Showing papers on "Binary number published in 2011"

Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors

Abstract: The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that i.i.d. random Gaussian matrices describe measurement mappings achieving, with overwhelming probability, nearly optimal error decay. Next, we consider reconstruction robustness to measurement errors and noise and introduce the Binary $\epsilon$-Stable Embedding (B$\epsilon$SE) property, which characterizes the robustness measurement process to sign changes. We show the same class of matrices that provide almost optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the Binary Iterative Hard Thresholding (BIHT) algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.

Modeling disjunctive constraints with a logarithmic number of binary variables and constraints

Abstract: Many combinatorial constraints over continuous variables such as SOS1 and SOS2 constraints can be interpreted as disjunctive constraints that restrict the variables to lie in the union of a finite number of specially structured polyhedra. Known mixed integer binary formulations for these constraints have a number of binary variables and extra constraints linear in the number of polyhedra. We give sufficient conditions for constructing formulations for these constraints with a number of binary variables and extra constraints logarithmic in the number of polyhedra. Using these conditions we introduce mixed integer binary formulations for SOS1 and SOS2 constraints that have a number of binary variables and extra constraints logarithmic in the number of continuous variables. We also introduce the first mixed integer binary formulations for piecewise linear functions of one and two variables that use a number of binary variables and extra constraints logarithmic in the number of linear pieces of the functions. We prove that the new formulations for piecewise linear functions have favorable tightness properties and present computational results showing that they can significantly outperform other mixed integer binary formulations.

Binary Microlensing Event OGLE-2009-BLG-020 Gives Verifiable Mass, Distance, and Orbit Predictions

Abstract: We present the first example of binary microlensing for which the parameter measurements can be verified (or contradicted) by future Doppler observations. This test is made possible by a confluence of two relatively unusual circumstances. First, the binary lens is bright enough (I = 15.6) to permit Doppler measurements. Second, we measure not only the usual seven binary-lens parameters, but also the "microlens parallax" (which yields the binary mass) and two components of the instantaneous orbital velocity. Thus, we measure, effectively, six "Kepler+1" parameters (two instantaneous positions, two instantaneous velocities, the binary total mass, and the mass ratio). Since Doppler observations of the brighter binary component determine five Kepler parameters (period, velocity amplitude, eccentricity, phase, and position of periapsis), while the same spectroscopy yields the mass of the primary, the combined Doppler + microlensing observations would be overconstrained by 6 + (5 + 1) – (7 + 1) = 4 degrees of freedom. This makes possible an extremely strong test of the microlensing solution. We also introduce a uniform microlensing notation for single and binary lenses, define conventions, summarize all known microlensing degeneracies, and extend a set of parameters to describe full Keplerian motion of the binary lenses.

Binary microlensing event OGLE-2009-BLG-020 gives a verifiable mass, distance and orbit predictions

Abstract: We present the first example of binary microlensing for which the parameter measurements can be verified (or contradicted) by future Doppler observations. This test is made possible by a confluence of two relatively unusual circumstances. First, the binary lens is bright enough (I=15.6) to permit Doppler measurements. Second, we measure not only the usual 7 binary-lens parameters, but also the 'microlens parallax' (which yields the binary mass) and two components of the instantaneous orbital velocity. Thus we measure, effectively, 6 'Kepler+1' parameters (two instantaneous positions, two instantaneous velocities, the binary total mass, and the mass ratio). Since Doppler observations of the brighter binary component determine 5 Kepler parameters (period, velocity amplitude, eccentricity, phase, and position of periapsis), while the same spectroscopy yields the mass of the primary, the combined Doppler + microlensing observations would be overconstrained by 6 + (5 + 1) - (7 + 1) = 4 degrees of freedom. This makes possible an extremely strong test of the microlensing solution. We also introduce a uniform microlensing notation for single and binary lenses, we define conventions, summarize all known microlensing degeneracies and extend a set of parameters to describe full Keplerian motion of the binary lenses.

An Exact Algorithm for F-Measure Maximization

Abstract: The F-measure, originally introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure remains a statistically and computationally challenging problem, since no closed-form maximizer exists. Current algorithms are approximate and typically rely on additional assumptions regarding the statistical distribution of the binary response variables. In this paper, we present an algorithm which is not only computationally efficient but also exact, regardless of the underlying distribution. The algorithm requires only a quadratic number of parameters of the joint distribution (with respect to the number of binary responses). We illustrate its practical performance by means of experimental results for multi-label classification.

High-precision Timing of Five Millisecond Pulsars:Space Velocities, Binary Evolution, and Equivalence Principles

Abstract: We present high-precision timing of five millisecond pulsars (MSPs) carried out for more than seven years; four pulsars are in binary systems and one is isolated. We are able to measure the pulsars' proper motions and derive an estimate for their space velocities. The measured two-dimensional velocities are in the range 70-210 km s{sup -1}, consistent with those measured for other MSPs. We also use all the available proper motion information for isolated and binary MSPs to update the known velocity distribution for these populations. As found by earlier works, we find that the velocity distribution of binary and isolated MSPs are indistinguishable with the current data. Four of the pulsars in our observing program are highly recycled with low-mass white dwarf companions and we are able to derive accurate binary parameters for these systems. For three of these binary systems, we are able to place initial constraints on the pulsar masses with best-fit values in the range 1.0-1.6 M{sub Sun }. The implications of the results presented here to our understanding of binary pulsar evolution are discussed. The updated parameters for the binary systems studied here, together with recently discovered similar systems, allowed us to update previous limits onmore » the violation of the strong equivalence principle through the parameter |{Delta}| to 4.6 Multiplication-Sign 10{sup -3} (95% confidence) and the violation of Lorentz invariance/momentum conservation through the parameter |{alpha}-hat3| to 5.5 Multiplication-Sign 10{sup -20} (95% confidence).« less

Tracking the precession of compact binaries from their gravitational-wave signal

Abstract: We present a simple method to track the precession of a black-hole-binary system during the inspiral, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitudes of the (l=2, |m|=2) modes are maximized, which we denote the “quadrupole-aligned” frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within (Δθ,Δφ)=(0.05°,0.2°). We then apply the method to a q=M_2/M_1=3 binary that exhibits significant precession. In general, a spinning binary’s orbital angular momentum L is not orthogonal to the orbital plane. Evidence that our method locates the direction of L rather than the normal of the orbital plane is provided by comparison with post-Newtonian results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-precessing binary, and that the frequency of the (l=2, |m|=2) modes is consistent with the “total frequency” of the binary’s motion. The simple form of the quadrupole-aligned waveform may be useful in attempts to analytically model the inspiral-merger-ringdown signal of precessing binaries, and in standardizing the representation of waveforms for studies of accuracy and consistency of source modelling efforts, both numerical and analytical.

High-Precision Timing of 5 Millisecond Pulsars: Space Velocities, Binary Evolution and Equivalence Principles

Abstract: We present high-precision timing of five millisecond pulsars (MSPs) carried out for more than seven years; four pulsars are in binary systems and one is isolated. We are able to measure the pulsars' proper motions and derive an estimate for their space velocities. The measured two-dimensional velocities are in the range 70-210 km/s, consistent with those measured for other MSPs. We also use all the available proper motion information for isolated and binary MSPs to update the known velocity distribution for these populations. As found by earlier works, we find that the velocity distribution of binary and isolated MSPs are indistinguishable with the current data. Four of the pulsars in our observing program are highly recycled with low-mass white dwarf companions and we are able to derive accurate binary parameters for these systems. For three of these binary systems we are able to place initial constraints on the pulsar masses with best-fit values in the range 1.0-1.6 M_sun. The implications of the results presented here to our understanding of binary pulsar evolution are discussed. The updated parameters for the binary systems studied here, together with recently discovered similar systems, allowed us to update previous limits on the the violation of the strong equivalence principle through the parameter |Delta| to 4.6x10^-3 (95% confidence) and the violation of Lorentz-invariance/momentum-conservation through the parameter |hat{alpha}_3| to 5.5x10^-20 (95% confidence).

A Robust and Compression-Combined Digital Image Encryption Method Based on Compressive Sensing

Abstract: This paper proposes a compression-combined digital image encryption method which is robust against consecutive packet loss and malicious shear attack. We utilize the characteristics of compressive sensing, dimensional reduction and random projection, to compress and encrypt a digital image simultaneously. On this basis, block Arnold scrambling is used to permutate the position of measurements. Bit wise XOR operation is executed on the quantized binary bit stream to dissipate the Gaussian distribution property of cipher image. In this paper, one dimensional Logistic mapping is used to generate chaotic sequences, which will be regarded as the parameters of block Arnold transformation and the pseudo-random sequence for XOR operation. Numerical experiments show that the cipher image has following features, robustness, low data volume, incoherence, key sensitivity, and resistance to brute force attack.

Speeding scalar multiplication over binary elliptic curves using the new carry-less multiplication instruction

Abstract: The availability of a new carry-less multiplication instruction in the latest Intel desktop processors significantly accelerates multiplication in binary fields and hence presents the opportunity for reevaluating algorithms for binary field arithmetic and scalar multiplication over elliptic curves. We describe how to best employ this instruction in field multiplication and the effect on performance of doubling and halving operations. Alternate strategies for implementing inversion and half-trace are examined to restore most of their competitiveness relative to the new multiplier. These improvements in field arithmetic are complemented by a study on serial and parallel approaches for Koblitz and random curves, where parallelization strategies are implemented and compared. The contributions are illustrated with experimental results improving the state-of-the-art performance of halving and doubling-based scalar multiplication on NIST curves at the 112- and 192-bit security levels and a new speed record for side-channel-resistant scalar multiplication in a random curve at the 128-bit security level. The algorithms presented in this work were implemented on Westmere and Sandy Bridge processors, the latest generation Intel microarchitectures.

Enhancement of "logical" responses by noise in a bistable optical system.

Abstract: We verify numerically the phenomenon of logical stochastic resonance in a polarization bistable laser. Namely, we show that when one presents two weak binary inputs to the laser system, the response mirrors a logical or(nor) output. The reliability of the logic operation is dependent on the noise intensity. As one increases the noise, the probability of the output reflecting the desired or(nor) operation increases to nearly unity and then decreases. We also demonstrate that changing the bias morphs the output into another logic operation, and(nand), whose probability displays analogous behavior. Furthermore, we highlight the possibility of processing two logic gates in parallel in our laser system by exploiting two coupled orthogonal polarizations that can be detected simultaneously. This suggests that the computational power of the optical system may be enhanced by this additional potential for parallel processing.

List decoding for binary Goppa codes

Abstract: This paper presents a Patterson-style list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n-√n(n - 2t - 2) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomial-time list-decoding algorithms for the same codes, the new algorithm corrects approximately t2/2n extra errors.

An analytical description of the evolution of binary orbital-parameter distributions in N-body computations of star clusters

Abstract: A new method is presented to describe the evolution of the orbital-parameter distributions for an initially universal binary population in star clusters by means of the currently largest existing library of N-body models. It is demonstrated that a stellar-dynamical operator exists, which uniquely transforms an initial orbital parameter distribution function for binaries into a new distribution depending on the initial cluster mass and half-mass radius, after some time of dynamical evolution. For the initial distribution the distribution functions derived by Kroupa (1995a,b) are used, which are consistent with constraints for pre-main sequence and Class I binary populations. Binaries with a lower energy and a higher reduced-mass are dissolved preferentially. The stellar-dynamical operator can be used to efficiently calculate and predict binary properties in clusters and whole galaxies without the need for further N-body computations. For the present set of N-body models it is found that the binary populations change their properties on a crossing time-scale such that the stellar dynamical operator can be well parametrized as a function of the initial cluster density. Furthermore it is shown that the binary-fraction in clusters with similar initial velocity dispersions follows the same evolutionary tracks as a function of the passed number of relaxation-times. Present-day observed binary populations in star clusters put constraints on their initial stellar densities which are found to be in the range 10^2 - 2x10^5 M_sun pc^-3 for open clusters and a few x 10^3 - 10^8 M_sun pc^-3 for globular clusters, respectively.

Hybrid Binary-Ternary Number System for Elliptic Curve Cryptosystems

Abstract: Single and double scalar multiplications are the most computational intensive operations in elliptic curve based cryptosystems. Improving the performance of these operations is generally achieved by means of integer recoding techniques, which aim at minimizing the scalars' density of nonzero digits. The hybrid binary-ternary number system provides both short representations and small density. In this paper, we present three novel algorithms for both single and double scalar multiplication. We present a detailed theoretical analysis, together with timings and fair comparisons over both tripling-oriented Doche-Ichart-Kohel curves and generic Weierstrass curves. Our experiments show that our algorithms are almost always faster than their widely used counterparts.

Existence of Binary $Z$ -Complementary Pairs

Abstract: The conventional binary complementary pairs exist only for very limited lengths, while binary Z -complementary pairs exist for many more lengths In this letter, an upper bound on zero correlation zone (ZCZ) width of binary Z-complementary pairs of odd length is established The existence conjecture of binary Z-complementary pairs with ZCZ widths 2, 3, 4, 5 and 6 is completely solved, and a new recursive construction of binary Z-complementary pairs is proposed

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 Energy-Efficient Communication Scheme for Wireless Networks: A Redundant Radix-Based Approach

Abstract: We propose a redundant radix based number (RBN) representation for encoding and transmitting data for applications which typically utilize low cost devices and demand low power operations with simple modulation techniques like ASK, OOK and FSK. Coupled with silent periods for communicating the digit zero, this encoded communication scheme, called as RBNSiZeComm, provides a highly energy-efficient technique for data transmission. Considering an n-bit data representation and assuming that each of the 2n binary strings is equally likely to occur, theoretically obtainable fraction of energy savings by using our proposed RBNSiZeComm transmission protocol is, on an average, 1 - n+2/4n. A hybrid modulation scheme using FSK and ASK with non-coherent detection based receiver for the RBNSiZeComm protocol has been presented. Assuming equal likelihood of all possible binary strings of a given length, there is nearly 53% savings in energy on an average at the transmitter relative to binary FSK, over additive white gaussian noise (AWGN) channels. Simulation results demonstrate that compared to binary FSK, our proposed implementation can extend the battery life of devices from about 33% to 62% on an average in applications like remote healthcare and wireless sensor networks for agriculture.

System for initializing an arithmetic coder

Abstract: Decoding an entropy slice using a context based adaptively binary arithmetic coding, based upon a pair of variables n and m, corresponding to a probability state index and the value of the most probable symbol.

Representations and evolutionary operators for the scheduling of pump operations in water distribution networks

Abstract: Reducing the energy consumption of water distribution networks has never had more significance. The greatest energy savings can be obtained by carefully scheduling the operations of pumps. Schedules can be defined either implicitly, in terms of other elements of the network such as tank levels; or explicitly, by specifying the time during which each pump is on/off. The traditional representation of explicit schedules is a string of binary values with each bit representing pump on/off status during a particular time interval. In this paper, we formally define and analyze two new explicit representations based on time-controlled triggers, where the maximum number of pump switches is established beforehand and the schedule may contain fewer than the maximum number of switches. In these representations, a pump schedule is divided into a series of integers with each integer representing the number of hours for which a pump is active/inactive. This reduces the number of potential schedules compared to the binary representation, and allows the algorithm to operate on the feasible region of the search space. We propose evolutionary operators for these two new representations. The new representations and their corresponding operations are compared with the two most-used representations in pump scheduling, namely, binary representation and level-controlled triggers. A detailed statistical analysis of the results indicates which parameters have the greatest effect on the performance of evolutionary algorithms. The empirical results show that an evolutionary algorithm using the proposed representations is an improvement over the results obtained by a recent state of the art hybrid genetic algorithm for pump scheduling using level-controlled triggers.

Full-complex amplitude modulation with binary spatial light modulators.

Abstract: Imperfections and nonrobust behavior of practical multilevel spatial light modulators (SLMs) degrade the performance of many proposed full-complex amplitude modulation schemes We consider the use of more robust binary SLMs for this purpose We propose a generic method, by which, out of K binary (or 1 bit) SLMs of size M×N, we effectively create a new 2K-level (or K bit) SLM of size M×N The method is a generalization of the well-known concepts of bit plane representation and decomposition for ordinary gray scale digital images and relies on forming a properly weighted superposition of binary SLMs When K is sufficiently large, the effective SLM can be regarded as a full-complex one Our method is as efficient as possible from an information theoretical perspective A 4f system is discussed as a possible optical implementation This 4f system also provides a means for eliminating the undesirable higher diffraction orders The components of the 4f system can easily be customized for different production technologies

Binary SIFT: Fast image retrieval using binary quantized SIFT features

Abstract: SIFT features are widely used in content based image retrieval. Typically, a few thousand keypoints are extracted from each image. Image matching involves distance computations across all pairs of SIFT feature vectors from both images, which is quite costly. We show that SIFT features perform surprisingly well even after quantizing each component to binary, when the medians are used as the quantization thresholds. Quantized features preserve both distinctiveness and matching properties. Almost all of the features in our 5.4 million feature test set map to distinct binary patterns after quantization. Furthermore, number of matches between images using both the original and the binary quantized SIFT features are quite similar. We investigate the distribution of SIFT features and observe that the space of 128-D binary vectors has sufficient capacity for the current performance of SIFT features. We use component median values as quantization thresholds and show through vector-to-vector distance comparisons and image-to-image matches that the resulting binary vectors perform comparable to original SIFT vectors. We also discuss computational and storage gains. Binary vector distance computation reduces to bit-wise operations. Square operation is eliminated. Fast and efficient indexing techniques such as the signatures used for chemical databases can also be considered.

All-optical binary to gray code and gray to binary code conversion scheme with the help of semiconductor optical amplifier-assisted sagnac switch

Abstract: Gray codes are widely used to facilitate error correction in digital communications. An all-optical four-bit binary to Gray code and Gray to binary code converter with the help of semiconductor optical amplifier-assisted Sagnac switch is proposed and described. This study describes all-optical conversion scheme using a set of all-optical switches. The new method promises both higher processing speed and accuracy. Numerical simulation result confirming the described methods and conclusion are given here.

Adaptive binarization for arithmetic coding

Abstract: The present invention first provides adaptive binarization in which a binarizer outputs binary symbol in length, which is variable adaptively to the probability of the source. When the probability is low, it is desirable to decrease the length of the binary symbols to improve the efficiency of arithmetic coding and reduce the complexity of coding calculation. On the other hand, when the probability is high, it is desirable to increase the length of the binary symbols to improve the overall process speed of a decoder. Specifically, a binarizer, according to the present invention, binarizes mapping unit values from a non-binary symbol into binary symbols. The number of binary symbols is inversely proportional to the size of the mapping unit value. In the present invention, the mapping unit value is made variable adaptively to the probability. Thus, the number of binary symbols from the binarizer is also variable adaptively to the probability parameter.

Semicoherent search strategy for known continuous wave sources in binary systems

Abstract: We present a method for detection of weak continuous signals from sources in binary systems via the incoherent combination of many short coherently analyzed segments. The main focus of the work is on the construction of a metric on the parameter space for such signals for use in matched-filter based searches. The metric is defined using a maximum likelihood detection statistic applied to a binary orbit phase model including eccentricity. We find that this metric can be accurately approximated by its diagonal form in the regime where the segment length is > the segment length) for all but the orbital angular frequency. Increased template density for this parameter scales linearly with the observation span. We also present two example search schemes. The first use a reparametrized phase model upon which we compute the metric on individual short coherently analyzed segments. The second assumes long >> the orbital period segment lengths from which we again compute the coherent metric and find itmore » to be approximately diagonal. In this latter case we also show that the semicoherent metric is equal to the coherent metric.« less

Software implementation of binary elliptic curves: impact of the carry-less multiplier on scalar multiplication.

Abstract: The availability of a new carry-less multiplication instruction in the latest Intel desktop processors significantly accelerates multiplication in binary fields and hence presents the opportunity for reevaluating algorithms for binary field arithmetic and scalar multiplication over elliptic curves. We describe how to best employ this instruction in field multiplication and the effect on performance of doubling and halving operations. Alternate strategies for implementing inversion and half-trace are examined to restore most of their competitiveness relative to the new multiplier. These improvements in field arithmetic are complemented by a study on serial and parallel approaches for Koblitz and random curves, where parallelization strategies are implemented and compared. The contributions are illustrated with experimental results improving the state-of-the-art performance of halving and doubling-based scalar multiplication on NIST curves at the 112and 192-bit security levels, and a new speed record for side-channel resistant scalar multiplication in a random curve at the 128-bit security level.

Some new distance-4 constant weight codes

Abstract: Improved binary constant weight codes with minimum distance 4 are constructed. A table with bounds on the chromatic number of small Johnson graphs is given.

Algebraic structure of the minimal support codewords set of some linear codes

Abstract: It has been widely known that complete decoding for binary linear codes can be regarded as a linear integer programming problem with binary arithmetic conditions. Conti and Traverso [9] have proposed an algorithm which uses Grobner bases to solve integer programming with ordinary integer arithmetic conditions. Ikegami and Kaji [12] extended the Conti-Traverso algorithm to solve integer programming with modulo arithmetic conditions. It is natural to consider for those problems the Graver basis associated to them which turns out to be the minimal cycles of the matroid associated to the code, i.e. minimal support codewords in the binary case and its geometry. This provides us a universal test set for the programs considered.