Noise Probability Research Articles

Optimum noise mechanism for differentially private queries in discrete finite sets

The differential privacy (DP) literature often centers on meeting privacy constraints by introducing noise to the query, typically using a pre-specified parametric distribution model with one or two degrees of freedom. However, this emphasis tends to neglect the crucial considerations of response accuracy and utility, especially in the context of categorical or discrete numerical database queries, where the parameters defining the noise distribution are finite and could be chosen optimally. This paper addresses this gap by introducing a novel framework for designing an optimal noise probability mass function (PMF) tailored to discrete and finite query sets. Our approach considers the modulo summation of random noise as the DP mechanism, aiming to present a tractable solution that not only satisfies privacy constraints but also minimizes query distortion. Unlike existing approaches focused solely on meeting privacy constraints, our framework seeks to optimize the noise distribution under an arbitrary (ϵ,δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\epsilon , \\delta )$$\\end{document} constraint, thereby enhancing the accuracy and utility of the response. We demonstrate that the optimal PMF can be obtained through solving a mixed-integer linear program. Additionally, closed-form solutions for the optimal PMF are provided, minimizing the probability of error for two specific cases. Numerical experiments highlight the superior performance of our proposed optimal mechanisms compared to state-of-the-art methods. This paper contributes to the DP literature by presenting a clear and systematic approach to designing noise mechanisms that not only satisfy privacy requirements but also optimize query distortion. The framework introduced here opens avenues for improved privacy-preserving database queries, offering significant enhancements in response accuracy and utility.

Color image hybrid noise filtering algorithm based on deep convolution neural network

To solve the problems of the classical color image hybrid noise filtering method, a deep convolutional neural network improved by evolutionary strategy and jump connection is proposed and applied to the filtering noise reduction of color images. First, the color information of the image is described quantitatively by digital means. The common method is to build color space model. According to the characteristics of color and the needs of human vision, mathematical algorithms are used to convert images into machine recognizable data. The distance between pixels is measured according to the difference of pixels in the color image determined above. Then, the probability density function and noise probability density function of Gaussian noise are calculated to determine the hybrid noise feature points of color image. The filtering algorithm structure designed this time is as follows: A color image hybrid noise filter is used to map the noise points in the mapped image to the feature space, and linear regression is performed on the noise point data. Relaxation variables are introduced in the network to improve the denoising ability. The experimental results show that the Peak Signal to Noise Ratio and structural similarity index values of the filtering algorithm designed in this study are higher than the two methods in the literature. The color image hybrid noise filtering model designed in this study has good filtering performance, good image cleanliness, and high filtering efficiency.

Which Is More Effective in Label Noise Cleaning, Correction or Filtering?

Most noise cleaning methods adopt one of the correction and filtering modes to build robust models. However, their effectiveness, applicability, and hyper-parameter insensitivity have not been carefully studied. We compare the two cleaning modes via a rebuilt error bound in noisy environments. At the dataset level, Theorem 5 implies that correction is more effective than filtering when the cleaned datasets have close noise rates. At the sample level, Theorem 6 indicates that confident label noises (large noise probabilities) are more suitable to be corrected, and unconfident noises (medium noise probabilities) should be filtered. Besides, an imperfect hyper-parameter may have fewer negative impacts on filtering than correction. Unlike existing methods with a single cleaning mode, the proposed Fusion cleaning framework of Correction and Filtering (FCF) combines the advantages of different modes to deal with diverse suspicious labels. Experimental results demonstrate that our FCF method can achieve state-of-the-art performance on benchmark datasets.

Object segmentation for image indexing in large database

It is a challenging task to devise an effective model for object segmentation considering numerous classes because different classes might have different features and different backgrounds. We propose a unique segmentation and classification model to detect and classify objects. We propose a extended version of the U-Net model for object segmentation whereas, for the classification task, we propose an effective fusion scheme by exploiting two popular CNN models including ResNet50 and MobileNet. We conduct experiments on the Caltech101 benchmark dataset which contains 8677 images grouped into 101 classes. Besides, to examine the performance of our proposed segmentation method on object detection, we devise a polygonal ground-truth dataset based on the Caltech101 benchmark dataset. The unique feature of polygon shape ground truth is that it creates a mask of the target image in which the probability of noise is very low where there is noise in the bounding box ground truth. Extensive experiments on the Caltech101 benchmark dataset demonstrate the efficacy of our proposed approaches compared to the other existing models with a segmentation accuracy of 95.94% and classification accuracy of 99.90%. We also achieve an average IoU score of 0.98 which validates the effective object recognition performance of our model.

Deep Learning-Based Analysis of Ancient Greek Literary Texts in English Version: A Statistical Model Based on Word Frequency and Noise Probability for the Classification of Texts

In our paper we intend to present a methodology that we elaborated for clustering texts based on the word fre quency in the English translations of selected old Greek texts. We used the classification system of the ancient Library of Alex andria, devised by the prominent Greek scholar-poet, Callima chus in the 3rd century BC., as a basis for categorizing literary masterpieces. In our content analysis, we could determine a tri plet of a, b, c values for describing a power function that appro priately fits a curve determined by the word frequencies in the texts. In addition, we have discovered 16 special features of the different texts that correspond to various token categories inves tigated in each text, such as part of speech of the word in the con text, numerals, subordinate conjunction, symbols, etc. We have developed a cognitive model in which several hundred different subtexts were utilized for supervised learning with the aim of subtext class recognition. Concerning 200 subtexts, the triplet of a, b, c values, the classes of the subtexts, and their 16-dimen sional feature vectors were learnt for the Recurrent Neural Net work (RNN). It turned out that the Long-Short Term Memory RNN could efficiently predict which class a chosen subtext could be categorized into without considering the interpretation of the content. The influence of the non-zero error rate of new com munication services on the meaning of the transferred texts was also investigated. The impact of the noise on the classification accuracy was found to be linear, dependent on the character error rate.

Fear conditioning and fear generalization in children and adolescents with anxiety disorders

Overgeneralization of conditioned fear is associated with anxiety disorders (AD). Most results stem from studies done in adult patients, but studies with children are rare, although the median onset of anxiety disorders lies already in childhood. Thus, the goal of the present study was to examine fear learning and generalization in youth participants, aged 10–17 years, with AD (n = 39) compared to healthy controls (HC) (n = 40). A discriminative fear conditioning and generalization paradigm was used. Ratings of arousal, valence, and US expectancy (the probability of an aversive noise following each stimulus) were measured, hypothesizing that children with AD compared to HC would show heightened ratings of arousal and US expectancy, and decreased positive valence ratings, respectively, as well as overgeneralization of fear. The results indicated that children with AD rated all stimuli as more arousing and less pleasant, and demonstrated higher US expectancy ratings to all stimuli when compared to HC. Thus, rather than displaying qualitatively different generalization patterns (e.g., a linear vs. quadratic slope of the gradient), differences between groups were more quantitative (similar, but parallel shifted gradient). Therefore, overgeneralization of conditioned fear does not seem to be a general marker of anxiety disorders in children and adolescents.

Modeling of truncated normal distribution for estimating hydraulic parameters in water distribution systems: taking nodal water demand as an example.

The normal probability density function (PDF) is widely used in parameter estimation in the modeling of dynamic systems, assuming that the random variables are distributed at infinite intervals. However, in practice, these random variables are usually distributed in a finite region confined by the physical process and engineering practice. In this study, we address this issue through the application of truncated normal PDF. This method avoids a non-differentiable problem inherited in the truncated normal PDF at the truncation points, a limitation that can limit the use of analytical methods (e.g., Gaussian approximation). A data assimilation method with the derived formula is proposed to describe the probability of parameter and measurement noise in the truncated space. In application to a water distribution system (WDS), the proposed method leads to estimating nodal water demand and hydraulic pressure key to hydraulic and water quality model simulations. Application results to a hypothetical and a large field WDS clearly show the superiority of the proposed method in parameter estimation for WDS simulations. This improvement is essential for developing real-time hydraulic and water quality simulation and process control in field applications when the parameter and measurement noise are distributed in the finite region.

NLIP: Noise-Robust Language-Image Pre-training

Large-scale cross-modal pre-training paradigms have recently shown ubiquitous success on a wide range of downstream tasks, e.g., zero-shot classification, retrieval and image captioning. However, their successes highly rely on the scale and quality of web-crawled data that naturally contain much incomplete and noisy information (e.g., wrong or irrelevant contents). Existing works either design manual rules to clean data or generate pseudo-targets as auxiliary signals for reducing noise impact, which do not explicitly tackle both the incorrect and incomplete challenges at the same time. In this paper, to automatically mitigate the impact of noise by solely mining over existing data, we propose a principled Noise-robust Language-Image Pre-training framework (NLIP) to stabilize pre-training via two schemes: noise-harmonization and noise-completion. First, in noise-harmonization scheme, NLIP estimates the noise probability of each pair according to the memorization effect of cross-modal transformers, then adopts noise-adaptive regularization to harmonize the cross-modal alignments with varying degrees. Second, in noise-completion scheme, to enrich the missing object information of text, NLIP injects a concept-conditioned cross-modal decoder to obtain semantic-consistent synthetic captions to complete noisy ones, which uses the retrieved visual concepts (i.e., objects’ names) for the corresponding image to guide captioning generation. By collaboratively optimizing noise-harmonization and noise-completion schemes, our NLIP can alleviate the common noise effects during image-text pre-training in a more efficient way. Extensive experiments show the significant performance improvements of our NLIP using only 26M data over existing pre-trained models (e.g., CLIP, FILIP and BLIP) on 12 zero-shot classification datasets (e.g., +8.6% over CLIP on average accuracy), MSCOCO image captioning (e.g., +1.9 over BLIP trained with 129M data on CIDEr) and zero-shot image-text retrieval tasks.

Integrated Navigation Method of Aerospace Vehicle Based on Rank Statistics

The large dynamic and high-speed flight of aerospace vehicle will bring unpredictable conditions to its navigation system, resulting in that its system random noise probability distribution will no longer meet the preconditions of Gaussian distribution preset by the existing filter algorithm, thus reducing the accuracy of the navigation system. So, it is very important to propose an effective method to solve the filter problem of the navigation system in non-Gaussian distribution to improve the accuracy of the navigation system. Therefore, an integrated navigation method of aerospace vehicle based on rank statistics (LRF) has been proposed in this paper. Firstly, based on the flight characteristics of aerospace vehicles, an accurate gravity calculation model has been established to improve the accuracy of system modelling. Then, the state equation and measurement equation of integrated navigation system have been established. In combination with the rank filter algorithm as well as the determined weights, sampling points are calculated and nonlinearly propagated through the transition matrix to achieve an accurate estimation about the predicted values of the state quantities and measurement quantities and the covariance matrix. In turn, it simulates the probability distribution of the system state effectively. Therefore, when the system random noise probability distribution of the aerospace vehicle does not meet the Gaussian distribution due to various interference factors in the actual flight process, the algorithm can simulate the probability distribution of the actual system to the greatest extent, to improve the accuracy of the integrated navigation system and enhance the reliability of the navigation system ultimately.

Fractional Spurs Reduction Technique Using Probability Density Shaping Sigma-Delta Modulator and Fractional Frequency Divider

A fractional spurs reduction technique using probability density shaping (PDS) sigma-delta modulator (SDM) and fractional frequency divider is presented. The PDS-SDM is utilized to reshape the quantization noise probability density. If a certain condition is obeyed, the loop nonlinearity would not induce fractional spurs. Moreover, in order to reduce the total quantization noise power, a fractional frequency divider, e.g., phase-interpolated (PI) frequency divider, is adopted to reduce the division ratio from 1 to 0.25, leading to 12 dB quantization noise suppression. By combining the PDS-SDM and fractional divider, the fractional spurs are greatly mitigated. A phase domain ADPLL Simulink model is proposed for verification and the simulation results demonstrate the proposed technique is effective for fractional spurs reduction.

The Rayleigh Problem (Random Flights) is Everywhere Redux

The phase noise problem (or Rayleigh problem) occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in an attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise.

An improved sparse identification of nonlinear dynamics with Akaike information criterion and group sparsity.

A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics (SINDy) algorithm is developed. First, the Akaike information criterion (AIC) is integrated to enforce model selection by hierarchically ranking the most informative model from several manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations (ODEs) to partial differential equations (PDEs), while group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to treat noise separate from signals and tends to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the Van der Pol, Rössler, Burgers’ and Kuramoto–Sivashinsky equations, can be identified correctly with the introduction of noise. Furthermore, except for normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possesses robustness.

Analysis of Theoretical Bounds in Noisy Threshold Group Testing

The objective of this study was to describe a noisy threshold group testing model where positive and negative cases could occur depending on virus concentration in coronavirus disease 2019 (COVID-19) diagnosis with output results flipped due to measurement noise. We investigated lower bounds for successful reconstruction of a small set of defective samples in the noisy threshold group testing framework. To this end, using Fano’s inequality, we derived the minimum number of tests required to find unknown signals with defective samples. Our results showed that the minimum number of tests on probability of error for reconstruction of unknown signals was a function of the defective rate and noise probability. We obtained lower bounds for performance of the noisy threshold group testing framework with respect to noise intervals. In addition, the relationship between defective rate of signals and sparsity of group matrices to design optimal noisy threshold group testing systems is presented.

Characterization of radiation damages on Silicon photomultipliers by X-rays up to 100 kGy

Silicon photomultipliers (SiPMs) are highly-sensitive photodetectors emerging as the technology of choice for many applications, including among the others, large high-energy physics experiments and detectors for space instruments, where they are often exposed to a large amount of radiation. In recent years, there has been an increasing interest in assessing the performance deterioration of such detectors after ionizing and non-ionizing radiation, such as protons, neutrons and X or gamma rays. It is therefore interesting to characterize the effect of irradiation on such Geiger-mode detectors, differentiating between the ionizing and non-ionizing energy-loss effects. Moreover, it is interesting to compare the radiation damage effects on several types of SiPMs, to assess the main phenomena and the deterioration mechanisms, aiming to a more radiation tolerant SiPM design.In this work we irradiated several types of SiPM structures, produced in FBK (Trento, Italy), with 40 keV X-rays, at several doses, up to 100 kGy (in silicon), performing both online measurements (after each irradiation step) and offline functional characterization, after one month of room temperature annealing. The SiPMs are made with many different technologies, in particular different layouts, junction polarities, internal structures and starting materials. We studied the variation in the reverse current–voltage curves, distinguishing the effects on multiplied and not-multiplied current components, the primary dark count rate, the correlated noise probabilities and photon detection efficiency. Comparing all the measurement results, knowing the internal structure and the fabrication processes, we were able to extract and distinguish different deterioration mechanisms, also supported by TCAD simulations on the different effects of ionizing radiation inside the microcells.

Optimization Method of RFID Reader Antenna Deployment in Obstacle Environment Based on Improved FA

The aim of this study is to solve the problem of RFID reader antenna deployment when an obstacle in the environment or the material itself is an obstacle. The article establishes a new reader antenna constraint model based on the rectangular obstacle RFID antenna deployment optimization environment model and the reader antenna sensing model containing Gaussian distribution noise probability and applies the improved firefly algorithm to find the optimum with coverage rate, interference degree, and load balance function as multiobjective functions. First, to obtain a uniform traversal of the target space, and a cube mapping is applied for chaos initialization. Second, a weighting model is proposed to control the speed of firefly variation and combine the variable step strategy of elite individuals to expand the movement step of elite individuals and reduce the movement step of nonelite individuals to improve population diversity. Finally, to improve the algorithm’s continuous optimality-seeking ability, a Gaussian variation operation strategy based on elite fireflies is introduced to ensure the algorithm’s optimality-seeking throughout the process.

Label noise detection under the noise at random model with ensemble filters

Label noise detection has been widely studied in Machine Learning because of its importance in improving training data quality. Satisfactory noise detection has been achieved by adopting ensembles of classifiers. In this approach, an instance is assigned as mislabeled if a high proportion of members in the pool misclassifies it. Previous authors have empirically evaluated this approach; nevertheless, they mostly assumed that label noise is generated completely at random in a dataset. This is a strong assumption since other types of label noise are feasible in practice and can influence noise detection results. This work investigates the performance of ensemble noise detection under two different noise models: the Noisy at Random (NAR), in which the probability of label noise depends on the instance class, in comparison to the Noisy Completely at Random model, in which the probability of label noise is entirely independent. In this setting, we investigate the effect of class distribution on noise detection performance since it changes the total noise level observed in a dataset under the NAR assumption. Further, an evaluation of the ensemble vote threshold is conducted to contrast with the most common approaches in the literature. In many performed experiments, choosing a noise generation model over another can lead to different results when considering aspects such as class imbalance and noise level ratio among different classes.

Gibbs measures as unique KMS equilibrium states of nonlinear Hamiltonian PDEs

The classical Kubo–Martin–Schwinger (KMS) condition is a fundamental property of statistical mechanics characterizing the equilibrium of infinite classical mechanical systems. It was introduced in the seventies by G. Gallavotti and E. Verboven as an alternative to the Dobrushin–Lanford–Ruelle (DLR) equation. In this article, we consider this concept in the framework of nonlinear Hamiltonian PDEs and discuss its relevance. In particular, we prove that Gibbs measures are the unique KMS equilibrium states for such systems. Our proof is based on Malliavin calculus and Gross–Sobolev spaces. The main feature of our work is the applicability of our results to the general context of white noise, abstract Wiener spaces and Gaussian probability spaces, as well as to fundamental examples of PDEs like the nonlinear Schrödinger, Hartree, and wave (Klein–Gordon) equations.

Characterization of Silicon Photomultipliers after proton irradiation up to [formula omitted

Silicon photomultipliers (SiPMs) are highly-sensitive photodetectors emerging as the technology of choice for many applications, including large high-energy physics experiments where they often are exposed to high radiation fluences. In recent years, there has been an increasing interest in assessing the performance deterioration of such detectors after the irradiation with proton or neutron, with different fluence levels.In this work, samples of different FBK SiPM technologies, made with different manufacturing technologies, were irradiated at the INFN-LNS facility (Italy) with protons reaching fluences up to about 1014 neq/cm2 (1 MeV neutron equivalent) and their performances were characterized in detail after about 30-days room temperature annealing. The results show a significant worsening of the primary noise (dark count rate) of the detectors, which increases with the irradiation fluence, whereas the other performance parameters like the micro-cell gain, the correlated noise probability and the photon detection efficiency do not show significant variations up to 1011 neq/cm2 at least. The breakdown voltage estimation after irradiation is another important aspect for a SiPM. In this contribution, we show several methods for its estimation and compare the results. We also introduced new methodologies to characterize the performance of the SiPMs when they present a very high level of noise, such as the estimation of the dark count rate based on the measured reverse current, the estimation of variations in the photon detection efficiency through the measurement of the responsivity, and the measurement of the correlated noise and the gain through the average charge in response to a pulsed light signal.Lastly, we also analyzed the spatial localization of the proton-induced defects inside the device, i.e. the defects that mostly contribute to the increase of the DCR of the device, through the emission microscopy (EMMI) technique. In particular, we analyzed the SiPMs at the single cell level, trying to identify and spatially localize the defects.

The Residual ISI for Which the Convolutional Noise Probability Density Function Associated with the Blind Adaptive Deconvolution Problem Turns Approximately Gaussian.

In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange’s Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the “eye diagram” is still very closed, namely, where the residual ISI can not be considered as small.

TECHNOLOGIES FOR MONITORING THE TECHNICAL CONDITION OF TRANSPORT INFRASTRUCTURE OBJECTS BASED ON THE COEFFICIENT OF CORRELATION BETWEEN CRITICAL VALUES OF NOISE AND USEFUL SIGNALS

Transport infrastructure objects are exposed to a large number of loads, which cause the formation of displacements, bends, wear, cracks, breakdowns, corrosion, and other defects. It is shown that at the moment of initiation of malfunctions in objects, the noise of the noisy signals coming from the corresponding sensor takes critical values that correlate with useful signals. Therefore, algorithms are developed for calculating the probability of random noise accepting critical values, a coefficient of correlation between the critical values of the noise and the useful component, and a relay cross-correlation function. Technologies for monitoring the technical condition of transport infrastructure objects are proposed based on the estimates of the developed noise characteristics. Computational experiments are conducted, and the reliability of the developed algorithms and technologies is confirmed.