Error Exponent Research Articles

Optimal 1-bit Error Exponent for 2-Hop Relaying With Binary-Input Channels

Optimal 1-bit Error Exponent for 2-Hop Relaying With Binary-Input Channels

Decoding error probability of random parity-check matrix ensemble over the erasure channel

AbstractIn this paper we carry out an in-depth study on the average decoding error probability of the random parity-check matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random parity-check matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random parity-check matrix ensemble and the error exponent of the variance, which implies a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random linear code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.

Assessing the Recreational Fishers and their Catches based on Social Media Platforms: Privacy and Ethical Data Analysis Considerations

Social Media (SM) can offer insights to track recreational Fishing (Rf); Many Limitations Hinder Its Practical Application. The proportion and characteristics of RFs that share their catches remain unidentified. The objective was to enhance the surveillance abilities of RF by utilizing SM information. This study focuses on the sharing economy information transmission, network optimization of SM platforms, and privacy protection issues during data transmission. The study starts with the data transmission characteristics in SM platforms, analyzes the data ethics in SM information transmission from the perspectives of natural and economic data attributes, and then focuses on the privacy protection principles in network information transmission. Then, a privacy protection scheme based on a locally sensitive hash algorithm is constructed, and finally, an information transmission scheme and method optimization based on a network optimization module are proposed. The research gathered data using physical (face-to-face) surveys and digital (email) surveys to define marine RF that post catches on online platforms (“sharers”), together with additional demographic and fishing data. A comparative analysis was conducted on the computational convergence and accuracy of different privacy protection methods, and the optimal rule framework for data privacy protection was discussed. The observation results show that the efficiency of information transmission using the Minhash-SSNR method is slightly inferior to that using the OSNR-SSNR method. Minhash technology is based on a similarity comparison of dimensionality-reduced data. This leads to data causing the initially highly similar two sets of lists to be misjudged as not having enough similarity, thereby reducing some potential information dissemination opportunities and affecting the efficacy of information transmission. It can be seen that the Minhash-SSNR strategy can effectively send information to nodes with high similarity, preventing excessive information duplication within the system. Although the Minhash-SSNR strategy has a certain degree of decline in information transmission efficiency, it accounts for only about 5% compared to the OSNR-SSNR strategy, ensuring the essential operational stability of SM opportunity networks without significant impact. With few learning and training times, the network information transmission optimization module proposed in this study quickly achieved a lower exponential error. As the number of training sessions gradually increases, the exponential error of the network information transmission optimization module in this study is small, and the prediction accuracy of the method is high. RFs who captured a prize, iconic, or symbolic species tended to discuss their catches more. This research signifies significant progress in incorporating SM information to oversee RFs.

Exponential error reduction for glueball calculations using a two-level algorithm in pure gauge theory

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional SU(3) pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multilevel method. We discuss the physical distance at which the multilevel sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels. Published by the American Physical Society 2024

Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

AbstractThe asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ranks. Over the complex numbers, a refinement of this problem, originating in the theory of quantum entanglement, is to find the optimal rate of entanglement transformations as a function of the error exponent. This trade-off can also be characterized in terms of the set of normalized, additive, multiplicative functionals that are monotone in a suitable sense, which includes the restriction-monotones as well. For example, the flattening ranks generalize to the (exponentiated) Rényi entanglement entropies of order $$\alpha \in [0,1]$$ α ∈ [ 0 , 1 ] . More complicated parameters of this type are known, which interpolate between the flattening ranks or Rényi entropies for special bipartitions, with one of the parts being a single tensor factor. We introduce a new construction of subadditive and submultiplicative monotones in terms of a regularized Rényi divergence between many copies of the pure state represented by the tensor and a suitable sequence of positive operators. We give explicit families of operators that correspond to the flattening-based functionals, and show that they can be combined in a nontrivial way using weighted operator geometric means. This leads to a new characterization of the previously known additive and multiplicative monotones, and gives new submultiplicative and subadditive monotones that interpolate between the Rényi entropies for all bipartitions. We show that for each such monotone there exist pointwise smaller multiplicative and additive ones as well. In addition, we find lower bounds on the new functionals that are superadditive and supermultiplicative.

Activation function optimization scheme for image classification

Activation function has a significant impact on the dynamics, convergence, and performance of deep neural networks. The search for a consistent and high-performing activation function has always been a pursuit during deep learning model development. Existing state-of-the-art activation functions are manually designed with human expertise except for Swish. Swish was developed using a reinforcement learning-based search strategy. In this study, we propose an evolutionary approach for optimizing activation functions specifically for image classification tasks, aiming to discover functions that outperform current state-of-the-art options. Through this optimization framework, we obtain a series of high-performing activation functions denoted as Exponential Error Linear Unit (EELU). The developed activation functions are evaluated for image classification tasks from two perspectives: (1) five state-of-the-art neural network architectures, such as ResNet50, AlexNet, VGG16, MobileNet, and Compact Convolutional Transformer, which cover computationally heavy to light neural networks, and (2) eight standard datasets, including CIFAR10, Imagenette, MNIST, Fashion MNIST, Beans, Colorectal Histology, CottonWeedID15, and TinyImageNet which cover from typical machine vision benchmark, agricultural image applications to medical image applications. Finally, we statistically investigate the generalization of the resultant activation functions developed through the optimization scheme. With a Friedman test, we conclude that the optimization scheme is able to generate activation functions that outperform the existing standard ones in 92.8% cases among 28 different cases studied, and −x⋅erf(e−x) is found to be the best activation function for image classification generated by the optimization scheme.

Soil Temperature and Moisture Forecasting Using Exponential Smoothing Method Based on Mean Absolute Percentage Error

Soil is an essential medium for almost all plants. Temperature and moisture in the soil become one of the factors that affect plant growth. Unbalanced or unfavorable soil conditions will adversely affect the plant. Therefore, soil conditions, including temperature and moisture, must be monitored to maintain plant health. Forecasting can be used to find out the soil condition in the future so that strategies can be prepared to deal with these conditions. This forecasting is carried out based on existing soil temperature and moisture data, which is then processed using the exponential smoothing method and mean absolute percentage error as a reference for the error rate or accuracy of the forecasting. The application of these methods succeeded in producing forecasting with very good overall accuracy.<em> </em>

A Survey on Error Exponents in Distributed Hypothesis Testing: Connections with Information Theory, Interpretations, and Applications.

A central challenge in hypothesis testing (HT) lies in determining the optimal balance between Type I (false positive) and Type II (non-detection or false negative) error probabilities. Analyzing these errors' exponential rate of convergence, known as error exponents, provides crucial insights into system performance. Error exponents offer a lens through which we can understand how operational restrictions, such as resource constraints and impairments in communications, affect the accuracy of distributed inference in networked systems. This survey presents a comprehensive review of key results in HT, from the foundational Stein's Lemma to recent advancements in distributed HT, all unified through the framework of error exponents. We explore asymptotic and non-asymptotic results, highlighting their implications for designing robust and efficient networked systems, such as event detection through lossy wireless sensor monitoring networks, collective perception-based object detection in vehicular environments, and clock synchronization in distributed environments, among others. We show that understanding the role of error exponents provides a valuable tool for optimizing decision-making and improving the reliability of networked systems.

Prime Orbit Theorems for expanding Thurston maps: Genericity of strong non-integrability condition

In the second paper [16] of this series, we obtained an analog of the prime number theorem for a class of branched covering maps on the 2-sphere S2 called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on S2 satisfying the α-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In this third and last paper of the series, we show that the α-strong non-integrability condition is generic in the class of α-Hölder continuous functions.

Model Selection for Exponential Power Mixture Regression Models.

Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.

Adaptive control of A class of nonlinear systems with guaranteed parameter estimation: A concurrent learning based approach

AbstractRecent advances in concurrent learning based adaptive controllers have relaxed the persistency of excitation condition required to achieve exponential tracking and parameter estimation error convergence. This was made possible via the use of additional concurrent learning stacks in the parameter estimation algorithm. However, the proposed concurrent learning components, that is, the history stacks, needed to be filled with “selected” values dependent on the actual system states. Therefore, the previously proposed concurrent learning adaptive controllers required the system to be stable initially for a finite time so that the corresponding history stacks can be filled (finite excitation condition). In this work, motivated to remove the finite excitation condition, a novel desired system state based concurrent learning adaptive controller is proposed. In order to remove the system state dependencies in the controller and estimation algorithms, a filtered version of the dynamics and a novel prediction error formulation have been designed. The overall exponential stability, parameter error convergence and boundedness of the system states during closed loop operations are ensured via Lyapunov based arguments. The main advantages of the proposed method are its dependence on the desired system states and the overall stability results that paved the way in removing the need for finite excitation condition. Numerical studies performed on a two link robotic device are also presented to illustrate the feasibility of the proposed method.

Exponential family measurement error models for single-cell CRISPR screens.

CRISPR genome engineering and single-cell RNA sequencing have accelerated biological discovery. Single-cell CRISPR screens unite these two technologies, linking genetic perturbations in individual cells to changes in gene expression and illuminating regulatory networks underlying diseases. Despite their promise, single-cell CRISPR screens present considerable statistical challenges. We demonstrate through theoretical and real data analyses that a standard method for estimation and inference in single-cell CRISPR screens-"thresholded regression"-exhibits attenuation bias and a bias-variance tradeoff as a function of an intrinsic, challenging-to-select tuning parameter. To overcome these difficulties, we introduce GLM-EIV ("GLM-based errors-in-variables"), a new method for single-cell CRISPR screen analysis. GLM-EIV extends the classical errors-in-variables model to responses and noisy predictors that are exponential family-distributed and potentially impacted by the same set of confounding variables. We develop a computational infrastructure to deploy GLM-EIV across hundreds of processors on clouds (e.g. Microsoft Azure) and high-performance clusters. Leveraging this infrastructure, we apply GLM-EIV to analyze two recent, large-scale, single-cell CRISPR screen datasets, yielding several new insights.

Universal Neyman–Pearson classification with a partially known hypothesis

Abstract We propose a universal classifier for binary Neyman–Pearson classification where the null distribution is known, while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between Hoeffding’s classifier and the likelihood ratio test and attains the same error probability prefactor as the likelihood ratio test, i.e. the same prefactor as if both distributions were known. In addition, such as Hoeffding’s universal hypothesis test, the proposed classifier is shown to attain the optimal error exponent tradeoff attained by the likelihood ratio test whenever the ratio of training to observation samples exceeds a certain value. We propose a lower bound and an upper bound to the optimal training to observation ratio. In addition, we propose a sequential classifier that attains the optimal error exponent tradeoff.

Quasi-Synchronization of Fractional Multiweighted Coupled Neural Networks via Aperiodic Intermittent Control.

This article investigates the quasi-synchronization for fractional multiweighted coupled neural networks (FMCNNs) with discontinuous activation functions and mismatched parameters. First, under the generalized Caputo fractional-order derivative operator, a novel piecewise fractional differential inequality is established to study the convergence of fractional systems, which significantly extends some related published results. Subsequently, by exploiting the new inequality and Lyapunov stability theory, some sufficient quasi-synchronization conditions of FMCNNs are presented by aperiodic intermittent control. Meanwhile, the exponential convergence rate and synchronization error's bound are given explicitly. Finally, the validity of theoretical analysis is confirmed by numerical examples and simulations.

MA-CNN based spindle thermal error modeling using the depth feature analysis with thermal error mechanism

The dynamic changes in the temperature fields make it unavoidable for the spindle to undergo thermal deformation. Thermal error modelling is helpful in enhancing the accuracy of machine tools. This paper proposes a spindle thermal error modelling method based on the mayfly algorithm (MA) for complex working conditions. First, different working conditions are set to obtain thermal deformation and temperature data. A thermal error model is established using MA. MA is used to optimize the number and size of convolutional kernels. Next, the depth features of the model are compared with the exponential thermal error model in logarithmic space. The model is compared with five other models. The results indicate that the MA-CNN model has a higher accuracy. Finally, the compensation is conducted in three directions. The results show that the average thermal error in the Z direction is reduced by 63.75 %, which demonstrates the good performance of the model.

Calculation of the total number of radiation decay of Radiolabelled-Octreotate using non-linear mixed effect models

Non-Linear Mixed Effect (NLME) is a method used in the area under the measured time-activity curve (AUC) calculations. The calculation of an accurate AUC is needed for an accurate determination of the radiation absorbed dose. In NLME, the error model might affect the accuracy of the estimation of the AUC. Therefore, the aim of this study was to determine the effect of error models on AUC calculations using NMLE. The data used in this study were from biokinetic data of the 111In-DOTATATE biodistribution in the tumour collected from the literature. The data were fitted using published bi-exponential function $f(t) = {{({{\rm{k}}_e} \times {{\rm{k}}_a})} \over {c({{\rm{k}}_a} - {{\rm{k}}_e})}}\left[ {{e^{ - ({{\rm{k}}_e})t}} - {e^{ - ({{\rm{k}}_a})t}}} \right]$ with several error models, namely constant, proportional, combined and exponential errors. The mean and standard deviation were determined from the AUC for each error model AUC values obtained from constant, proportional, combined, and exponential error were (4.40 ± 1.93) nmol·min, (3.13 ± 2.74) nmol·min, (3.22 ± 2.85) nmol·min and (3.14 ± 2.75) nmol·min, respectively. Based on the research results, the proportional, combined and exponential error were relatively produced better results compared to the constant error model in our dataset.

Reliable Simulation of Quantum Channels: the Error Exponent

Reliable Simulation of Quantum Channels: the Error Exponent

A novel processor for dynamic evolution of constrained SAT problems: The dynamic evolution variant of the discrete Hopfield neural network satisfiability model

The Boolean satisfiability problem, a renowned NP-complete challenge in computer science, has recently garnered interest in the Discrete Hopfield Neural Network - Satisfiability model. This model adeptly integrates logical rules into Hopfield networks, excelling in locating global minima for traditional SAT problems. However, it faces efficiency challenges when dealing with SAT problems characterized by dynamic evolution constraints due to its static network architecture. During dynamic evolution iterations, there is a significant exponential increase in the computational costs due to redundant and repetitive computations.In order to address this challenge, this paper introduces a dynamic evolution variant of the Discrete Hopfield Neural Network - Satisfiability model. In extensive simulation experiments, we progressively augmented the number of constraint clauses from 1 to 1500, seeking global minima for CNF problems. The proposed model exhibited congruent performance with the traditional model, achieving a Global Minimum Ratio of 1 and a Hamming distance of 0. Crucially, the proposed model minimized CPU utilization and neared zero error metrics, while the traditional model experienced exponential CPU and error metric escalation. These outcomes affirm the proposed model's robust global search capabilities and high precision, aligning with the traditional model. Furthermore, owing to this model's incorporation of not only temporal constraint increment operator but also innovative real-time learning techniques and clever integration methods, along with the establishment of a novel real-time decision mechanism, the proposed model effectively addresses the issues of redundancy and repeated calculations inherent in traditional models. This results in a stable and significantly improved computational speed. Additionally, this model's dynamic evolution network architecture is specifically designed to accommodate arbitrary and efficient extensions of dynamic constraints, while also featuring a built-in preprocessing function to filter out duplicate variables. In the future, as a dynamic evolution processor, this model exhibits immense potential for solving large-scale SAT problems with dynamic evolution constraints and holds broad application prospects in emerging fields such as automated reasoning, intelligent recommendation systems, and machine learning.

MHD Casson Fluid with Radiative Heat and Mass Transfer past an Impulsively Moving Inclined Plate

This paper explores the flow of Casson fluid that passes a moving inclined plate with the influence of double diffusions and radiation, where the fluid is imposed electrically conductive and moves through a porous medium. Several suitable non-dimensional variables are suggested in the model using partial differential equations with initial and boundary conditions. The corresponding non-dimensional governing equations are solved with the help of Laplace transform method. Analytical solutions to momentum, energy, and concentration are obtained, and the expression is in exponential and complementary error functions of Gauss. Finding solutions is limited to similar solutions for previous studies on Casson and viscous fluids as a special case. Computations are performed, where the outcomes are examined for embedded flow parameters.

Field experimental investigation on bearing characteristics of super-long pile under dynamic compaction in land reclamation area

To investigate the bearing mechanism of super-long piles in reclamation, this study performed a series of field tests on super-long cast-in-place piles. The load distribution and bearing characteristics of the piles were analyzed, and the bearing capacity calculation method was evaluated. The findings revealed that dynamic compaction (8000 kN·m) improved the compactness and bearing capacity of the filled soil, and was capable of avoiding negative friction around the pile. The pile bearing characteristics were friction type, and bearing capacity was mainly borne by axial friction resistance. The pile end resistance accounted for 15.7 %–35.1 % of the bearing capacity, and the peak friction resistance was distributed in the upper soil at a depth range of 0.13–0.31 times pile length. The measured value of friction resistance was 9.8 %–90.2 % higher in the upper soil layer and 46.7 %–60.8 % lower in the rock layer than the value recommended by the current Chinese code. The hyperbolic model overestimated the bearing capacity by 26.8 %–50.4 % and the exponential model error was -4.5 % – +18.9 %. The hyperbolic model was corrected, and the correction factor was determined as 0.73. This study provides guidance for the structural design and theoretical calculation of super-long piles in reclamation areas.