conceptual structure of fraction division than those who solved all of the fraction problems together. Thus, implicit analogies across shared concepts can affect children’s mathematical thinking. Moreover, specific analogies between whole number and fraction concepts can yield a positive, rather than a negative, whole number bias.

Wasan geometry with the division by 0

Abstract: Results in Wasan geometry of tangents circles can still be considered in a singular case by the division by 0.

Comparison of CD(C) ROADM architectures for space division multiplexed networks

Abstract: We compare different architectures of CD and CDC ROADMs supporting spatial superchannel routing in terms of required components, revealing the most cost-effective designs.

Studies of The Durability of Belt Conveyor Idlers with Working Loads Taken into Account

Abstract: The results of laboratory and operational studies conducted in the Machinery Systems Division of Wroclaw University of Technology in recent years have became the basis for selecting proper belt conveyor roller designs optimized for specific strength and operational criteria. The usefulness of the results for assessing the energy intensity of idlers, estimating their durability and determining modernization policies has been confirmed. Methods of estimating the durability of carrying idlers on the basis of the identified output stream distributions are presented. Results of studies carried out using an analytical method and a laboratory method are reported. It has been shown that the operational durability of a roller is determined by its design, the roller set parameters (the spacing and the angle of bevel) and the operating conditions having a bearing on the irregularity of the transported output stream.

Pre-service teachers’ flexibility with referent units in solving a fraction division problem

Abstract: This study investigated 111 pre-service teachers’ (PSTs’) flexibility with referent units in solving a fraction division problem using a length model. Participants’ written solutions to a measurement fraction division problem were analyzed in terms of strategies and types of errors, using an inductive content analysis approach. Findings suggest that most PSTs could calculate fraction division and make equivalent fractions procedurally but did not have the quantitative meanings of measurement division with fraction quantities or of making equivalent fractions. Implications are discussed for the improvement of PSTs’ specialized knowledge for teaching fraction division.

Motivation Cards to Support Students’ Understanding on Fraction Division

Abstract: This design research aims to develop a learning activity which supports the fifth-grade students to understand measurement fraction division problems (A whole number divided by a fraction that result in a whole number answer ) conceptually. Furthermore, how students solve the fraction division problem using models is also analyzed. Data for the retrospective analysis is collected through two teaching experiments in the form of students’ work, field notes, and some part of classroom discussions. The important findings in this research are: 1) the developed learning activity namely Motivation Cards support students understand that 3 divided by one-half means how many one-half are in 3 through models. However, when the divisor is not a unit fraction they could not directly relate the unshaded part in area model for example. 2) area model is proper model to be firstly introduced when the students work on fraction division. 3) understanding this kind of fraction division help students understand other measurement fraction division where both divisor and dividend are fractions. 4) the learning activity supports the development of character values for students.

Fuzzy number division and the multi-granularity phenomenon

Abstract: Manuscript submitted 2016-01-26, revised 2016-07-08, 2016-10-26 and 2016-12-30, initially accepted for publication 2017-01-20, published in August 2017. Abstract. The paper presents difficulties connected with fuzzy and interval division. If operations such as fuzzy addition, subtraction and multiplication provide as a result one compact, multidimensional granule, then a result of the fuzzy division can consists of few separated granules. Such results are more difficult to use in next calculations. The paper shows that the number of solution granules can be higher than 2 and that in certain problems division does not occur explicitly. In certain problems, separation of particular solution granules can be considerable. The paper also shows how to realize the fuzzy division when its denominator contains zero. Most types of fuzzy arithmetics forbid such operation. However, the paper shows that it is possible. Multidimensional fuzzy RDM arithmetic and horizontal membership functions which facilitate detecting of solution granules are also described. The considered problems are visualized by examples.

Hardware Division by Small Integer Constants

Abstract: This article studies the design of custom circuits for division by a small positive constant. Such circuits can be useful for specific FPGA and ASIC applications. The first problem studied is the Euclidean division of an unsigned integer by a constant, computing a quotient and remainder. Several new solutions are proposed and compared against the state-of-the-art. As the proposed solutions use small look-up tables, they match well with the hardware resources of an FPGA. The article then studies whether the division by the product of two constants is better implemented as two successive dividers or as one atomic divider. It also considers the case when only a quotient or only a remainder is needed. Finally, it addresses the correct rounding of the division of a floating-point number by a small integer constant. All these solutions, and the previous state-of-the-art, are compared in terms of timing, area, and area-timing product. In general, the relevance domains of the various techniques are different on FPGA and on ASIC.

The New Theory of International Values: An Overview

Abstract: This chapter is a general introduction of the new theory of international values, which is an extension of the cost-of-production theory of value to the international trade situations. Within a general framework comprising input trade and choice of production techniques, the new theory analyzes the international values (i.e., the system that consists of wages of each country and prices of goods), gains and losses from trade, and the patterns of specializations. It is the first theory to treat traded input goods in this general form. It facilitates the analysis of recent conspicuous trade aspects, such as rapidly increasing trade volume of intermediate goods, fragmentations of production processes, and the complex network of global value chains. Besides the Introduction (Division I), this work is divided into four parts: (1) the presentation of the theory (Division II), (2) extensions of the theory to more complex situations (Division III), (3) some examples of applications of the theory (Division IV), and (4) possible implications to three neighboring fields (Division V). Terms and concepts are explained in detail and theorems are fully stated. A mathematical proof of the fundamental theorem is given in the Appendix.

Subtraction and Division of Neutrosophic Numbers

Abstract: In this paper, we define the subtraction and the division of neutrosophic single-valued numbers. The restrictions for these operations are presented for neutrosophic singlevalued numbers and neutrosophic single-valued overnumbers / undernumbers / offnumbers. Afterwards, several numeral examples are presented.

Asymmetric Cell Division in the One-Cell C. elegans Embryo: Multiple Steps to Generate Cell Size Asymmetry.

Abstract: The first division of the one-cell C. elegans embryo has been a fundamental model in deciphering the mechanisms underlying asymmetric cell division. Polarization of the one-cell zygote is induced by a signal from the sperm centrosome and results in the asymmetric distribution of PAR proteins. Multiple mechanisms then maintain PAR polarity until the end of the first division. Once asymmetrically localized, PAR proteins control several essential aspects of asymmetric division, including the position of the mitotic spindle along the polarity axis. Coordination of the spindle and cytokinetic furrow positions is the next essential step to ensure proper asymmetric division. In this chapter, I review the different mechanisms underlying these successive steps of asymmetric division. Work from the last 30 years has revealed the existence of multiple and redundant regulatory pathways which ensure division robustness. Besides the essential role of PAR proteins, this work also emphasizes the importance of both microtubules and actomyosin throughout the different steps of asymmetric division.

The relationship between non-symbolic multiplication and division in childhood

Abstract: Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving appro...

Optical multi-beam forming method based on a liquid crystal optical phased array

Abstract: Three multi-beam forming methods based on optical phased array technology are presented in this paper. These methods can achieve simultaneous multiple-beam pointing in the optical band. The principles of these methods are introduced, the far-field pattern calculation formulas of the subaperture method and the array division multiplexing method are derived, and the algorithm flow of the iterative Fourier transform method is described in detail. Simulations and experiments have been conducted to verify the validity of these methods.

Origin of life: Division for multiplication

Abstract: Early forms of life could have started by molecular compounds coming together under conditions dense enough to promote reactions. But how might these droplets have undergone what we now know as cell division? The answer may be simpler than we think.

Calculation of passive magnetic force in a radial magnetic bearing using general division approach

Abstract: This paper represents the force calculation in a radial passive magnetic bearing using Monte Carlo technique with general division approach (s-MC). The expression of magnetic force is obtained using magnetic surface charge density method which incurs a multidimensional integration with complicated integrand. This integration is solved using Monte Carlo technique with 1-division (1-MC) and 2-division (2-MC) approaches with a MATLAB programming. Analysis using established methods such as finite element method (FEM), semi-analytical method, and adaptive Monte Carlo (AMC) method has been carried out to support the proposed technique. Laboratory experiment has been conducted to validate the proposed method. 2-MC gives better result than 1-MC. The computation time of the proposed method is compared with the quadrature method, FEM and AMC. It is observed that the proposed method invites less computational burden than those methods as the algorithm adaptively traverses the domain for promising parts of the domain only, and all the elementary regions are not considered with equal importance.

New observation on division property

Abstract: Integral cryptanalysis [1–5] is among the most important cryptanalytic vectors. With some special inputs, we check whether the sum of the corresponding ciphertexts is 0 or not. In some other literatures, integral cryptanalysis is also known as square attack, saturation attack, multi-set attack, higher-order differential attack and so on. Usually, it is difficult to determine the property of a multi-set which has the balaced property B after applying a nonlinear transformation. Thus if we could determine the property of the output multi-set, the integral distinguishers could be improved. Todo [6] proposed in EUROCRYPT 2015 the division property to evaluate the sum of the outputs of a nonlinear function. A multi-set X has the division property D k if and only if for all Boolean functions f : F2 → F2, deg f < k, the sum of f on X is always 0. It has been pointed out that the division property D 2 is equivalent to the property B. However, there is a gap between D n and A. Let X and Y be the input and output sets of an S-box, respectively, and d be the algebraic degree of the Sbox. The newly proposed methods of constructing integrals for both Feistel and SPN structures are based on the following fact: If X has the division property D k , Y has the division property D n ⌈k/d⌉. The result shows that for a given Feistel structure, we can always construct a 3-round and a 5-round integral distinguisher in case the round function is non-bijective and bijective, respectively. In CRYPTO 2015, Sun et al. [7] proved that a zero correlation linear hull always implies the existence of an integral distinguisher. Therefore, we can construct integrals of a block cipher by finding zero correlation linear hulls. For example, based on the known zero correlation linear hulls of 3-round/5-round Feistel structures with non-bijective/bijective round functions, they theoretically proved that there always exist 3-round/5round integral distinguishers for Feistel structures with non-bijective/bijective round functions. In [6], Todo constructed a special subset with the division property D k . Since the number of elements in this subset is 2, we wonder whether we could construct some other subsets with the division property D k , however with less elements than 2, to reduce the data complexity of the integral distinguishers of Feistel structures. Many block ciphers are designed based on the Feistel structure, such as DES [8] and Camellia [9]. A Feistel structure consists of r rounds, each of which is defined as follows. Denote by (Li−1, Ri−1) the 2n-bit input to the i-th round, and (Li, Ri) the output of the i-th round. Then

Method and apparatus for encoding and decoding video using picture division information

Abstract: Disclosed are a method and an apparatus for encoding and decoding a video using picture division information. Each of the pictures of the video is divided into tiles or slices on the basis of the picture division information. Each picture is divided in one of at least two different ways on the basis of the picture division information. The picture division information may indicate two or more picture division schemes. The picture division scheme may be changed periodically or may be changed according to a specified rule. The picture division information may describe these periodic changes or specified rules.