Showing papers on "Binary number published in 2005"

A Computational Guide to Physics of Eclipsing Binaries. I. Demonstrations and Perspectives

Abstract: PHOEBE (PHysics Of Eclipsing BinariEs) is a modeling package for eclipsing binary stars, built on top of the widely used WD program of Wilson & Devinney. This introductory paper gives an overview of the most important scientific extensions (incorporating observational spectra of eclipsing binaries into the solution-seeking process, extracting individual temperatures from observed color indices, main-sequence constraining, and proper treatment of the reddening), numerical innovations (suggested improvements to WD's differential corrections method, the new Nelder & Mead downhill simplex method), and technical aspects (back-end scripter structure, graphical user interface). While PHOEBE retains 100% WD compatibility, its add-ons are a powerful way to enhance WD by encompassing even more physics and solution reliability. The operability of all these extensions is demonstrated on a synthetic main-sequence test binary; applications to real data will be published in follow-up papers. PHOEBE is released under the GNU General Public License, which guarantees it to be free and open to anyone interested in joining in on future development.

The evolution of binary fractions in globular clusters

Abstract: We study the evolution of binary stars in globular clusters using a new Monte Carlo approach combining a population synthesis code (StarTrack), and a simple treatment of dynamical interactions in the dense cluster core using a new tool for computing 3-body and 4-body interactions (Fewbody). We find that the combination of stellar evolution and dynamical interactions (binary–single and binary–binary) leads to a rapid depletion of the binary population in the cluster core. The maximum binary fraction today in the core of a typical dense cluster like 47 Tuc, assuming an initial binary fraction of 100%, is only about 5–10%. We show that this is in good agreement with recent HST observations of close binaries in the core of 47 Tuc, provided that a realistic distribution of binary periods is used to interpret the results. Our findings also have important consequences for the dynamical modeling of globular clusters, suggesting that “realistic models” should incorporate much larger initial binary fractions than has usually been done in the past.

Discrete tomography by convex-concave regularization and D.C. programming

Abstract: We present a novel approach to the tomographic reconstruction of binary objects from few projection directions within a limited range of angles. A quadratic objective functional over binary variables comprising the squared projection error and a prior penalizing non-homogeneous regions, is supplemented with a concave functional enforcing binary solutions. Application of a primal-dual subgradient algorithm to a suitable decomposition of the objective functional into the difference of two convex functions leads to an algorithm which provably converges with parallel updates to binary solutions. Numerical results demonstrate robustness against local minima and excellent reconstruction performance using five projections within a range of 90^@?. Our approach is applicable to quite general objective functions over binary variables with constraints and thus applicable to a wide range of problems within and beyond the field of discrete tomography.

High-mass X-ray binaries in the Magellanic Clouds

Abstract: We present a catalogue of high-mass X-ray binaries in the Magellanic Clouds. The catalogue lists source name(s), coordinates, apparent magnitudes, orbital parameters, and X-ray luminosity of 128 high-mass X-ray binaries, together with stellar parameters of the components, other characteristic properties and a comprehensive selection of the relevant literature. The aim of this catalogue is to provide easy access to the basic information on the X-ray sources and their counterparts in other wavelength ranges (UV, optical, IR, radio). Most of the sources are identified to be Be/X-ray binaries. Some sources, however, are only tentatively identified as high-mass X-ray binaries on the basis of a transient character and/or a hard X-ray spectrum. Further identification in other wavelength bands is needed to finally determine the nature of these sources. In cases where there is some doubt about the high-mass nature of the X-ray binary this is mentioned. Literature published before 1 May 2005 has, as far as possible, been taken into account.

Bit-error rate of binary digital modulation schemes in generalized gamma fading channels

Abstract: We derive a closed-form expression for the bit-error rate of binary digital modulation schemes in a generalized fading channel that is modeled by the three-parameter generalized gamma distribution. This distribution is very versatile and generalizes or accurately approximates many of the commonly used channel models for multipath, shadow, and composite fading. The result is expressed in terms of Meijer's G-function, which can be easily evaluated numerically.

Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies

Abstract: We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 400K are considered. The results are compared with the predictions of loss-cone theory, under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binary's influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that the hardening rate of the binary stabilizes when N exceeds a particular value, or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave coalescence in a Hubble time.

Design of a reversible binary coded decimal adder by using reversible 4-bit parallel adder

Abstract: In this paper, we have proposed a design technique for the reversible circuit of binary coded decimal (BCD) adder. The proposed circuit has the ability to add two 4-bits binary variables and it transforms the addition into the appropriate BCD number with efficient error correcting modules where the operations are reversible. We also show that the proposed design technique generates the reversible BCD adder circuit with minimum number of gates as well as the minimum number of garbage outputs.

Design And Implementation Of 2 Bit Ternary ALU Slice

Abstract: This paper describes the architecture, design & implementation of 2 bit ternary ALU (T-ALU) slice. The proposed ALU is designed for two -bit operation & can be used for n bit operations by cascading n/2 ALU slices. This ALU is implemented using C-MOS ternary logic gates (T-Gates) for ternary arithmetic & logic circuits. Ternary gates are implemented using enhancement / depletion MOSFET technology, thus proposed ALU is suitable for LSI / VLSI implementation. The designed technique used here requires only two stages i.e . decoder & T-gates, as against three stages i.e. decoder, binary gates & encoder require in conventional ternary logic implementation . Index Terms : Ternary, Unary function, T -Gates, Literal. I. Introduction Alexander [1964] showed that natural base (e= 2.71828) is the most efficient radix for implementation of switching circuits. It seems that most efficient radix for the implementation of digital system is 3 than 2. Ternary logic system, meaning that it has 3 valued switching. Ternary system has several important advantages over binary. It can be summarized as reductions in the interconnections require to implement logic functions, thereby reducing chip area, more information can be transmitted over a given set of lines, lesser memory requirement for a given data length. Besides this serial & some serial-parallel operations can be carried out at higher speed [1][2][3]. Its advantages have been confirmed in the application like memories, communications and digital signal processing etc. [7]. It has been proven that realization & implementation of combinational & sequential function is possible for ternary systems [4][5][6][7]. The implementation is based around bipolar transistors, MOSFETs etc. a basic switching elements, which is refereed to as T-Ga tes [8]. Besides this several authors have proposed reduction techniques to realize ternary functions [9][10][11][12]. In this contribution, we propose ALU capable of performing basic ternary arithmetic & logic operations as mentioned in table 1. We also suggest a scheme that takes the advantage of minimization techniques proposed by [9][11][13] & implemented using T-gates designed for ternary operations. This scheme shows reduction in the number of gate count to implement ternary functions. Firstly we describe the design of 2 bit ALU and then integrate over ALU slice. The organization of paper is: Section II describes basic T-Gate implementation, 2 bit ALU architecture is given in section III, section IV describes 2 bit ALU design and ALU slice design. Experimental results & performance evaluation is given in section V. Finally conclusion is given in section VI. Table 1:Functional Table of T -ALU

Inclusion of binaries in evolutionary population synthesis

Abstract: Using evolutionary population synthesis we present integrated colours, integrated spectral energy distributions and absorption-line indices defined by the Lick Observatory image dissector scanner (referred to as the Lick/IDS) system, for an extensive set of instantaneous-burst binary stellar populations with and without binary interactions. The ages of the populations are in the range 1-15 Gyr and the metallicities are in the range 0.0001-0.03. By comparing the results for populations with and without binary interactions we show that the inclusion of binary interactions makes the integrated U-B, B-V, V-R and R-I colours and all Lick/IDS spectral absorption indices (except for H) substantially smaller. In other words, binary evolution makes a population appear bluer. This effect raises the derived age and metallicity of the population. We calculate several sets of additional solar-metallicity binary stellar populations to explore the influence of the binary evolution algorithm input parameters (the common-envelope ejection efficiency and the stellar wind mass-loss rate) on the resulting integrated colours. We also look at the dependence on the choice of distribution functions used to generate the initial binary population. The results show that variations in the choice of input model parameters and distributions can significantly affect the results. However, comparing the discrepancies that exist between the colours of various models, we find that the differences are less than those produced between the models with and those without binary interactions. Therefore it is very necessary to consider binary interactions in order to draw accurate conclusions from evolutionary population synthesis work.

Data Analysis for Detection and Localization of MultilMe Abnormalities with AoDlication to Mammography

Abstract: Obuchowski et al describe a statistical method that applies to the observer performance tasks involved in detecting and localizing lesions. Their work represents an effort to improve observer performance methods, which are the foundation of imaging system performance assessment. Experts in perception research have voiced a need for alternatives to receiver operating characteristic (ROC) curve analysis (1). The ubiquitous ROC paradigm requires binary truth and binary observer response, requirements not satisfied by the task of detection and localization. The basic idea behind the method developed by Obuchowski et al is to divide each patient image into mutually exclusive regions of interest (ROIs) and to regard each ROI, rather than each patient, as an observational unit. An ROI is regarded as abnormal if it contains a malignant lesion, and otherwise it is regarded as normal. Sensitivity and specificity are calculated by appropriately modifying the usual expressions, and the area under the ROC curve is calculated by using a nonparametric method. Statistical methods for clustered data, which include intrapatient ROI-ROI correlations, are used to compare the readers' accuracies. The authors illustrate their method by applying it to previously published work involving the detection and localization of malignant breast lesions with mammography, and they compare their method with alternative free-response ROC (AFROC) analysis and other patient-based strategies.

Logic Functions and Equations: Binary Models for Computer Science

Abstract: I. Theoretical Foundations.- 1. Basic Algebraic Structures.- 2. Logic Functions.- 4. Boolean Differential Calculus.- 5. The Solution of Logic Equations.- II. Applications.- 6. Logics and Arithmetics.- 7. Combinational Circuits.- 8. Finite-State Machines.- III. Tools.- 9. Xboole.

Cellular wave computers for brain-like spatial-temporal sensory computing

Abstract: Present day classical computers, developed during the last sixty years are logic machines, based on binary logic and arithmetic, acting on discrete valued (binary coded) data. Its unique property is algorithmic (stored) programmability, invented by John von Neumann. The mathematical concept is based on a universal machine on integers (Turing machine). Cellular automata, introduced also by J. von Neumann, are fully parallel array processors with all discrete space, time and state values. Their beautiful properties have been recently rediscovered showing the deeper qualitative properties, if we allow the states and time to be continuous values like in CNN, a broader class of dynamics will be generated. Even more, the fundamental conditions to generate complex features at the edge of chaos have been established: the need of local activity. Taking one step further, and using the CNN-UM architecture, a new world of algorithms is opening.

The Power of the Middle Bit of a P Functiona

Abstract: This paper studies the class MP of languages which can be solved in poly nomial time with the additional information of one bit from a P function f The middle bit of f x is shown to be as powerful as any other bit whereas the O logn bits at either end are apparently weaker The polynomial hierarchy and the classes ModkP k are shown to be low for MP They are also low for a class we call AmpMP which is de ned by abstracting the ampli cation methods of Toda SIAM J Comput Consequences of these results for circuit complexity are obtained using the concept of a Mid Bit gate which is de ned to take binary inputs x xw and output the blog w c th bit in the binary representation of the number Pw i xi Every language in ACC can be computed by a family of depth deterministic cir cuits of size logn O with a MidBit gate at the root and AND gates of fan in logn O at the leaves This result improves the known upper bounds for the class ACC

Context-based adaptive binary arithmetic coding method and apparatus

Abstract: There are provided a context-based adaptive binary arithmetic decoding method and apparatus. The context-based adaptive binary arithmetic decoding apparatus includes: a context extractor extracting a plurality of contexts from a storage unit storing contexts each including a state value for probability characteristic; a first ROM table storing current probability information so that a current binary symbol of the bit stream is decoded according to a state value of each context; a second ROM table storing predicted probability information so that a next binary symbol of the bit stream is decoded according to a state value of each context; a general mode arithmetic decoder, which performs pipeline processing, loading current probability information from the first ROM table on the basis of a current state value of a context extracted from the context extractor to decode a first binary symbol, and loading predicted probability information from the second ROM table to decode a next remaining binary symbol while decoding the remaining binary symbols; and a bypass mode arithmetic decoder, including a plurality of calculators for parallel processing, simultaneously decoding a plurality of corresponding binary symbols of the bit stream, to perform arithmetic decoding on the remaining symbols if a predetermined condition is satisfied while the general mode arithmetic decoder performs arithmetic decoding on the corresponding symbols of the bit stream. Therefore, by implementing a hardware suitable for context-based adaptive binary arithmetic decoding, it is possible to enhance a decoding speed.

Bounds on the Average Binary Minimum Distance and the Maximum Likelihood Performance of Reed

Abstract: In this paper, an average binary weight enumerator of Reed Solomon (RS) codes is derived assuming a binomial distribution of the bits in a non-zero symbol. Lower bounds on the average binary minimum distance are shown. The averaged binary image of the RS code is shown to be asymptotically good for sufficiently high rates. These results are used to bound the maximum likelihood performance of RS codes, whose binary image is modulated using binary phase shift keying on AWGN channels, for both hard and soft decision decoding.

XTE J1550–564: INTEGRAL Observations of a Failed Outburst

Abstract: The well-known black hole X-ray binary transient XTE J1550-564 underwent an outburst during the spring of 2003, which was substantially underluminous in comparison to previous periods of peak activity in that source. In addition, our analysis shows that it apparently remained in the hard spectral state over the duration of that outburst. This is again in sharp contrast to major outbursts of that source in 1998/1999, during which it exhibited an irregular light curve, multiple state changes, and collimated outflows. This leads us to classify it as a "failed outburst." We present the results of our study of the spring 2003 event, including light curves based on observations from both INTEGRAL and RXTE. In addition, we studied the evolution of the high-energy 3-300 keV continuum spectrum using data obtained with three main instruments on INTEGRAL. These spectra are consistent with typical low-hard-state thermal Comptonization emission. We also consider the 2003 event in the context of a multisource, multievent period-peak luminosity diagram, in which it is a clear outlier. We then consider the possibility that the 2003 event was due to a discrete accretion event rather than limit-cycle instability. In that context, we apply model fitting to derive the timescale for viscous propagation in the disk and infer some physical characteristics.

Binary encodings of non-binary constraint satisfaction problems: algorithms and experimental results

Abstract: A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally accepted that the translated problem can be solved by applying well-established techniques for binary CSPs. In this paper we evaluate the applicability of the latter approach. We demonstrate that the use of standard techniques for binary CSPs in the encodings of non-binary problems is problematic and results in models that are very rarely competitive with the non-binary representation. To overcome this, we propose specialized arc consistency and search algorithms for binary encodings, and we evaluate them theoretically and empirically. We consider three binary representations; the hidden variable encoding, the dual encoding, and the double encoding. Theoretical and empirical results show that, for certain classes of non-binary constraints, binary encodings are a competitive option, and in many cases, a better one than the non-binary representation.

An efficient method of elliptic curve encryption using Ancient Indian Vedic Mathematics

Abstract: The major time consuming arithmetic operations in ECC are point additions and doubling. Exponentiation operations like square and cube are the major bottlenecks in the efficiency of point additions and doubling. This paper presents efficient hardware circuitry for point doubling using square algorithms of Ancient Indian Vedic Mathematics. In order to calculate the square of a number, "Duplex" D property of binary numbers is proposed

On the stability of 2/sup n/-periodic binary sequences

Abstract: The k-error linear complexity of a periodic binary sequence is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits per period. This contribution focuses on the case of 2n-periodic binary sequences. For k=1,2, the exact formula for the expected k-error linear complexity of a sequence having maximal possible linear complexity 2n, and the exact formula of the expected 1-error linear complexity of a random 2n-periodic binary sequence are provided. For k ges 2, lower and upper bounds on the expected value of the k-error linear complexity of a random 2n-periodic binary sequence are established

The massive binary CPD-41degr7742 II. Optical light curve and X-ray observations

Abstract: In the first paper of this series, we presented a detailed high-resolution spectroscopic study of CPD - 41degr7742, deriving for the first time an orbital solution for both components of the system. In this second paper, we focus on the analysis of the optical light curve and on recent XMM-Newton X-ray observations. In the optical, the system presents two eclipses, yielding an inclination i ~ 77degr. Combining the constraints from the photometry with the results of our previous work, we derive the absolute parameters of the system. We confirm that the two components of CPD - 41degr7742 are main sequence stars (O9 V + B1-1.5 V) with masses (M_1 ~ 18 Msol and M_2 ~ 10 Msol) and respective radii (R_1 ~ 7.5 Rsol and R_2 ~ 5.4 Rsol) close to the typical values expected for such stars. We also report an unprecedented set of X-ray observations that almost uniformly cover the 2.44-day orbital cycle. The X-ray emission from CPD - 41degr7742 is well described by a two-temperature thermal plasma model with energies close to 0.6 and 1.0 keV, thus slightly harder than typical early-type emission. The X-ray light curve shows clear signs of variability. The emission level is higher when the primary is in front of the secondary. During the high emission state, the system shows a drop of its X-ray emission that almost exactly matches the optical eclipse. We interpret the main features of the X-ray light curve as the signature of a wind-photosphere interaction, in which the overwhelming primary O9 star wind crashes into the secondary surface. Alternatively the light curve could result from a wind-wind interaction zone located near the secondary star surface. As a support to our interpretation, we provide a phenomenological geometric model that qualitatively reproduces the observed modulations of the X-ray emission.

Results on the nonlinear span of binary sequences

Abstract: The problem of finding the length of a shortest feedback shift register that generates a given finite-length sequence is considered. An efficient algorithm for the determination of the span is proposed, that takes advantage of the special block structure of the associated system of linear equations. The span distribution of finite-length binary sequences is also studied.

Apparatus and method for dynamic binary translator to support precise exceptions with minimal optimization constraints

Abstract: A method and apparatus for dynamic binary translator to support precise exceptions with minimal optimization constraints. In one embodiment, the method includes the translation of a source binary application generated for a source instruction set architecture (ISA) into a sequential, intermediate representation (IR) of the source binary application. In one embodiment, the sequential IR is modified to incorporate exception recovery information for each of the exception instructions identified from the source binary application to enable a dynamic binary translator (DBT) to represent exception recovery values as regular values used by IR instructions. In one embodiment, the sequential IR may be optimized with a constraint on movement of an exception instruction downward past an irreversible instruction to form a non-sequential IR. In one embodiment, the non-sequential IR is optimized to form a translated binary application for a target ISA. Other embodiments are described and claimed.

A binary neural k -nearest neighbour technique

Abstract: K-Nearest Neighbour (k-NN) is a widely used technique for classifying and clustering data. K-NN is effective but is often criticised for its polynomial run-time growth as k-NN calculates the distance to every other record in the data set for each record in turn. This paper evaluates a novel k-NN classifier with linear growth and faster run-time built from binary neural networks. The binary neural approach uses robust encoding to map standard ordinal, categorical and real-valued data sets onto a binary neural network. The binary neural network uses high speed pattern matching to recall the k-best matches. We compare various configurations of the binary approach to a conventional approach for memory overheads, training speed, retrieval speed and retrieval accuracy. We demonstrate the superior performance with respect to speed and memory requirements of the binary approach compared to the standard approach and we pinpoint the optimal configurations.

VLT Observations of the Ultraluminous X-Ray Source NGC 1313 X-2

Abstract: We present archive ESO VLT photometric and spectroscopic data of the ultraluminous X-ray source NGC 1313 X-2. The superb quality of the VLT images reveals that two distinct objects, with R magnitudes 23.7 and 23.6, are visible inside the Chandra error box. The two objects, separated by 075, were unresolved in our previous ESO 3.6 m+EFOSC image. We show that both are stars in NGC 1313, the first a B0-O9 main-sequence star of ~20 M☉, the second a G supergiant of ~10 M☉. Irrespective of which of the two objects the actual counterpart is, this implies that NGC 1313 X-2 is a high-mass X-ray binary with a very massive donor.

Higher radix floating-point representations for FPGA-based arithmetic

Abstract: FPGA implementations of floating-point operators have historically been designed to use binary floating-point representations. The general computing world settled on binary floating-point representations over three decades ago, and more recently, the FPGA community followed their example. Binary representations were chosen to maximize numerical accuracy per bit of data, however, the unique nature of FPGA-based computation makes numerical accuracy per unit of FPGA resources a more important measure of the usefulness of a given floating-point representation. In this paper, we show that higher radix floating-point representations are well suited to FPGA-based computations, especially high precision calculations which require the support of denormalized numbers. Higher radix representations use FPGA resources more efficiently. For example, a hexadecimal floating-point adder has a 30% smaller area-time product than its binary counterpart, while still delivering equal worst-case and better average-case numerical accuracy. Contrary to established belief, higher radix representations are useful for FPGA applications requiring IEEE 754 compliance, since they can deliver superior numerical performance while still using less FPGA resources.

A new bound for the zero-error capacity region of the two-user binary adder channel

Abstract: A new uniquely decodable (UD) code pair for the two-user binary adder channel (BAC) is presented. This code pair leads to an improved bound for the zero-error capacity region of such a channel. The highest known rate for a UD code pair for the two-user BAC is thereby improved to (log/sub 2/240)/6/spl ap/1.3178. It is also demonstrated that the problem of finding UD code pairs for the closely related binary XOR channel is in one-to-one correspondence with a certain construction of binary one-error-correcting codes.

Bipartite modular multiplication

Abstract: This paper proposes a new fast method for calculating modular multiplication. The calculation is performed using a new representation of residue classes modulo M that enables the splitting of the multiplier into two parts. These two parts are then processed separately, in parallel, potentially doubling the calculation speed. The upper part and the lower part of the multiplier are processed using the interleaved modular multiplication algorithm and the Montgomery algorithm respectively. Conversions back and forth between the original integer set and the new residue system can be performed at speeds up to twice that of the Montgomery method without the need for precomputed constants. This new method is suitable for both hardware implementation; and software implementation in a multiprocessor environment. Although this paper is focusing on the application of the new method in the integer field, the technique used to speed up the calculation can also easily be adapted for operation in the binary extended field GF(2m).

Binary arithmetic decoding apparatus and methods using a pipelined structure

Abstract: Binary arithmetic decoding methods and apparatus are provided. A first decoded bit and a first set of decoding parameters are generated using a previously generated set of decoding parameters. A second decoded bit and a second set of decoding parameters are generated using the first set of decoding parameters. If the first decoded bit is a last bit of a syntax element, the second set of decoding parameters is disregarded in generating subsequent decoded bits. The generation of the first and second decoded bits and determination of whether the first decoded bit is a last bit of a syntax element, e.g., a de-binarizing operation, may be pipelined such that the determination of whether the first decoded bit is a last bit of a syntax element occurs concurrent with and/or after generation of the second decoded bit and the second set of decoding parameters.

Granular Computing and Rough Sets

Abstract: This chapter gives an overview and refinement of recent works on binary granular computing. For comparison and contrasting, granulation and partition are examined in parallel from the prospect of rough Set theory (RST).The key strength of RST is its capability in representing and processing knowledge in table formats. Even though such capabilities, for general granulation, are not available, this chapter illustrates and refines some such capability for binary granulation. In rough set theory, quotient sets, table representations, and concept hierarchy trees are all set theoretical, while in binary granulation, they are special kind of pretopological spaces, which is equivalent to a binary relation Here a pretopological space means a space that is equipped with a neighborhood system (NS). A NS is similar to the classical NS of a topological space, but without any axioms attached to it1.