Non-unique Results Research Articles

New-generation maximum entropy method: a Lagrangian-based algorithm for dynamic reconstruction of interferometric data

ABSTRACT Imaging interferometric data in radio astronomy requires the use of non-linear algorithms that rely on different assumptions on the source structure and may produce non-unique results. This is especially true for very long baseline interferometry (VLBI) observations, where the sampling of Fourier space is very sparse. A basic tenet in standard VLBI imaging techniques is to assume that the observed source structure does not evolve during the observation. However, the recent VLBI results of the supermassive black hole at our Galactic Centre (Sagittarius A*), recently reported by the Event Horizon Telescope Collaboration, require the development of dynamic imaging algorithms, since it exhibits variability at minute time-scales. In this paper, we introduce a new non-convex optimization problem that extends the standard maximum entropy method (MEM), for reconstructing intra-observation dynamical images from interferometric data that evolve in every integration time. We present a rigorous mathematical formalism to solve the problem via the primal–dual approach. We build a Newton strategy and we give its numerical complexity. We also give a strategy to iteratively improve the obtained solution and, finally, we define a novel figure of merit to evaluate the quality of the recovered solution. Then, we test the algorithm, called the new-generation MEM (ngMEM), in different synthetic data sets, with increasing difficulty. Finally, we compare it with another well-established dynamical imaging method. Within this comparison, we have identified a significant improvement of the ngMEM reconstructions. Moreover, the evaluation of the integration time evolution scheme and the time contribution showed that this method can play a crucial role in obtaining good dynamic reconstructions.

Ring Repeating Unit: An Upgraded Structure Representation of Linear Condensation Polymers for Property Prediction.

Unique structure representation of polymers plays a crucial role in developing models for polymer property prediction and polymer design by data-centric approaches. Currently, monomer and repeating unit (RU) approximations are widely used to represent polymer structures for generating feature descriptors in the modeling of quantitative structure-property relationships (QSPR). However, such conventional structure representations may not uniquely approximate heterochain polymers due to the diversity of monomer combinations and the potential multi-RUs. In this study, the so-called ring repeating unit (RRU) method that can uniquely represent polymers with a broad range of structure diversity is proposed for the first time. As a proof of concept, an RRU-based QSPR model was developed to predict the associated glass transition temperature (Tg) of polyimides (PIs) with deterministic values. Comprehensive model validations including external, internal, and Y-random validations were performed. Also, an RU-based QSPR model developed based on the same large database of 1321 PIs provides nonunique prediction results, which further prove the necessity of RRU-based structure representation. Promising results obtained by the application of the RRU-based model confirm that the as-developed RRU method provides an effective representation that accurately captures the sequence of repeat units and thus realizes reliable polymer property prediction by data-driven approaches.

Hybrid Fourier series and smoothing spline path non-parametrics estimation model

Pathway analysis is one way to determine whether there is a causal relationship between extrinsic and intrinsic factors. The linearity assumption is something that can change the model. The shape of the model is subject to linearity assumptions. Path analysis is parametric when the linearity assumption is true, whereas non-parametric path analysis is used when the non-linear shape is unknown and there is no knowledge of the data pattern. Non-linear path analysis is used when the non-linear shape and data pattern are unknown. This work aimed to combine the smoothing spline method and the Fourier series method to compute non-parametric path function and it is believed that they would be able to produce more flexible function estimations for data patterns since both have the benefit of being accurate or close to the real data pattern. As a result, we found that Fourier series and smoothing splines can be used in non-parametric path analysis only if the linearity assumption is violated. Non-parametric regression-based path analysis estimators were then obtained using the ordinary least squares (OLS) approach. It uses a non-parametric approach and therefore gives non-unique estimation results.

Non-unique Fixed Points of Self Mappings in Bi-metric Spaces

In this paper, we prove a few non-unique fixed-point results of mapping on a set with bi-metrics using θ – contraction. We also give an example that justifies our results. In the literature, our result generalized many results

Effects of Skin Stimulation on Sensory-Motor Networks Excitability: Possible Implications for Physical Training in Amyotrophic Lateral Sclerosis.

BackgroundMany different trials were assessed for rehabilitation of patients with amyotrophic lateral sclerosis (ALS), with non-unique results. Beside the effects on muscle trophism, some of the encouraging results of physical training could be ascribed to the modulation of cortical excitability, which was found hyperexcited in ALS.ObjectiveThe effects of tactile skin stimulation in the modulation of the sensory-motor integrative networks in healthy subjects were assayed through the paired associative stimulation (PAS) protocol.MethodsIn total, 15 healthy subjects were enrolled. In the standard PAS session, the average amplitude of the motor evoked potential (MEP) after 10 stimuli of transcranial magnetic stimulation (TMS) was measured at the baseline and after the PAS protocol (0, 10, 20, 30, and 60 min). In the skin stimulation session, the average amplitude of the MEP was measured before and after 10 min of skin stimulation over the hand. Subsequently, each subject underwent the PAS stimulation and the measure of the average amplitude of the MEP (0, 10, 20, 30, and 60 min).ResultsThe tactile skin stimulation on healthy subjects increases the PAS-induced sensory-motor network hyperexcitability in healthy subjects.ConclusionSkin stimulation should be avoided in the physiotherapeutic approaches for patients with ALS, given the possible hyperexciting effects on the already upmodulated sensory-motor networks. They can be taken into account for diseases characterized by downregulation of cortical and transcortical networks.

Two‐Dimensional Quantitative Comparison of Density Distributions in Detrital Geochronology and Geochemistry

AbstractDetrital geochronology provides insight into a broad range of Earth Science questions. However, detrital zircon U‐Pb age distributions are inherently univariate, and thus quantitative comparison methods are limited to one‐dimension (1D) and subject to nonunique results due to overlapping age groups. We developed two‐dimensional (2D) quantitative comparison measures for bivariate kernel density estimates (KDEs) and cumulative distribution functions (CDFs). These methods are extensions of 1D quantitative comparison measures commonly used in detrital geochronology: Similarity, Likeness, and Cross‐correlation of KDEs and Kolmogorov‐Smirnov (K‐S) and Kuiper tests of CDFs. We demonstrate the efficacy of these methods by applying them to a global compilation of detrital and igneous zircon univariate U‐Pb data (n = 767,660) and bivariate U‐Pb and Hf (i.e., εHfT) data (n = 114,311) parsed geographically into eight continental landmasses demarcated by Paleozoic sutures. The 2D quantitative comparison measures behave in a similar fashion to their 1D counterparts in terms of sensitivity and consistency regardless of parameterization (e.g., kernel bandwidth and discretization interval). Results show that the detrital record reliably reflects the igneous record for both univariate U‐Pb and bivariate εHfT distributions between 4,400 and 0 Ma. In contrast, 1D and 2D quantitative comparison results differ over the narrower Ediacaran‐Cambrian time interval due to nonunique univariate zircon U‐Pb age groups; the 2D quantitative results consistently identify continental landmasses involved in the formation of Gondwana. We implemented the 2D methods in a new MATLAB‐based graphical user interface, DZstats2D, which is available as open‐source code and as standalone applications for macOS and Windows.

A Novel Scaling Process for the Computation of Multiconductor Transmission-Line Modal Properties Using the Basis Invariance of Total Current and Power

Some modal (or decoupled) transmission-line properties such as per-unit-length impedance, admittance, or characteristic impedance have long been held to be, in general, non-unique. This ambiguity arises from the nature of the similarity transformations used to relate the terminal and modal domains, for which the voltage transformation matrix has been shown to be only loosely related to the corresponding current transformation matrix. Modern methods have attempted to relate the two, but these relations typically rely on arbitrary normalizations, leading to strictly incorrect and/or non-unique results. This work introduces relations between the two transformations, derived from the physical equivalence of total power and currents between the two domains, by which the transformation matrices can be unambiguously related to each other, and the modal properties uniquely solved. This technique allows for the correct extraction of the modal transmission-line properties for any arbitrary system of conductors. Multiple examples are studied to validate the proposed solution process.

Discrete fracture networks modeling of shale gas production and revisit rate transient analysis in heterogeneous fractured reservoirs

Horizontal wells with multiple hydraulic fractures are necessary stimulation technique for economically developing tight and shale gas reservoirs. In such reservoirs, the conventional well-test techniques are not suitable because of ultralow formation permeability. Rate transient analysis (RTA) is the widely used tool for analyzing these reservoirs for the purpose of reserves estimation, hydraulic fracture stimulation optimization, and development planning. However, the conventional rate transient analysis is based on the models that were derived from idealistic assumptions for homogenous reservoirs. In this article, we first review the industry's common practice for rate transient analysis and discuss why the idealized conceptual model may not be adequate for analyzing production data from shale gas reservoirs. Then, a unified shale gas reservoir model based on Discrete Fracture Networks (DFN) is presented to investigate how each mechanism influences shale gas production and the corresponding rate transient behavior. It is found that shale gas production and rate transient behavior are significantly impacted by reservoir heterogeneity, fracture networks, non-Darcy flow, gas adsorption and completion efficiency. Short early-time linear flow with long transitional flow period is an indication of either existence of abundant complex fracture networks or heterogeneous completion with unevenly distributed hydraulic fractures. Consider the nature of non-unique results of RTA, information from other independent sources is required to achieve a consistent and holistic interpretation.

A simple method for calculating in-situ settling velocities of cohesive sediment without fractal dimensions

The settling velocity of sediment flocs is central to the study of the transportation process of contaminants in aqueous ecosystems. To describe the irregular shape of flocs, fractal theory based on the image analysis method is commonly used. However, this method usually leads to non-unique results as it requires the selection of a threshold intensity. Therefore, the main objective of this study is to develop a method to determine the settling velocity of both flocs and particles without using the fractal dimension. To achieve this goal, porosity was introduced as a substitute for the fractal dimension, and a simple method with three variables, floc diameter, mass concentration, and volume concentration of flocs, was developed. A density function method was used to obtain the floc porosity from a laser particle sizer which could obtain the volume concentration of sediment and an optical backscatter point sensor (OBS). Laboratory tests on two sediments from two different lakes were conducted. Results indicate that this method has a higher accuracy than traditional methods such as the Stokes equation and the Rubey equation. The variable density function performed better than the uniform density function and was, therefore, recommended for calculating the settling velocities for both micro and macro flocs. Using the developed method, the drag coefficient for the flocs was calculated and its accuracy analyzed. The method presented in this paper, which is simpler in determining in-situ settling velocities than traditional methods, also allows for direct inter-comparison between results derived from various studies.

Morphometric analysis of plunge pools and sediment wave fields along western Great Bahama Bank

A systematic assessment of morphometric parameters of over 200 plunge pools along the steep escarpment base of western Great Bahama Bank and ~2000km2 of sediment wave fields of upslope migrating cyclic steps documents the importance of cascading density currents for sedimentation on the slope. The abrupt downslope termination of the Holocene mud wedge with the cyclic steps shows that strike parallel bottom currents interacting with the off-bank currents are responsible for slope sediment distribution. The plunge pools and sediment waves were generated by density-cascading and both are related to a hydraulic jump caused by two gradient changes along the slope profile. The bedforms highlight both the erosional and depositional nature of this current regime, which is controlled by slope gradient and the directional confinement by either grooves on the steep escarpment or gullies on the middle to lower slope. The >20m deep plunge pools are ellipsoidal, with an average width of 211m and length of 283m, but variations between 80–360m and 100–650m for width and length occur. They are caused by an average gradient break of 16° on the cemented upper slope. Gradient breaks of as low as 2° are reported to be sufficient to scour a plunge pool like the ones in the study area, but higher gradient breaks between 10 and 20° are quite common for consistent plunge pool development. A second gradient break further down slope changes flow conditions for the generation of cyclic steps, with asymmetric waveforms of 4m high (average) in large wave fields in the entire the study area. Orientation is mainly orthogonal to the main slope direction but wave lengths and sinuosity vary, depending on the morphologic location of the wave field. The comparison with sediment wave fields with similar geometries or in similar environments shows that flow reconstruction based on the wave height and wave length alone along with a characterization of sediment grain size, however, yields non-unique results and is site specific.

On the Brodutch and Modi method of constructing geometric measures of classical and quantum correlations

Recently, Brodutch and Modi proposed a general method of constructing meaningful measures of classical and quantum correlations. We systematically apply this method to obtain geometric classical and quantum correlations based on the Bures and the trace distances for two-qubit Bell diagonal states. Moreover, we argue that in general the Brodutch and Modi method may provide non-unique results, and we show how to modify this method to avoid this issue.

Asymptotic approximation method of force reconstruction: Proof of concept

An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. An alternative approach is developed that draws upon concepts from control systems theory, the equilibrium analysis of linear dynamical systems with time-dependent inputs, and asymptotic approximation analysis. This paper presents the theoretical development of the proposed method. A simple application of the method is presented to demonstrate the procedure. A more complex application to a continuous system is performed to demonstrate the applicability of the method.

Nonunique steady flow solutions for pressure correction equations applied in the regime of natural convection inside free vented enclosures

ABSTRACTThermal buoyancy-driven natural convection in partial enclosures with multiple free openings is investigated regarding the coupling of the pressure correction algorithm with inner-loop iterations of the pressure correction equation. Unexpected steady flow phenomena, i.e., nonunique steady flow states, are observed when different inner-loop iterations m and relaxation factors α of the pressure correction equation are implemented, after the appropriate assumptions on the free opening boundary conditions are made. Numerical experiments and benchmark exercises confirm that definitions on the free openings could be too weak to ensure global similarity to the results of extended domain methodology. Furthermore, inner-loop iteration m and relaxation factor α could have similar effects on the nonunique steady flow results. As thermal Rayleigh number is relatively low, a linear relationship could be established among inner-loop iteration m, relaxation factor α, and mass exchange rate, MER. In addition, harmonic arrangements on the iteration residuals of the momentum equation and the pressure correction equation could accelerate convergence of the whole pressure correction algorithm.

Non-unique results of collisions of quasi-one-dimensional dissipative solitons.

We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counter-propagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasi-one-dimensional objects. As a model, we use coupled cubic-quintic complex Ginzburg-Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic-quintic complex Ginzburg-Landau equation with effective parameters.

Structural identification with incomplete instrumentation and global identifiability requirements under base excitation

Estimating the mass and stiffness parameters of a structural system via its vibration response measurements is the primary objective in the field of modal testing and structural health monitoring. The attainment of this objective, however, is hindered by various practical and theoretical issues. One such issue is incomplete instrumentation, leading to spatially incomplete mode shapes and often nonunique identification results. When the excitation is induced by ground motion, the problem is further complicated because of arbitrary normalization of mode shapes. This study attempts to address these issues for shear-building type structures. Mode shape normalization and expansion approaches are developed that utilize the topology of the structural matrices. Theoretical constraints regarding minimal instrumentation and the necessity for any a priori information are addressed vis-à-vis the requirements for global identifiability. Some practical implementation issues are discussed. The performance of the method is evaluated using numerical simulations and shake table experiments. Copyright © 2015 John Wiley & Sons, Ltd.

Class of compound dissipative solitons as a result of collisions in one and two spatial dimensions.

We study the interaction of quasi-one-dimensional (quasi-1D) dissipative solitons (DSs). Starting with quasi-1D solutions of the cubic-quintic complex Ginzburg-Landau (CGL) equation in their temporally asymptotic state as the initial condition, we find, as a function of the approach velocity and the real part of the cubic interaction of the two counterpropagating envelopes: interpenetration, one compound state made of both envelopes or two compound states. For the latter class both envelopes show DSs superposed at two different locations. The stability of this class of compound states is traced back to the quasilinear growth rate associated with the coupled system. We show that this mechanism also works for 1D coupled cubic-quintic CGL equations. For quasi-1D states that are not in their asymptotic state before the collision, a breakup along the crest can be observed, leading to nonunique results after the collision of quasi-1D states.

Accurate Prediction of Device Performance Based on 2-D Carrier Profiles in the Presence of Extensive Mobile Carrier Diffusion

In this paper, we illustrate how high-resolution 2-D carrier profiles from scanning spreading resistance microscopy (SSRM) can be used to predict and understand device performance of dynamic random access memory peripheral transistors with high-k metal gate and ultrashallow junctions. In an earlier study on high-speed complementary metal-oxide-semiconductor logic, the 2-D carrier profiles from SSRM were used as the active 2-D dopant profile input to the device simulator as they are virtually identical. The extensive mobile carrier diffusion caused by the lower concentrations, however, implies a strong difference between the mobile carrier distribution and the dopant distribution such that the same approach is no longer valid. Ideally one would have to generate, based on the carrier profiles, the active dopant distribution through the inverse solution of the Poisson equation (in two dimensions) which is, however, numerically nontrivial and often leads to nonunique results. Therefore, an alternative approach is proposed here, whereby we fine-tune the process simulations such that the resulting simulated carrier profiles match the 2-D SSRM profiles. Upon reaching satisfactory agreement, the simulated profiles can be used as input for a device simulator and be used to predict sensitive device parameters such as drain-induced barrier lowering and threshold voltage rolloff.

Assessing Vadose Zone Biodegradation by a Multicomponent Gas Transport Model

This study calibrated a gas transport model that uses multicomponent approaches, i.e., the dusty gas model (DGM) and Stefan–Maxwell (SM) equations, to soil gas concentration depth profiles to determine aerobic biodegradation rates of hydrocarbons in unsaturated soils. I found that viscous advection induced by multicomponent gas transport in porous systems and Knudsen diffusion may be neglected for soil systems with intrinsic permeabilities >10−13 m2, and intrinsic permeability of low‐permeability layers, such as cemented limestone or concrete pavement on the ground surface, calibrated by the DGM model ranged from 10−15 to 10−18 m2. The SM model may be applicable for gas transport in soil systems with low‐permeability layers if low obstruction factor values are assigned for these layers. The obstruction factor defined in the DGM and SM equations accounts for impedance to gas diffusion in unsaturated soils and is similar to tortuosity for Fick's law of diffusion. Results further showed that flux rates of hydrocarbon vapors from sources in unsaturated soils need to be measured or assessed before models are fitted to hydrocarbon vapor depth profiles. If the flux rates are not assessed, and if the obstruction factor and intrinsic permeability in the low‐permeability layers are of uncertain magnitudes, models may produce nonunique results for biodegradation rates of hydrocarbons. Thus, I propose a two‐step procedure for determining aerobic biodegradation rates of hydrocarbons.

Modal parameter based structural identification using input–output data: Minimal instrumentation and global identifiability issues

It is of interest to the modal testing and structural health monitoring community to be able to identify the mass and stiffness parameters of a system from its vibration response measurements. On the other hand, incomplete instrumentation of the monitored system results in measured mode shapes which are incomplete and may lead to non-unique identification results. In this study, the problem of mass normalized mode shape expansion, and subsequent physical parameter identification, for shear-type structural systems with input–output measurements is investigated. While developing a mode shape expansion algorithm, the issue of global identifiability of the system is also addressed vis-à-vis instrumentation set-ups. Several possible minimal and near-minimal instrumentation set-ups which guarantee a unique estimation of the unmeasured mode shape components from the measured components are identified for various experimental designs. An input–output balance approach, applicable to any general structural model, is proposed to mass normalize the mode shape components observed at the instrumented degrees of freedom. Using the proposed mode shape expansion and the input–output balance procedures, along with the modal orthogonality relations, the mass and stiffness matrices of the system can be estimated. The advantage of the algorithm lies in its ability to obtain a reliably accurate identification using the minimal necessary instrumentation with no a priori mass or stiffness information. The performance of the proposed algorithm is finally discussed through numerical simulations of forced vibration experiments on a 7 degree of freedom shear-type system.

A procedure for the three-mode analysis of compositions

The Tucker3 model is one of the most widely used tools for factorial analysis of three-way data arrays. When orthogonal factors are extracted this model can be seen as a three-way PCA (principal component analysis). The Tucker3 model is characterized by extreme flexibility as it allows for the use of a different number of factors in each mode and it yields non-unique results. This adaptability makes the Tucker3 model extremely effective for decomposition and compression of data in many applications and fields. When this model is applied to vectors of non-negative values with a sum constraint all problems connected with the statistical analysis of compositions must be taken into consideration. Like other standard statistical techniques, this model cannot be directly applied. The aim of this paper is to present the theory behind the correct application of the Tucker3 model on compositional data and to describe the TUCKALS3 algorithm.