Deterministic Correlations Research Articles

CAB‐Net: Convolutional attention BLSTM network for enhanced leukocyte classification

AbstractIn recent years, deep learning techniques have been increasingly utilized to automate and reduce human errors in leukocyte classification. However, reliability and accuracy issues remain a challenge. This paper proposes CAB‐Net, an end‐to‐end deep learning‐based model that integrates a convolutional neural network with an attention mechanism and BLSTM. The model uses a stack of convolutional and pooling layers to extract initial features from input images, which are then fed into the attention block to generate class‐specific discriminative features and BLSTM employed to model deterministic class correlations between highlighted discriminative features and labels. Experimental results show that CAB‐Net outperforms state‐of‐the‐art methods in term of accuracy, precision, recall, F1‐Score, and AUC‐ROC. In addition, the CAB‐Net model demonstrates good performance even with low‐resolution images. Consequently, CAB‐Net can be considered as the current state‐of‐the‐art prediction model for improving leukocyte classification in clinical environments.

Deterministic correlations enhance synchronization in oscillator populations with heterogeneous coupling.

Synchronization is a critical phenomenon that displays a pivotal role in a wealth of dynamical processes ranging from natural to artificial systems. Here, we untangle the synchronization optimization in a system of globally coupled phase oscillators incorporating heterogeneous interactions encoded by the deterministic-random coupling. We uncover that, within the given restriction, the added deterministic correlations can profoundly enhance the synchronizability in comparison with the uncorrelated scenario. The critical points manifesting the onset of synchronization and desynchronization transitions, as well as the level of phase coherence, are significantly shaped by the increment of deterministic correlations. In particular, we provide an analytical treatment to properly ground the mechanism underlying synchronization enhancement and substantiate that the analytical predictions are in fair agreement with the numerical simulations. This study is a step forward in highlighting the importance of heterogeneous coupling among dynamical agents, which provides insights for control strategies of synchronization in complex systems.

Features of the Relaxation Process in an RC Circuit under the Influence of a Sinusoidal Voltage

The article is devoted to the study of the properties of the relaxation process in a nonlinear electrical circuit under the sinusoidal voltage influence. Electronic devices and processes the operation of which is based on relaxation principles are sources of specific series of pulses, the monitoring of which allows one to draw conclusions about the technical parameters of these devices and processes. The occurrence of a series of partial discharges in a high-voltage device can serve as an example. An essential factor of partial discharges is their multiplicity both in time and in space, which are dispersed in an a priori unknown number of defects. The aim is to determine the number of defects and to perform appropriate grouping of the entire set of partial discharges by defects. Internal deterministic correlations derived as a result of solving the problem and presented in terms of the classical theory of electrical circuits should be regarded as a key to solving the problem that was set forth. Analytical correlations for the deterministic component of partial discharges in potential electrical insulation defects are revealed. The obtained correlations characterize the time intervals between individual discharges inside the insulation defect. These time intervals are uniquely related to the defect parameters and can serve as a basis for identifying this defect against the background of other partial discharges. As an example, the result of mathematically modeling a relaxation process with the specified parameters is given.

Investigation of Unsteady Rotor–Stator Interaction and Deterministic Correlation Analysis in a Transonic Compressor Stage

Abstract Unsteady blade row interaction (UBRI) has a large impact on performance in high-speed axial compressors. Thus, the influence of UBRI should be accurately predicted in compressor routine design. In this study, the unsteady rotor–stator interaction in a transonic single-stage compressor, NASA Stage 35, is studied by steady and unsteady Reynolds-Averaged Navier–Stokes methods. First, the UBRI is analyzed. Periodic separation bubbles on the stator suction surface induced by the rotor wake are observed. Comparisons between steady and unsteady results show that the radial distribution of flow angle near the hub and tip region of the stator is strongly influenced by UBRI. Second, deterministic correlations are analyzed based on the average-passage equation system. The distribution of deterministic stress and the relationship between spatial correlations and deterministic correlations are analyzed. Results show that a strong nonlinear interaction caused by the rotor wake and the stator potential field is found in the rotor–stator gap, which is responsible for the generation of spatial–time correlation. Then, the anisotropy of deterministic correlations is analyzed using the Lumley triangle. Results show that the deterministic stress is highly anisotropic in the stator passage, which can be considered in the modeling using a similar strategy of turbulence modeling. At last, the relationships between the harmonics and decay rate of deterministic correlations are analyzed. The decay rate of deterministic correlation is highly related to the corresponding harmonics, and the higher-order harmonic exhibits a higher decay rate. A modified exponential decay model is proposed for deterministic correlation based on harmonics, which provides improved performance.

Dancing with Bubbles: Deterministic versus Probabilistic Bubble Models in Dense Phase Sand Fluidized Beds for Biomass Gasification

This study addresses the need to model bubble flow in a fluidized bed using a probabilistic approach, which includes intrinsic bubble flow randomness. It is shown that the proposed probabilistic predictive model (PPM) overcomes the limitations of deterministic correlations, commonly used to describe bubble dynamics in high-density (above 2000 kg/m3) sand-beds of Type B particles of the Geldart classification. It is proven that a PPM can describe the relationship between bubble axial chord and bubble rise velocity using minimum and maximum behavioral bands. This probabilistic model, which applies to a wide range of operating conditions, as shown in the present study, can be considered applicable to single bubbles injected at incipient fluidization, as well as to bubbly beds with and without loaded biomass pellets.

Correlations and Bath’s law

Bath’s empirical law is derived from the magnitude-difference statistical distribution of earthquake pairs. The pair (two-event, bivariate) distribution related to earthquake correlations is presented. The single-event distribution of dynamically-correlated earthquakes is derived, by means of the geometric-growth model of energy accumulation in the focal region. It is shown that the dynamical correlations may account, at least partially, for the roll-off effect in the Gutenberg-Richter distributions. The extension of the magnitude difference to negative values (by observing the order of the members of the pair) leads to a vanishing mean value of the magnitude difference and to the standard deviation as a measure of its variations. It is suggested that the standard deviation of the magnitude difference is the average difference in magnitude between the main shock and its largest aftershock (foreshock), thus providing an insight into the nature and the origin of Bath’s law. Earthquake purely statistical correlations and deterministic time-magnitude correlations of the accompanying seismic activity are also presented.

Privacy-Preserving Correlated Data Publication: Privacy Analysis and Optimal Noise Design

The privacy issue in data publication is critical and has been extensively studied. Correlation is unavoidable in data publication, which universally manifests intrinsic correlations owing to social, physical, behavioral, and genetic relationships. However, most of the existing works assume that private data is independent, i.e., the correlation among data is neglected. In this paper, we investigate the privacy concern of data publication where deterministic and probabilistic correlations are considered, respectively. Specifically, $(\varepsilon, \delta)$ -multi-dimensional data-privacy (MDDP) is proposed to quantify the correlated data privacy. It characterizes the disclosure probability of the published data being jointly estimated with the correlation under a given accuracy. Then, we explore the effects of deterministic and probabilistic correlations on privacy disclosure, respectively. For both kinds of correlations, it is shown that the privacy disclosure with correlations increases compared to the one without correlation knowledge. Meanwhile, a closed-form expression of disclosure probability and a strict bound of privacy disclosure gain are derived, respectively. To minimize the disclosure probability, we provide the optimal noise distribution in the sense of $(\varepsilon, \delta)$ -MDDP. Extensive simulations on a real dataset verify our analytical results.

Variance Swaps with Deterministic and Stochastic Correlations

As market observations say that many financial quantities are correlated in a time dependent, nonlinear or unpredictable way, in this study, we present an approach to price discretely sampled variance swaps based on the Heston model extended by incorporating deterministic or stochastic correlation between an underlying asset and its variance. We obtain a closed form exact formula for the fair delivery prices under the deterministic correlation model and an affine approximation formula under the stochastic correlation model. A comparison with Monte–Carlo simulations supports the validity of the pricing formulas. Based on the analytic results, we find that the fair delivery price increases as time to maturity or leverage effect increases or sampling frequency decreases. On the other hand, the impact scale of the correlation volatility is so imperceptible that the time dependent deterministic correlation model can still be a good proxy of the stochastic correlation environment in the case of variance swap pricing, while the approximation formula with the stochastic correlation is better than the exact formula with the deterministic correlation in computing sense.

An Exponential Decay Model for the Deterministic Correlations in Axial Compressors

The unsteady blade row interaction (UBRI) is inherent and usually has a large effect on performance in multistage axial compressors. The effect could be considered by using the average-passage equation system (APES) in steady-state environment by introducing the deterministic correlations (DC). How to model the DC is the key in APES method. The primary purpose of this study is to develop a DC model for compressor routine design. The APES technique is investigated by using a 3D viscous unsteady and time-averaging Computational fluid dynamics (CFD) flow solver developed in our previous studies. Based on DC characteristics and its effects on time-averaged flow, an exponential decay DC model is proposed and implemented into the developed time-averaging solver. Steady, unsteady, and time-averaging simulations are conducted on the investigation of the UBRI and the DC model in the first transonic stage of NASA 67 and the first two stages of a multistage compressor. The DC distributions and mean flow fields from the DC model are compared with the unsteady simulations. The comparison indicates that the proposed model can take into account the major part of UBRI and provide significant improvements for predicting compressor characteristics and spanwise distributions of flow properties in axial compressors, compared with the steady mixing plane method.

Development of region-specific soil behavior type index correlations for evaluating liquefaction hazard in Christchurch, New Zealand

Utilizing an unprecedented database of field and laboratory test data from Christchurch, New Zealand, this study develops deterministic and probabilistic correlations relating the soil behavior type index (Ic) to laboratory test-based liquefaction susceptibility and fines content. The proposed Ic correlations are in turn used to assess liquefaction hazard for 9623 case studies compiled from three earthquakes that impacted Christchurch, New Zealand, wherein the predicted liquefaction severity is compared to post-earthquake field observations. Furthermore, the accuracy of the predictions based on the region-specific Ic correlations are compared to those made using generic Ic correlations. The use of the Christchurch-specific Ic correlations, in general, only slightly improved the liquefaction severity predictions. These findings could be a result of shortcomings in the procedures used to predict liquefaction triggering and/or liquefaction manifestations. Nevertheless, the findings give credence to the use of generic correlations for typical projects. Finally, the overall framework of the study used herein can be applied to worldwide locals and is not just limited for use in the Canterbury region of New Zealand.

Investigation of Unsteady Flow Interactions in a Transonic High Pressure Turbine Using Nonlinear Harmonic Method

The performance of a transonic high pressure turbine is mainly influenced by the unsteady interactions associated with the passing blades. In this paper, the unsteady flow interactions in a transonic turbine have been numerically investigated using the nonlinear harmonic (NLH) method in comparison with the steady and unsteady Reynolds-averaged Navier–Stokes (RANS). The comparison shows that the NLH method using three harmonics could capture the main unsteady flow interactions efficiently with about seven times smaller computational cost than the unsteady RANS, resulting in a more accurate time-averaged flow than for steady RANS. However, the continuity of the flow variables across the rotor-stator interface has shown some discrepancies compared with the unsteady RANS, which can be further satisfied by increasing the numbers of harmonics. The unsteady interactions are analyzed in detail; the results show that the wake and trailing edge shock from the upstream stator are the major sources of unsteadiness in the downstream rotor passage. The stator trailing edge shock impinges on the suction side of the passing rotor blades and generates pressure waves. These pressure waves are periodically reflected back to trigger the stator wake shedding. These waves are strong enough to travel through the rotor passage, and eventually affect the flow at the rotor’s trailing edge. The stator wakes are chopped by the downstream rotor, and travel through the rotor passage. This significantly enhances the unsteadiness of the flow near the rotor trailing edge. Lastly, the deterministic stresses and enthalpy distributions extracted from the NLH method have revealed that the effects of the unsteadiness are relatively weaker in the axial direction. Furthermore, the deterministic correlations analysis has shown that, some empirical deterministic correlations models based on the decay concept of compressors are not suitable for turbines.

Covariance Bell inequalities

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Monte Carlo Approach for Estimating Density and Atomic Number From Dual‐Energy Computed Tomography Images of Carbonate Rocks

AbstractWe develop a new Monte Carlo‐based inversion method for estimating electron density and effective atomic number from 3‐D dual‐energy computed tomography (CT) core scans. The method accounts for uncertainties in X‐ray attenuation coefficients resulting from the polychromatic nature of X‐ray beam sources of medical and industrial scanners, in addition to delivering uncertainty estimates of inversion products. Estimation of electron density and effective atomic number from CT core scans enables direct deterministic or statistical correlations with salient rock properties for improved petrophysical evaluation; this condition is specifically important in media such as vuggy carbonates where CT resolution better captures core heterogeneity that dominates fluid flow properties. Verification tests of the inversion method performed on a set of highly heterogeneous carbonate cores yield very good agreement with in situ borehole measurements of density and photoelectric factor.

WEAK DIFFUSION LIMITS OF DYNAMIC CONDITIONAL CORRELATION MODELS

The properties of dynamic conditional correlation (DCC) models, introduced more than a decade ago, are still not entirely known. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a nondegenerate diffusion limit can be obtained. Alternative sets of conditions are considered for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the often used quasi-approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may provide reasonable approximations for sufficiently large frequencies and sample sizes.

Investigation of model development for deterministic correlations associated with impeller-diffuser interactions in centrifugal compressors

The average-passage equation system (APES) provides a rigorous framework to account for the deterministic unsteady effects by the so-called deterministic correlations (DC), which include both deterministic stress correlations (DCS) and deterministic total enthalpy correlations (DCH). These correlations should be modeled to close the system of equations. In this paper, the distribution of DC in a transonic centrifugal compressor is presented, and its relative importance is revealed. The assumption made by Adamczyk that the pure unsteady fluctuation is significantly smaller than the spatial fluctuation is verified at the impeller-diffuser interface. The decomposition of DCH is also discussed to determine its two different physical mechanisms. Finally, the transport equations in terms of DCS in cylindrical coordinates are derived, and the terms are evaluated to determine the ones that are necessary to model. All these analyses significantly contribute to our model development for DC in centrifugal compressors.

Assessing the challenges of a pulse wave velocity based blood pressure measurement in surgical patients.

Development of a continuous noninvasive blood pressure (cNIBP) monitor that is unobtrusive to patients is an attractive alternative to the cuff based measurements performed on medical-surgical floors in the hospital. Pulse wave velocity (PWV) provides a means to continuously monitor blood pressure in these patients. However, a PWV based cNIBP monitor faces a number of challenges in order to accurately measure blood pressure. In our study, we investigated some of the challenges faced by a body-worn cNIBP monitor (i.e. ViSi Mobile) on data collected on patients undergoing surgery. Results indicated that 1) pulse arrival time (PAT) values from ViSi Mobile were well correlated with PAT values obtained from an invasive reference; 2) the reciprocal of the PAT measurements were linearly correlated with blood pressure but the calibration curve was altered by administration of certain vasoactive substances; and 3) there are deterministic correlations between systolic pressure, diastolic pressure and the corresponding mean arterial pressure over a wide range of blood pressure values.

Numerical investigations of impeller–diffuser interactions in a transonic centrifugal compressor stage using nonlinear harmonic method

Numerical investigations have been conducted on a transonic centrifugal compressor stage with a vaned diffuser. Due to the high loading and small radial gap between the impeller and diffuser, the unsteady impeller–diffuser interactions can be very large compared with axial compressors, and this has a significant impact on the time-averaged performance of a centrifugal compressor stage. Steady, unsteady and NonLinear Harmonic (NLH) simulations have been carried out to study the interactions in a transonic centrifugal compressor. Comparisons have been made against the overall performance and flow details. The distribution of deterministic correlations are extracted and compared to show the effect of unsteadiness due to impeller–diffuser interactions. All of these analyses show that the NLH method gains more accuracy compared with the steady-state mixing plane simulation and saves CPU time compared with an unsteady time-accurate computation. NLH and unsteady methods are in good agreement in overall performance predictions compared with the steady-state mixing plane method while small differences still exist in flow details. In general, the NLH method obtains good accuracy in terms of both deterministic stress and enthalpy correlations which are sufficiently accurate to be directly used in model development in the average-passage equation system instead of the more time-consuming unsteady simulation.

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique. Then steady and unsteady simulations are conducted in a transonic compressor stage. The results from both simulations are compared to highlight the significance of the unsteady interactions. Furthermore, the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC). Lastly, steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results. The results from steady and time-averaging simulations are compared with the time-averaged unsteady results. The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system. The primary purpose of this study was to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 2 of this two-part paper, the influence of DC on the time-averaged flow field was systematically studied. Several time-averaging computations were conducted with various boundary conditions and DC for the downstream stator in a transonic compressor stage, by employing the CFD solver developed in Part 1 of this two-part paper. These results were compared with the time-averaged unsteady flow field and the steady one. The study indicated that the circumferential-averaged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compressors. Furthermore, it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.

Complex Networks, Fractals and Topology Trends for Oxidative Activity of DNA in Cells for Populations of Fluorescing Neutrophils in Medical Diagnostics

A novel nonlinear statistical method of immunofluorescence data analysis is presented. The data of DNA fluorescence due to oxidative activity in neutrophils nuclei of peripheral blood is analyzed. Histograms of photon counts statistics are generated using flow cytometry method. The histograms represent the distributions of fluorescence flash frequency as functions of intensity for large populations∼104-105 of fluorescing cells. We have shown that these experiments present 3D-correlations of oxidative activity of DNA for full chromosomes set in cells with spatial resolution of measurements is about few nanometers in the flow direction the jet of blood. Detailed analysis showed that large-scale correlations in oxidative activity of DNA in cells are described as networks of small- worlds (complex systems with logarithmic scaling) with self own small-world networks for given donor at given time for all states of health. We observed changes in fractal networks of oxidative activity of DNA in neutrophils in vivo and during medical treatments for classification and diagnostics of pathologies for wide spectra of diseases. Our approach based on analysis of changes topology of networks (fractal dimension) at variation the scales of networks. We produce the general estimation of health status of a given donor in a form of yes/no of answers (healthy/sick) in the dependence on the sign of plus/minus in the trends change of fractal dimensions due to decreasing the scale of nets. We had noted the increasing biodiversity of neutrophils and stochastic (Brownian) character of intercellular correlations of different neutrophils in the blood of healthy donor. In the blood of sick people we observed the deterministic cell-cell correlations of neutrophils and decreasing their biodiversity.