scispace - formally typeset
Search or ask a question

Showing papers on "Division (mathematics) published in 2020"


Journal ArticleDOI
TL;DR: It is shown, for three different strains, that S. aureus cells do not regularly divide in three alternating perpendicular planes as previously thought, and one out of the multiple planes perpendicular to the septum can be used in daughter cells irrespective of its orientation in relation to the penultimate division plane.
Abstract: Staphylococcus aureus is generally thought to divide in three alternating orthogonal planes over three consecutive division cycles. Although this mode of division was proposed over four decades ago, the molecular mechanism that ensures this geometry of division has remained elusive. Here we show, for three different strains, that S. aureus cells do not regularly divide in three alternating perpendicular planes as previously thought. Imaging of the divisome shows that a plane of division is always perpendicular to the previous one, avoiding bisection of the nucleoid, which segregates along an axis parallel to the closing septum. However, one out of the multiple planes perpendicular to the septum which divide the cell in two identical halves can be used in daughter cells, irrespective of its orientation in relation to the penultimate division plane. Therefore, division in three orthogonal planes is not the rule in S. aureus. Staphylococcus aureus is thought to divide in three alternating orthogonal planes over three consecutive divisions. Here the authors dispel this idea, showing that one out of the multiple planes perpendicular to the septum can be used in daughter cells irrespective of its orientation in relation to the penultimate division plane.

46 citations


Journal ArticleDOI
TL;DR: A theory based on stochastic hybrid systems which could explain the main division strategies, including not only the adder strategy but the whole range from sizer to timer, is developed.
Abstract: Recent experiments support the adder model for E. coli division control. This model posits that bacteria grow, on average, a fixed size before division. It also predicts decorrelation between the noise in the added size and the size at birth. Here we develop a theory based on stochastic hybrid systems which could explain the main division strategies, including not only the adder strategy but the whole range from sizer to timer. We use experiments to explore the division control of E. coli growing with glycerol as carbon source. In this medium, the division strategy is sizerlike, which means that the added size decreases with the size at birth. We found, as our theory predicts, that in a sizerlike strategy the mean added size decreases with the size at birth while the noise in added size increases. We discuss possible molecular mechanisms underlying this strategy and propose a general model that encompasses the different division strategies.

38 citations


Book ChapterDOI
07 Dec 2020
TL;DR: Under the framework of the monomial prediction, it is formally prove that most algorithms for detecting division properties in literature raise no false alarms but may miss, and establishes the equivalence between themonomial prediction and the three-subset bit-based division property without unknown subset presented at EUROCRYPT 2020.
Abstract: Since it was proposed in 2015 as a generalization of integral properties, the division property has evolved into a powerful tool for probing the structures of Boolean functions whose algebraic normal forms are not available. We capture the most essential elements for the detection of division properties from a pure algebraic perspective, proposing a technique named as monomial prediction, which can be employed to determine the presence or absence of a monomial in any product of the coordinate functions of a vectorial Boolean function \(\textit{\textbf{f}}\) by counting the number of the so-called monomial trails across a sequence of simpler functions whose composition is \(\textit{\textbf{f}}\). Under the framework of the monomial prediction, we formally prove that most algorithms for detecting division properties in literature raise no false alarms but may miss. We also establish the equivalence between the monomial prediction and the three-subset bit-based division property without unknown subset presented at EUROCRYPT 2020, and show that these two techniques are perfectly accurate.

31 citations


Journal ArticleDOI
TL;DR: A simple yet effective scheme using an azimuth-scaling spiral transformation that can accomplish both OAM multiplication and division by arbitrary rational factors in a single stage is proposed and experimentally demonstrated.
Abstract: Multiplication and division of the orbital angular momentum (OAM) of light are important functions in the exploitation of the OAM mode space for such purposes as high-dimensional quantum information encoding and mode division multiplexed optical communications. These operations are possible with optical transformations that reshape optical wave fronts according to azimuthal scaling. However, schemes proposed thus far have been limited to OAM multiplication by integer factors and require complex beam-copying or multitransformation diffraction stages; a result of the limited phase excursion 2πl around the annulus of an OAM state exp(ilθ). Based on the key idea that the phase excursion along spirals in the transverse plane of a vortex is theoretically unlimited, we propose and experimentally demonstrate a simple yet effective scheme using an azimuth-scaling spiral transformation that can accomplish both OAM multiplication and division by arbitrary rational factors in a single stage.

29 citations


Journal ArticleDOI
TL;DR: The main objective of this study is to minimize optical node resources, such as transponders, multiplexers and wavelength selective switches, needed to provide and maintain high quality of network services, in ultra-wideband wavelength division multiplexed networks, at low cost.
Abstract: Ultra-wideband wavelength division multiplexed networks enable operators to use more effectively the bandwidth offered by a single fiber pair and thus make significant savings, both in operational and capital expenditures. The main objective of this study is to minimize optical node resources, such as transponders, multiplexers and wavelength selective switches, needed to provide and maintain high quality of network services, in ultra-wideband wavelength division multiplexed networks, at low cost. A model based on integer programming is proposed, which includes a detailed description of optical network nodal resources. The developed optimization tools are used to study the ultra-wideband wavelength division multiplexed network performance when compared with the traditional C-band wavelength division multiplexed networks. The analysis is carried out for realistic networks of different dimensions and traffic demand sets.

24 citations


Journal ArticleDOI
TL;DR: A floating-point division and square root unit is presented, which implements a radix-64 floating- point division and a Radix-16 floating- Point square root, requiring 11, 6, and 4 cycles for double, single and half-precision division with normalized operands and result, and 15, 8 and 5 cycles for square root.
Abstract: Digit-recurrence algorithms are widely used in actual microprocessors to compute floating-point division and square root. These iterative algorithms present a good trade-off in terms of performance, area and power. We present a floating-point division and square root unit, which implements a radix-64 floating-point division and a radix-16 floating-point square root. To have an affordable implementation, each radix-64 division iteration and radix-16 square root iteration are made of simpler radix-4 iterations: 3 radix-4 iterations in division and 2 in square root. Speculation is used between consecutive radix-4 iterations to get a reduced timing. There are three different parts in digit-recurrence implementations: initialization, digit iterations, and rounding. The digit iteration is the iterative part and it uses the same logic for several cycles. Division and square root share partially the initialization and rounding stages, whereas each one has different logic for the digit iterations. The result is a low-latency floating-point divider and square root, requiring 11, 6, and 4 cycles for double, single and half-precision division with normalized operands and result, and 15, 8 and 5 cycles for square root. One or two additional cycles are needed in case of subnormal operand(s) or result.

19 citations


Journal ArticleDOI
TL;DR: A practical algorithm for computing the propagation tables of 16-bit Super-Sboxes is described for the first time, increasing the precision of the division property by removing a lot of false division trails.
Abstract: In this paper we propose new techniques related to division property. We describe for the first time a practical algorithm for computing the propagation tables of 16-bit Super-Sboxes, increasing the precision of the division property by removing a lot of false division trails. We also improve the complexity of the procedure introduced by Lambin et al. (Design, Codes and Cryptography, 2020) to extend a cipher with linear mappings and show how to decrease the number of transitions to look for. While search procedures for integral distinguishers most often rely on MILP or SAT solvers for their ease of programming the propagation constraints, such generic solvers can only handle small 4/8-bit Sboxes. Thus we developed an ad-hoc tool handling larger Sboxes and all the improvements described in the paper. As a result, we found new integral distinguishers on SKINNY-64, HIGHT and Midori-64.

17 citations


Journal ArticleDOI
TL;DR: A map of the ship encounter azimuth division was constructed that can serve as an accurate numerical basis for the division of marine encounter situations, maritime accident responsibility division, and intelligent ship collision avoidance decisions.

15 citations


Journal ArticleDOI
TL;DR: In this paper, the demagnetization characteristics and eddy current loss of a BLDC motor generator are analyzed according to magnet segments and the rotor temperature is measured to determine the difference in heating caused by the change in EDD current loss.
Abstract: Permanent magnet motor is used in various fields because of their relatively small size, high power and high efficiency. However, an electric machine performance using permanent magnet can be decreased as temperature, humidity, and magnetic field related demagnetization phenomenon. Therefore, the motor should be designed considering the demagnetization characteristics. In this paper, the demagnetization characteristics and eddy current loss of a BLDC motor generator are analyzed according to magnet segments. For the comparison of eddy current loss, 3D analysis is performed by dividing the magnet into Non segment, three segments, five segments, and seven segments. The magnet demagnetization according to the change in eddy current is analyzed. The rotor temperature is measured to determine the difference in heating caused by the change in eddy current loss. The electromagnetic characteristics are analyzed by ANSYS EM 19.0. The validity of the results is verified by comparing the simulation and experimental data.

14 citations


Journal ArticleDOI
TL;DR: In this paper, a photonic-assisted regenerative microwave frequency divider with a tunable frequency division factor of 2 to 6 was proposed to improve the phase noise performance of a microwave signal.
Abstract: A photonic-assisted microwave frequency divider that is able to perform frequency division with a tunable division factor is presented. It is realized based on the regenerative approach in which frequency mixing and filtering operations are implemented using a dual-parallel Mach–Zehnder modulator (DPMZM) and an optical filter in an optoelectronic oscillator loop. The frequency division factor can be tuned by controlling the optical filter passband, the round-trip gain, and the time delay of the optoelectronic oscillator loop. The proposed approach is analyzed theoretically and verified experimentally. The phase conditions to achieve frequency division for a given division factor are analyzed. Experimental results demonstrate, for the first time, a photonic-assisted regenerative microwave frequency divider with a tunable frequency division factor of 2 to 6. One key application of a microwave frequency divider is to improve the phase noise performance of a microwave signal. In our experiment, the phase noise is reduced by 16.2 dB when a microwave signal is frequency divided by 6 times.

13 citations


Journal ArticleDOI
TL;DR: Experimental results on real-life trajectory datasets illustrate that the proposed ST-TSD method significantly improves the quality of traffic sub-area division over existing methods.

Journal ArticleDOI
TL;DR: A new model is built that only includes that the sub-matrix corresponding to a valid trail should be invertible, which provides more choices for future designs and removes the restriction of the ZR method that the matrix has to be inversionible.
Abstract: The bit-based division property (BDP) is the most effective technique for finding integral characteristics of symmetric ciphers. Recently, automatic search tools have become one of the most popular approaches to evaluating the security of designs against many attacks. Constraint-aided automatic tools for the BDP have been applied to many ciphers with simple linear layers like bit-permutation. Constructing models of complex linear layers accurately and efficiently remains hard. A straightforward method proposed by Sun et al. (called the S method), decomposes a complex linear layer into basic operations like COPY and XOR, then models them one by one. However, this method can easily insert invalid division trails into the solution pool, which results in a quicker loss of the balanced property than the cipher itself would. In order to solve this problem, Zhang and Rijmen propose the ZR method to link every valid trail with an invertible sub-matrix of the matrix corresponding to the linear layer, and then generate linear inequalities to represent all the invertible sub-matrices. Unfortunately, the ZR method is only applicable to invertible binary matrices (defined in Definition 3).To avoid generating a huge number of inequalities for all the sub-matrices, we build a new model that only includes that the sub-matrix corresponding to a valid trail should be invertible. The computing scale of our model can be tackled by most of SMT/SAT solvers, which makes our method practical. For applications, we improve the previous BDP for LED and MISTY1. We also give the 7-round BDP results for Camellia with FL/FL−1, which is the longest to date.Furthermore, we remove the restriction of the ZR method that the matrix has to be invertible, which provides more choices for future designs. Thanks to this, we also reproduce 5-round key-dependent integral distinguishers proposed at Crypto 2016 which cannot be obtained by either the S or ZR methods.

Journal ArticleDOI
TL;DR: In this paper, a new balanced-to-balanced filtering power divider with an arbitrary power division ratio was proposed by utilizing the circular patch resonator, which achieved good performance at the resonant frequency of TM ∼ 11.
Abstract: Here, a new balanced-to-balanced filtering power divider with an arbitrary power division ratio is proposed by utilising the circular patch resonator. To clarify the working principle, the resonant property of the circular patch resonator is firstly investigated. A prototype of the balanced-to-balanced power divider with arbitrary power division ratio is then developed. This prototype consists of only one circular patch resonator, three pairs of balanced ports, and two ports terminated with matching impedances. With this simple arrangement, the desired performance of a balanced-to-balanced power divider with an arbitrary power division ratio can be satisfactorily achieved at the resonant frequency of TM 11 . Afterwards, a second-order filtering circuit is constructed. In this context, two circular patches are arranged at the two sides of the ground and good signal transmission is realised by virtue of proper coupling apertures etched on the ground. Apart from coupling, the apertures can be further used for harmonic suppression. Therefore, this proposed structure not only has improved in-band and out-of-band performances, but also has good harmonic suppression. To verify the design concept, two balanced-to-balanced filtering power dividers with division ratios of 1:1 and 15:1 are finally designed and fabricated. All the measured results agree well with the simulated ones.

Proceedings ArticleDOI
04 May 2020
TL;DR: This work introduces the process of Maxpolynomial Division, a geometric method which simulates division of polynomials in the max-plus semiring, while highlighting its key properties and noting its connection to neural networks.
Abstract: In this work, we further the link between neural networks with piecewise linear activations and tropical algebra. To that end, we introduce the process of Maxpolynomial Division, a geometric method which simulates division of polynomials in the max-plus semiring, while highlighting its key properties and noting its connection to neural networks. Afterwards, we generalize this method and apply it in the context of neural network minimization, for two-layer networks used for binary classification problems, attempting to reduce the size of the hidden layer before the output. A tractable method to find an appropriate divisor and perform the division is introduced and evaluated in the IMDB Movie Review and MNIST datasets, with preliminary experiments demonstrating a capacity of this method to reduce the size of the network, without major loss of performance.

Posted Content
TL;DR: In this paper, it was shown that a subfamily of fields is not linearly disjoint over a CM elliptic curve defined over a number field containing the CM field (K) if it contains more than one element.
Abstract: For every CM elliptic curve $E$ defined over a number field $F$ containing the CM field $K$, we prove that the family of $p^{\infty}$-division fields of $E$, with $p \in \mathbb{N}$ prime, becomes linearly disjoint over $F$ after removing an explicit finite subfamily of fields. If $F = K$ and $E$ is obtained as the base-change of an elliptic curve defined over $\mathbb{Q}$, we prove that this finite subfamily is never linearly disjoint over $K$ as soon as it contains more than one element.

Journal ArticleDOI
01 Feb 2020
TL;DR: Computational simulations confirm that a timer division control model alone cannot lead to size homeostasis if the single‐cell growth model is exponential, and timer and adder division control models cannot be distinguished if thesingle‐cellgrowth model is linear.
Abstract: Three models of division control are proposed to achieve cell size homeostasis: sizer, timer, and adder. However, few published studies of division control take into account the dynamics of single-cell growth and most assume that single-cell growth is exponential. Here, computational simulations considering exponential, linear, and bilinear growth models are performed. These simulations confirm that a timer division control model alone cannot lead to size homeostasis if the single-cell growth model is exponential. Furthermore, timer and adder division control models cannot be distinguished if the single-cell growth model is linear. Models of division control cannot be easily differentiated by analysis of average cell behavior because the birth sizes of the majority of cells are close to the population average. However, the differences between division control models are amplified in outlier cells whose birth size is far from the average. A method is introduced for vector field analysis of the speed of convergence of outlier lineages toward the steady-state birth size, which can help to distinguish between division control models and single-cell growth models.

Journal ArticleDOI
TL;DR: In this paper, it was shown that if K is N-invariant and N is non-central, then K is central and some examples of almost subnormal subgroups in division rings that are not subnormal are also given.
Abstract: Let D be a division ring with infinite center, K a proper division subring of D and N an almost subnormal subgroup of the multiplicative group $$D^*$$ of D. The aim of this paper is to show that if K is N-invariant and N is non-central, then K is central. Some examples of almost subnormal subgroups in division rings that are not subnormal are also given.

Journal ArticleDOI
TL;DR: In this paper, the authors show that even if the previous techniques fail to find a distinguisher based on the division property over a given function, they can potentially find a relevant distinguisher over a linearly equivalent function.
Abstract: Division property is a cryptanalysis method that proves to be very efficient on block ciphers Computer-aided techniques such as MILP have been widely and successfully used to study various cryptanalysis techniques, and it especially led to many new results for the division property Nonetheless, we claim that the previous techniques do not consider the full search space We show that even if the previous techniques fail to find a distinguisher based on the division property over a given function, we can potentially find a relevant distinguisher over a linearly equivalent function We show that the representation of the block cipher heavily influences the propagation of the division property, and exploiting this, we give an algorithm to efficiently search for such linear mappings As a result, we exhibit a new distinguisher over 10 rounds of RECTANGLE, while the previous best was over 9 rounds, and rule out such a distinguisher over more than 9 rounds of PRESENT We also give some insight about the construction of an S-box to strengthen a block cipher against our technique We prove that using an S-box satisfying a certain criterion is optimal in term of resistance against classical division property Accordingly, we exhibit stronger variants of RECTANGLE and PRESENT, improving the resistance against division property based distinguishers by 2 rounds

Journal ArticleDOI
27 Mar 2020-Top
TL;DR: This paper extends the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utilities cooperative games with a priori unions and provides axiomatic characterizations of the new values.
Abstract: In this paper, we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal surplus division value we propose three possible extensions. We provide axiomatic characterizations of the new values. Furthermore, we apply the proposed modifications to a particular motivating example and compare the numerical results with those obtained with the original values.

Journal ArticleDOI
16 Dec 2020
TL;DR: In this paper, the transrational numbers are constructed as a transfield of the field of rational numbers and considered as an abstract data type, and given an equational specification under initial algebra semantics.
Abstract: In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to its opposite, and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.


Journal ArticleDOI
TL;DR: In this article, the authors present a general algorithm for quantum annealing for any number of dimensions and provide results from the D-Wave quantum anneler for 2x2 and 3x3 general matrices.
Abstract: Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore\rq{}s Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, gated systems and quantum annealers. In this paper, we express floating point operations such as division and matrix inversion in terms of a {\em quadratic unconstrained binary optimization} (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, but we provide results from the D-Wave quantum anneler for 2x2 and 3x3 general matrices. Our algorithm scales to very large numbers of linear equations. We should also mention that our algorithm provides the full solution the the matrix problem, while HHL provides only an expectation value.

Posted Content
TL;DR: In this paper, the inner ideals of Lie algebras obtained from the Tits-Kantor-Koecher construction were used to construct Moufang sets, Moufangs triangles and Moufans hexagons.
Abstract: We construct Moufang sets, Moufang triangles and Moufang hexagons using inner ideals of Lie algebras obtained from structurable algebras via the Tits--Kantor--Koecher construction. The three different types of structurable algebras we use are, respectively: (1) structurable division algebras, (2) algebras $D \oplus D$ for some alternative division algebra $D$, equipped with the exchange involution, (3) matrix structurable algebras $M(J,1)$ for some cubic Jordan division algebra $J$. In each case, we also determine the root groups directly in terms of the structurable algebra.

Journal ArticleDOI
18 Jun 2020-Sensors
TL;DR: This article addresses the area division problem in a distributed manner providing a solution for cooperative monitoring missions with multiple UAVs by presenting a distributed online algorithm to accelerate the convergence of the system to the optimal solution, following a frequency-based approach.
Abstract: This article addresses the area division problem in a distributed manner providing a solution for cooperative monitoring missions with multiple UAVs. Starting from a sub-optimal area division, a distributed online algorithm is presented to accelerate the convergence of the system to the optimal solution, following a frequency-based approach. Based on the "coordination variables" concept and on a strict neighborhood relation to share information (left, right, above and below neighbors), this technique defines a distributed division protocol to determine coherently the size and shape of the sub-area assigned to each UAV. Theoretically, the convergence time of the proposed solution depends linearly on the number of UAVs. Validation results, comparing the proposed approach with other distributed techniques, are provided to evaluate and analyze its performance following a convergence time criterion.

Journal ArticleDOI
01 May 2020
TL;DR: It is proved that the bias phenomenon, the non-randomness widely utilized in dynamic cube attacks and cube testers, can also be reflected by the division property, and new secure bounds are derived for Grain-like primitives against both the zero-sum and bias cube testers.
Abstract: A theoretically reliable key-recovery attack should evaluate not only the non-randomness for the correct key guess but also the randomness for the wrong ones as well. The former has always been the main focus but the absence of the latter can also cause self-contradicted results. In fact, the theoretic discussion of wrong key guesses is overlooked in quite some existing key-recovery attacks, especially the previous cube attack variants based on pure experiments. In this paper, we draw links between the division property and several variants of the cube attack. In addition to the zero-sum property, we further prove that the bias phenomenon, the non-randomness widely utilized in dynamic cube attacks and cube testers, can also be reflected by the division property. Based on such links, we are able to provide several results: Firstly, we give a dynamic cube key-recovery attack on full Grain-128. Compared with Dinur et al.’s original one, this attack is supported by a theoretical analysis of the bias based on a more elaborate assumption. Our attack can recover 3 key bits with a complexity 297.86 and evaluated success probability 99.83%. Thus, the overall complexity for recovering full 128 key bits is 2125. Secondly, now that the bias phenomenon can be efficiently and elaborately evaluated, we further derive new secure bounds for Grain-like primitives (namely Grain-128, Grain-128a, Grain-V1, Plantlet) against both the zero-sum and bias cube testers. Our secure bounds indicate that 256 initialization rounds are not able to guarantee Grain-128 to resist bias-based cube testers. This is an efficient tool for newly designed stream ciphers for determining the number of initialization rounds. Thirdly, we improve Wang et al.’s relaxed term enumeration technique proposed in CRYPTO 2018 and extend their results on Kreyvium and ACORN by 1 and 13 rounds (reaching 892 and 763 rounds) with complexities 2121.19 and 2125.54 respectively. To our knowledge, our results are the current best key-recovery attacks on these two primitives.

Journal ArticleDOI
TL;DR: Inspired by the fact that many TU games base the profit distribution strategies not only on the egalitarian principle but also on the utility principle, the equal contribution division value and the weighted equal contribution Division value based on the least square method and players’ contribution excess vector are spontaneously generated.


Proceedings ArticleDOI
01 Jan 2020
TL;DR: An iterative/pipelined parameterized POSIT fused division and square-root module using Verilog HDL and implemented, validated on Xilinx Virtex UltraScale VCU108 FPGA board and achieved a throughput of 400 Mega POSIT operations per second.
Abstract: In modern computing systems and devices, Floating-Point Unit (FPU) plays a significant role on performance-oriented, compute-intensive, Machine Learning/AI related applications. Currently two types of representations for floating-point numbers have been followed, viz. conventional IEEE-754-2008 and recently proposed Type-III Unum POSIT number which has wider dynamic range. Most of the modern processors have FPU as co-processor in order to improve the floating-point performance. Among various FP computations, division and square-root are generally the least-likely performed operations. These hardware operations are typically expensive in-terms of area, speed and power. The overall performance of floating-point division and square-root unit can be significantly affected by the chosen algorithm and the architecture of the implementation. A novel, modified, non-restoring algorithm and a POSIT iterative/pipelined architecture which performs fused division and square-root operation in a single unit, is proposed in this research work. For parameterized POSIT, a one-bit, modified, non-restoring fused division and square-root unit is the core component and can be reused/configured for different exponent and mantissa sizes. We have developed an iterative/pipelined parameterized POSIT fused division and square-root module using Verilog HDL and implemented, validated on Xilinx Virtex UltraScale VCU108 FPGA board (544 LUTs and achieved a throughput of 400 Mega POSIT operations per second). The results have been analyzed and compared in-terms of area-utilization and throughput with known published equivalent IEEE-754-2008 implementations and other POSIT divider units. The proposed design has less data-path delay, uses less hardware and achieves better throughput as compared to published results. The design has also been synthesized targeting SCL 180nm ASIC and achieved a throughput of 250 Mega POSIT operations per second.

Book ChapterDOI
03 Jun 2020
TL;DR: A method widely used to obtain IEEE 754 binary floating-point numbers with a standard uniform distribution involves drawing an integer uniformly at random and dividing it by another larger integer.
Abstract: A method widely used to obtain IEEE 754 binary floating-point numbers with a standard uniform distribution involves drawing an integer uniformly at random and dividing it by another larger integer. We survey the various instances of the algorithm that are used in actual software and point out their properties and drawbacks, particularly from the standpoint of numerical software testing and data anonymization.

Journal ArticleDOI
TL;DR: It is proposed that co-actors are sensitive to changes within their environment, which allows them to choose a labor division that maximizes use of their individual attentional capacities.
Abstract: In daily life, humans frequently perform visuospatial tasks together (e.g., visual search) and distribute the labor in such tasks. Previous research has shown that humans prefer a left and right labor division in a joint multiple object tracking (MOT) task. Yet, findings from studies investigating individuals’ tracking ability suggest attentional capacities may be more maximally used with a top and bottom labor division. We investigated whether co-actors’ labor division preference is influenced by how they are seated (neighboring vs. opposite of each other) or how the MOT task is displayed (portrait vs. landscape). We find that pairs attain a higher performance using a top and bottom labor division and preferred this labor division compared to a left and right division. This preference was unaffected by the seating arrangement. For the landscape display, however, we find that participants no longer attain a higher performance for the top and bottom labor division and accordingly participants’ preference for this labor division was greatly reduced as well. Overall, we propose that co-actors are sensitive to changes within their environment, which allows them to choose a labor division that maximizes use of their individual attentional capacities.