Exponential Loss Research Articles

Cumulative Residual Extropy for Pareto Distribution in the Presence of Outliers: Bayesian and Non-Bayesian Methods

The extropy is considered to be a complementary dual of the well-known Shannon’s entropy and has wide applications in many fields. This article discusses estimating the extropy and cumulative residual extropy of the Pareto distribution using the maximum likelihood and Bayesian methods. We obtain the maximum likelihood of extropies measures in presence of outliers. These estimators are specialized to homogenous case. The Bayesian estimators of both extropy measures are derived based on symmetric and asymmetric loss functions. The Markov chain Monte Carlo methods are used to accomplish some complex calculations. The precision of the Bayesian and the maximum likelihood estimates for extropy estimates are examined through simulations. Regarding results of simulation study, we conclude that the performances of both estimation methods improve with sample sizes. Also, Bayesian estimates of the extropy and cumulative residual extropy under linear exponential loss function are superior to the other Bayesian estimates under the other loss functions in most of cases. The performance for the extropy and cumulative residual extropy estimates increase with number of outliers in almost cases. Generally, there is a great agreement between the theoretical and empirical results. Further performance comparison is conducted by the experiments with real data.

Asymmetric Power Hazard Distribution for COVID-19 Mortality Rate under Adaptive Type-II Progressive Censoring: Theory and Inferences.

This article investigates the estimation of the parameters for power hazard function distribution and some lifetime indices such as reliability function, hazard rate function, and coefficient of variation based on adaptive Type-II progressive censoring. From the perspective of frequentism, we derive the point estimations through the method of maximum likelihood estimation. Besides, delta method is implemented to construct the variances of the reliability characteristics. Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under squared error and linear exponential loss functions. Also, the corresponding credible intervals are constructed. A simulation study is utilized to assay the performance of the proposed methods. Finally, a real data set of COVID-19 mortality rate is analyzed to validate the introduced inference methods.

A tighter proof for CCA secure inner product functional encryption: Genericity meets efficiency

Inner product functional encryption (IPFE) is a primitive which produces, from a master secret key, decryption keys skk associated to vectors k over some specified base ring. Decrypting an encryption of vector m with skk only reveals 〈k,m〉. Benhamouda et al. [7] provided a generic construction for CCA-secure IPFE from projective hash functions (PHFs), unfortunately their security reduction suffers an exponential loss. Their only instantiation capable of decrypting inner products of large sizes, which relies on the decisional composite residuosity (DCR) assumption, is impractical due to the large size of ciphertexts, decryption keys, and the prohibitive speed of the scheme. Our core contribution is a new approach to proving CCA security. Our constructions maintain the genericity of [7], while our security proof relaxes the requirements on the underlying PHFs and gains in reduction tightness. We instantiate these constructions from the DCR assumption, an assumption in class groups (HSMCL) and the decision Diffie Hellman (DDH) assumption. Our CCA-secure constructions from DCR and HSMCL are the first such schemes to efficiently decrypt inner products of large size, improving by multiple orders of magnitude upon the work of [7]. A single-core C implementation of these schemes shows that, for a 112 bit security, and 100-dimensional vectors, their DCR-based scheme takes 1 h 20 min to encrypt, and over 5 min to decrypt, whereas our slowest scheme takes 5.2 s to encrypt and 0.5 s to decrypt. Similarly a ciphertext for their scheme is of 283 MB; those of our HSMCL-based scheme are of 30 kB.

Posterior Estimates for the Parameter of the Poisson Distribution by Using Two Different Loss Functions

In this paper, Bayes estimators of Poisson distribution have been derived by using two loss functions: the squared error loss function and the proposed exponential loss function in this study, based on different priors classified as the two different informative prior distributions represented by erlang and inverse levy prior distributions and non-informative prior for the shape parameter of Poisson distribution. The maximum likelihood estimator (MLE) of the Poisson distribution has also been derived. A simulation study has been fulfilled to compare the accuracy of the Bayes estimates with the corresponding maximum likelihood estimate (MLE) of the Poisson distribution based on the root mean squared error (RMSE) for different cases of the parameter of the Poisson distribution and different sample sizes.

Exponential Loss Minimization for Learning Weighted Naive Bayes Classifiers

The naive Bayesian classification method has received significant attention in the field of supervised learning. This method has an unrealistic assumption in that it views all attributes as equally important. Attribute weighting is one of the methods used to alleviate this assumption and consequently improve the performance of the naive Bayes classification. This study, with a focus on nonlinear optimization problems, proposes four attribute weighting methods by minimizing four different loss functions. The proposed loss functions belong to a family of exponential functions that makes the optimization problems more straightforward to solve, provides analytical properties of the trained classifier, and allows for the simple modification of the loss function such that the naive Bayes classifier becomes robust to noisy instances. This research begins with a typical exponential loss which is sensitive to noise and provides a series of its modifications to make naive Bayes classifiers more robust to noisy instances. Based on numerical experiments conducted using 28 datasets from the UCI machine learning repository, we confirmed that the proposed scheme successfully determines optimal attribute weights and improves the classification performance.

Autoencoders with Exponential Deviation Loss for Weakly Supervised Anomaly Detection

Autoencoders with Exponential Deviation Loss for Weakly Supervised Anomaly Detection

Bayesian Risk Analysis for Length Biased Log Logistic Distribution Under Different Loss

The aim of this paper is parametric and reliability estimation for the two parameter length biased log-logistic distribution under squared error, generalized exponential, linear exponential and precautionary loss functions. Bayes estimates obtained under non informative priors through Lindleys approximation and through Markov Chain Monte Carlo are then compared with the classical parametric estimates. Bayesian risk analysis based on a simulated and a real data set are used to demonstrate application of the theoretic results.

Security Performance Analysis of a NOMA-Assisted Underwater VLC System Under Imprecise Channel Estimations

The accurate estimation of underwater Visible Light Communication (VLC) channel conditions is challenging due to its widespread attenuation and scattering effects. The channel attenuation is a linear function of frequency and causes exponential signal power loss whereas due to the scattering effect, numerous photons are statistically generated as light beams strike water molecules and there arise security concerns. Assuming realistic underwater conditions, this paper investigates the security performance of a typical Non-Orthogonal Multiple Access (NOMA)-assisted underwater VLC system. It consists of a Floating Vehicle Transmitter (FVT), equipped with multiple Light Emitting Diodes (LEDs) to transmit the signal to two legitimate near-end and far-end Underwater Vehicles (UVs) in presence of an active/passive eavesdropper. The Channel State Information (CSI) of each transmitting link is estimated with the use of a Minimum Mean Square Error (MMSE) technique. Furthermore, we propose a LED selection mechanism to select an LED that can achieve the highest secrecy rate defined under the constraints of known and unknown CSI of legitimate and/or eavesdropping links. Using the Successive Interference Cancellation (SIC) technique, a novel closed-form secrecy outage probability expressions for the conventional single-LED and multi-LED NOMA-VLC links for both known and unknown CSI scenarios is derived. The security performance of the proposed multi-LED NOMA-VLC system is compared with the conventional single-LED NOMA-VLC system under the effect of air bubbles for both fresh and salty water. Finally, we verify the validity of the numerical results through Monte-carlo simulation analysis.

Applicability Analysis of Different Runoff Schemes of the Gulang River Basin in Arid Region of Gansu Province, China

[Background] Mountain torrent disasters are one of the deadliest weather-related natural disasters in the world, often causing extremely serious economic and property losses and casualties; in recent years, due to heavy rainfall and complex geological and geomorphological conditions, mountain torrent disasters have occurred frequently in Gansu Province. An effective rainfall-runoff model is the key to prevent them. There are still many problems about how to establish suitable hydrological models in the arid basin of China. [Methods] Therefore, the Gulang River Basin in Gansu Province was selected as the research area to construct the HEC-HMS rainfall-runoff model; through the screening of different runoff methods, different runoff schemes were established to explore the optimal runoff algorithm for the arid basin; there are mainly SCS-CN method, initial and constant method, Green and Ampt method and exponential loss method in runoff generation; SCS unit hydrograph and Clark unit hydrograph methods are selected for slope transform, kinematic wave and lag algorithms for channel routing, totally 16 different runoff schemes. Three floods in the Gulang River Basin are selected to analyze the simulation effect of different runoff schemes in Gulang River Basin. [Results]1) If the Nash-Sutcliffe efficiency coefficient is selected as the evaluation index, the best simulation results are schemes 1 and 16 in the 20180826 flood, schemes 2 and 1 in the 20190626 flood and schemes 1 and 3 in the 20190911 flood. If the percentage of flood peak error is selected as the evaluation index, the best simulation results are schemes 16 and 1 in the 20180826 flood, schemes 9 and 6 in the 20190626 flood and schemes 13 and 4 in the 20190911 flood.If the percentage of runoff depth error is selected as indicator, the best simulation results are schemes 1 and 8 in the 20180826 flood, schemes 7 and 8 in the 20190626 flood and schemes 6 and 13 in the 20190911 flood. 2)The mean value of Nash-Sutcliffe efficiency coefficient obtained by the SCS-CN method for runoff generation, the SCS unit hydrograph for slope transform and the lag algorithm for channel routing are 0.8, 0.65 and 0.65, respectively; the mean absolute percentage errors of flood peak are 9.29%, 9.71% and 8.47%, respectively; the mean absolute percentage errors of runoff depth are 6.07%, 7.17% and 7.74%, respectively; the mean time difference of flood peak of SCS unit hydrograph for slope transform and lag algorithm for channel routing are 1.21 hour and 1.5 hour, respectively.[Conclusion]The most suitable scheme is the combination of the SCS-CN method for runoff generation, SCS unit hydrograph for slope transform, and lag algorithm for channel routing. The results can provide a certain reference for the prevention of flood disasters in the arid region of Gansu Province.

Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application

In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one‐selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.

A proof of consistency of the MLE for nonlinear Markov-switching AR processes

We propose a new approach to demonstrate the consistency of the maximum likelihood estimator for nonlinear Markov-switching AR processes (abbreviated MS-NAR). We obtain a uniform exponential memory loss property for the prediction filter by approximating it by a filter with finite memory. From the α-mixing property for the MS-NAR process we obtain an ergodic theorem. Finally, we show that in the linear and Gaussian case our assumptions are fully satisfied.

Utilizing a degradation prediction pathway system to understand how a novel methacrylate derivative polymer with flipped external ester groups retains physico-mechanical properties following esterase exposure

ObjectiveThe region of failure for current methacrylates (i.e. derivatives of acrylates) are ester bond linkages that hydrolyze in the presence of salivary and bacterial esterases that break the polymer network backbone. This effect decreases the mechanical properties of methacrylate-based materials. MethodsThe ethylene glycol dimethacrylate (EGDMA) or novel ethylene glycol ethyl methacrylate (EGEMA) discs were prepared using 40 µL of the curing mixture containing photo/co-initiators for 40 s in a PTFE mold at 1000 mW/cm2. The degree of conversion was used as a quality control measure for the prepared discs, followed by physical, mechanical, and chemical characterization of discs properties before and after cholesterol esterase treatment. ResultsAfter 9 weeks of standardized cholesterol esterase (CEase) exposure, EGDMA discs showed exponential loss of material (p = 0.0296), strength (p = 0.0014) and increased water sorption (p = 0.0002) compared to EGEMA discs. We integrated a degradation prediction pathway system to LC/MS and GC/MS analyses to elucidate the degradation by-products of both EGEMA and EGDMA polymers. GC/MS analysis demonstrated that the esterase catalysis was directed to central polymer backbone breakage, producing ethylene glycol, for EGDMA, and to side chain breakage, producing ethanol, for EGEMA. The flipped external ester group linkage design is attributed to EGEMA showing higher resistance to esterase biodegradation and changes in mechanical and physical properties than EGDMA. SignificanceEGEMA is a potential substitute for common macromer diluents, such as EGDMA, based on its resistance to biodegradation effects. This work inspires the flipped external group design to be applied to analogs of current larger, hydrophobic strength bearing macromers used in future dental material formulations.

Classical and objective Bayesian estimation and confidence intervals of an asymmetric loss based capability index Cpmk′$\mathcal {C}^{\prime }_{pmk}$

AbstractIn this paper, we introduce a new process capability index, based on an asymmetric loss function (linear exponential) for normal process. To estimate , we first obtain eight different classical methods of estimation and then consider objective Bayesian methods of estimation under the squared error loss function and the linear exponential loss function. Extensive simulations are carried out to investigate the performance of these estimation methods in terms of the mean squared errors. In addition, we compare the performance of four bootstrap confidence intervals and the highest posterior density interval of in terms of average width and coverage probability. Finally, three real‐data applications from electronic industries are provided for illustrative purposes.

Quantum entanglement creation for distant quantum memories via time-bin multiplexing

Quantum networks require parallel quantum entanglement between pairs of distant quantum memories (QMs) for practical applications. However, usually one pair of QMs is entangled using a single photonic pulse and multiple pulses are consumed to generate parallel entanglement between pairs of QMs. We propose a multiplexing method for simultaneously entangling multiple pairs of QMs located in two distant nodes. A single photon with high-dimensional encoding first entangles with all QMs in one node, leading to hybrid entanglement between a high-dimensional photon and two-dimensional QMs, and then it interacts with QMs in the other node and converts the hybrid entanglement to entanglement between multiple pairs of QMs in a heralded way. This can significantly increase the efficiency of large-scale quantum networks by reducing the exponential transmission loss via time-bin multiplexing. Furthermore, this protocol presents a specific connection between high-dimensional and two-dimensional quantum systems.

Breaking down chipping and fragmentation in sediment transport: the control of material strength

Abstract. As rocks are transported, they primarily undergo two breakdown mechanisms: fragmentation and chipping. Fragmentation is catastrophic breakup by fracture in the bulk – either by subcritical crack growth under repeated collisions, or from a single high-energy (supercritical) collision – and produces angular shards. Chipping is a distinct low-energy mechanism of impact attrition that involves shallow cracking; this process rounds river pebbles in a universal manner under bed-load transport. Despite its geophysical significance, the transition from chipping to fragmentation is not well studied. Here, we examine this transition experimentally by measuring the shape and mass evolution of concrete particles of varying strength, subject to repeated collisions in a rotating drum. For sufficiently strong particles, chipping occurred and was characterized by the following: attrition products were orders of magnitude smaller than the parent; attrition rate was insensitive to material strength; and particles experienced monotonic rounding toward a spherical shape. As strength decreased, we observed the onset of a subcritical cracking regime associated with fragmentation: mass of attrition products became larger and more varied; attrition rate was inversely proportional to material strength; and shape evolution fluctuated and became non-monotonic. Our results validate conceptual and numerical models for impact attrition: chipping follows “Sternberg's law” of exponential mass loss through time; for fragmentation, the lifetime of particles increases nonlinearly with material strength, consistent with “Basquin's law” of fatigue failure. We suggest that bedrock erosion models must be clarified to incorporate distinct attrition mechanisms, and that pebble or bedrock-channel shape may be utilized to deduce the operative mechanism in a given environment.

A New Two-Parameter Burr-Hatke Distribution: Properties and Bayesian and Non-Bayesian Inference with Applications

This article introduces a two-parameter flexible extension of the Burr-Hatke distribution using the inverse-power transformation. The failure rate of the new distribution can be an increasing shape, a decreasing shape, or an upside-down bathtub shape. Some of its mathematical properties are calculated. Ten estimation methods, including classical and Bayesian techniques, are discussed to estimate the model parameters. The Bayes estimators for the unknown parameters, based on the squared error, general entropy, and linear exponential loss functions, are provided. The ranking and behavior of these methods are assessed by simulation results with their partial and overall ranks. Finally, the flexibility of the proposed distribution is illustrated empirically using two real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, Fréchet, gamma, exponential, inverse log-logistic, inverse weighted Lindley, inverse Pareto, inverse Nakagami-M, and Burr-Hatke distributions.

Abstract 10882: Validation of a Continuous Flow Pressure Gradient for Coarctation Severity Assessment

Introduction: Coarctation of the aorta (CoA) severity is assessed via trans-CoA blood pressure gradient (BPG) estimated using simplified Bernoulli equation (SBE) with indices from noninvasive Doppler echocardiography (echo). However, simplifications of the SBE and inconsistent readings through a suboptimal insonation window limit diagnostic accuracy (DA). In a rabbit model mimicking human CoA (Fig. 1A), catheter vs. Doppler comparison of BPG revealed diastolic continuous-flow pressure gradient (CFPG) was independently associated with severity. We therefore hypothesized the unique properties of CFPG would improve DA in humans. Methods: SBE and CFPG were quantified using color flow Doppler in humans and rabbits with discrete non-recurrent CoA before repair (Fig. 1B). Quantifications used peak velocity proximal to (V p ) and at the CoA (V pk ), early diastolic velocity (V d ), doppler velocity index (DVI), and normalized diastolic pressure half-time (dPHT; see Fig. 1B and C for definitions). Results were compared with measured BPG in rabbits (peak-to-peak catheter BPG) and humans (upper-lower extremity BPG). There was a total of 18 human and 26 rabbit cases; significance was defined a priori as a BPG of ≥20 mmHg. A CFPG ≥4 mmHg threshold was identified by maximizing sensitivity plus specificity in receiver operative curves (ROC). Results: Accuracy measures (Fig. 1D) revealed the superior performance of CFPG vs. SBE. Although reports suggest <60% of measured BPG can be explained with SBE, CFPG yielded a specificity of 78% in humans. Similar improvements were observed in rabbits. Results confirm the potential DA of CFPG in echo-based CoA assessment. Fig. 1- (A) MRI confirming morphological similarities between rabbit and human CoA, (B) Spectral Doppler images show diastolic continuous flow, (C) indices derived from the generalized Bernoulli equation assuming exponential diastolic pressure loss, (D) diagnostic performance for CFPG vs. conventional SBE.

Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

A New Extended Cosine—G Distributions for Lifetime Studies

In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.

Automatic segmentation of organs-at-risks of nasopharynx cancer and lung cancer by cross-layer attention fusion network with TELD-Loss.

Radiotherapy is one of the main treatments of nasopharyngeal cancer (NPC) and lung cancer. Accurate segmentation of organs at risks (OARs) in CT images is a key step in radiotherapy planning for NPC and lung cancer. However, the segmentation of OARs is influenced by the highly imbalanced size of organs, which often results in very poor segmentation results for small and difficult-to-segment organs. In addition, the complex morphological changes and fuzzy boundaries of OARs also pose great challenges to the segmentation task. In this paper, we propose a cross-layer attention fusion network (CLAF-CNN) to solve the problem of accurately segmentingOARs. In CLAF-CNN, we integrate the spatial attention maps of the adjacent spatial attention modules to make the segmentation targets more accurately focused, so that the network can capture more target-related features. In this way, the spatial attention modules in the network can be learned and optimized together. In addition, we introduce a new Top-K exponential logarithmic Dice loss (TELD-Loss) to solve the imbalance problem in OAR segmentation. The TELD-Loss further introduces a Top-K optimization mechanism based on Dice loss and exponential logarithmic loss, which makes the network pay more attention to small organs and difficult-to-segment organs, so as to enhance the overall performance of the segmentationmodel. We validated our framework on the OAR segmentation datasets of the head and neck and lung CT images in the StructSeg 2019 challenge. Experiments show that the CLAF-CNN outperforms the state-of-the-art attention-based segmentation methods in the OAR segmentation task with average Dice coefficient of 79.65% for head and neck OARs and 88.39% for lungOARs. This work provides a new network named CLAF-CNN which contains cross-layer spatial attention map fusion architecture and TELD-Loss for OAR segmentation. Results demonstrated that the proposed method could obtain accurate segmentation results for OARs, which has a potential of improving the efficiency of radiotherapy planning for nasopharynx cancer and lung cancer.