Showing papers on "Division (mathematics) published in 2016"

Applying MILP Method to Searching Integral Distinguishers Based on Division Property for 6 Lightweight Block Ciphers

Abstract: Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and very recently, Todo et al. proposed bit-based division property and applied to SIMON32 at FSE 2016. However, this technique can only be applied to block ciphers with block size no larger than 32 due to its high time and memory complexity. In this paper, we extend Mixed Integer Linear Programming (MILP) method, which is used to search differential characteristics and linear trails of block ciphers, to search integral distinguishers of block ciphers based on division property with block size larger than 32.

Cell division plane orientation based on tensile stress in Arabidopsis thaliana.

Abstract: Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson–Dumais rule generalizes Errera’s rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson–Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth. We found that the Besson–Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants.

Applying MILP Method to Searching Integral Distinguishers Based on Division Property for 6 Lightweight Block Ciphers.

Abstract: Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and very recently, Todo et al. proposed bit-based division property and applied to SIMON32 at FSE 2016. However, this technique can only be applied to block ciphers with block size no larger than 32 due to its high time and memory complexity. In this paper, we extend Mixed Integer Linear Programming (MILP) method, which is used to search differential characteristics and linear trails of block ciphers, to search integral distinguishers of block ciphers based on division property with block size larger than 32.

Teleportation-based quantum information processing with Majorana zero modes

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

SEERAD: A high speed yet energy-efficient rounding-based approximate divider

Abstract: In this paper, a high speed yet energy-efficient approximate divider for error resilient applications is proposed. For the division operation, the divisor is rounded to a value with a specific form resulting in the transformation of the division operation to the multiplication one. The proposed approximate divider enjoys the flexibility of increasing the accuracy at the price of higher delay and hardware usage. The efficacy of the proposed approximate divider is evaluated in comparison to three different implementations of the SRT divider. The results show that the delay and energy consumption of the proposed approximate divider are, on average, 14 and 300 times smaller than those of the Radix-2 SRT with the carry-save reminder computation. Additionally, the effectiveness of the proposed approximate divider is studied in an image division operation performed in image processing applications. The results suggest the appropriateness of the proposed approximate divider for digital signal processing applications.

Division operations on variable length elements in memory

Abstract: Examples of the present disclosure provide apparatuses and methods for performing variable bit-length division operations in a memory. An example method comprises performing a variable length division operation on a first vector comprising variable length elements representing a number of dividends and stored in a group of memory cells coupled to a first access line and a number of sense lines of a memory array and a second vector comprising variable length elements representing a number of divisors stored in a group of memory cells coupled to a second access line and the number of sense lines of the memory array. The method can include dividing the first vector by the second vector by performing a number of operations. The method can include performing at least one of the number of operations without transferring data via an input/output (I/O) line.

Design of Division Circuits for Stochastic Computing

Abstract: Stochastic computing (SC) encodes data in the signal probabilities associated with pseudo-random bit-streams. It enables very low-area and low-power arithmetic operations using standard VLSI circuits, it is also highly error-tolerant. While addition, subtraction and multiplication have extremely simple SC implementations, this is not true for division. Known stochastic dividers employ sequential logic circuits whose accuracy, convergence properties, etc., are unsatisfactory or not well under-stood. As a result, division is usually avoided or approximated in SC design. We first review and analyze in depth the existing design approaches to stochastic division. We then propose a novel division technique called CORDIV that exploits correlation between the input parameters. CORDIV not only has lower cost than previous stochastic dividers, but is also significantly more accurate. Area is reduced mainly because CORDIV requires less overhead for stochastic number conversion. We provide experimental data showing a typical 3x reduction in area and about a 10x improvement in accuracy.

Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations

Abstract: The interval-valued intuitionistic fuzzy set (IVIFS) generalizes Atanassov's intuitionistic fuzzy set (A-IFS) with the membership and non-membership degrees being intervals instead of real numbers, so it can contain more information. In this paper, we study the derivatives and differentials under interval-valued intuitionistic fuzzy environment. Firstly, we discuss the four change directions (the addition, subtraction, multiplication and division directions) of the interval-valued intuitionistic fuzzy values (IVIFVs); Secondly, we propose four kinds of limits (the addition, subtraction, multiplication and division limits) for different sequences of IVIFVs, and then we define the concepts of interval-valued intuitionistic fuzzy function (IVIFF) and study the continuities of IVIFFs; Thirdly, we develop two kinds of derivatives (the subtraction and division derivatives) of IVIFFs and give an equivalent condition for the existence of the derivative of an IVIFF. At last, we define the concepts of two k...

Time-Division Cellular Networks With Full-Duplex Base Stations

Abstract: A joint user pairing and resource allocation algorithm is proposed to maximize the system throughput in a time-division (TD) cellular network while guaranteeing the quality-of-service (QoS) requirement of users. Full-duplex communication (FDC) is enabled at the base station (BS) with imperfect self interference (SI) cancellation while the user equipments can only work in the traditional half-duplex way because of hardware limitation. We first formulate a nonconvex optimization problem and then utilize the constrained concave-convex procedure (CCCP) to develop a suboptimal solution. A two-step heuristic algorithm with low computational complexity is also proposed. Numerical results show that both user diversity gain and full-duplex (FD) gain can be achieved and the performance of FDC highly depends on the strength of the residual self-interference.

Optical frequency divider with division uncertainty at the 10−21 level

Abstract: Optical clocks with unprecedented accuracy of 10−18 promise innovations in many research areas. Their applications rely to a large extent on the ability of precisely converting the frequency from one optical clock to another, or particularly to the frequencies in the fiber telecom band for long-distance transmission. This report demonstrates a low-noise, high-precision optical frequency divider, which realizes accurate optical frequency conversion and enables precise measurement of optical frequency ratios. By measuring against the frequency ratio between the fundamental and the second harmonic of a 1064-nm laser instead of a second copy of the same system, we demonstrate that the optical frequency divider has a fractional frequency division instability of 6 × 10−19 at 1 s and a fractional frequency division uncertainty of 1.4 × 10−21. The remarkable numbers can support frequency division of the best optical clocks in the world without frequency-conversion-caused degradation of their performance.

Crystallization of space: Space-time fractals from fractal arithmetic

Abstract: Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetic allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated with appropriate Lie groups. The construction is illustrated by explicit examples.

Anti Aristotle—The Division of Zero by Zero

Abstract: Today, the division of zero by zero (0/0) is a concept in philosophy, mathematics and physics without a definite solution. On this view, we are left with an inadequate and unsatisfactory situation that we are not allowed to divide zero by zero while the need to divide zero by zero (i.e. divide a tensor component which is equal to zero by another tensor component which is equal to zero) is great. A solution of the philosophically, logically, mathematically and physically far reaching problem of the division of zero by zero (0/0) is still not in sight. The aim of this contribution is to solve the problem of the division of zero by zero (0/0) while relying on Einstein’s theory of special relativity. In last consequence, Einstein’s theory of special relativity demands the division of zero by zero. Due to Einstein’s theory of special relativity, it is (0/0) = 1. As we will see, either we must accept the division of zero by zero as possible and defined, or we must abandon Einstein’s theory of special relativity as refuted.

A reconstruction of Peters's six-place table of trigonometric functions for the new division (1938)

Abstract: This document provides a reconstruction of Peters's table of trigonometric functions for the centesimal division and to six places (1938).

Subtraction-Free Complexity, Cluster Transformations, and Spanning Trees

Abstract: Subtraction-free computational complexity is the version of arithmetic circuit complexity that allows only three operations: addition, multiplication, and division. We use cluster transformations to design efficient subtraction-free algorithms for computing Schur functions and their skew, double, and supersymmetric analogues, thereby generalizing earlier results by P. Koev. We develop such algorithms for computing generating functions of spanning trees, both directed and undirected. A comparison to the lower bound due to M. Jerrum and M. Snir shows that in subtraction-free computations, "division can be exponentially powerful." Finally, we give a simple example where the gap between ordinary and subtraction-free complexity is exponential.

Three-dimensional multiway power dividers based on transformation optics.

Abstract: The two-dimensional (2D) or three-dimensional (3D) multiway power dividers based on transformation optical theory are proposed in this paper. It comprises of several nonisotropic mediums and one isotropic medium without any lumped and distributed elements. By using finite embedded coordinate transformations, the incident beam can be split and bent arbitrarily in order to achieve effective power division and transmission. In addition, the location of the split point can be employed to obtain unequal power dividers. Finally, several typical examples of the generalized power divider without limitation in 3D space are performed, which shows that the proposed power divider can implement required functions with arbitrary power division and arbitrary transmission paths. The excellent simulated results verify the novel design method for power dividers.

Cell division detection method based on deep learning

Abstract: The invention discloses a cell division detection method based on deep learning, relates to the technical field including cytobiology and the like, and solves the problem of inaccurate cell division detection results. The cell division detection method comprises the following steps: obtaining an image in a cell culture process, and forming a continuous image sequence according to the images obtained at certain time intervals; judging and comparing all cell division processes in the image sequence, and labelling a position where a process that a paternal cell is divided into two daughter cell membranes can be clearly observed in cell division, and forming a labelled dataset; constructing a full convolutional neural network model, determining the parameter of the full convolutional neural network model, loading the labelled dataset into the full convolutional neural network model, using a deep learning method to directly carry out feature learning on an image sequence, and obtaining the trained full convolutional neural network model; and deploying the trained full convolutional neural network model for automatically detecting the cell division of the cell culture data of a similar type. The cell division detection method is used for cell division detection.

Exploitation, Domination, Competitive Markets, and Unfair Division

Abstract: Saying that one agent exploits another is not always casting any aspersions, as when we praise a football team for exploiting the opponent’s poor pass defense in a close game. But sometimes to be described as exploiting is to be characterized as behaving in a way that is morally wrong or at least pro tanto morally wrong. What is this wrong? This essay considers this question mainly with a view to exploring under what conditions engaging in mutually beneficial voluntary interaction with others, as in market exchange, qualifies as exploitation with a connotation of moral wrongness.

Dividing by Zero -- How Bad Is It, Really?

Abstract: In computable analysis testing a real number for being zero is a fundamental example of a non-computable task. This causes problems for division: We cannot ensure that the number we want to divide by is not zero. In many cases, any real number would be an acceptable outcome if the divisor is zero - but even this cannot be done in a computable way. In this note we investigate the strength of the computational problem Robust division: Given a pair of real numbers, the first not greater than the other, output their quotient if well-defined and any real number else. The formal framework is provided by Weihrauch reducibility. One particular result is that having later calls to the problem depending on the outcomes of earlier ones is strictly more powerful than performing all calls concurrently. However, having a nesting depths of two already provides the full power. This solves an open problem raised at a recent Dagstuhl meeting on Weihrauch reducibility. As application for Robust division, we show that it suffices to execute Gaussian elimination.

Division algebras of prime degree with infinite genus

Abstract: The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D′] ∈ Br(F), where D′ is a central division F-algebra having the same maximal subfields as D. For any prime p, we construct a division algebra of degree p with infinite genus. Moreover, we show that there exists a field K such that there are infinitely many nonisomorphic central division K-algebras of degree p and any two such algebras have the same genus.

Division and Slope Factorization of p-Adic Polynomials

Abstract: We study two important operations on polynomials defined over complete discrete valuation fields: Euclidean division and factorization. In particular, we design a simple and efficient algorithm for computing slope factorizations, based on Newton iteration. One of its main features is that we avoid working with fractional exponents. We pay particular attention to stability, and analyze the behavior of the algorithm using several precision models.

Enhanced Rate Division Multiple Access for Electromagnetic Nanonetworks

Abstract: An electromagnetic (EM) nanonetowork is considered to be a key technology in realizing Internet of Nano-Things. However, the traditional communication schemes cannot be directly applied at nanoscale level due to extreme limitation in energy, memory, computational resources, and hardware designs. Due to unique properties of pulse-based communication in nanonetoworks, rate division time-spread ON–OFF keying is considered to be appropriate modulation and channel access mechanism. As such, a symbol in EM nanonetwork would be is represented by either a single pulse or absence of pulse. In rate division, the symbol streams transmitted by multiple users are interleaved by assigning different time periods between two symbols of each user referred as symbol interval. The symbol interval is required to be derived from prime or coprime numbers to minimize the number of collisions. In this paper, we propose a scheme to derive the symbol interval by generating unique prime number at each user node using Prime Mod algorithm. Our scheme do not require coordination between transmitter and receiver and it can be easily implemented in both infrastructure based and ad hoc nanonetworks. Moreover, we show the statistical properties of the computed prime numbers, bounds on prime numbers that can be used, collision probability, and comparison of computational complexity with conventional schemes.

Map information update apparatus and map information update system

Abstract: A map information update apparatus includes: a map information storage unit that stores district map information including a plurality of division areas; a receiver that receives a broadcast wave carrying information of one or more of the plurality of division areas; a wireless communication unit that receives a radio wave carrying information of one or more of the plurality of division areas by wireless communication; and an information update unit that updates, when the district map information does not satisfy a first basis, the district map information for each division area based on the information carried by the broadcast wave received by the receiver and updates, when the district map information satisfies the first basis, the district map information for each division area based on the information carried by the radio wave received by the wireless communication unit.

Rapid extraction method and system for target central point

Abstract: The invention provides a rapid extraction method and system for a target central point All connecting areas in an obtained binary image are marked; a target connecting area is detected according to the marked connecting areas; an external rectangular area is determined based on the target connecting area; and thus a target central point coordinate in the external rectangular area is obtained In the prior art, the multiplication and division operation load for the employed edge detection, Hessian matrix, Hough conversion, and fitting algorithms is heavy However, according to the provided method, the most operation of the image binaryzation, connecting area marking and center of mass method belongs to the logic operation and adding and subtraction operation, so that the execution efficiency is high

A novel method for 3D reconstruction: Division and merging of overlapping B-spline surfaces☆

Abstract: B-spline surfaces, extracted from scanned sensor data, are usually required to represent objects in inspection, surveying technology, metrology and reverse engineering tasks. In order to express a large object with a satisfactory accuracy, multiple scans, which generally lead to overlapping patches, are always needed due to, inter-alia, practical limitations and accuracy of measurements, uncertainties in measurement devices, calibration problems as well as skills of the experimenter. In this paper, we propose an action sequence consisting of division and merging. While the former divides a B-spline surface into many patches with corresponding scanned data, the latter merges the scanned data and its overlapping B-spline surface patch. Firstly, all possible overlapping cases of two B-spline surfaces are enumerated and analyzed from a view of the locations of the projection points of four corners of one surface in the interior of its overlapping surface. Next, the general division and merging methods are developed to deal with all overlapping cases, and a simulated example is used to illustrate aforementioned detailed procedures. In the sequel, two scans obtained from a three-dimensional laser scanner are simulated to express a large house with B-spline surfaces. The simulation results show the efficiency and efficacy of the proposed method. In this whole process, storage space of data points is not increased with new obtained overlapping scans, and none of the overlapping points are discarded which increases the representation accuracy. We believe the proposed method has a number of potential applications in the representation and expression of large objects with three-dimensional laser scanner data.

Frequency Control in the European Power System Considering the Organisational Structure and Division of Responsibilities

Abstract: One of the core responsibilities of a transmission system operator is real-time control of mismatches between scheduled production and actual consumption of electric power, i.e. frequency control. Since the liberalisation of electricity markets and the increase of decentralised intermittent generation, the Continental European power system has been exposed to high and persisting frequency deviations. This thesis investigates technical and organisational shortcomings of the existing frequency control framework in Continental Europe. The objective is to contribute to future concepts of frequency control that ensure an efficient and high frequency quality in the interconnected power system. Historical data are statistically analysed and used for time-sequential Monte Carlo simulations which enable the investigation of the current frequency control structure as well as frequency control coupling processes in future demand and production portfolios. Although the domination of hourly imbalance periods and respective hourly products imposes a highly predictable operational pattern, market-induced imbalances have a severe impact on frequency quality. In this context, the benefits of harmonised ramping requirements and the reduction of the imbalance period are discussed. The current frequency control setup can be gradually centralised across Europe. Imbalance and reserve sharing can be practically implemented, and transfer capacities can be managed. Imbalance sharing does not require additional harmonisation of active power reserve processes and products. Reserve sharing, on the contrary, can only be managed on a non-discriminatory and fair basis if the active power reserve dimensioning as well as the activation rules are harmonised to grant a comparable performance. The findings imply that system operators and national regulatory authorities should focus more closely on the dependency between schedule-based operation and market activity as well as on local active power reserves and cross-border frequency control processes.

Efficient intelligent screw locking equipment

Abstract: The invention relates to efficient intelligent screw locking equipment The efficient intelligent screw locking equipment comprises an equipment matrix, motion mechanisms, a feeding mechanism, a nail rejecting mechanism, lock fetching mechanisms and visual systems, wherein the feeding mechanism and the nail rejecting mechanism are fixedly mounted on the equipment matrix, and the lock fetching mechanisms and the visual systems are connected to the terminals of the motion mechanisms The efficient intelligent screw locking equipment is characterized by further comprising a control system which is used for importing point location information of screw holes; driving mechanisms are connected with scale division rotating discs through direct connection transmission mechanisms; incomplete filling sensors are mounted on material paths, and feeding sensors are mounted at joints between material distribution discs and material paths; scale division decoders are mounted on output shafts of material distribution driving motors, and first scale division sensors are mounted on one sides of the scale division decoders; reeds are mounted on the outer edges of the scale division rotating discs, and second scale division sensors are mounted at positions, corresponding to the reeds, on the main body brackets; baffle ring sensors are arranged at the positions, corresponding to the baffle rings, of the main body brackets; and nail detection sensors are mounted at the positions, corresponding to the lower ends of suction months, of the main body brackets Compared with the prior art, the efficient intelligent screw locking equipment has the characteristics of high production change speed and high working efficiency