Sum Of Covariances Research Articles

Genome-wide identification of overexpression and downregulation gene targets based on the sum of covariances of the outgoing reaction fluxes

In metabolic engineering, predicting gene overexpression targets remains challenging because both endogenous and heterologous genes in a large metabolic space can be candidates, in contrast to gene knockout targets that are confined to endogenous genes. We report the development of iBridge that identifies positive and negative metabolites exerting positive and negative impacts on product formation, respectively, based on the sum of covariances of their outgoing (consuming) reaction fluxes for a target chemical. Then, "bridge" reactions converting negative metabolites to positive metabolites are identified as overexpression targets, while the opposites as downregulation targets. Using iBridge, overexpression and downregulation targets are suggested for the production of 298 chemicals and validated for 36 chemicals experimentally demonstrated in previous studies. Finally, iBridge is employed to engineer Escherichia coli strains capable of producing 10.3 g/L of D-panthenol, a compound not previously produced, as well as putrescine and 4-hydroxyphenyllactate at enhanced titers, 63.7 and 8.3 g/L, respectively.

Recent Trends in Individual and Multivariate Compound Flood Drivers in Canada's Coasts

AbstractOver half of the global population and the majority of the cities in coastal zones are at risk of coastal flooding. Changes in the occurrence of individual extremes and the interactions between hydrological and coastal variables can exacerbate flood risks. While extensive research has been conducted to understand and predict different types of flood hazards in isolation, spatial and temporal trends and variability of compound flooding, that is, flooding caused by multiple drivers, remain an open question. This study investigates the individual and joint temporal variations of multiple drivers that can cause compound flooding in Canada's coasts including total water level, storm surge, precipitation, and streamflow. Long‐term changes in the frequency and intensity of extremes are analyzed over the Atlantic, Pacific, and the Great Lakes regions. Univariate and multivariate trend tests including Mann Kendall, Covariance Inversion Test, Covariance Sum Test, and Covariance Eigenvalue Test are applied. In addition, a new multivariate index based on the contributing flood drivers transformed into a probability space is proposed, and its application to study compound flooding is investigated. Overall, results show increased risks of individual and compound flooding over the Atlantic coast and varying trends in the Pacific and Great Lakes regions. The multivariate trend indices show consistent results in most scenarios. The proposed index provides a simple and flexible measure to analyze the spatial and temporal variation of compound flooding risks at different thresholds. The results highlight the importance of considering nonstationary compound flood events to develop resilience strategies in coastal environments.

Dust storm frequency change in relation to climate drivers

AbstractClimate variability and change in arid regions are important factors in controlling emission, frequency and movement of dust storms. This study provides robust statistical methods including univariate Mann‐Kendall block bootstrapping method and three bivariate trend assessment methods, Covariance Inversion Test, Covariance Sum Test and The Covariance Eigenvalue to detect trends in dust storm frequency across arid regions of Iran in relation to climate variability and trend in recent decades. In this regard, the annual number of dust storms from 25 stations in central arid and semi‐arid regions of Iran were selected. In addition, five major climatic variables including annual rainfall, annual maximum and average wind speed, annual maximum and average temperature were also collected. The univariate trend test indicates both increasing and decreasing trend in dust storm frequency and climate variables. The bivariate trend test shows a strong and statistically significant relationship between trend of climate variables and dust storm frequency for most of the stations across the region. Among climate variables, rainfall change has an inverse impact on dust storm frequency while wind speed and temperature have direct covariance structure with dust storm frequency. The wind speed also seems to be the most effective climate driver on dust storm frequency in arid regions of Iran, followed by temperature. The results also shows that local conditions that are not considered in this study may also play a significant role in dust storm emission in some parts of the region.

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

ABSTRACTThis article presents SPSTS, an automated sequential procedure for computing point and Confidence-Interval (CI) estimators for the steady-state mean of a simulation-generated process subject to user-specified requirements for the CI coverage probability and relative half-length. SPSTS is the first sequential method based on Standardized Time Series (STS) area estimators of the steady-state variance parameter (i.e., the sum of covariances at all lags). Whereas its leading competitors rely on the method of batch means to remove bias due to the initial transient, estimate the variance parameter, and compute the CI, SPSTS relies on the signed areas corresponding to two orthonormal STS area variance estimators for these tasks. In successive stages of SPSTS, standard tests for normality and independence are applied to the signed areas to determine (i) the length of the warm-up period, and (ii) a batch size sufficient to ensure adequate convergence of the associated STS area variance estimators to their limiting chi-squared distributions. SPSTS's performance is compared experimentally with that of recent batch-means methods using selected test problems of varying degrees of difficulty. SPSTS performed comparatively well in terms of its average required sample size as well as the coverage and average half-length of the final CIs.

Monitoring autocorrelated processes using a distribution-free tabular CUSUM chart with automated variance estimation

We formulate and evaluate distribution-free statistical process control (SPC) charts for monitoring shifts in the mean of an autocorrelated process when a training data set is used to estimate the marginal variance of the process and the variance parameter (i.e., the sum of covariances at all lags). Two alternative variance estimators are adapted for automated use in DFTC-VE, a distribution-free tabular CUSUM chart, based on the simulation-analysis methods of standardized time series and a simplified combination of autoregressive representation and non-overlapping batch means. Extensive experimentation revealed that these variance estimators did not seriously degrade DFTC-VE's performance compared with its performance using the exact values of the marginal variance and the variance parameter. Moreover, DFTC-VE's performance compared favorably with that of other competing distribution-free SPC charts. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplementary resource: Appendix]

Detecting compensatory dynamics in competitive communities under environmental forcing

Competition is assumed to generate compensatory dynamics where an increase in one species is compensated by a decrease in others. Recently, using a community covariance technique, Houlahan et al. found that compensatory dynamics are only visible in 25–30% of natural communities studied. The study was based on scoring the sum of covariances of population densities. In contrast to the theory, and as a cautionary reminder to the interpretation of natural time series data, we show that negative community covariance can be absent even in strongly competitive communities and can be found present in communities without competitive interactions. Precise knowledge of various features of the underlying species’ biology and characteristics of the environmental variation is required before community covariance can be correctly interpreted as a proxy for the importance of competition or environmental forcing in driving community fluctuations. Other tools may therefore be more appropriate, e.g. explicit modelling of competition using modern time series analytical tools.

Where Do Alphas Come From?: A New Measure of the Value of Active Investment Management

The value of active investment management is traditionally measured by alpha, beta, tracking error, and the Sharpe and information ratios. These are essentially static characteristics of the marginal distributions of returns at a single point in time, and do not incorporate dynamic aspects of a manager's investment process. In this paper, I propose a new measure of the value of active investment management that captures both static and dynamic contributions of a portfolio manager's decisions. The measure is based on a decomposition of a portfolio's expected return into two distinct components: a static weighted-average of the individual securities' expected returns, and the sum of covariances between returns and portfolio weights. The former component measures the portion of the manager's expected return due to static investments in the underlying securities, while the latter component captures the forecast power implicit in the manager's dynamic investment choices. This measure can be computed for long-only investments, long/short portfolios, and asset allocation rules, and is particularly relevant for hedge-fund strategies where both components are significant contributors to their expected returns, but only one should garner the high fees that hedge funds typically charge. Several analytical and empirical examples are provided to illustrate the practical relevance of these new measures.

Overlapping Variance Estimators for Simulation

To estimate the variance parameter (i.e., the sum of covariances at all lags) for a steady-state simulation output process, we formulate certain statistics that are computed from overlapping batches separately and then averaged over all such batches. We form overlapping versions of the area and Cramér–von Mises estimators using the method of standardized time series. For these estimators, we establish (i) their limiting distributions as the sample size increases while the ratio of the sample size to the batch size remains fixed; and (ii) their mean-square convergence to the variance parameter as both the batch size and the ratio of the sample size to the batch size increase. Compared with their counterparts computed from nonoverlapping batches, the estimators computed from overlapping batches asymptotically achieve reduced variance while maintaining the same bias as the sample size increases; moreover, the new variance estimators usually achieve similar improvements compared with the conventional variance estimators based on nonoverlapping or overlapping batch means. In follow-up work, we present several analytical and Monte Carlo examples, and we formulate efficient procedures for computing the overlapping estimators with only order-of-sample-size effort.

Efficient Computation of Overlapping Variance Estimators for Simulation

For a steady-state simulation output process, we formulate efficient algorithms to compute certain estimators of the process variance parameter (i.e., the sum of covariances at all lags), where the estimators are derived in principle from overlapping batches separately and then averaged over all such batches. The algorithms require order-of-sample-size work to evaluate overlapping versions of the area and Cramér–von Mises estimators arising in the method of standardized time series. Recently, Alexopoulos et al. showed that, compared with estimators based on nonoverlapping batches, the estimators based on overlapping batches achieve reduced variance while maintaining similar bias asymptotically as the batch size increases. We provide illustrative analytical and Monte Carlo results for M/M/1 queue waiting times and for a first-order autoregressive process. We also present evidence that the asymptotic distribution of each overlapping variance estimator can be closely approximated using an appropriately rescaled chi-squared random variable with matching mean and variance.

Exact expected values of variance estimators for simulation

AbstractWe formulate exact expressions for the expected values of selected estimators of the variance parameter (that is, the sum of covariances at all lags) of a steady‐state simulation output process. Given in terms of the autocovariance function of the process, these expressions are derived for variance estimators based on the simulation analysis methods of nonoverlapping batch means, overlapping batch means, and standardized time series. Comparing estimator performance in a first‐order autoregressive process and the M/M/1 queue‐waiting‐time process, we find that certain standardized time series estimators outperform their competitors as the sample size becomes large. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

A wavelet-based spectral procedure for steady-state simulation analysis

We develop WASSP, a wavelet-based spectral method for steady-state simulation analysis. First WASSP determines a batch size and a warm-up period beyond which the computed batch means form an approximately stationary Gaussian process. Next WASSP computes the discrete wavelet transform of the bias-corrected log-smoothed-periodogram of the batch means, using a soft-thresholding scheme to denoise the estimated wavelet coefficients. Then taking the inverse discrete wavelet transform of the thresholded wavelet coefficients, WASSP computes estimators of the batch means log-spectrum and the steady-state variance parameter (i.e., the sum of covariances at all lags) for the original (unbatched) process. Finally by combining the latter estimator with the batch means grand average, WASSP provides a sequential procedure for constructing a confidence interval on the steady-state mean that satisfies user-specified requirements concerning absolute or relative precision as well as coverage probability. An experimental performance evaluation demonstrates WASSP’s effectiveness compared with other simulation analysis methods.

A simultaneous CONCOR algorithm for the analysis of two partitioned matrices

A standard approach to derive underlying components from two or more data matrices, holding data from the same individuals or objects, is the (generalized) canonical correlation analysis. This technique finds components (canonical variates) with maximal sums of correlations between them. The components do not necessarily explain much variance in the matrices they were derived from. This observation has given rise to alternative techniques, which maximize the sum of covariances between the components, subject to orthonormality constraints on the weight matrices applied to generate the components from the data matrices. However, a method called ConcorGM, maximizing the sum of squared covariances, has also been proposed. It has the additional feature that it allows for the analysis of two sets of data matrices which may, but need not coincide. The ConcorGM algorithm maximizes the sum of squared covariances successively, by first finding the best single-component solution, and repeating that process in the respective residual spaces. An algorithm for maximizing the sum of squared covariances simultaneously is offered.

MULTIVARIATE NONPARAMETRIC TESTS FOR TREND IN WATER QUALITY1

ABSTRACT: National and state fixed station stream quality monitoring networks have now been in existence for over ten years. The resulting data bases provide opportunities and challenges for statistical trend assessment. Although nonparametric tests have been developed that are well suited to such problems, the interpretation of variations in trend significance between seasons and variables remains a problem. One recently developed test is based on the sum of Mann‐Kendall statistics over seasons or variables, with the test statistic variance computed as the sum of the covariances of the individual Mann‐Kendall statistics. In this method, up‐ and downtrends can cancel, giving an overall indication of no trend. A related test which is sensitive to trend regardless of direction has been shown to behave poorly for typical stream quality record lengths. An alternative formulation which is sensitive to up‐ and downtrends and has power approaching that of the covariance sum method, is described. In addition, a variation of a contrast test for discriminating trend directions and magnitudes among variables or seasons where correlation between seasons or variables is present is described, and tests of its performance reported.

Linear error analysis of slope-area discharge determinations

The slope-area method can be used to calculate peak flood discharges when current-meter measurements are not possible. This calculation depends on several quantities, such as water-surface fall, that are subject to large measurement errors. Other critical quantities, such as Manning's n, are not even amenable to direct measurement but can only be estimated. Finally, scour and fill may cause gross discrepancies between the observed condition of the channel and the hydraulic conditions during the flood peak. The effects of these potential errors on the accuracy of the computed discharge have been estimated by statistical error analysis using a Taylor-series approximation of the discharge formula and the well-known formula for the variance of a sum of correlated random variates. The resultant error variance of the computed discharge is a weighted sum of covariances of the various observational errors. The weights depend on the hydraulic and geometric configuration of the channel. The mathematical analysis confirms the rule of thumb that relative errors in computed discharge increase rapidly when velocity heads exceed the water-surface fall, when the flow field is expanding and when lateral velocity variation (alpha) is large. It also confirms the extreme importance of accurately assessing the presence of scour or fill.

On DFIs' liability management: Deposit capacity, multideposit supply, and risk-efficient rate setting

Beyond reference rate-setting strategies derived in a CAPM framework, the paper addresses two related questions: (i) limited deposit accommodation under capital regulation, and (ii) characterization of rate differentials in correlated-uncorrelated multideposit markets. Under certain circumstances, an optimal rate/capacity choice policy will imply deposit capacity is not fully utilized all the time. Since capacity is not costless, excess liability capacity may be an optimal financial decision when the intermediary must meet adequacy test assorted with financial penalties or with enforceable limitations on its balance-sheet growth. In the other case, the intermediary is likely to introduce risky rate differentials to the extent risk is actually reduced enough to increase its market valuation. For correlated multideposit markets, this obtains whenever pairs of supplies are sufficiently negative to make their weighted covariance sum larger than the segment own variance. Alternatively, for uncorrelated segments, higher rates will be offered to steady depositors whose standard deviation of class supply contributes little to total risk.