Independent Perturbations Research Articles

Robust Inversion of Time-domain Electromagnetic Data: Application to Unexploded Ordnance Discrimination

We invert time-domain electromagnetic data for the purpose of discriminating between buried unexploded ordnance (UXO) and non-hazardous metallic clutter. The observed secondary magnetic field radiated by a conductor is forward modeled as a linear combination of decaying, orthogonal dipoles. We show via a perturbation analysis that errors in the measurement of sensor position propagate to non-normal errors on the observed data. A least squares (L2) inversion assumes normal errors on the data, so non-normal errors have the potential to bias dipole parameter estimates. In contrast, robust norms are designed to downweight the effect of outlying (noisy) data and so can provide useful parameter estimates when there is a non-normal component to the noise. When positional errors are modeled as independent Gaussian perturbations, we find that weighted least squares and robust inversions have comparable performance. Both inversion techniques estimate data uncertainties from observed data, and this has the effect of making the least squares inversion robust to outliers. However, when simulated errors are correlated, robust inversion with a bisquare norm provides a marked improvement over L2 inversion. Application of robust inversion to real data sets from Camp Sibert, Alabama produced an incremental improvement to the initial L2 inversion, identifying outlying ordnance items and improving discrimination performance.

Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations

In this work we study dynamical systems on the torus modeling Josephson junctions in the theory of superconductivity, and also perturbations of these systems. We show that, in the family of equations that describe resistively shunted Josephson junctions, phase lock occurs only for integer rotation numbers and propose a simple method for calculating the boundaries of the corresponding Arnold tongues. This part is a simplification of known results about the quantization of rotation number [4]. Moreover, we show that the quantization of rotation number only at integer points is a phenomenon of infinite codimension. Namely, there is an infinite set of independent perturbations of systems that give rise to countably many nondiscretely located phase-locking regions.

Uncoordinated Loss of Chromatid Cohesion Is a Common Outcome of Extended Metaphase Arrest

Chromosome segregation requires coordinated separation of sister chromatids following biorientation of all chromosomes on the mitotic spindle. Chromatid separation at the metaphase-to-anaphase transition is accomplished by cleavage of the cohesin complex that holds chromatids together. Here we show using live-cell imaging that extending the metaphase bioriented state using five independent perturbations (expression of non-degradable Cyclin B, expression of a Spindly point mutant that prevents spindle checkpoint silencing, depletion of the anaphase inducer Cdc20, treatment with a proteasome inhibitor, or treatment with an inhibitor of the mitotic kinesin CENP-E) leads to eventual scattering of chromosomes on the spindle. This scattering phenotype is characterized by uncoordinated loss of cohesion between some, but not all sister chromatids and subsequent spindle defects that include centriole separation. Cells with scattered chromosomes persist long-term in a mitotic state and eventually die or exit. Partial cohesion loss-associated scattering is observed in both transformed cells and in karyotypically normal human cells, albeit at lower penetrance. Suppressing microtubule dynamics reduces scattering, suggesting that cohesion at centromeres is unable to resist dynamic microtubule-dependent pulling forces on the kinetochores. Consistent with this view, strengthening cohesion by inhibiting the two pathways responsible for its removal significantly inhibits scattering. These results establish that chromosome scattering due to uncoordinated partial loss of chromatid cohesion is a common outcome following extended arrest with bioriented chromosomes in human cells. These findings have important implications for analysis of mitotic phenotypes in human cells and for development of anti-mitotic chemotherapeutic approaches in the treatment of cancer.

Gene Expression Network Reconstruction by Convex Feature Selection when Incorporating Genetic Perturbations

Cellular gene expression measurements contain regulatory information that can be used to discover novel network relationships. Here, we present a new algorithm for network reconstruction powered by the adaptive lasso, a theoretically and empirically well-behaved method for selecting the regulatory features of a network. Any algorithms designed for network discovery that make use of directed probabilistic graphs require perturbations, produced by either experiments or naturally occurring genetic variation, to successfully infer unique regulatory relationships from gene expression data. Our approach makes use of appropriately selected cis-expression Quantitative Trait Loci (cis-eQTL), which provide a sufficient set of independent perturbations for maximum network resolution. We compare the performance of our network reconstruction algorithm to four other approaches: the PC-algorithm, QTLnet, the QDG algorithm, and the NEO algorithm, all of which have been used to reconstruct directed networks among phenotypes leveraging QTL. We show that the adaptive lasso can outperform these algorithms for networks of ten genes and ten cis-eQTL, and is competitive with the QDG algorithm for networks with thirty genes and thirty cis-eQTL, with rich topologies and hundreds of samples. Using this novel approach, we identify unique sets of directed relationships in Saccharomyces cerevisiae when analyzing genome-wide gene expression data for an intercross between a wild strain and a lab strain. We recover novel putative network relationships between a tyrosine biosynthesis gene (TYR1), and genes involved in endocytosis (RCY1), the spindle checkpoint (BUB2), sulfonate catabolism (JLP1), and cell-cell communication (PRM7). Our algorithm provides a synthesis of feature selection methods and graphical model theory that has the potential to reveal new directed regulatory relationships from the analysis of population level genetic and gene expression data.

The temporal weighting of loudness: effects of the level profile

In four experiments, we studied the influence of the level profile of time-varying sounds on temporal perceptual weights for loudness. The sounds consisted of contiguous wideband noise segments on which independent random-level perturbations were imposed. Experiment 1 showed that in sounds with a flat level profile, the first segment receives the highest weight (primacy effect). If, however, a gradual increase in level (fade-in) was imposed on the first few segments, the temporal weights showed a delayed primacy effect: The first unattenuated segment received the highest weight, while the fade-in segments were virtually ignored. This pattern argues against a capture of attention to the onset as the origin of the primacy effect. Experiment 2 demonstrated that listeners adjust their temporal weights to the level profile on a trial-by-trial basis. Experiment 3 ruled out potentially inferior intensity resolution at lower levels as the cause of the delayed primacy effect. Experiment 4 showed that the weighting patterns cannot be explained by perceptual segmentation of the sounds into a variable and a stable part. The results are interpreted in terms of memory and attention processes. We demonstrate that the prediction of loudness can be improved significantly by allowing for nonuniform temporal weights.

Multiparametric sensitivity analysis of the additive model in data envelopment analysis

AbstractIn this paper, we study multiparametric sensitivity analysis of the additive model in data envelopment analysis using the concept of maximum volume in the tolerance region. We construct critical regions for simultaneous and independent perturbations in all inputs/outputs of an efficient decision making unit. Necessary and sufficient conditions are derived to classify the perturbation parameters as “focal” and “nonfocal.” Nonfocal parameters can have unlimited variations because of their low sensitivity in practice and these parameters can be deleted from the final analysis. For focal parameters a maximum volume region is characterized. Theoretical results are illustrated with the help of a numerical example.

Quantitative stability analysis for vector problems of 0–1 programming

We consider multiple objective 0–1 programming problems in the situation where parameters of objective functions and linear constraints are exposed to independent perturbations. We study quantitative characteristics of stability (stability radii) of problem solutions. An approach to deriving formulae and estimations of stability radii is presented. This approach is applied to stability analysis of the linear 0–1 programming problem and problems with two types of nonlinear objective functions: linear absolute value and quadratic.

High frequency elastic wave inversion

This thesis is concerned with the problem of high frequency elastic wave inversion. This is the problem of determining sharp, localised changes in the properties of materials beneath the surface of the earth using only measurements of reflected seismic waves taken at or near the surface. The central objective of this thesis is to construct multiparameter inversion operators which map data from surface wave measurements into accurate estimates for the high frequency perturbations in the density, ρ, and in the 21 independent Hooke’s tensor components, cijkl, of subsurface anisotropic inclusions. Using results from the field of microlocal analysis of Fourier Integral Operators, it is shown that asymptotically valid inversion operators exist which can invert all 22 independent elastic parameter perturbations directly, without relying on statistical estimates. To gather the required data, the technique of using ensembles of linked seismic experiments is introduced and extensively analysed in the context of a standard linearised single scattering model for elastic waves based on the Born approximation. This technique builds on work by Burridge and others in [10:Burridge R. ; De Hoop M. V. ; Miller D. ; Spencer C. ; 1998], and by Nolan in [17:Clifford J. Nolan 1997][49:Nolan and Ryan 2007]. In addition, a fundamental theoretical analysis of the seismic inversion problem is carried out. By analysing important components of the seismic forward problem, a theoretical framework is introduced which allows the determination of whether or not multiparameter inversion is possible, and specifically with what types of seismic ensembles and elastic wave modes. In particular, this framework will show under which circumstances multiparameter inversion is not possible, both for the case of point anisotropic inclusions, and in particular for larger volume inclusions. It is shown that these results can be extended to inversion in multiple type of seismic backgrounds. To complement the theoretical results, an application of evolutionary algorithm is presented which is used to find practical invertible seismic ensembles which allow inversion to be carried out feasibly. The thesis also presents a introductory overview of the techniques of Fourier Integral Operators and microlocal analysis, which are used to construct later inversion models. Other more elaborate mathematical techniques used in the thesis are also introduced or expanded on in the appendices for the benefit of the general reader. Finally, supporting lemmas in the appendices introduce a new method for determining the component dependencies of linear elastic materials.

H 2 optimal control for a wide class of discrete-time linear stochastic systems

In this article, the problem of H 2-control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Different H 2 performance criteria (often called H 2-norms) are introduced and characterised via solutions of some suitable linear equations on certain spaces of symmetric matrices. Some aspects specific to the discrete-time framework are revealed. The problem of optimisation of H 2-norms is solved under the assumption that full state vector is available for measurements. One shows that among all stabilising controllers of higher dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilising solution of a system of discrete-time generalised Riccati equations.

Long-term prediction of solar and geomagnetic activity daily time series using singular spectrum analysis and fuzzy descriptor models

Abstract Of the various conditions that affect space weather, Sun-driven phenomena are the most dominant. Cyclic solar activity has a significant effect on the Earth, its climate, satellites, and space missions. In recent years, space weather hazards have become a major area of investigation, especially due to the advent of satellite technology. As such, the design of reliable alerting and warning systems is of utmost importance, and international collaboration is needed to develop accurate short-term and long-term prediction methodologies. Several methods have been proposed and implemented for the prediction of solar and geomagnetic activity indices, but problems in predicting the exact time and magnitude of such catastrophic events still remain. There are, however, descriptor systems that describe a wider class of systems, including physical models and non-dynamic constraints. It is well known that the descriptor system is much tighter than the state-space expression for representing real independent parametric perturbations. In addition, the fuzzy descriptor models as a generalization of the locally linear neurofuzzy models are general forms that can be trained by constructive intuitive learning algorithms. Here, we propose a combined model based on fuzzy descriptor models and singular spectrum analysis (SSA) (FD/SSA) to forecast a number of geomagnetic activity indices in a manner that optimizes a fuzzy descriptor model for each of the principal components obtained from singular spectrum analysis and recombines the predicted values so as to transform the geomagnetic activity time series into natural chaotic phenomena. The method has been applied to predict two solar and geomagnetic activity indices: geomagnetic aa and solar wind speed (SWS) of the solar wind index. The results demonstrate the higher power of the proposed method—compared to other methods—for predicting solar activity.

Multiple Perturbation Two-Dimensional Correlation Analysis of Cellulose by Attenuated Total Reflection Infrared Spectroscopy

An extension of the two-dimensional (2D) correlation analysis scheme for multi-dimensional perturbation is described. A simple computational form is provided to construct synchronous correlation and disrelation maps for the analysis of microscopic imaging data based on two independent perturbation variables. Sets of time-dependent attenuated total reflection infrared (ATR-IR) spectra of water and cellulose mixtures were collected during the evaporation of water from finely ground cellulose. The system exhibits complex behaviors in response to two independent perturbations, i.e., evaporation time and grinding time. Multiple perturbation 2D analysis reveals a specific difference in the rate of evaporation of water molecules when accompanied by crystallinity changes of cellulose. It identifies subtle differences in the volatility of water, which is related to the crystalline structure of cellulose.

Two-Sample Kalman Filter for Steady-State Data Assimilation

Abstract In this paper, a new iterative algorithm for computing a steady-state Kalman gain is proposed. This algorithm utilizes two model forecasts with statistically independent random perturbations to determine the error covariance used to define a Kalman gain matrix for steady-state data assimilation. It is based on the assumption that the error process is weakly stationary and ergodic. The algorithm consists of an iterative procedure for improving the covariance estimate, which requires a fixed observation network. Two twin experiments using a simple wave model and an operational storm surge prediction model are performed to demonstrate the performance of the proposed algorithm. The experiments show that the results obtained by using the proposed algorithm converge to the ones produced by the classic Kalman filter algorithm. An additional experiment using the three-variable Lorenz model is also performed to demonstrate its potential applicability in unstable dynamical systems.

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain. The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions. The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.

Electric field dependence of phase equilibria of binary Stockmayer fluid mixtures

A perturbation theory based study of the effect of an external electric field on the phase equilibrium properties of binary Stockmayer fluids is presented. The dipole–dipole interaction and the applied field are treated as independent perturbations to a Lennard–Jones mixture, and the reference fluid is treated by the van der Waals one-fluid approximation. A third-order free energy expression in the electric field strength is established, and the dielectric constant is calculated for a needle-shaped sample parallel to the field direction. We present and discuss vapour–liquid and liquid–liquid equilibrium curves at a given temperature for some dipolar mixtures exposed to an electric field, including chlorodifluoromethane + difluoromethane and acetonitrile + methanol. A sufficiently high electric field may result in massive shifts of vapour pressures and critical or azeotropic points, and can considerably alter the properties of coexisting phases. The vapour pressure decreases with increasing field strength.

Multi-parametric sensitivity analysis in piecewise linear fractional programming

In this paper, we study multi-parametric sensitivity analysis forprogramming problems with the piecewise linear fractional objective function in the tolerance region. We construct critical regions for simultaneous and independent perturbations in the objective function coefficients and in the right-hand-side vector of the given problem. Necessary and sufficient conditions are derived to classify perturbation parameters as 'focal' and 'non-focal'. Non-focal parameters can be deleted from the analysis, because of their low sensitivity in practice. Theoretical results are illustrated with the help of a numerical example.

Uncertainties in Air Toxics Calculated by the Dispersion Models AERMOD and ISCST3 in the Houston Ship Channel Area

Abstract The uncertainties in simulations of annually averaged concentrations of two air toxics (benzene and 1,3-butadiene) are estimated for two widely used U.S. air quality models, the Industrial Source Complex Short-Term, version 3, (ISCST3) model and the American Meteorological Society–Environmental Protection Agency Model (AERMOD). The effects of uncertainties in emissions input, meteorological input, and dispersion model parameters are investigated using Monte Carlo probabilistic uncertainty methods, which involve simultaneous random and independent perturbations of all inputs. The focus is on a 15 km × 15 km domain in the Houston, Texas, ship channel area. Concentrations are calculated at hypothetical receptors located at the centroids of population census tracts. The model outputs that are analyzed are the maximum annually averaged maximum concentration at any single census tract or monitor as well as the annually averaged concentration averaged over the census tracts. The input emissions uncertainties are estimated to be about a factor of 3 (i.e., covering the 95% range) for each of several major categories. The uncertainties in meteorological inputs (such as wind speed) and dispersion model parameters (such as the vertical dispersion coefficient σz) also are estimated. The results show that the 95% range in predicted annually averaged concentrations is about a factor of 2–3 for the air toxics, with little variation by model. The input variables whose variations have the strongest effect on the predicted concentrations are on-road mobile sources and some industrial sources (dependent on chemical), as well as wind speed, surface roughness, and σz. In most scenarios, the uncertainties of the emissions input group contribute more to the total uncertainty than do the uncertainties of the meteorological/dispersion input group.

Cobalt targets multiple metabolic processes in Salmonella enterica.

Cobalt is essential for growth of Salmonella enterica and other organisms, yet this metal can be toxic when present in excess. Wild-type Salmonella exhibits several metabolic defects when grown in the presence of cobalt, some of which generate visible growth consequences. Work herein identifies sulfur assimilation, iron homeostasis, and Fe-S cluster metabolism as targets for cobalt toxicity. In each case it is proposed that cobalt exerts its effect by one of two mechanisms: direct competition with iron or indirectly through a mechanism that involves the status of reduced thiols in the cell. Cobalt toxicity results in decreased siroheme production, increased expression of the Fur regulon, and decreased activity of Fe-S cluster proteins. The consequences of reduced sulfite reductase activity in particular are exacerbated by the need for glutathione in cobalt resistance. Significantly, independent metabolic perturbations could be detected at cobalt concentrations below those required to generate a detectable growth defect.

The influence of imperfections on the flow structure of steady vortex breakdown bubbles

Vortex breakdown bubbles in the flow in a closed cylinder with a rotating end-cover have previously been successfully simulated by axisymmetric codes in the steady range. However, high-resolution experiments indicate a complicated open bubble structure incompatible with axisymmetry. Numerical studies with generic imperfections in the flow have revealed that the axisymmetric bubble is highly sensitive to imperfections, and that this may resolve the apparent paradox. However, little is known about the influence of specific, physical perturbations on the flow structure. We perform fully three-dimensional simulations of the flow with two independent perturbations: an inclination of the fixed cover and a displacement of the rotating cover. We show that perturbations below a realistic experimental uncertainty may give rise to flow structures resembling those obtained in experiments, that the two perturbations may interact and annihilate their effects, and that the fractal dimension associated with the emptying of the bubble can quantitatively be linked to the visual bubble structure.

Observability and detectability of a class of discrete-time stochastic linear systems

In this paper, the problem of stochastic observability and stochastic detectability of a class of discrete-time linear systems affected by independent random perturbations and Markovian jumping is investigated. The definition of stochastic observability adopted here extends to this framework the definition of the wellknown uniform observability of a deterministic discrete-time time-varying linear system. By several examples, we show that the concept of stochastic observability introduced in this paper is less restrictive than those introduced in other existing works and it does not imply always the stochastic detectability as it would be expected. Finally, one proves that this kind of stochastic observability allows us to derive a Barbashin–Krasovskii-type result for exponential stability in mean square.

El Niño and similar perturbation effects on the benthos of the Humboldt, California, and Benguela Current upwelling ecosystems

Abstract. To a certain degree, Eastern Boundary Current (EBC) ecosystems are similar: Cold bottom water from moderate depths, rich in nutrients, is transported to the euphotic zone by a combination of trade winds, Coriolis force and Ekman transport. The resultant high primary production fuels a rich secondary production in the upper pelagic and nearshore zones, but where O2 exchange is restricted, it creates oxygen minimum zones (OMZs) at shelf and upper slope (Humboldt and Benguela Current) or slope depths (California Current). These hypoxic zones host a specifically adapted, small macro- and meiofauna together with giant sulphur bacteria that use nitrate to oxydise H2S. In all EBC, small polychaetes, large nematodes and other opportunistic benthic species have adapted to the hypoxic conditions and co-exist with sulphur bacteria, which seem to be particularly dominant off Peru and Chile. However, a massive reduction of macrobenthos occurs in the core of the OMZ. In the Humboldt Current area the OMZ ranges between <100 and about 600 m, with decreasing thickness in a poleward direction. The OMZ merges into better oxygenated zones towards the deep sea, where large cold-water mega- and macrofauna occupy a dominant role as in the nearshore strip. The Benguela Current OMZ has a similar upper limit but remains shallower. It also hosts giant sulphur bacteria but little is known about the benthic fauna. However, sulphur eruptions and intense hypoxia might preclude the coexistence of significant mega- und macrobenthos. Conversely, off North America the upper limit of the OMZ is considerably deeper (e.g., 500–600 m off California and Oregon), and the lower boundary may exceed 1000m. The properties described are valid for very cold and cold (La Niña and "normal") ENSO conditions with effective upwelling of nutrient-rich bottom water. During warm (El Niño) episodes, warm water masses of low oxygen concentration from oceanic and equatorial regions enter the upwelling zones, bringing a variety of (sub)tropical immigrants. The autochthonous benthic fauna emigrates to deeper water or poleward, or suffers mortality. However, some local macrofaunal species experience important population proliferations, presumably due to improved oxygenation (in the southern hemisphere), higher temperature tolerance, reduced competition or the capability to use different food. Both these negative and positive effects of El Niño influence local artisanal fisheries and the livelihood of coastal populations. In the Humboldt Current system the hypoxic seafloor at outer shelf depths receives important flushing from the equatorial zone, causing havoc on the sulphur bacteria mats and immediate recolonisation of the sediments by mega- and macrofauna. Conversely, off California, the intruding equatorial water masses appear to have lower oxygen than ambient waters, and may cause oxygen deficiency at upper slope depths. Effects of this change have not been studied in detail, although shrimp and other taxa appear to alter their distribution on the continental margin. Other properties and reactions of the two Pacific EBC benthic ecosystems to El Niño seem to differ, too, as does the overall impact of major episodes (e.g., 1982/1983(1984) vs. 1997/1998). The relation of the "Benguela Niño" to ENSO seems unclear although many Pacific-Atlantic ocean and atmosphere teleconnections have been described. Warm, low-oxygen equatorial water seems to be transported into the upwelling area by similar mechanisms as in the Pacific, but most major impacts on the eukaryotic biota obviously come from other, independent perturbations such as an extreme eutrophication of the sediments ensuing in sulphidic eruptions and toxic algal blooms. Similarities and differences of the Humboldt and California Current benthic ecosystems are discussed with particular reference to ENSO impacts since 1972/73. Where there are data available, the authors include the Benguela Current ecosystem as another important, non-Pacific EBC, which also suffers from the effects of hypoxia.