Correct Probability Research Articles

Distributed-Satellite-Clusters-Based Spectrum Sensing with Two-Stage Phase Alignment.

We investigate a distributed-satellite-clusters (DSC)-system-based spectrum sensing, to enhance the ability for sensing weak signals. However, the spectrum-sensing performance may be significantly decreased by the phase deviations among different satellite clusters, where the deviations may be caused by the movement and the perturbation of satellites. To eliminate such a decrement, we propose a cooperative spectrum-sensing scheme in the presence of phase deviations, where the deviations are alleviated by a special two-stage phase synchronization. Specifically, the phase compensation is first performed relying on broadcasting reference signals and the ephemeris, to address the challenges of the deviations caused by the movement. Then, a two-bit feedback algorithm, having a dynamic disturbance step size, is further adopted for controlling and mitigating the deviations caused by the perturbation. Additionally, we provide the closed-form expression of the correct detection probability of the proposed spectrum-sensing scheme, using the specially derived probability density function of the sum of the shadowed-Rician random variables with independently identical distribution. Simulation results show that the proposed scheme can achieve the best spectrum-sensing performance, comparing with the traditional energy detection, eigenvalue ratio test and the generalized likelihood ratio test.

Error detection and correction in one mBnB class code

The article deals with the issues of error detection and correction in the second order bi-pulse code. The analysis of the code generation algorithm is carried out, based on which it is shown that the code has 4 allowed four-bit combinations. The article considers own resources of a code which allow detecting and correcting both single errors and packets of errors. It is shown that errors are detected with probability of 1 when one, two and three bits of the code combination are distorted, while the probability of their correction does not exceed 0.5, in the case of distortion of all four symbols, both detection and correction of errors is impossible. To increase the probability of error correction, it is proposed to use a well-known method based on determining the parity or oddness of the allowed combinations in separate fragments of a linear signal, a brief description of the method is given, its analysis is carried out in relation to this code. It is shown that the use of this method makes it possible to correct all single, paired and three-time errors, as well as to detect all four-time errors, on the basis of which it can be concluded that it significantly improves the correcting properties of the signal under consideration.

A fine frequency estimation algorithm based on DFT samples and fuzzy logic for a real sinusoid

The study on the frequency estimation of a real sinusoid has been addressed in this article. Discrete-Fourier-transform (DFT)-based frequency estimation always uses the maximum bin of DFT as a coarse estimation followed by a fine estimation algorithm, which computes a correction term to compensate for the initial frequency offset caused by the coarse estimation. To enhance the frequency estimation accuracy, a fine estimation algorithm based on DFT samples and fuzzy logic (FL) is proposed in this study. Firstly, a modified phase-based algorithm is presented to estimate the sign of the correction term. Then, a main-lobe coefficient and a side-lobe coefficient are constructed using the amplitude of three spectral lines to calculate the correction term. A FL controller is utilised to generate a weighted factor to adjust the weight of the main-lobe coefficient and the side-lobe coefficient in the formula of the correction term. Compared with other existing fine algorithms, the proposed algorithm improves the correct probability of sign estimation by 10%–20%, and improves the estimation accuracy by 5%–8% at lower carrier-to-noise ratios (CNRs). In addition, the performance of the proposed algorithm is less affected by the initial frequency offset than other algorithms.

A note on the abundance of primordial black holes: Use and misuse of the metric curvature perturbation

The formation of Primordial Black Holes (PBHs) through the collapse of large fluctuations in the early universe is a rare event. This manifests itself, for instance, through the non-Gaussian tail of the formation probability. To compute such probability and the abundance of PBHs, the curvature perturbation is frequently adopted. In this note we emphasize that its use does not provide the correct PBH formation probability. Through a path-integral approach we show that the exact calculation of the PBH abundance demands the knowledge of multivariate joint probabilities of the curvature perturbation or, equivalently, of all the corresponding connected correlators.

Misidentification errors in reencounters result in biased estimates of survival probability from CJS models: Evidence and a solution using the robust design

Abstract Misidentification of marked individuals is unavoidable in most studies of wild animal populations. Models commonly used for the estimation of survival from such capture–recapture data ignore misidentification errors potentially resulting in biased parameter estimates. With a simulation study, we show that ignoring misidentification in Cormack–Jolly–Seber (CJS) models results in systematic positive biases in the estimates of survival and in spurious declines of survival over time. We developed an extended robust design capture mark–resight (RDM) model that includes correct identification parameters to get unbiased survival estimates when resighting histories are prone to misidentification. The model assumes that resightings occur repeatedly within a season, which in practice is often the case when resightings of colour‐marked individuals are collected. We implemented the RDM model in a state‐space formulation and also an approximate, but computationally faster, model (RDMa) in JAGS and evaluated their performances using simulated and empirical capture–resight data on black‐tailed godwits Limosa limosa. The CJS models applied to simulated data under an imperfect identification scenario data produced strongly positively biased estimates of survival. For a range of degrees of correct identification probabilities, the RDM model provided unbiased and accurate estimates of survival, reencounter and correct‐identification probabilities. The RDMa model performed well for large datasets (>25 individuals), with high resighting (>0.3) and high correct identification (>0.7) probabilities. For the empirical data, the CJS model estimated average juvenile survival at 0.997% and adult survival at 0.939% and also detected a strong decline in adult survival over time at a rate of −0.14 ± 0.029. In contrast, the RDMa model estimated a probability of correct identification of 0.94, annual juvenile survival at 0.234%, adult at 0.834% and less strong decline over time (−0.046 ± 0.016). We conclude that estimates of survival probabilities obtained from data that include misidentification errors and analysed with standard CJS model are unlikely to be correct. The bias in survival increases with the magnitude of misidentification errors, which is inevitable as datasets become longer. Since misidentification due to tag misreads is common in empirical data, we recommend the use of the here presented RDM model to provide unbiased parameter estimates.

Lightweight Automatic Modulation Classification Based on Decentralized Learning

Due to the implementation and performance limitations of centralized learning automatic modulation classification (CentAMC) method, this paper proposes a decentralized learning AMC (DecentAMC) method using model consolidation and lightweight design. Specifically, the model consolidation is realized by a central device (CD) for edge device (ED) model averaging (MA) and multiple EDs for ED model training. The lightweight is designed by separable convolutional neural network (S-CNN), in which the separable convolutional layer is utilized to replace the standard convolution layer and most of fully connected layers are cut off. Simulation results show that the proposed method substantially reduces the storage and computational capacity requirements of the EDs and communication overhead. The training efficiency also shows remarkable improvement. Compared with convolutional neural network (CNN), the space complexity (i.e., model parameters and output feature map) is decreased by about 94&#x0025; and the time complexity (i.e., floating point operations) of S-CNN is decreased by about 96&#x0025; while degrading the average correct classification probability by less than 1&#x0025;. Compared with S-CNN-based CentAMC, without considering model weights uploading and downloading, the training efficiency of our proposed method is about <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> times of it, where <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> is the number of EDs. Considering the model weights uploading and downloading, the training efficiency of our proposed method can still be maintained at a high level (e.g., when the number of EDs is 12, the training efficency of the proposed AMC method is about 4 times that of S-CNN-based CentAMC in dataset <inline-formula> <tex-math notation="LaTeX">$D_{1} = \{2{\mathrm {FSK, 4FSK, 8FSK, BPSK, QPSK, 8PSK, 16QAM}}\}$ </tex-math></inline-formula> and about 5 times that of S-CNN-based CentAMC in dataset <inline-formula> <tex-math notation="LaTeX">$D_{2} = \{2 {\mathrm {FSK, 4FSK, 8FSK, BPSK, QPSK, 8PSK, PAM2, PAM4, PAM8, 16QAM}}\}$ </tex-math></inline-formula>), while the communication overhead is reduced more than 35&#x0025;.

Novel Cooperative Automatic Modulation Classification Using Vectorized Soft Decision Fusion for Wireless Sensor Networks.

Cooperative automatic modulation classification (CAMC) using a swarm of sensors is intriguing nowadays as it would be much more robust than the conventional single-sensing-node automatic modulation classification (AMC) method. We propose a novel robust CAMC approach using vectorized soft decision fusion in this work. In each sensing node, the local Hamming distances between the graph features acquired from the unknown target signal and the training modulation candidate signals are calculated and transmitted to the fusion center (FC). Then, the global CAMC decision is made by the indirect vote which is translated from each sensing node’s Hamming-distance sequence. The simulation results demonstrate that, when the signal-to-noise ratio (SNR) was given by ≥ , our proposed new CAMC scheme’s correct classification probability could reach up close to . On the other hand, our proposed new CAMC scheme could significantly outperform the single-node graph-based AMC technique and the existing decision-level CAMC method in terms of recognition accuracy, especially in the low-SNR regime.

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production.

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself.

CNN Confidence Estimation for Rejection-Based Hand Gesture Classification in Myoelectric Control

Convolutional neural networks (CNNs) have been widely utilized to identify hand gestures from surface electromyography (sEMG) signals. However, due to the nonstationary characteristics of sEMG, the classification accuracy usually degrades significantly in the daily living environment involving complex hand movements. To further improve the reliability of a classifier, unconfident classifications are expected to be identified and rejected. In this study, we propose a novel approach to estimate the probability of correctness for each classification. Specifically, a confidence estimation model is established to generate confidence scores (ConfScore) based on posterior probabilities of CNN, and an objective function is designed to train the parameters of this model. In addition, a comprehensive metric that combines the true acceptance rate (TAR) and the true rejection rate (TRR) is proposed to evaluate the rejection performance of ConfScore, so that the tradeoff between system security and control lag could be fully considered. The effectiveness of ConfScore is verified using data from public databases and our online platform. The experimental results illustrate that ConfScore can better reflect the correctness of CNN classifications than traditional confidence features, i.e., maximum posterior probability and entropy of the probability vector. Moreover, the rejection performance is observed to be less sensitive to variations in rejection thresholds.

Runtime verification in uncertain environment based on probabilistic model learning.

Runtime verification (RV) is a lightweight approach to detecting temporal errors of system at runtime. It confines the verification on observed trajectory which avoids state explosion problem. To predict the future violation, some work proposed the predictive RV which uses the information from models or static analysis. But for software whose models and codes cannot be obtained, or systems running under uncertain environment, these predictive methods cannot take effect. Meanwhile, RV in general takes multi-valued logic as the specification languages, for example the true, false and inconclusive in three-valued semantics. They cannot give accurate quantitative description of correctness when inconclusive is encountered. We in this paper present a RV method which learns probabilistic model of system and environment from history traces and then generates probabilistic runtime monitor to quantitatively predict the satisfaction of temporal property at each runtime state. In this approach, Hidden Markov Model (HMM) is firstly learned and then transformed to Discrete Time Markov Chain (DTMC). To construct incremental monitor, the monitored LTL property is translated into Deterministic Rabin Automaton (DRA). The final probabilistic monitor is obtained by generating the product of DTMC and DRA, and computing the probabilities for each state. With such a method, one can give early warning once the probability of correctness is lower than a pre-defined threshold, and have the chance to do adjustment in advance. The method has been implemented and experimented on real UAS (Unmanned Aerial Vehicle) simulation platform.

An Effective Source Number Enumeration Approach Based on SEMD

In signal processing, empirical mode decomposition (EMD) first decomposes the received single-channel signal into several intrinsic mode functions (IMFs) and a residual, and then uses machine learning methods for source number enumeration. EMD, however, has an end effect that can undermine the accuracy of source number enumeration. To address this issue, this paper proposed a new EMD method named Supplementary Empirical Mode Decomposition (SEMD), which improved the accuracy by extending the signal length. The proposed method can be better applied to the modal parameter identification of non-stationary and nonlinear data in the engineering field. This method first identifies two candidate extreme points, which are the closest to the function value of the first extreme point near the endpoint. Then, on one side of the candidate point, it finds a waveform similar to that at the endpoint. Finally, the maximum and minimum points at each end of the signal will be added to extend the length of the signal. The added extreme points are candidate extreme points in similar waveforms. For the improved source number enumeration method based on SEMD, the instantaneous phase is obtained first by SEMD and Hilbert transform (HT). Then, the instantaneous phase feature is extracted to obtain a high-dimensional eigenvalue vector. Finally, the back propagation (BP) neural network is used to predict the number of sources. Experiment shows that SEMD can effectively restrain the end effect, and the source number enumeration algorithm based on SEMD has a higher correct detection probability than others.

Spectrum Sensing With Energy Detection in Multiple Alternating Time Slots

Energy detection (ED) represents a low complexity approach used by secondary users (SU) to sense spectrum occupancy by primary users (PU) in cognitive radio (CR) systems. In this paper, we present a new algorithm that senses the spectrum occupancy by performing ED in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> consecutive sensing time slots starting from the current slot and continuing by alternating before and after the current slot. We consider a PU traffic model specified in terms of an average duty cycle value, and derive analytical expressions for the false alarm probability (FAP) and correct detection probability (CDP) for any value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> . Our analysis is corroborated with numerical results in which Monte-Carlo simulations are used to determine FAP and CDP to confirm the validity of the analytical expressions obtained and to illustrate that good receiver operating characteristic (ROC) performance is reached for reasonably small values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> .

Discrete Atomic Transform-Based Lossy Compression of Three-Channel Remote Sensing Images with Quality Control

Lossy compression of remote sensing data has found numerous applications. Several requirements are usually imposed on methods and algorithms to be used. A large compression ratio has to be provided, introduced distortions should not lead to sufficient reduction of classification accuracy, compression has to be realized quickly enough, etc. An additional requirement could be to provide privacy of compressed data. In this paper, we show that these requirements can be easily and effectively realized by compression based on discrete atomic transform (DAT). Three-channel remote sensing (RS) images that are part of multispectral data are used as examples. It is demonstrated that the quality of images compressed by DAT can be varied and controlled by setting maximal absolute deviation. This parameter also strictly relates to more traditional metrics as root mean square error (RMSE) and peak signal-to-noise ratio (PSNR) that can be controlled. It is also shown that there are several variants of DAT having different depths. Their performances are compared from different viewpoints, and the recommendations of transform depth are given. Effects of lossy compression on three-channel image classification using the maximum likelihood (ML) approach are studied. It is shown that the total probability of correct classification remains almost the same for a wide range of distortions introduced by lossy compression, although some variations of correct classification probabilities take place for particular classes depending on peculiarities of feature distributions. Experiments are carried out for multispectral Sentinel images of different complexities.

Specific Radar Recognition Based on Characteristics of Emitted Radio Waveforms Using Convolutional Neural Networks.

With the increasing complexity of the electromagnetic environment and continuous development of radar technology we can expect a large number of modern radars using agile waveforms to appear on the battlefield in the near future. Effectively identifying these radar signals in electronic warfare systems only by relying on traditional recognition models poses a serious challenge. In response to the above problem, this paper proposes a recognition method of emitted radar signals with agile waveforms based on the convolutional neural network (CNN). These signals are measured in the electronic recognition receivers and processed into digital data, after which they undergo recognition. The implementation of this system is presented in a simulation environment with the help of a signal generator that has the ability to make changes in signal signatures earlier recognized and written in the emitter database. This article contains a description of the software’s components, learning subsystem and signal generator. The problem of teaching neural networks with the use of the graphics processing units and the way of choosing the learning coefficients are also outlined. The correctness of the CNN operation was tested using a simulation environment that verified the operation’s effectiveness in a noisy environment and in conditions where many radar signals that interfere with each other are present. The effectiveness results of the applied solutions and the possibilities of developing the method of learning and processing algorithms are presented by means of tables and appropriate figures. The experimental results demonstrate that the proposed method can effectively solve the problem of recognizing raw radar signals with agile time waveforms, and achieve correct probability of recognition at the level of 92–99%.

Reference Governor-based fault-tolerant constrained control

This paper presents a fault-tolerant control scheme for constrained linear systems. First, a new variant of the Reference Governor (RG) called At Once Reference Governor (AORG) is introduced. The AORG is distinguished from the conventional RG by computing the Auxiliary Reference (AR) sequence so that to optimize performance over a prescribed time interval instead of only at the current time instant; this enables the integration of the AORG with fault detection schemes. In particular, it is shown that, when the AORG is combined with a Multi-Model Adaptive Estimator (MMAE), the AR sequence can be determined such that the tracking properties are guaranteed and constraints are satisfied at all times, while the detection performance is optimized, i.e., faults can be detected with a high probability of correctness. In addition a reconfiguration scheme is presented that ensures system viability despite the presence of faults based on recoverable sets. Simulations on a Boeing 747-100 aircraft model are carried out to evaluate the effectiveness of the AORG scheme in enforcing constraints and tracking the desired roll and side-slip angles. The effectiveness of the presented fault-tolerant control scheme in maintaining the airplane viability in the presence of damaged vertical stabilizer is also demonstrated.

Analysing detection bands of two-spectral reflection method to identify forest species composition

The optical reflection method is considered for detection of the forest areas where coniferous or broadleaved trees are dominant. Statistical modelling of correct detection and false alarm probabilities for identifying dominant (coniferous or broadleaved) tree species by the two-spectral reflection method has been conducted. It has been shown that monitoring enables us to identify dominant (coniferous or broadleaved) tree species with correct detection probability close to 1 and false alarms probability ~ second decimal places for the temperate climate zone at the wavelengths of 532 and 1540 nm or 532 and 1480 nm. As to the subtropical climate zone, due to a great variety of reflection spectra of vegetation, a selection of the spectral detection bands for reliable identification of dominant coniferous or broadleaved tree species is possible only for specific forestlands where the number of evergreen broadleaved and coniferous tree species is relatively small.

Dimensionality reduction via path integration for computing mRNA distributions.

Inherent stochasticity in gene expression leads to distributions of mRNA copy numbers in a population of identical cells. These distributions are determined primarily by the multitude of states of a gene promoter, each driving transcription at a different rate. In an era where single-cell mRNA copy number data are more and more available, there is an increasing need for fast computations of mRNA distributions. In this paper, we present a method for computing separate distributions for each species of mRNA molecules, i.e. mRNAs that have been either partially or fully processed post-transcription. The method involves the integration over all possible realizations of promoter states, which we cast into a set of linear ordinary differential equations of dimension [Formula: see text], where M is the number of available promoter states and [Formula: see text] is the mRNA copy number of species j up to which one wishes to compute the probability distribution. This approach is superior to solving the Master equation (ME) directly in two ways: (a) the number of coupled differential equations in the ME approach is [Formula: see text], where [Formula: see text] is the cutoff for the probability of the jth species of mRNA; and (b) the ME must be solved up to the cutoffs [Formula: see text], which must be selected a priori. In our approach, the equation for the probability to observe n mRNAs of any species depends only on the the probability of observing [Formula: see text] mRNAs of that species, thus yielding a correct probability distribution up to an arbitrary n. To demonstrate the validity of our derivations, we compare our results with Gillespie simulations for ten randomly selected system parameters.

Predicting Rapid Changes in Evaporative Stress Index (ESI) and Soil Moisture Anomalies over the Continental United States.

AbstractProbabilistic forecasts ofchangesin soil moisture and an Evaporative Stress Index (ESI) on sub-seasonal time scales over the contiguous U.S. are developed. The forecasts use the current land surface conditions and numerical weather prediction forecasts from the Sub-seasonal to Seasonal (S2S) Prediction Project. Changes in soil moisture are quite predictable 8-14 days in advance with 50% or more of the variance explained over the majority of the contiguous U.S.; however, changes in ESI are significantly less predictable. A simple red noise model of predictability shows that the spatial variations in forecast skill are primarily a result of variations in the autocorrelation, or persistence, of the predicted variable, especially for the ESI. The difference in overall skill between soil moisture and ESI, on the other hand, is due to the greater soil moisture predictability by the numerical model forecasts. As the forecast lead time increases from 8-14 days to 15-28 days, however, the autocorrelation dominates the soil moisture and ESI differences as well. An analysis of modelled transpiration, and bare soil and canopy water evaporation contributions to total evaporation, suggests improvements to the ESI forecasts can be achieved by estimating the relative contributions of these components to the initial ESI state. The importance of probabilistic forecasts for reproducing the correct probability of anomaly intensification is also shown.

Optimization of a GIS sensor layout based on global detection probability distribution evaluation

Gas-insulated switchgear (GIS) is an important power equipment. The implementation of health monitoring is limited by the number of sensors, and the global detection results of the system should be highly credible to ensure the reliability of the power supply system. To solve this problem, this study proposes a sensor layout optimization method based on global detection probability performance evaluation. Starting from the cost function, the GIS discharge detection problem is transformed into a Bayesian risk decision problem, the binary state of ‘with discharge’ and ‘without discharge’ is adopted to simplify the cost function and reduce the computing workload, and the objective function representing the global detection performance of the system is obtained. The solution of layout optimization is realized by the improved genetic algorithm. 3-sensor, 4-sensor and 6-sensor layouts, which are digitally simulated at different detection rates, and then the distribution diagram of the global detection rate is obtained. On this basis, the feasibility and effectiveness of the optimization method are verified through an experiment. The results show that, compared with other sensor layout optimization methods, this optimization method can obtain the correct probability distribution of the detection rate globally and realize the graphical quantization of the detection performance distribution of the system so as to ensure the system performance.

How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering

Abstract Recent works have shown that language models (LM) capture different types of knowledge regarding facts or common sense. However, because no model is perfect, they still fail to provide appropriate answers in many cases. In this paper, we ask the question, “How can we know when language models know, with confidence, the answer to a particular query?” We examine this question from the point of view of calibration, the property of a probabilistic model’s predicted probabilities actually being well correlated with the probabilities of correctness. We examine three strong generative models—T5, BART, and GPT-2—and study whether their probabilities on QA tasks are well calibrated, finding the answer is a relatively emphatic no. We then examine methods to calibrate such models to make their confidence scores correlate better with the likelihood of correctness through fine-tuning, post-hoc probability modification, or adjustment of the predicted outputs or inputs. Experiments on a diverse range of datasets demonstrate the effectiveness of our methods. We also perform analysis to study the strengths and limitations of these methods, shedding light on further improvements that may be made in methods for calibrating LMs. We have released the code at https://github.com/jzbjyb/lm-calibration.