Sums Of Variables Research Articles

Disparity fluctuations in Jurassic ammonoids by means of conch geometry

We investigated the Jurassic ammonoids of southern Germany with respect to their temporal patterns of morphospace occupation. A Fourier analysis of whorl outline shapes was performed based on 1200 species within 72 discriminated biostratigraphic zones. Three general modes of temporal patterns in morphospace occupation can be distinguished by combining the sum of range, the sum of variance, and the position of the centroid of the morphological spectrum: (1) Morphospace stasis, (2) morphospace enlargement, and (3) morphospace reduction. We applied this classification scheme in the study of the Jurassic ammonoids, demonstrating that the evolutionary history of Jurassic ammonoids in southern Germany can be subdivided into three phases with increased morphological range, ending with incisions in the early Aalenian, late Bathonian, and end-Tithonian. Morphological variance differs partly from the range, showing a general increase during the Jurassic with incisions at the Toarcian–Aalenian boundary, within the Callovian, and the late Tithonian. A conducted subsampling as well as the comparison of disparity analyses of different temporal resolutions shows strikingly varying effects in morphospace patterns. Different resolutions and subsampled data provide strong correlations between sample size and the sum of range in particular.

A resampling variance estimator for the k nearest neighbours technique

Current estimators of variance for the k nearest neighbours (kNN) technique are designed for estimates of population totals. Their efficiency in small-area estimation problems can be poor. In this study, we propose a modified balanced repeated replication estimator of variance (BRR) of a kNN total that performs well in small-area estimation problems and under both simple random and cluster sampling. The BRR estimate of variance is the sum of variances and covariances of unit-level kNN estimates in the area of interest. In Monte Carlo simulations of simple random and cluster sampling from seven artificial populations with real and simulated forest inventory data, the agreement between averages of BRR estimates of variance and Monte Carlo sampling variances was good both for population and for small-area totals. The modified BRR estimator is currently limited to sample sizes no larger than 1984. An accurate approximation to the proposed BRR estimator allows significant savings in computing time.

Shrinkage Estimation of Effect Sizes as an Alternative to Hypothesis Testing Followed by Estimation in High-Dimensional Biology: Applications to Differential Gene Expression

Research on analyzing microarray data has focused on the problem of identifying differentially expressed genes to the neglect of the problem of how to integrate evidence that a gene is differentially expressed with information on the extent of its differential expression. Consequently, researchers currently prioritize genes for further study either on the basis of volcano plots or, more commonly, according to simple estimates of the fold change after filtering the genes with an arbitrary statistical significance threshold. While the subjective and informal nature of the former practice precludes quantification of its reliability, the latter practice is equivalent to using a hard-threshold estimator of the expression ratio that is not known to perform well in terms of mean-squared error, the sum of estimator variance and squared estimator bias. On the basis of two distinct simulation studies and data from different microarray studies, we systematically compared the performance of several estimators representing both current practice and shrinkage. We find that the threshold-based estimators usually perform worse than the maximum-likelihood estimator (MLE) and they often perform far worse as quantified by estimated mean-squared risk. By contrast, the shrinkage estimators tend to perform as well as or better than the MLE and never much worse than the MLE, as expected from what is known about shrinkage. However, a Bayesian measure of performance based on the prior information that few genes are differentially expressed indicates that hard-threshold estimators perform about as well as the local false discovery rate (FDR), the best of the shrinkage estimators studied. Based on the ability of the latter to leverage information across genes, we conclude that the use of the local-FDR estimator of the fold change instead of informal or threshold-based combinations of statistical tests and non-shrinkage estimators can be expected to substantially improve the reliability of gene prioritization at very little risk of doing so less reliably. Since the proposed replacement of post-selection estimates with shrunken estimates applies as well to other types of high-dimensional data, it could also improve the analysis of SNP data from genome-wide association studies.

Note on the variance of the sum of Gaussian functionals

Note on the variance of the sum of Gaussian functionals

Buffer Optimization in Network-on-Chip Through Flow Regulation

For network-on-chip (NoC) designs, optimizing buffers is an essential task since buffers are a major source of cost and power consumption. This paper proposes flow regulation and has defined a regulation spectrum as a means for system-on-chip architects to control delay and backlog bounds. The regulation is performed per flow for its peak rate and burstiness. However, many flows may have conflicting regulation requirements due to interferences with each other. Based on the regulation spectrum, this paper optimizes the regulation parameters aiming for buffer optimization. Three timing-constrained buffer optimization problems are formulated, namely, buffer size minimization, buffer variance minimization, and multiobjective optimization, which has both buffer size and variance as minimization objectives. Minimizing buffer variance is also important because it affects the modularity of routers and network interfaces. A realistic case study exhibits 62.8% reduction of total buffers, 84.3% reduction of total latency, and 94.4% reduction on the sum of variances of buffers. Likewise, the experimental results demonstrate similar improvements in the case of synthetic traffic patterns. The optimization algorithm has low run-time complexity, enabling quick exploration of large design spaces. This paper concludes that optimal flow regulation can be a highly valuable instrument for buffer optimization in NoC designs.

A novel statistical image thresholding method

Classic statistical thresholding methods based on maximizing between-class variance and minimizing class variance fail to achieve satisfactory results when segmenting a kind of image, where variance discrepancy between the object and background classes is large. The reason is that they take only class variance sum of some form as criterions for threshold selection, but neglect discrepancy of the variances. In this paper, a novel criterion combining the above two factors is proposed to eliminate the described limitation for classic statistical approaches and improve segmentation performance. The proposed method determines the optimal threshold by minimizing the criterion. The method was compared with several classic thresholding methods on a variety of images including some NDT images and laser cladding images, and the experimental results show the effectiveness of the algorithm.

Repeatability of nerve conduction measurements derived entirely by computer methods

BackgroundNerve conduction studies are an objective, quantitative, and reproducible measure of peripheral nerve function and are widely used in the diagnosis of neuropathies. The purpose of this study is to determine the reliability of nerve conduction parameters derived entirely from computer based data acquisition and waveform cursor assignments and to quantify the relative contributions of test variability sources.MethodsThirty volunteers, some with symptoms suggestive of neuropathies; of these, 29 completed the study. The median, ulnar, deep peroneal, posterior tibial, and sural nerves were evaluated bilaterally at two test sessions 3-7 days apart. Within each session, nerves were tested twice within 10 minutes. The analyzed nerve conduction parameters include motor latencies, motor conduction velocity (CV), compound muscle action potential (CMAP) amplitude, F-wave latencies (minimum, mean and maximum), sensory peak latency (DSL), sensory CV, and sensory nerve action potential (SNAP) amplitude. The primary outcome measure is variance component analysis and the corresponding coefficient of variation (CoV). The between-session-test variance is the sum of within-session variance and between-session variance, quantifying the total variation between test sessions. Additional statistical measures include the intraclass correlation coefficient (ICC) and relative interval variation (RIV).ResultsMotor and sensory latencies, CV and F-wave latency parameters have low between-session-test CoVs, ranging from 4.2% to 9.8%. Amplitude parameters have a higher between-session-test CoVs in the range of 15.6--19.8%. Between-test CoVs are about 30--80% lower than between-session CoVs with the exception of F-wave latency parameters. Between-test ICC values are 0.96 or above for all parameters. Between-session ICC ranges from 0.98 for F-wave latency to 0.77 for sural sensory CV. All latency-related between-session ICCs have a value 0.83 or above. The RIVs are the tightest for F-wave latency parameters and widest for CMAP amplitude parameters. Repeatability in a sub-group of subjects with more severe symptom grades follows the same trend as the overall study population without substantial quantitative differences.ConclusionThe study demonstrates the high repeatability of nerve conduction parameters acquired by modern electrodiagnostic instruments using computer based waveform cursor assignment. The reliability is comparable to benchmark studies in which the nerve conduction measurements were performed manually in controlled multi-center clinical trials. Furthermore, the ranking of reliability, whereby F-wave latencies have the best reproducibility and amplitudes the worst, is also consistent with the benchmark studies.

On the nature of nicotine addiction: A taxometric analysis.

Taxometric procedures were used to determine whether nicotine addiction is best conceptualized as a dimensional or a categorical (i.e., taxonic) phenomenon. Using data from the 2003 National Survey on Drug Use and Health (NSDUH; N = 12,467), results from MAMBAC, MAXEIG, and LMODE taxometric analyses provided strong evidence that nicotine addiction has a taxonic latent structure. Members of the addiction taxon, which constituted approximately 48% of those who reported smoking in the past 30 days, consumed a higher number of cigarettes per day, had stronger craving, higher levels of nicotine tolerance, more inflexible smoking patterns, and shorter latencies to smoking their first cigarette on waking compared with nontaxon members. These findings of a distinct addiction taxonic structure were replicated using a 2002 NSDUH sample (N = 12,224). Finally, the predictive validity of the taxon variable was compared with a continuous indicator sum. The taxon accounted for most of the predictive variance in the indicator sum, but the latter generally showed significant predictive power even after controlling for the former. Thus, these smoking variables may have both a categorical and a dimensional structure.

A comparative study of the performances of some estimators of linear model with fixed and stochastic regressors

In linear regression model, regressors are assumed fixed in repeated sampling. This assumption is not always satisfied especially in business, economics and social sciences. Consequently in this paper, effort is made to compare the performances of some estimators of linear model with autocorrelated error terms when normally distributed regressors are fixed (non – stochastic) with when they are stochastic. The estimators are the ordinary least square (OLS) estimator and four feasible generalized least estimators which are Cochrane Orcutt (CORC), Hidreth – Lu (HILU), Maximum Likelihood (ML), Maximum Likelihood Grid (MLGD) estimator. These estimators are compared using the finite properties of estimators' criteria namely; sum of biases, sum of variances and sum of the mean squared error of the estimated parameter of the model at different levels of autocorrelation and sample size through Monte – Carlo studies. Results show that at each level of autocorrelation the estimated value of the criteria with stochastic regressor are much lesser than that of the fixed regressor for all the estimators except CORC when the sample size is small (n=20) and the level of autocorrelation is very high . More comparatively, it is observed that the same estimator(s) that is more efficient with fixed regressors is also more efficient with stochastic regressors except when the sample size is large (n = 80) and the level of autocorrelation is either low or high . At these instances, the CORC / HILU estimator is more efficient with fixed regressors while the ML / MLGD estimator is more efficient with stochastic regressors Keywords : Fixed Regressors, Stochastic Regressors, Linear Model, Autocorrelated error, OLS estimator, Feasible GLS estimators Global Journal of Pure and Applied Sciences Vol. 14 (3) 2008: pp. 363-370

A Pragmatic PHY Abstraction Technique for Link Adaptation and MIMO Switching

MIMO (multiple input multiple output) techniques are widely employed to improve the performance of wireless systems. These techniques are used to overcome multipath fading and/or improve the peak throughput of wireless systems. It is well known that there is a fundamental tradeoff between diversity gain and multiplexing gain [1]. Orthogonal space time codes such as the Alamouti code (also known as space time block codes (STBC)) exploit multiple antennas as a diversity source, and thus improve packet error rate (PER) and the average throughput. However, space time block codes are not designed to increase the peak data rate of the system. On the other hand, spatial multiplexing (SM) techniques offer higher peak throughput by transmitting parallel streams of data from different antennas. In order to successfully decode the parallel streams, the channel must exhibit a small eigenvalue spread. Otherwise, the streams will interfere with one another and it is difficult to decode the information data. The performance improvement from SM is therefore highly dependent on the channel characteristics. It is possible to use multiple encoders and rate control per layer to improve the SM performance. However, there are instances of channel where STBC is more beneficial than SM with a single encoder. In order to resolve the shortcomings of STBC and SM, a hybrid technique can be applied where depending on the instantaneous channel conditions either STBC or SM is selected. This technique is commonly referred to as adaptive MIMO switching (AMS) [5]-[11]. One important aspect of the technique is the switching criteria, namely the PHY abstraction method which estimates a packet error event as a function of the instantaneous channel condition, transmission profiles, and receiver characteristics. We show that the proposed algorithm outperforms other techniques such as determinant and Demmel condition number based techniques in flat fading channel. In selective fading channels where a codeword sees a finite number of multiple channel qualities, estimating the resulting PER is very challenging. Existing techniques rely on an estimate of the average of the channel qualities seen by each codeword. In this paper, we propose a PHY abstraction and switching algorithm hereby referred to by weighted sum of instantaneous qualities (WSIQ) whereby the channel qualities are ordered in order to reduce the variance of channel qualities and then a weighted sum of the qualities is applied. The weighting vector is chosen to minimize the variance of the linear sum. We have provided simulations to show the superiority of WSIQ even when channel statistics are unknown. In addition, computationally efficient techniques suited for practical implementation are proposed.

Study on subset size selection in digital image correlation for speckle patterns

Digital Image Correlation (DIC) is a flexible and effective technique to measure the displacements on specimen surfaces by matching the reference subsets in the undeformed image with the target subsets in the deformed image. With the existing DIC techniques, the user must rely on experience and intuition to manually define the size of the reference subset, which is found to be critical to the accuracy of measured displacements. In this paper, the problem of subset size selection in the DIC technique is investigated. Based on the Sum of Squared Differences (SSD) correlation criterion as well as the assumption that the gray intensity gradients of image noise are much lower than that of speckle image, a theoretical model of the displacement measurement accuracy of DIC is derived. The theoretical model indicates that the displacement measurement accuracy of DIC can be accurately predicted based on the variance of image noise and Sum of Square of Subset Intensity Gradients (SSSIG). The model further leads to a simple criterion for choosing an optimal subset size for the DIC analysis. Numerical experiments have been performed to validate the proposed concepts, and the calculated results show good agreements with the theoretical predictions.

Evaluation of new laryngoscope blade for tracheal intubation, Truview EVO2©;

Difficult airways present a clinical challenge for anaesthetists. The Truphatek Truview EVO2 (Truphatek International Ltd, Netanya, Israel) is a new laryngoscope blade used for endotracheal intubation that could be used where there is difficulty in visualizing the laryngeal inlet. Twenty anaesthetists (12 trainees and eight consultants) compared the Truphatek Truview EVO2 with a conventional Macintosh size 3 blade. The Trucorp Airsim Bronchi (Trucorp Ltd, Belfast, Northern Ireland, UK) manikin was intubated under normal conditions and under simulated difficult conditions such as tongue inflation and neck rigidity. In each scenario, the Cormack-Lehane grade, time needed for successful intubation, perceived difficulty of tracheal intubation and personal preference of blade were compared. The results were analysed with t-test (time of intubation), Wilcoxon signed-rank sum (Cormack-Lehane grade, ease of manoeuvre, preferred blade) and analysis of variance with Bonferroni correction (augmentation of difficulties in different scenarios). The Truview EVO2 blade allowed the best laryngeal view as judged by the Cormack-Lehane grade (P < 0.05) in two separate situations: under simulated tongue inflation and under simulated neck rigidity. However, this blade did not reduce the intubation time or the ease of tracheal tube placement with respect to conventional Macintosh blade. Compared with the classical Macintosh blade, the Truview EVO2 blade allowed a better view of the larynx, but did not facilitate endotracheal intubation in any of the difficult scenarios created with the adjustable manikin and in most scenarios in fact prolonged the intubation time.

A wavelet-based optimal texture feature set for classification of brain tumours

In this work, the classification of brain tumours in magnetic resonance images is studied by using optimal texture features. These features are used to classify three sets of brain images—normal brain, benign tumour and malignant tumour. A wavelet-based texture feature set is derived from the region of interest. Each selected brain region of interest is characterized with both its energy and texture features extracted from the selected high frequency subband. An artificial neural network classifier is employed to evaluate the performance of these features. Feature selection is performed by a genetic algorithm. Principal component analysis and classical sequential methods are compared against the genetic approach in terms of the best recognition rate achieved and the optimal number of features. A classification performance of 98% is achieved in a genetic algorithm with only four of the available 29 features. Principal component analysis and classical sequential methods require a larger feature set to attain the similar classification accuracy of 98%. The optimal texture features such as range of angular second moment, range of sum variance, range of information measure of correlation II and energy selected by the genetic algorithm provide best classification performance with lower computational effort.

Priority sampling for estimation of arbitrary subset sums

From a high-volume stream of weighted items, we want to create a generic sample of a certain limited size that we can later use to estimate the total weight of arbitrary subsets. Applied to Internet traffic analysis, the items could be records summarizing the flows of packets streaming by a router. Subsets could be flow records from different time intervals of a worm attack whose signature is later determined. The samples taken in the past thus allow us to trace the history of the attack even though the worm was unknown at the time of sampling. Estimation from the samples must be accurate even with heavy-tailed distributions where most of the weight is concentrated on a few heavy items. We want the sample to be weight sensitive, giving priority to heavy items. At the same time, we want sampling without replacement in order to avoid selecting heavy items multiple times. To fulfill these requirements we introduce priority sampling, which is the first weight-sensitive sampling scheme without replacement that works in a streaming context and is suitable for estimating subset sums. Testing priority sampling on Internet traffic analysis, we found it to perform an order of magnitude better than previous schemes. Priority sampling is simple to define and implement: we consider a steam of items i = 0,…, n − 1 with weights w i . For each item i , we generate a random number α i ∈ (0,1] and create a priority q i = w i /α i . The sample S consists of the k highest priority items. Let τ be the ( k + 1)th highest priority. Each sampled item i in S gets a weight estimate ŵ i = max{ w i , τ}, while nonsampled items get weight estimate ŵ i = 0. Magically, it turns out that the weight estimates are unbiased, that is, E[ ŵ i ] = w i , and by linearity of expectation, we get unbiased estimators over any subset sum simply by adding the sampled weight estimates from the subset. Also, we can estimate the variance of the estimates, and find, surprisingly, that the covariance between estimates ŵ i and ŵ j of different weights is zero. Finally, we conjecture an extremely strong near-optimality; namely that for any weight sequence, there exists no specialized scheme for sampling k items with unbiased weight estimators that gets smaller variance sum than priority sampling with k + 1 items. Szegedy settled this conjecture at STOC'06.

Genetic Analysis of Salt Stress Responses in Asparagus Bean (Vigna unguiculata (L.) ssp. sesquipedalis Verdc.)

Salt stress responses of 23 asparagus bean cultivars were evaluated using 14-day-old seedlings after 15-day exposure to 75 mM NaCl in a hydroponics culture system. Salt-induced changes in plant growth and morphology, photosynthetic capacity, cell membrane integrity, and cellular protection enzyme systems as well as other physiological and biochemical traits were investigated to identify genotypic variability in salt response. This study also analyzed heredity parameters and correlation of the salt response index (SRI). Salt stress suppressed seedling growth and simultaneously reduced leaf area, content of chlorophyll and soluble proteins, net assimilation rate, as well as dry matter accumulation. In contrast, leaf blade cell membrane relative permeability, content of malondialdehyde, and antioxidant enzyme activity were elevated after salt treatment. Analysis of the heredity parameters has identified that the 18 investigated traits have different genotypic variance of the SRI values. Based on Ward's distances estimated for the sum of square variance in the SRI values, all the cultivars were classified into 2 discrete salt-tolerant and salt-sensitive clusters. Findings from this study will provide theoretical bases for identification and breeding of salt-tolerant cultivars in asparagus bean.

Dominant species constrain effects of species diversity on temporal variability in biomass production of tallgrass prairie

Species diversity is thought to stabilize functioning of plant communities. An alternative view is that stability depends more on dynamics of dominant species than on diversity. We compared inter‐annual variability (inverse of stability) of aboveground biomass in paired restored and remnant tallgrass prairies at two locations in central Texas, USA. Data from these two locations were used to test the hypothesis that greater richness and evenness in remnant than restored prairies would reduce variability in aboveground biomass in response to natural variation in rainfall. Restored prairies were chosen to be similar to paired remnant prairies in characteristics other than species diversity that affect temporal variability in biomass. Variability was measured as the coefficient of variation among years (square root of variance/mean; CV), where variance in community biomass equals the sum of variances of individual plant species plus the summed covariances between species pairs. Species diversity over five years was greater by a factor of 2 or more in remnant than restored prairies because richness and evenness were greater in remnant than restored prairies. Still, the CV of community biomass during spring and CV of annual biomass production did not differ consistently between prairie types. Neither the sum of species covariances nor total community biomass differed between prairies. Biomass varied relatively little in restored compared to remnant prairies because biomass of the dominant species in restored prairies (the grassSchizachyrium scoparium) varied less than did biomass of other dominant and sub‐dominant species. In these grasslands, biomass response to natural variation in precipitation depended as much on characteristics of a dominant grass as on differences in diversity.

Localized large sums of random variables

We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.

Error compensation during finger force production after one- and four-finger voluntarily fatiguing exercise

The effect of muscle fatigue on error compensation strategies during multi-finger ramp force production tasks was investigated. Thirteen young, healthy subjects were instructed to produce a total force with four fingers of the right hand to accurately match a visually displayed template. The template consisted of a 3-s waiting period, a 3-s ramp force production [from 0 to 30% maximal voluntary contraction (MVC)], and a 3-s constant force production. A series of 12 ramp trials was performed before and after fatigue. Fatigue was induced by a 60-s maximal isometric force production with either the index-finger only or with all four fingers during two separate testing sessions. The average percent of drop was 38.2% in the MVC of the index finger after index-finger fatiguing exercise and 38.3% in the MVC of all fingers after four-finger fatiguing exercise. The ability of individual fingers to compensate for each other's errors in order for the total force to match the preset template was quantified as the error compensation index (ECI), i.e., the ratio of the sum of variances of individual finger forces and the variance of the total force. By comparing pre- and post-fatigue performance during four-finger ramp force production, we observed that the variance of the total force was not significantly changed after one- or four-finger fatiguing exercise. The ECI significantly decreased after four-finger fatiguing exercise, especially during the last second of the ramp; while the ECI remained unchanged after index finger single-finger fatiguing exercise. These results suggest that the central nervous system is able to utilize the abundant degrees of freedom to compensate for partial impairment of the motor apparatus induced by muscle fatigue to maintain the desired performance. However, this ability is significantly decreased when all elements of the motor apparatus are impaired.

Some asymptotic results on the sum of variances of order statistics

Some results on the asymptotic behaviour of n=1 Var[ψ(X(k))], where (X(k))1≤k≤n is a set of order statistics, are given. A Central Limit Theorem for ranked set sampling estimators is also provided. These results may be applied when an auxiliary variable induces a stratification on the target variable in a design-based approach. Mathematics Subject Classification: Primary 60F15, Secondary 60F05

Combined Statistical and Multiscale View on Ultrasonic Liver Images for Characterization

Combined Statistical and Multiscale View on Ultrasonic Liver Images for Characterization