Factor Of Square Root Research Articles

Quadriphase DS-CDMA with pulse shaping and the accuracy of the Gaussian approximation for matched filter receiver performance analysis

Probability of bit-error (P/sub e/) performance of asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems is analyzed. In particular, the effects of pulse shaping, quadriphase (or direct-sequence quadriphase shift keying (DS-QPSK)) spreading, aperiodic spreading sequences and the coherent correlator or, equivalently, the matched filter (MF) receiver are considered. An exact P/sub e/ expression and several approximations: one using the characteristic function (CF) method, a simplified expression for the improved Gaussian approximation (IGA) and the simplified improved Gaussian approximation (SIGA) are derived. Two main results are presented. Under conditions typically satisfied in practice and even with a small number of interferers, the standard Gaussian approximation (SGA) for the multiple-access interference component of the MF statistic and for MF P/sub e/ performance is shown to be accurate. Moreover, the IGA is shown to reduce to the SGA for pulses with zero excess bandwidth. Second, the P/sub e/ performance of quadriphase DS-CDMA is shown to be superior or equivalent to that of biphase DS-CDMA. Numerical examples with Monte Carlo simulation are presented to illustrate P/sub e/ performance for square-root raised-cosine (Sqrt-RC) pulses and spreading factors of moderate to large values.

Multivariate extremes, aggregation and risk estimation

We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high frequency data can considerably improve quality of estimates of extreme movements in financial markets. Secondly we present an empirical exploration of what the tails really look like for four foreign exchange rates sampled at varying frequencies. Both temporal and spatial dependence is considered. In particular we estimate the spectral measure, which along with the tail index, completely determines the extreme value distribution. Lastly we apply our results to the problem of portfolio optimisation or risk minimization. We analyze how the expected shortfall and VaR scale with time horizon and find that this scaling is not by a factor of square root of time as is frequently used, but by a different power of time. We show that the accuracy of risk estimation can be drastically improved by using hourly or bihourly data.

Multivariate Extremes, Aggregation and Risk Estimation

We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high frequency data can considerably improve quality of estimates of extreme movements in financial markets. Secondly we present an empirical exploration of what the tails really look like for four foreign exchange rates sampled at varying frequencies. Both temporal and spatial dependence is considered. In particular we estimate the spectral measure, which along with the tail index, completely determines the extreme value distribution. Lastly we apply our results to the problem of portfolio optimization or risk minimization. We analyze how the expected shortfall and VaR scale with time horizon and find that this scaling is not by a factor of square root of time as is frequently used, but by a different power of time. We show that the accuracy of risk estimation can be drastically improved by using hourly or bihourly data.

The effects of k-space data undersampling and discontinuities in keyhole functional MRI.

The effects of the k-space data undersampling and the discontinuities associated with the keyhole approach in functional magnetic resonance imaging (fMRI) have been addressed. Undersampling of high k-space data increases the high spatial-frequency noise by a factor of square root m, where m is the number of images sharing the high k-space data. However, the effects of the noise can be effectively removed using clustered-pixel statistical analysis. The amplitude and phase discontinuities may result in an increase in the low spatial-frequency noise level, which has no impact on specificity and only a minimal impact on sensitivity. Although dramatically reducing acquisition time and preserving the spatial resolution of functional magnetic resonance imaging, the keyhole technique may have a limited capability in detecting highly focal activations.

Alfven cyclotron instability and ion cyclotron emission

Two-dimensional solutions of compressional Alfven eigenmodes (CAEs) are studied in the cold plasma approximation. For finite inverse aspect ratio tokamak plasmas the two-dimensional eigenmode envelope is localized at the low magnetic field side with the radial and poloidal localization on the order of a/ square root m and a/4 square root m, respectively, where m is the dominant poloidal mode number. Charged fusion product driven Alfven cyclotron instability (ACI) of the compressional Alfven eigenmodes provides the explanation for the ion cyclotron emission (ICE) spectrum observed in tokamak experiments. The ACI is excited by fast charged fusion products via Doppler shifted cyclotron wave-particle resonances. The ion cyclotron and electron Landau dampings and fast particle instability drive are calculated perturbatively for deuterium-deuterium (DD) and deuterium-tritium (DT) plasmas. Near the plasma edge at the low field side the velocity distribution function of charged fusion products is localized in both pitch angle and velocity. The poloidal localization of the eigenmode enhances the ACI growth rates by a factor of square root m in comparison with the previous results without poloidal envelope. The thermal ion cyclotron damping determines that only modes with eigenfrequencies at multiples of the edge cyclotron frequency of the background ions can be easily excited and form an ICE spectrum similar to the experimental observations. Theoretical understanding is given for the results of TFTR DD and DT experiments with valpha 0/vA approximately=1 and JET experiments with valpha 0/vA>1

Estimating propulsive forces in swimming from three‐dimensional kinematic data

Propulsive forces are important determinants of swimming performance. The aim of this study was to quantify the measurement error (uncertainty) in propulsive forces calculated from kinematic data. Ten operators digitized underwater video recordings of a breaststroke swimmer's right arm action. Four landmarks on the hand were digitized at 50 Hz and their three-dimensional coordinates obtained using a DLT algorithm. Two angles (alpha and psi) defining the orientation of the hand relative to the fluid flow were calculated following the procedures of Schleihauf et al. (1983). The hydrodynamic force acting on the hand (FR) was calculated using the force coefficients of Schleihauf (1979). Errors in single measurements of hand speed, alpha and psi were estimated for each video field analysed. Errors in alpha and psi led to average errors in the lift and drag coefficients of 27 and 20% respectively, which, when combined with an average hand speed error of 6%, produced an average error in FR of 26%. Each of these errors was reduced by a factor of square root 10 when the mean of 10 measurements was used to calculate FR. Researchers should report both the estimated errors in their hydrodynamic data and the procedures used to reduce them.

Noise reduction by frame averaging: A numerical simulation for portal imaging systems

We have studied the usefulness of both pre- and post-ADC frame summing for the purpose of reducing the effect of quantum noise and digitization noise in portal imaging systems. The study is based on the fluorescent-screen video-camera type of system. The study predicts the not-surprising result that provided the noise level at the ADC input is sufficiently large, the overall SNR can be increased by a factor of square root of M1M2, where M1 and M2 are the number of frames summed before and after the ADC. The study also predicts, somewhat unexpectedly, that there is an operating region in which increasing M1 actually decreases the SNR in the final image. To avoid this region M1 must be less than approximately 6 x 2(2B) (1 + -delta-1)1/2/(iaccf), where B is the number of ADC bits, -delta is the mean number of optical photons detected by the video camera per detected x-ray photon, iacc is the open-field number of detected x-ray photons per accelerator pulse per pixel, and f is the patient transmission factor. An equivalent statement is that the rms noise at the input to the ADC, sigma in, must exceed approximately 0.4q where q is the quantization interval of the ADC. It is possible that some systems operate in or close to this region. A second feature of this anomalous behavior is that the final image is not necessarily improved by increasing the number M2 of post-ADC-summed frames. For example, when sigma in/q = 0.2, there is no improvement in the overall rms error for M2 > 32.(ABSTRACT TRUNCATED AT 250 WORDS)

A New Square-root Balancing-Free Stochastic Truncation Model Reduction Algorithm

The paper proposes a new computational approach with enhanced numerical robustness for computing reduced order models of continuous systems by using the balanced stochastic truncation model reduction method. The new approach circumvents the computation of possibly III-conditioned stochastic balancing transformations. Instead, well-conditioned projection matrices are determined for computing directly the state-space representations of the reduced order models. The projection matrices are computed in a numerically reliable way, by using exclusively the Cholesky (square-root) factors of systems Gramians. The proposed algorithm can handle both minimal and non-minimal systems.

Improved square-root forms of fast linear least squares estimation algorithms

Improving the numerical stability of fast algorithms by square-root factorization generally requires the use of hypernormal transformations which do not always exhibit a satisfactory numerical behavior. An alternate approach, adapted from a paper by A.W. Bojanczyk and A. O. Steinhardt (see ibid., vol.37, p.1286-8, 1989), is proposed. It uses orthogonal transformations, which leads to more stable fast square-root algorithms. Applications to the generalized Levinson algorithm and the Chandrasekhar equations are detailed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Energy consumption in multilective and boundary VLSI computations

A VLSI computation is said to be m-way multilective when each input bit is available m times in either space or time or both. The repeated availability of input bits can save computational energy. For a uniswitch m-way multilective computation, where a wire can switch at most once, it is shown that the energy savings can be as much as a factor of m. A multiswitch m-way multilective computation can save up to a factor of square root m switching energy. Tighter energy lower bounds are derived for a circuit with the input/output (I/O) pads located on the border. These boundary computations seem to cost an additional factor ranging from square root log n to log n in switching energy. The author extends the energy lower bounds for the multilective case, for a chip with aspect ratio a. The additional energy cost ranges from a factor of square root a to a factor of a.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of Microcomputer-Based Model Reference Adaptive Control to a Hydraulic Positioning System

Publisher Summary This chapter discusses the application of a microcomputer-based model reference adaptive control to a hydraulic positioning system model. A direct adaptive control scheme based on the model reference principle guarantees stable operation. This is achieved by augmenting the plant output signal using a so called correction network connected in parallel to the plant, which acts as a dynamic weighting filter for the manipulating signal. This network is designed using root locus or pole assignment theory. For parameter estimation, several methods and algorithms such as stochastic approximation and recursive least squares have been employed. Only numerically stable update algorithms such as square-root filtering or UDUT factorization of the covariance matrix are used. The chapter presents some experiments that show that adaptive model reference control assures zero steady-state error for non-negligible load, even in the absence of integral action in the control law.

Temporal integration of trains of tone pulses by normal and by cochlearly impaired listeners

Two experiments investigated the temporal integration of trains of tone pulses by normal and by cochlearly impaired listeners. In the first experiment, thresholds were measured for a single 5-ms, 4-kHz tone pulse, and for ten such tone pulses as a function of interpulse interval (delta t). For normal listeners, temporal integration, defined as the threshold difference between one and ten pulses, was about 8 dB for delta t less than 20 ms, and about 5 dB at longer delta t's. For impaired listeners, temporal integration was only about 2-3 dB across the range of delta t's (5-160 ms) studied. A second experiment measured psychometric functions (log d' versus log signal power) for a single pulse and for ten pulses with delta t's of 5 ms and 80 ms. The normal listeners' functions had slopes close to unity in all three conditions, with a few exceptions. The impaired listeners' functions had slopes close to unity for ten pulses with delta t = 5 ms, but had slopes significantly greater than unity for delta t = 80 ms, and for a single pulse. At delta t = 80 ms, the increase in d' relative to the condition with a single tone was similar (a factor of square root of 10) for both impaired and normal listeners, but the threshold difference was smaller for the impaired listeners due to their steeper psychometric functions. For impaired listeners, then, temporal integration at delta t = 80 ms was normal in terms of a change in d' but abnormal when measured as a threshold difference.(ABSTRACT TRUNCATED AT 250 WORDS)

Approximate treatment of the Holstein-Primakoff-type boson mapping

The generalised Holstein-Primakoff boson representation of the bifermion operators is used to construct a boson image of the microscopic nuclear Hamiltonian. The microscopic analogue of the interacting boson model (IBM) Hamiltonian is obtained. It is shown how the square-root factor in the IBM Hamiltonian can be generalised so as to take into account its dependence on the angular momentum and seniority of the collective state. The method is applicable to systems where the assumption that the projection operator P is approximately equal to unity can be used. The method is proposed to include, apart from the collective quadrupole, other collective and non-collective degrees of freedom in the Hamiltonian.

Quantitative phenotypic variation in single normal and malignant cells from liver and breast occurs along a geometric series.

Single-cell variability in albumin content of normal rat hepatocytes and hepatoma cells and in a specific breast surface antigen content in normal and malignant human mammary epithelial cells was studied by a quantitative immunoperoxidase method. The range of variability was nearly 10-fold for both normal and malignant cells. This wide range of single cell heterogeneity was generated very rapidly in clonal colonies of less than 30 hepatoma cells. By a grid test for periodicity that we devised, and also by Fourier transform analysis, the distribution of albumin content in single hepatocytes and hepatoma cells, and of a breast surface antigen content in normal and malignant breast cells, was shown to be discontinuous, where the cells distributed with a periodicity that fit a geometric series, of which consecutive values differed by a factor of square root 2. The fit to this geometric series was best for normal cells. Significant quantal shifts occurred at a high rate (greater than 10(-2) per cell per generation) and to higher and lower levels with equal probability. These results demonstrate that geometric phenotypic variability is a normal phenomenon and should be taken into account when studying gene regulation and population dynamics.

A linear biopolymer in the vicinity of the triple point. The homopolymer case.

This is a theoretical study of a situation where each residue of a linear biopolymer may adopt one of three conformational states. Such a situation exists in the case of DNA, since it may be in helical A, B, . . ., Z forms as well as the melted state. In the vicinity of the triple point in the phrase diagram three states, e.g. the A form, the B form and the denatured state, co-exist within a given molecule. We present an exact analytical solution of the simplest homopolymer model. Theory predicts that the presence of two helical states in one molecule should affect the helix-coil transition in two ways. The melting temperature experiences an upward shift and the melting range width is increased, by a factor of square root of two as a maximum.

Distributed Processor Scheduling and User Countermeasures

Consider an m-processor distributed system having both local node and network traffic. Because users have incomplete information about the state of the queues at remote nodes, they can be tempted to shorten the expected completion time of a job by running multiple incarnations of each task in parallel on all m processors. To assess the temptation of such a “user countermeasure,” a job consisting of a sequence of n tasks to be performed sequentially is considered. Under simple assumptions about execution and network times, users can cut their expected job completion time by a factor of the square root of m. The implications of such user countermeasures on system design are discussed.