Sample Variance Research Articles

The Lyman Continuum Escape Fraction of Star-forming Galaxies at 2.4 ≲ z ≲ 3.0 from UVCANDELS

Abstract The UltraViolet Imaging of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey Fields (UVCANDELS) survey is a Hubble Space Telescope (HST) Cycle-26 Treasury Program, allocated in total 164 orbits of primary Wide-Field Camera 3 Ultraviolet and VISible light F275W imaging with coordinated parallel Advanced Camera for Surveys F435W imaging, on four of the five premier extragalactic survey fields: GOODS-N, GOODS-S, EGS, and COSMOS. We introduce this survey by presenting a comprehensive analysis of the absolute escape fraction ( f esc abs ) of Lyman continuum radiation through stacking the UV images of a population of star-forming galaxies with secure redshifts at 2.4 ≤ z ≤ 3.0. Our stacking benefits from the catalogs of high-quality spectroscopic redshifts compiled from archival ground-based data and HST slitless spectroscopy, carefully vetted by dedicated visual inspection efforts. We develop a robust stacking method to apply to 10 samples of in total 56 galaxies, and perform detailed Monte Carlo simulations of the intergalactic medium (IGM) attenuation, to take into account the sample variance of the mean IGM transmission when measuring f esc abs . The full stack at z ≈ 2.44 from 28 galaxies places a stringent 1σ upper limit of f esc abs ≲ 5 % , whereas the full stack at z ≈ 2.72 of an equal number of galaxies gives an upper limit of f esc abs ≲ 26 % at 1σ confidence level. These new F275W and F435W imaging mosaics from UVCANDELS have been made publicly available on the Barbara A. Mikulski Archive for Space Telescopes.

Path integral molecular dynamics approximations of quantum canonical observables

Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the Monte Carlo sampling from the Gibbs density of the electron operator, which due to the fermion sign problem has a computational complexity that scales exponentially with the number of electrons. In this work, we construct an algorithm that approximates the mean-field Hamiltonian by path integrals for fermions. The algorithm is based on the determinant of a matrix with components based on Brownian bridges connecting permuted electron coordinates. The computational work for n electrons is O(n3), which reduces the computational complexity associated with the fermion sign problem. We analyze a bias resulting from this approximation and provide a rough computational error indicator. It remains to rigorously explain the surprisingly high accuracy for high temperatures. The method becomes infeasible at low temperatures due to a large sample variance.

Evaluation of unitary conductance of gap junction channels based on stationary fluctuation analysis.

Gap junction (GJ) channels, formed of connexin (Cx) protein, enable direct intercellular communication in most vertebrate tissues. One of the key biophysical characteristics of these channels is their unitary conductance, which can be affected by mutations in Cx genes and various biochemical factors, such as posttranslational modifications. Due to the unique intercellular configuration of GJ channels, recording single-channel currents is challenging, and precise data on unitary conductances of some Cx isoforms remain limited. In this study, we applied stationary noise analysis, a method successfully used for ion channels with very low unitary conductances, to GJ channels. We modified this technique to account for the residual conductance of GJ channels and present three strategies for estimating unitary conductance, including model-based evaluation of open-state probability and subtraction of residual conductance. To assess the validity, advantages, and limitations of these approaches, we performed mathematical analysis and simulation experiments. We also addressed practical issues such as the underestimation of sample variance in autocorrelated recordings and channel rundown, proposing solutions to these issues. Finally, we applied these strategies to electrophysiological data recorded from cells expressing Cx45. Our findings showed that noise-based estimates of Cx45 unitary conductance from macroscopic currents align well with those obtained from single-channel recordings.

Suppressing the sample variance of DESI-like galaxy clustering with fast simulations

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM.Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit.We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance.Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively.We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k 2 = 2k 1 = 0.2 h Mpc-1 by a factor of 1.6.With smaller sample variance on galaxy clustering, we are able to constrain thebaryon acoustic oscillations (BAO)scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordialnon-Gaussianity (NG).

Constraining primordial non-Gaussianity with Density-Split Clustering

Obtaining tight constraints on primordial non-Gaussianity (PNG) is a key step in discriminating between different models for cosmic inflation. The constraining power from large-scale structure (LSS) measurements is expected to overtake that from cosmic microwave background (CMB) anisotropies with the next generation of galaxy surveys including the Dark Energy Spectroscopic Instrument (DESI) and Euclid. We consider whether Density-Split Clustering (DSC) can help improve PNG constraints from these surveys for local, equilateral and orthogonal types. DSC separates a surveyed volume into regions based on local density and measures the clustering statistics within each environment. Using the Quijote simulations and the Fisher information formalism, we compare PNG constraints from the standard halo power spectrum, DSC power spectra and joint halo/DSC power spectra. We find that the joint halo/DSC power spectra outperform the halo power spectrum by factors of ∼ 1.4, 8.8, and 3.6 for local, equilateral and orthogonal PNG, respectively. This is driven by the higher-order information that DSC captures on small scales. We find that applying DSC to a halo field does not allow sample variance cancellation on large scales by providing multiple tracers of the same volume with different local PNG responses. Additionally, we introduce a Fourier space analysis for DSC and study the impact of several modifications to the pipeline, such as varying the smoothing radius and the number of density environments and replacing random query positions with lattice points.

HOD-dependent systematics in Emission Line Galaxies for the DESI 2024 BAO analysis

The Dark Energy Spectroscopic Instrument (DESI) will provide precise measurements of Baryon Acoustic Oscillations (BAO) to constrain the expansion history of the Universe and set stringent constraints on dark energy. Therefore, precise control of the global error budget due to various systematic effects is required for the DESI 2024 BAO analysis. In this work, we estimate the level of systematics induced in the DESI BAO analysis due the assumed Halo Occupation Distribution (HOD) model for the Emission Line Galaxy (ELG) tracer. We make use of mock galaxy catalogs constructed by fitting various HOD models to early DESI data, namely the One-Percent survey data. Our analysis includes typical HOD models for the ELG tracer used in the literature as well as extensions to the baseline models. Among the extensions, we consider various recipes for galactic conformity and assembly bias. We use 25 AbacusSummit simulations under the ΛCDM cosmology for each HOD model and perform independent analyses in Fourier space and in configuration space. To recover the BAO signal from our mocks we perform BAO reconstruction and apply the control variates technique to reduce sample variance noise. Our BAO analyses can recover the isotropic BAO parameter α iso within 0.1% and the Alcock Paczynski parameter α AP within 0.3%. Overall, we find that the systematic error due to the HOD dependence is below 0.17%, with the Fourier space analysis being more robust against the HOD systematics. We conclude that our analysis pipeline is robust enough against the HOD systematics for the ELG tracer in the DESI 2024 BAO analysis, for the assumptions made.

Observing kinematic anisotropies of the stochastic background with LISA

We propose a diagnostic tool for future analyses of stochastic gravitational wave background signals of extra-galactic origin in LISA data. Next-generation gravitational wave detectors hold the capability to track unresolved gravitational waves bundled into a stochastic background. This composite background contains cosmological and astrophysical contributions, the exploration of which offers promising avenues for groundbreaking new insights into very early universe cosmology as well as late-time structure formation. In this article, we develop a full end-to-end pipeline for the extraction of extra-galactic signals, based on kinematic anisotropies arising from the galactic motion, via full-time-domain simulations of LISA's response to the gravitational wave anisotropic sky. Employing a Markov-Chain-Monte-Carlo map-making scheme, multipoles up to ℓ=2 are recovered for scale-free spectra in the case of a high signal-to-noise ratio. We demonstrate that our analysis is consistently beating sample variance and is robust against statistical and systematic errors. The impact of instrumental noise on the extraction of kinematic anisotropies is investigated, and we establish a detection threshold of Ω GW ≳ 5 × 10-8 in the presence of instrument-induced noise. Potential avenues for improvement in our methodology are highlighted.

Integrating the maximum mean discrepancy metric with time–frequency enhanced convolutional neural networks for fault diagnosis

In the operation of rotating machinery, the condition monitoring of key components such as bearings and gears is very important. However, due to the complexity of the real environment and the diversity of equipment operating conditions, the collected mechanical vibration signals of bearings and gears often contain irrelevant noise, which brings challenges to signal processing. Traditional convolutional neural networks (CNNs), lacking denoising structures, have limited effectiveness in processing interfered vibration signals. In addressing these challenges, this paper introduces a novel approach, namely the Gramian-based CNN model and maximum mean square discrepancy (MMSD). For the model, we first propose a simple yet effective denoising strategy, namely Gramian noise reduction (GNR) based on the self-similarity of vibration signal cycles. Second, considering the limitations of traditional CNNs in handling interfered vibration signals, we develop a novel end-to-end GNR-based CNN model - Gramian Time–Frequency Enhanced Network (GTFE-Net), applied to bearing fault diagnosis. GTFE-Net consists of three parallel branches, each processing the original signal, the GNR-denosed signal, and spectral information. By integrating GNR into GTFE-Net, the network focuses more on feature extraction. Additionally, we introduce MMSD as a metric that comprehensively reflects differences in sample mean and variance information in the reproducing kernel Hilbert space, thereby enhancing domain confusion. The experimental results indicate that this method achieved a diagnostic accuracy of 77.19% for various transmission tasks in noisy environments. This finding provides reliable support for bearing fault diagnosis, demonstrating the method’s effectiveness and potential for application in complex environments.

A comprehensive guide to study the agreement and reliability of multi-observer ordinal data

BackgroundA recent systematic review revealed issues in regard to performing and reporting agreement and reliability studies for ordinal scales, especially in the presence of more than two observers. This paper therefore aims to provide all necessary information in regard to the choice among the most meaningful and most used measures and the planning of agreement and reliability studies for ordinal outcomes.MethodsThis paper considers the generalisation of the proportion of (dis)agreement, the mean absolute deviation, the mean squared deviation and weighted kappa coefficients to more than two observers in the presence of an ordinal outcome.ResultsAfter highlighting the difference between the concepts of agreement and reliability, a clear and simple interpretation of the agreement and reliability coefficients is provided. The large sample variance of the various coefficients with the delta method is presented or derived if not available in the literature to construct Wald confidence intervals. Finally, a procedure to determine the minimum number of raters and patients needed to limit the uncertainty associated with the sampling process is provided. All the methods are available in an R package and a Shiny application to circumvent the limitations of current software.ConclusionsThe present paper completes existing guidelines, such as the Guidelines for Reporting Reliability and Agreement Studies (GRRAS), to improve the quality of reliability and agreement studies of clinical tests. Furthermore, we provide open source software to researchers with minimum programming skills.

A Normative Model Representing Autistic Individuals Amidst Autism Spectrum Phenotypic Heterogeneity.

Currently, there is a need for approaches to understand and manage the multidimensional autism spectrum and quantify its heterogeneity. The diagnosis is based on behaviors observed in two key dimensions, social communication and repetitive, restricted behaviors, alongside the identification of required support levels. However, it is now recognized that additional modifiers, such as language abilities, IQ, and comorbidities, are essential for a more comprehensive assessment of the complex clinical presentations and clinical trajectories in autistic individuals. Different approaches have been used to identify autism subgroups based on the genetic and clinical heterogeneity, recognizing the importance of autistic behaviors and the assessment of modifiers. While valuable, these methods are limited in their ability to evaluate a specific individual in relation to a normative reference sample of autistic individuals. A quantitative score based on axes of phenotypic variability could be useful to compare individuals, evaluate the homogeneity of subgroups, and follow trajectories of an individual or a specific group. Here we propose an approach by (i) combining measures of phenotype variability that contribute to clinical presentation and could impact different trajectories in autistic persons and (ii) using it with normative modeling to assess the clinical heterogeneity of a specific individual. Using phenotypic data available in a comprehensive reference sample, the Simons Simplex Collection (n = 2744 individuals), we performed principal component analysis (PCA) to find components of phenotypic variability. Features that contribute to clinical heterogeneity and could impact trajectories in autistic people were assessed by the Autism Diagnostic Interview-Revised (ADI-R), Vineland Adaptive Behavior Scales (VABS) and the Child Behavior Checklist (CBCL). Cognitive assessment was estimated by the Total Intelligence Quotient (IQ). Three PCs embedded 72% of the normative sample variance. PCA-projected dimensions supported normative modeling where a multivariate normal distribution was used to calculate percentiles. A Multidimensional General Functionality Score (MGFS) to evaluate new prospective single subjects was developed based on percentiles. Our approach proposes a basis for comparing individuals, or one individual at two or more times and evaluating homogeneity in phenotypic clinical presentation and possibly guides research sample selection for clinical trials.

Polarisation results from the GOODS-N field with Apertif and polarised source counts

We analysed six Apertif datasets, covering the GOODS-N LOFAR deep field region, aiming to improve our understanding of the faint radio source composition, their polarisation behaviour, and how this affects our interpretation of polarised source counts. Using a semi-automatic routine, we ran rotation measure synthesis to generate a polarised intensity mosaic for each observation. The routine also performs source finding and cross-matching with the total power catalogue, as well as NVSS, SDSS and allWISE, to obtain a catalogue of 1182 polarised sources in an area of 47.4\,deg$^2$. Using the mid-infrared (MIR) radio correlation, we found no indication of any polarised emission from star formation. To robustly estimate the source counts, we performed an investigation of our sample's completeness as a function of the polarised flux via synthetic source injection. In contrast to previous works, we find no strong dependency of fractional polarisation on the total intensity flux density. We argue that differences regarding previous (small-scale, deep field) analyses can be attributed to sample variance. Relative to the findings of previous works, here we find a steeper slope for our Euclidean-normalised differential source counts. This is also visible as a flattening in cumulative source counts. We attribute the observed steeper slope in Euclidean normalised differential source counts to a change in the source composition and properties at low total intensities.

Spatial analysis of femtosecond laser generated plasma using principal component analysis

The appearance of plasma generated during femtosecond laser machining depends strongly on the features present on the sample before machining occurs. However, the complexity of femtosecond light-matter interaction means that development of a theoretical understanding of plasma generation is challenging. In this work, principal component analysis is applied to experimental images of plasma generated during femtosecond laser machining of silicon to calculate the orthogonal spatial patterns of the plasma variance (plasma modes), and to identify which sample variance (sample modes) are associated with these plasma modes. The results demonstrate the potential of principal component analysis for data-driven scientific discovery in the field of femtosecond light-matter interactions.

Practical Considerations When Using Mendelian Sampling Variances for Selection Decisions in Genomic Selection Programs

ABSTRACTThe purpose of this work was to test the application of selection criteria that consider the genetic variances of future generations. This has not been done previously in numerically large livestock breeding programs based on estimated rather than assumed known marker effects. A generic pure‐line pig breeding program was simulated in which 40 males and 400 females were selected every generation. Daily gain was used as an example trait. Three variance‐considering criteria as well as different reference population sizes were compared to investigate the effect of differences in genomic prediction accuracy on selection decisions. All variance‐considering criteria retained more genetic variance than if selection was based on estimated breeding values (max. 20%). This effect was more pronounced for higher prediction accuracies and criteria assessing the variance more generations ahead. After 20 generations, the criterion with the longest planning horizon combined with the largest reference population resulted in a 2% higher genetic level of boars selected to produce finisher pigs. While the advantage of accounting for future generations diminished with lower accuracy or shorter planning horizons, the variance‐considering criteria never performed worse than selection based on genomic estimated breeding values (GEBV) with respect to commercial genetic gain. We are reporting various accuracy metrics to help judge the effectiveness of using one of our tested criteria in real breeding programs. While we did not find large benefits for genetic gain when considering future variances in selection decisions, we also did not find negative side effects, while considerably more genetic variance was maintained. This means that using variance‐considering criteria results in either equally good or better performance than truncation selection based on estimated breeding values. Our criteria can be applied to any genomic breeding program as long as phased genotypes, estimated marker effects and a genetic map are available.

Optimizing Falling Drop Hemoglobin Method by Comparing Capillary Versus Venous Blood and Determining the Stability of the Copper Sulfate Solution.

Anemia is a global health issue that affects over 1 billion people and contributes to maternal mortality and birth defects. Low-resource, tropical areas face a dual challenge: high prevalence of anemia and inability to access affordable testing methods. The falling drop hemoglobin method has been developed by our lab to quantify hemoglobin concentration and assess anemia by timing the descent of venous blood in a column of copper sulfate solution, without using electricity or batteries. This research aimed to optimize the falling drop hemoglobin method by evaluating the use of capillary blood to reduce within sample variance and assessing copper sulfate stability to determine shelf life in expected working conditions. The falling drop hemoglobin method was performed on both venous and capillary blood samples collected directly from the fingertip by dispensing 44 µL of blood in a copper sulfate column. A microhematocrit was performed on the venous blood sample and converted mathematically to a hemoglobin level to serve as the standard. Copper sulfate stability was assessed for 32 weeks among three solutions: solution prepared fresh on day of testing, solution incubated at room temperature, and solution incubated at 37.7 °C. Capillary blood yielded higher average descent times and higher standard deviations than venous blood. Collecting precisely 44 µL of capillary blood proved challenging and impractical. In copper sulfate stability testing, freshly prepared solution yielded the highest average descent time. A one-way analysis of variance (ANOVA) test and Tukey's honestly significant difference (HSD) post hoc testing revealed no significant difference between mean descent times of freshly prepared and 37.7 °C solutions (P = 0.26) and between room temperature and 37.7 °C solutions (P = 0.64), but a significant difference between freshly prepared and room temperature solutions (P = 0.04). This study found that capillary blood did not present a more accurate alternative to venous blood in the falling drop hemoglobin test, and copper sulfate did not degrade over 32 weeks at 37.7 °C. This lends support for the current use of venous blood in the test, and for use of copper sulfate solution in tropical climates, where the test is most necessary, with a shelf life of at least 32 weeks.

The Influence of Canva-Based Learning Media on Creativity and Critical Thinking of Vocational School Students

The creativity and critical thinking of class XI students at SMK Plus Bustanul Ma'arif is still relatively low. One of the reasons for this is that teachers in carrying out learning do not use media. The aim of this research is to describe the influence of Canva-based learning media on the creativity and critical thinking of class XI students at SMK Plus Bustanul Ma'arif. The method used is Quasi Experiment with a Pretest-Posttest Only Control Group Design. The research instruments used were creativity and critical thinking tests. The homogeneity test results show that the sig value. creativity of 0.115 and a sig value. critical thinking is 0.773, so it can be concluded that the sample variance is homogeneous. Meanwhile, the normality test results show that the sig. creativity and critical thinking in the control group and experimental group were normally distributed because > 0.05. After fulfilling the prerequisite tests, the researcher collected posttest data on creativity and critical thinking in the control class and experimental class which were analyzed using the MANOVA test with an error degree of 5%. The results show that there is the significant influence of Canva-based learning media on the creativity and critical thinking of class XI students at SMK Plus Bustanul Ma'arif; Ha accepted and rejected H0.

BSDA: Bayesian Random Semantic Data Augmentation for Medical Image Classification.

Data augmentation is a crucial regularization technique for deep neural networks, particularly in medical imaging tasks with limited data. Deep learning models are highly effective at linearizing features, enabling the alteration of feature semantics through the shifting of latent space representations-an approach known as semantic data augmentation (SDA). The paradigm of SDA involves shifting features in a specified direction. Current SDA methods typically sample the amount of shifting from a Gaussian distribution or the sample variance. However, excessive shifting can lead to changes in data labels, which may negatively impact model performance. To address this issue, we propose a computationally efficient method called Bayesian Random Semantic Data Augmentation (BSDA). BSDA can be seamlessly integrated as a plug-and-play component into any neural network. Our experiments demonstrate that BSDA outperforms competitive methods and is suitable for both 2D and 3D medical image datasets, as well as most medical imaging modalities. Additionally, BSDA is compatible with mainstream neural network models and enhances baseline performance. The code is available online.

Optimality of novel estimators for variance estimation under successive sampling

This article presents a class of estimators allied with Searls (1964) using a novel approach to estimate population variance on two occasion under successive sampling. Isaki (1983) encourages us to address the problem of estimating finite population variance in survey sampling, its application to the case of successive sampling is highly captivating, and the methodology proposed here will be useful to those involved in similar studies in the future. To the best of our knowledge, this is any authors’ first foray into this field to provide more efficient estimators than the regression type estimator. An empirical study based on real population and artificial population proves the utility of the proposed methods.

A GENERAL LIMIT THEORY FOR NONLINEAR FUNCTIONALS OF NONSTATIONARY TIME SERIES

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self-normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self-normalized statistics similar to the bimodality that can arise in t-ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications, new self-normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.

Depressive and anxiety symptoms in current, previous, and no history of ME/CFS: NHIS 2022 analysis.

Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is associated with anxiety and depressive symptoms. Psychological symptoms are predisposing factors for, as well as symptoms of, ME/CFS. Recovery from ME/CFS is poorly understood and heterogenous, and it is unclear how psychological symptoms may change with recovery. The aim of this study was to examine the associations of depressive and anxious symptoms among individuals with current, previous, and no history of ME/CFS. National Health Interview Survey 2022 data were analyzed to assess ME/CFS status, as well as anxiety and depression burden. Adults (unweighted N = 27,651) in the United States reported sociodemographic and health behavior characteristics, with 453 adults reporting current ME/CFS, while 119 reported previous ME/CFS. Sample weights and variance estimation variables were implemented. Multivariable linear regression models were used to analyze the associations between ME/CFS status and anxiety and depression severity after adjusting for sociodemographic and health behavior variables. Participants were on average 48.1 years of age, and most identified as female (51.3%), white (76.6%), and not Hispanic or Latine (82.8%). Current and previous ME/CFS were associated with anxiety and depressive symptoms compared to individuals with no history of ME/CFS. Clinically significant levels of anxiety and depressive symptoms were substantial for individuals with current (37.6%; 49.0%) and previous (26.5%; 33.4%) ME/CFS compared to individuals with no history of ME/CFS (6.1%; 6.7%). ME/CFS, regardless of current presence, was related to significantly greater anxiety and depressive symptom burden.

STATISTICAL SIMULATION OF RELIABILITY OF NETWORKS WITH EXPONENTIALLY DISTRIBUTED UNIT LIFETIMES

In this paper, there were deduced three new lifetime distributions of serial-parallel and parallel-serial networks, their distribution being approached by means of analytical and Monte-Carlo methods. The novelty of the distribution consists in the fact that the number of subnets is random, governed by the Poisson and Logarithmic distributions, the lifetimes of the units in each subnet being independent, identically, exponentially distributed random variables, the number of units in each subnet is the same constant integer number. It was shown that the most important theoretical characteristics of lifetime for such networks, as the mean value, the variance, the survival/reliability function, my be approximated, with desired accuracy, by the same corresponding characteristics, as the sample mean value, sample variance, empirical survival/reliability function simulated by Monte-Carlo methods. Results are illustrated tabularly and graphically for some concrete examples.