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This paper presents a significant extension of perturbation theory techniques for estimating the roots of polynomials. Building upon foundational results and recent work by Pakdemirli and Yurtsever, as well as taking inspiration from the concept of probabilistic bounds introduced by Sheikh et al., we develop and prove several novel theorems that address a wide range of polynomial structures. These include polynomials with multiple large coefficients, coefficients of different orders, alternating coefficient orders, large linear and constant terms, and exponentially decreasing coefficients. Among the key contributions is a theorem that establishes an upper bound on the expected maximum modulus of the zeros of polynomials with uniformly distributed perturbations in their coefficients. The theorem considers the case where all but the leading coefficient receive a uniformly and independently distributed perturbation in the interval [ − 1 , 1 ] . Our approach provides a comprehensive framework for estimating the order of magnitude of polynomial roots based on the structure and magnitude of their coefficients without the need for explicit root-finding algorithms. The results offer valuable insights into the relationship between coefficient patterns and root behavior, extending the applicability of perturbation-based root estimation to a broader class of polynomials. This work has potential applications in various fields, including random polynomials, control systems design, signal processing, and numerical analysis, where quick and reliable estimation of polynomial roots is crucial. Our findings contribute to the theoretical understanding of polynomial properties and provide practical tools for engineers and scientists dealing with polynomial equations in diverse contexts. [ABSTRACT FROM AUTHOR]

Wearable sensors for sweat trace metal monitoring have the challenges of effective sweat collection and the real-time recording of detection signals. The existing detection technologies are implemented by generating enough sweat through exercise, which makes detecting trace metals in sweat cumbersome. Generally, it takes around 20 min to obtain enough sweat, resulting in dallied and prolonged detection signals that cannot reflect the endogenous fluctuations of the body. To solve these problems, we prepared a multifunctional hydrogel as an electrolyte and combined it with a flexible patch electrode to realize real-time monitoring of sweat Zn2+. Such hydrogel has magnetic and porous properties, and the porous structure of hydrogel enables a fast absorption of sweat, and the magnetic property of the addition of fabricated Fe3O4 NPs not only improves the conductivity but also ensures the adjustable internal structures of the hydrogel. Such a sensing platform for sweat Zn2+ monitoring shows a satisfied linear relationship in the concentration range of 0.16–16 µg/mL via differential pulsed anodic striping voltammetry (DPASV) and successfully detects the sweat Zn2+ of four volunteers during exercise and resting, displaying a promising path for commercial application. [ABSTRACT FROM AUTHOR]

In this paper, we perform statistical analysis for the decisional problem which is fundamental for the security of the key exchange protocol based on matrix power function. We have proven previously that the considered decisional problem is NP-complete and hence our proposal could potentially be quantum-safe. However, we did not explore the dependence of the complexity of the considered problem on the security parameters. Here we show that for small matrices certain information could be gained from the distribution of the entries of the public key matrices. On the other hand, we show that as the size of the matrices grows, the public key matrices are indistinguishable from truly random matrices. [ABSTRACT FROM AUTHOR]

In this paper, we revisited the previously proposed key exchange protocol based on the matrix power function. We prove that the entries of the public key matrices of both parties of the protocol are uniform. Using this result we defined a security game for our protocol and show that the malicious attacker cannot gain any significant advantage in winning this game by applying faithful representation or the linearization approaches. Moreover, we showed that the shared key is computationally indistinguishable from the imitation key if the security parameters are properly chosen.

We examine a property of sequences called Poissonian pair correlations with parameter 0 ⩽ β ⩽ 1 (abbreviated as β -PPC). We prove that when β < 1 , the property of β -PPC, also known as weak Poissonian correlations, can be detected at the behaviour of sequences at small scales, and show that this does not happen for the classical notion of PPC, that is, when β = 1 . Furthermore, we show that whenever 0 ⩽ α < β ⩽ 1 , β -PPC is stronger than α -PPC. We also include a discussion on weak Poissonian correlations of higher orders, showing that for β < 1 , Poissonian β -correlations of order k + 1 imply Poissonian β -correlations of k-th order with the same parameter β . [ABSTRACT FROM AUTHOR]

This paper proposes a novel multi-attribute decision-making (MADM) method for interval rough numbers (IRNs) considering different distribution types, namely uniform, exponential, and normal distributions. Upper and lower approximate interval dominance degrees are defined and aggregated using dynamic weights to obtain pairwise comparisons of IRNs. The properties of dominance are verified, and an attribute weight determination method based on the dominance balance degree is introduced. The proposed MADM method is data-driven and does not rely on the subjective preferences of decision-makers. Case analysis demonstrates the effectiveness and rationality of the proposed method, revealing that the distribution type of IRNs significantly impacts decision results, potentially leading to reversed ranking outcomes. The proposed method offers a comprehensive framework for handling MADM problems with IRNs under different distributions. [ABSTRACT FROM AUTHOR]

Although regular expressions do not correspond univocally to regular languages, it is still worthwhile to study their properties and algorithms. For the average case analysis one often relies on the uniform random generation using a specific grammar for regular expressions, that can represent regular languages with more or less redundancy. Generators that are uniform on the set of expressions are not necessarily uniform on the set of regular languages. Nevertheless, it is not straightforward that asymptotic estimates obtained by considering the whole set of regular expressions are different from those obtained using a more refined set that avoids some large class of equivalent expressions. In this paper we study a set of expressions that avoid a given absorbing pattern. It is shown that, although this set is significantly smaller than the standard one, the asymptotic average estimates for the size of the Glushkov automaton for these expressions does not differ from the standard case. Furthermore, for this set the asymptotic density of 휀-accepting expressions is also the same as for the set of all standard regular expressions. [ABSTRACT FROM AUTHOR]

Subsets of rational numbers are specified as preimages of values of arithmetical functions. The uniformity of distribution of elements of these sets is proved and interpreted in the context of Diophantine approximation to real numbers. [ABSTRACT FROM AUTHOR]

We study the behavior of the failure rate associated with the distribution of a random variable of the form X = Y + U , where Y, U are independent and U has bounded support. First, we obtain monotonicity results and bounds for the failure rate of X in the case where U has a uniform distribution and, in particular we show that, asymptotically, the failure rates of X and Y tend to the same limit. Some of the results are generalized for the case where the distribution of U is not uniform, but has bounded support. Further, we show that if the failure rate of a non negative variable X is constant in some interval (L , ∞) , then X can be written as the sum of two independent random variables, one of which is exponential and the other (which is not necessarily uniform) has support [ 0 , L ] . [ABSTRACT FROM AUTHOR]

When utilizing high-dimensional chaotic signals for frequency modulation, achieving a uniformly distributed power spectrum is a challenging task. This paper addresses this challenge by proposing a power spectrum homogenization strategy based on distribution transformation. The strategy transforms the task of achieving a uniformly distributed power spectrum in frequency modulation of high-dimensional chaotic signals to solve and equalize the probability density function of the chaotic signals, thereby further enhancing the ability of high-dimensional chaotic signals to suppress electromagnetic interference. Firstly, the difficulty of obtaining a smooth probability density function of chaotic modulation signals is solved using the kernel density estimation algorithm. Then, a distribution transformation algorithm is proposed to convert non-uniformly distributed chaotic modulation signals into uniformly distributed chaotic modulation signals. By using uniformly distributed chaotic modulation signals for frequency modulation, the objective of power spectrum equalization is achieved. Finally, taking the Chua's chaotic signal as an example, the effectiveness of the proposed strategy is verified using an experimental platform based on a digital signal processor-controlled active clamping flyback converter. [ABSTRACT FROM AUTHOR]

Given the constraints on the invariant distribution in chaotic systems, flexibly setting the probability distribution of chaotic signals poses a significant challenge. To tackle this issue, this paper proposes a strategy that transforms the task into solving and modifying the probability density function of the chaotic intrinsic signal. Initially, kernel density estimation algorithms are employed to address the issue of obtaining smooth probability density functions for high-dimensional chaotic signals. Any chaotic signal can serve as the intrinsic signal source, with its probability density function and distribution function being solvable using this algorithm. Subsequently, a graph-based transformation algorithm is introduced for the flexible adjustment of chaotic signal probability distribution. This algorithm can convert the intrinsic signal into a chaotic signal with the desired distribution type based on the characteristics of the target distribution, providing an analytical expression for the transformation relationship. Finally, the effectiveness of this strategy is validated by generating uniform distribution chaotic signals using a Chua chaotic signal as the intrinsic source. The outstanding performance of this signal in suppressing common-mode conducted electromagnetic interference in high-frequency converters is highlighted. The experimental results demonstrate this strategy's ability to flexibly configure probability distribution types of chaotic signals. Additionally, chaotic signals with a uniform distribution can achieve uniform power spectrum shaping, with a suppression effect on maximum common-mode conducted electromagnetic interference reaching 16.56 dB. [ABSTRACT FROM AUTHOR]

The use of life distributions has increased over the past decade, receiving particular attention in recent years, both from a practical and theoretical point of view. Life distributions can be used in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. This paper presents and investigates a new life distribution. The proposed model shows favorable characteristics in terms of reliability theory, which makes it competitive against other commonly used life distributions, such as the exponential, gamma, and Weibull distributions. The methods of maximum likelihood and moments are used to estimate the parameters of the proposed model. Additionally, real-life data drawn from different fields are used to illustrate the usefulness of the new distribution. Further, the R programming language is used to perform all computations and produce all graphs. [ABSTRACT FROM AUTHOR]

In any dimension d ≥ 2 , there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β -Poissonian pair correlations for all 0 < β < 1 d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β = 1 d). In this paper, we further elaborate on the closeness of the two notions. We show that d -dimensional Kronecker sequences for badly approximable vectors α → with an arbitrary small uniformly distributed stochastic error term generically have β = 1 d -Poissonian pair correlations. [ABSTRACT FROM AUTHOR]

Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized—from a stochastic point of view—as so-called self-consistent curves based on the conditional expectation and—from the variational-calculus point of view—as saddle points of the expected difference of a random variable and its projection onto some curve, where the current curve acts as argument of the energy functional. Beyond that, Duchamp and Stützle (1993, 1996) showed that planar curves can be computed as solutions of a system of ordinary differential equations. The aim of this paper is to generalize this characterization of principal curves to R d with d ≥ 3. Having derived such a dynamical system, we provide several examples for principal curves related to uniform distribution on certain domains in R 3. [ABSTRACT FROM AUTHOR]

A probabilistic model has been constructed to describe the physical state of a dielectric film that contains randomly distributed air inclusions with random radius . Analysis of this model has shown that the statistical distribution of electrical strength, which is less than that of a defect-free film, has exactly two maxima. It is realized at a sufficiently low density of air inclusions of random radius , which has an almost uniform probability distribution within the limits > > 0. Moreover, the position of the first maximum is determined by the value of the parameter . With increasing defect density or film thickness, the first maximum disappears and the electrical strength distribution becomes unimodal. [ABSTRACT FROM AUTHOR]

This paper introduced the neutrosophic uniform distribution and innovative simulation methods to generate random numbers from the neutrosophic uniform distribution and the neutrosophic Weibull distribution. We introduced simulation methods and algorithms designed to handle indeterminacy for both of these distributions. We provided random numbers generated from both distributions across a range of parameter values and degrees of indeterminacy. Furthermore, we conducted a comparative analysis between the classical simulation method in classical statistics and the neutrosophic simulation method. Our findings reveal that the proposed neutrosophic simulation method generates random numbers of smaller magnitudes compared to the classical simulation method under classical statistics. This observation forms the basis of our conclusion.

This paper introduced the neutrosophic uniform distribution and innovative simulation methods to generate random numbers from the neutrosophic uniform distribution and the neutrosophic Weibull distribution. We introduced simulation methods and algorithms designed to handle indeterminacy for both of these distributions. We provided random numbers generated from both distributions across a range of parameter values and degrees of indeterminacy. Furthermore, we conducted a comparative analysis between the classical simulation method in classical statistics and the neutrosophic simulation method. Our findings reveal that the proposed neutrosophic simulation method generates random numbers of smaller magnitudes compared to the classical simulation method under classical statistics. This observation forms the basis of our conclusion. [ABSTRACT FROM AUTHOR]

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Given a labeled tree topology t , consider a population P of k leaves chosen among those of t. The clade of P is the minimal subtree of t containing P and its size is given by the number of leaves in the clade. When t is selected under the Yule or uniform distribution among the labeled topologies of size n , we study the "clade size" random variable determining closed formulas for its probability mass function, its mean, and its variance. Our calculations show that for large n the clade size tends to be smaller under the uniform model than under the Yule model, with a larger variability in the first scenario for values of k ≥ 5. We apply our probability formulas to investigate set-theoretic relationships between the clades of two populations in a random tree, determining how likely one clade is contained in or it is equal to the other. Our study relates to earlier calculations for the probability that under the Yule model the clade size of P equals the size of P – that is, the population P forms a monophyletic group – and extends known results for the probability that the minimal (non-trivial) clade containing a random taxon has a given size. [ABSTRACT FROM AUTHOR]

The ubiquitous adoption of network-based technologies has left organizations vulnerable to malicious attacks. It has become vital to have effective intrusion detection systems (IDS) that protect the network from attacks. In this paper, we study the intrusion detection problem through the lens of probability theory. We consider a situation where a network receives random malicious signals at discrete time instances, and an IDS attempts to capture these signals via a random check process. We aim to develop a probabilistic framework for intrusion detection under the given scenario. Concretely, we calculate the detection rate of a network attack by an IDS and determine the expected number of detections. We perform extensive theoretical and experimental analyses of the problem. The results presented in this paper would be helpful tools for designing and analyzing intrusion detection systems. We propose a probabilistic framework that could be useful for IDS experts; for a network-based IDS that monitors in real-time, analyzing the entire traffic flow can be computationally expensive. By probabilistically sampling only a fraction of the network traffic, the IDS can still perform its task effectively while reducing the computational cost. However, checking only a fraction of the traffic increases the possibility of missing an attack. This research can help IDS designers achieve appropriate detection rates while maintaining a low false alarm rate. The groundwork laid out in this paper could be used for future research on understanding the probabilities related to intrusion detection. [ABSTRACT FROM AUTHOR]

This paper considers two models of queuing with a varying structure based on the introduction of additional transient intensities into known models or their combinations, which create stationary distributions convenient for calculation. In the first model, it is a probabilistic mixture of known stationary distributions with given weights. In the second model, this uniform distribution is repeatedly used in physical statistics. Both models are based on the selection of states, between which additional transient intensities are introduced. The algorithms used in this paper for introducing new transient intensities are closely related to the concept of flow in a deterministic transport network. The introduced controls are selected so that the marginal distribution of the combined system is a mixture of the marginal distributions of the combined systems with different weights determined by the introduced transient intensities. As a result, the process of functioning of the combined system is obtained by switching processes corresponding to different combined systems at certain points in time.

The CDT subproblem, which minimizes a quadratic function over the intersection of two ellipsoids, is a classical quadratic programming problem. In this paper, we study a method of solving CDT with a positive Lagrangian duality gap. An efficient splitting algorithm is proposed for finding the global optimal solutions. A cutting plane is firstly added to divide the feasible set of CDT into two subsets, and then two new quadratic programming problems with ellipsoidal and linear constraints are generated accordingly. Using the newly developed technique — second-order cone constraints to enhance the efficiencies of the SDP relaxation-based algorithms on the two subproblems, an optimal solution of CDT can be acquired by comparing the objective values of the two subproblems. Numerical experiments show that the new algorithm outperforms the two recent SDP relaxation-based algorithms, the two-parameter eigenvalue-based algorithm and the solver Gurobi 9.5 for certain types of CDT. [ABSTRACT FROM AUTHOR]

M. I. Yadrenko discovered that the expectation of the minimum number N1 of independent and identically distributed uniform random variables on (0, 1) that have to be added to exceed 1 is e. For any threshold a > 0, K. G. Russell found the distribution, mean, and variance of the minimum number Na of independent and identically distributed uniform random summands required to exceed a. Here we calculate the distribution and moments of Na when the summands obey the negative exponential and Lévy distributions. The Lévy distribution has infinite mean. We compare these results with the results of Yadrenko and Russell for uniform random summands to see how the expected first-passage time E (N a) , a > 0 , and other moments of Na depend on the distribution of the summand. [ABSTRACT FROM AUTHOR]

In response to the issues of low-velocity zones and non-uniform jet velocity distribution in the airflow field of traditional air-assisted orchard sprayers, an arc-shaped air outlet suitable for axial-flow air-assisted systems is designed. This article employs the method of CFD numerical simulation and experimental verification to compare and analyze the internal flow field of the air-assisted system and validates the reliability of the numerical simulation results through calculation error and chi-square test. The wind speed of the cross-section is measured at different distances from the outlet, and the distribution characteristics of the outflow field wind speed before and after the structural optimization of the air-assisted system are compared. The horizontal distribution of fog droplets is collected using a fog collection chamber. The experimental results show that the design of the arc-shaped outlet increases the average wind speed of the annular outlet from 14.95 m/s to 18.20 m/s and reduces the proportion of low-speed area from 20.83% to 0.71%. When the rounded corner radius of the air outlet is 50 mm, optimal parameters are attained. The maximum error between the simulated and experimental values is 9.52%. At a significance level of 0.05, the χ2 value is 0.252, indicating that the simulated values follow the distribution of the actual measurement values. On the cross-sections located at distances of 0.5, 0.75, 1, 1.25, and 1.5 m from the air outlet, the wind speed distribution with no arc-shaped air outlets exhibits a "low left and high right" type, tending to shift towards the right as a whole. Fog droplets also display a drift tendency towards the right side. The wind speed distribution with arc-shaped air outlets shows a symmetric "high in the middle and low on the sides" type. Fog droplets concentrate in the central position. The optimized air-assisted system can reduce the air field's low-flow area, increase the airflow distribution uniformity, improve the average wind speed at the outlet, and decrease fog droplet drift. This provides a reference for the structural design of air-assisted systems in current orchard sprayers of the same type. [ABSTRACT FROM AUTHOR]

The tax gap can be considered as the criterion and principle of the effectiveness and efficiency of the tax system. Inadequate collection of taxes as well as non-realization of tax revenues is called tax gap, which is one of the factors that aggravate the budget deficit. In this paper, the issue of tax gap is investigated with two approaches. The first approach is a situation where two groups of investigators who are willing and unwilling to collude with two groups of taxpayers who are willing and unwilling to collude with a uniform distribution are placed in the game. The second approach also shows a situation where the probability of not discovering a taxpayer's violation is shown by a mathematical function and the quality of investigating groups for taxpayers who are uniformly distributed is unknown. The results of the first approach show that with the increase in the number of taxpayers unwilling to collude and the increase in the number of groups willing to collude with taxpayers, the tax gap decreases. Also, with the reduction of the tax rate and the increase in the number of groups unwilling to collude, the tax gap increases. The results of the second approach show that the tax gap increases with the increase in the number of investigators and also the increase in the probability of dishonesty of the taxpayer.

Wearable sensors for sweat trace metal monitoring have the challenges of effective sweat collection and the real-time recording of detection signals. The existing detection technologies are implemented by generating enough sweat through exercise, which makes detecting trace metals in sweat cumbersome. Generally, it takes around 20 min to obtain enough sweat, resulting in dallied and prolonged detection signals that cannot reflect the endogenous fluctuations of the body. To solve these problems, we prepared a multifunctional hydrogel as an electrolyte and combined it with a flexible patch electrode to realize real-time monitoring of sweat Zn2+. Such hydrogel has magnetic and porous properties, and the porous structure of hydrogel enables a fast absorption of sweat, and the magnetic property of the addition of fabricated Fe3O4 NPs not only improves the conductivity but also ensures the adjustable internal structures of the hydrogel. Such a sensing platform for sweat Zn2+ monitoring shows a satisfied linear relationship in the concentration range of 0.16–16 µg/mL via differential pulsed anodic striping voltammetry (DPASV) and successfully detects the sweat Zn2+ of four volunteers during exercise and resting, displaying a promising path for commercial application.

Given the constraints on the invariant distribution in chaotic systems, flexibly setting the probability distribution of chaotic signals poses a significant challenge. To tackle this issue, this paper proposes a strategy that transforms the task into solving and modifying the probability density function of the chaotic intrinsic signal. Initially, kernel density estimation algorithms are employed to address the issue of obtaining smooth probability density functions for high-dimensional chaotic signals. Any chaotic signal can serve as the intrinsic signal source, with its probability density function and distribution function being solvable using this algorithm. Subsequently, a graph-based transformation algorithm is introduced for the flexible adjustment of chaotic signal probability distribution. This algorithm can convert the intrinsic signal into a chaotic signal with the desired distribution type based on the characteristics of the target distribution, providing an analytical expression for the transformation relationship. Finally, the effectiveness of this strategy is validated by generating uniform distribution chaotic signals using a Chua chaotic signal as the intrinsic source. The outstanding performance of this signal in suppressing common-mode conducted electromagnetic interference in high-frequency converters is highlighted. The experimental results demonstrate this strategy’s ability to flexibly configure probability distribution types of chaotic signals. Additionally, chaotic signals with a uniform distribution can achieve uniform power spectrum shaping, with a suppression effect on maximum common-mode conducted electromagnetic interference reaching 16.56 dB.

In order to establish the projection properties of computer uniform designs of experiments on Sobol’s sequences, an empirical comparative statistical analysis of the homogeneity of 2D projections of the best known improved designs of experiments was carried out using the novel objective indicators of discrepancies. These designs show an incomplete solution to the problem of clustering points in low-dimensional projections graphically and numerically, which requires further research for new Sobol’s sequences without the drawback mentioned above. In the article, using the example of the first 20 improved Sobol’s sequences, a methodology for creating refined designs is proposed, which is based on the unconventional use of these already found sequences. It involves the creation of the next dimensional design based on the best homogeneity and projection properties of the previous one. The selection of sequences for creating an initial design is based on the analysis of numerical indicators of the weighted symmetrized centered discrepancy for two-dimensional projections. According to the algorithm, the combination of sequences is fixed for the found variant and a complete search of the added one-dimensional sequences is performed until the best one is detected. According to the proposed methodology, as an example, a search for more perfect variants of designs for factor spaces from two to nine dimensions was carried out. New combinations of Sobol’s sequences with better projection properties than those already known are given. Their effectiveness is confirmed by statistical calculations and graphically demonstrated box plots and histograms of the projection indicators distribution of the weighted symmetrized centred discrepancy. In addition, the numerical results of calculating the volumetric indicators of discrepancies for the created designs with different number of points are given.

This study mainly considers the scheduling problems with learning effects, where the learning rate is a random variable and obeys a uniform distribution. In the first part, we introduce a single machine model with location-based learning effects. We have given the theoretical proof of the optimal solution for the five objective functions. In the second part, we study the problem with group technology. Both intra-group and inter-group have location-based learning effects, and the learning rate of intra-group jobs follows a uniform distribution. We also give the optimal ranking method and proof for the two problems proposed.

In this paper, we explore the integration of a stochastic input-output model based on uniform distribution into management accounting systems to enhance operational efficiency in enterprises. The model is formulated as the mathematical expression of an input-output table, focusing on the structure of the direct consumption coefficient matrix. By applying this model to the financial data of Y Iron and Steel Enterprise in W City, we evaluate the enterprise’s competitiveness and input-output performance. From 2019 to 2023, the company’s capital rate increased markedly from 0.0235 to 0.0868, reflecting a stronger resilience against lousy debt risks. Furthermore, we observed substantial growth in assets, deposits, and loans, with 2023 figures at 0.4965, 0.5839, and 0.3899, respectively. These metrics highlight the rapid development of the financial market and expansion opportunities. Our analysis demonstrates the utility of input-output models in management accounting to qualitatively assess and optimize product output and sales, thus ensuring greater overall operational efficiency.

In the realm of building demolition, ensuring the uniform distribution of energy from multiple sources is of paramount significance for the systematic deconstruction of large structures. This study presents an integrated methodology that combines genetic optimization and potential energy balance to determine the most suitable locations for multiple energy release points, thereby enhancing the efficiency and reliability of the demolition process. We initiate our approach by randomly selecting energy release points within a building model and subsequently simulate energy dispersion utilizing a potential function until reaching stable boundaries. In instances where the discrepancy in the area between the regions with maximum and minimum energy dispersion exceeds a predefined threshold, we instigate an optimization process employing genetic algorithms. This optimization process involves genetic crossover and mutation operations, followed by subsequent energy balance calculations. The result is not only an improvement in demolition efficiency but also an assurance of even energy coverage throughout the target area. [ABSTRACT FROM AUTHOR]

The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a lattice in the Euclidean space. We aim to characterize the cases when the output distribution is close to the uniform distribution on the space, as measured by the Rényi divergence of order α ∈ (1 , ∞ ] . A version of this question is known as the channel resolvability problem in information theory, and it has implications for security guarantees in wiretap channels, error correction, discrepancy, worst-to-average case complexity reductions, and many other problems. Our work quantifies the requirements for asymptotic uniformity (perfect smoothing) and identifies explicit code families that achieve it under the action of the Bernoulli and ball noise operators on the code. We derive expressions for the minimum rate of codes required to attain asymptotically perfect smoothing. In proving our results, we leverage recent results from harmonic analysis of functions on the Hamming space. Another result pertains to the use of code families in Wyner's transmission scheme on the binary wiretap channel. We identify explicit families that guarantee strong secrecy when applied in this scheme, showing that nested Reed–Muller codes can transmit messages reliably and securely over a binary symmetric wiretap channel with a positive rate. Finally, we establish a connection between smoothing and error correction in the binary symmetric channel. [ABSTRACT FROM AUTHOR]

The outcomes of many real-life experiments are sequences of record-breaking data sets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. Records are needed when it is difficult to obtain observations or when observations are being destroyed when subjected to an experimental test. Records are applied in many real-life applications, such as hydrology, industrial stress testing, demise of glaciers, crop production, meteorological analysis, sporting and athletic events, and oil and mining surveys. For instance, in the threshold modeling the observations are those that cross a certain threshold value. Effectively estimating the location parameters for equally likely (uniformly distributed) records is needed in many real-life experiments. The practice demonstrated that the widely used estimators, such as the best linear unbiased estimator (BLUE) and maximum likelihood estimator (MLE), have some defects. This manuscript improves the MLE and BLUE of the location parameters for uniformly distributed records by investigating the corresponding shrinkage estimator using prior information about the BLUE and MLE. To measure the accuracy and precision of the proposed shrinkage estimator, the bias and mean square error (MSE) of the proposed estimators are investigated that provide sufficient conditions to get unbiased estimator with minimum MSE. The numerical results demonstrated that the proposed estimator are dominating over the existing estimators. [ABSTRACT FROM AUTHOR]

For a given positive number 'δ′, we consider a sequence of δ − neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U (0 , 1) distribution, and "stop as soon as their union contains the interval (0 , 1). " We call such a union "a cover." To find the distributions of N (δ) , the stopping time random variable, we need the joint distribution of order statistics from a U (0 , 1) distribution. For each δ > 0 and n = 1 , 2 , ... , we obtain a general expression for P (N (δ) ≤ n) , and for a fixed value of δ , it is the distribution function of N (δ). For a given n, let Δ (n) be the minimum value of δ , so that the union of the n δ − neighborhoods of the first n observations contains the interval (0 , 1). Because N (δ) ≤ n if and only if Δ (n) ≤ δ , the distributions of Δ (n) can be obtained by fixing n in the general expression for P (N (δ) ≤ n). To describe the impact of δ on the distribution of N (δ) and that of n on Δ (n) , we sketch the graphs of distribution functions and the empirical distribution functions. [ABSTRACT FROM AUTHOR]

The tax gap can be considered as the criterion and principle of the effectiveness and efficiency of the tax system. Inadequate collection of taxes as well as non-realization of tax revenues is called tax gap, which is one of the factors that aggravate the budget deficit. In this paper, the issue of tax gap is investigated with two approaches. The first approach is a situation where two groups of investigators who are willing and unwilling to collude with two groups of taxpayers who are willing and unwilling to collude with a uniform distribution are placed in the game. The second approach also shows a situation where the probability of not discovering a taxpayer's violation is shown by a mathematical function and the quality of investigating groups for taxpayers who are uniformly distributed is unknown. The results of the first approach show that with the increase in the number of taxpayers unwilling to collude and the increase in the number of groups willing to collude with taxpayers, the tax gap decreases. Also, with the reduction of the tax rate and the increase in the number of groups unwilling to collude, the tax gap increases. The results of the second approach show that the tax gap increases with the increase in the number of investigators and also the increase in the probability of dishonesty of the taxpayer. [ABSTRACT FROM AUTHOR]

In this paper, the representability of the generalized Student's distribution as uniform and normal-scale mixtures is considered. It is also shown that the generalized Burr and the Snedecor–Fisher distributions can be represented as the scale mixtures of uniform, folded normal, exponential, Weibull or Fréchet distributions. New multiplication-type theorems are proven for these and related distributions. The relation between the generalized Student and generalized Burr distribution is studied. It is shown that the Snedecor–Fisher distribution is a special case of the generalized Burr distribution. Based on these mixture representations, some limit theorems are proven for random sums in which the symmetric and asymmetric generalized Student or symmetric and asymmetric two-sided generalized Burr distributions are limit laws. Also, limit theorems are proven for maximum and minimum random sums and absolute values of random sums in which the generalized Burr distributions are limit laws. [ABSTRACT FROM AUTHOR]

The use of life distributions has increased over the past decade, receiving particular attention in recent years, both from a practical and theoretical point of view. Life distributions can be used in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. This paper presents and investigates a new life distribution. The proposed model shows favorable characteristics in terms of reliability theory, which makes it competitive against other commonly used life distributions, such as the exponential, gamma, and Weibull distributions. The methods of maximum likelihood and moments are used to estimate the parameters of the proposed model. Additionally, real-life data drawn from different fields are used to illustrate the usefulness of the new distribution. Further, the R programming language is used to perform all computations and produce all graphs.

Dunbar's number is the cognitive limit of an individual to maintain stable relationships with others in his network. It is based on the size of the neocortex of the human brain. On the other hand, trust is one of the major issues for one while selecting members for his social network and the evolution of his social network with time. Trust and Dunbar's number are interconnected in the case of one's stable social network. Trust needs time to be built after several social interactions, intimacy, etc. In this paper, we try to provide answers to the following important questions related to social networks:(i) Do trust levels remain the same for individuals from one's perspective in his social network when the network size increases?(ii) What is the relation between the power-law exponent α and the trust cutoff?(iii) Do trust levels help to diffuse information quickly or vice versa to reach Dunbar's number 150 along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes?We find that there is a requirement for trust levels to increase among the same individuals in one's social network if the size of the network increases. As a relation between the power-law exponent α and the trust cutoff, it is found that α∝ 1/(trust cutoff). Moreover, we also find that trust levels never help to diffuse information quickly or vice versa to reach Dunbar's number 150, along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes.

This study mainly considers the scheduling problems with learning effects, where the learning rate is a random variable and obeys a uniform distribution. In the first part, we introduce a single machine model with location-based learning effects. We have given the theoretical proof of the optimal solution for the five objective functions. In the second part, we study the problem with group technology. Both intra-group and inter-group have location-based learning effects, and the learning rate of intra-group jobs follows a uniform distribution. We also give the optimal ranking method and proof for the two problems proposed. [ABSTRACT FROM AUTHOR]

For every flat surface, almost every flat surface in its SL (2 , R) orbit has the following property: the sequence of its saddle connection lengths in non-decreasing order is uniformly distributed in the unit interval. [ABSTRACT FROM AUTHOR]

Ensuring the uniformity of solar irradiance distribution on photovoltaic cells is a major challenge in low-concentrating photovoltaic systems based on a small-scale linear Fresnel reflector. A novel sawtooth V-cavity design method based on an optimization algorithm to achieve uniform irradiance distribution on photovoltaic cells is presented. The reliability of the design was verified using the Monte Carlo ray-tracing method and a laser experiment. A prototype was built using 3D printing technology with a biodegradable green polymer material known as polylactic acid. The new cavity was compared to the standard V-trough cavity, keeping the cavity aperture, reflective surface area, and photovoltaic cell width constant. In addition, the focal height, number of mirrors, mirror width, and mirror spacing were also kept constant; so, the cost of the two configurations was the same from the point of view of the primary reflector system. The new design ensured the uniform distribution of solar irradiation and significantly reduced the height of the cavity. The significant decrease in the height of the proposed cavity has the following advantages: (i) a decrease in the dimensions of the fixed structure of the small-scale linear Fresnel reflector, thus reducing its cost, (ii) a significant decrease in the surface area exposed to wind loads, thus reducing the cost of the fixed structure and secondary system structures, (iii) a reduction in the difficulty of the manufacture, maintenance, and transportation of the cavity's reflecting walls, and (iv) an increase in the cooling surface area, which increases the electrical efficiency of the photovoltaic cells. [ABSTRACT FROM AUTHOR]

This article serves as a continuation of our previously published work and focuses on loose material transport via sandwich belt conveyors. Experimental, analytical, stochastic, and numerical approaches are used to obtain and utilize the moduli of a bilateral Winkler elastic foundation that represent a loose material, which is wheat (Triticum aestivum) that is free of bran in this case. The solutions were obtained for a uniformly and nonuniformly distributed loose material. The task of the conveyor with loose material is simplified into a symmetric task, i.e., a beam on an elastic bilateral Winkler foundation, for an analytical solution and stochastic solution (Anthill and Matlab sw). In a numerical approach, this is considered a plane strain problem within the finite element method (Ansys and MSC.Marc sw). The experimental data are evaluated and used to obtain the functions of Winkler elastic foundation moduli, which are further considered in the numerical solution. The finite element method mainly serves as a verification tool. The acquired histograms of the elastic foundation moduli can be further applied in various scientific and research fields. [ABSTRACT FROM AUTHOR]

With the development of modern electronic countermeasure technology, the fight between radar jamming and anti-jamming in aviation military has become increasingly fierce. There are some special requirements for radar countermeasure experiments. For example, such experiments are often divided into several stages, and responses of the previous stages will become factors of the next stages. Moreover, the experiment design can only consider some typical level values of the factors. However, the experiment factors are mostly continuous variables. Thus when there are some jumps in the response, and the value granularity of the factor level is large, the responses fail to reflect the distortion process, which makes it difficult to explore the radar performance boundary. Therefore, it is necessary to study the sequential experiment design method with the optimization goals of response uniformization and response distortion process characterization. In this paper, a sequential experiment design strategy based on Kriging model is established. Firstly, Kriging model is used to fit the initial experimental data to obtain the response surface. In order to enhance the uniformity of response distribution, Shannon entropy is applied to the objective function as the measure of uniformity. While for the situation of response distortion, we consider replacing the existing experiment points with those whose corresponding responses have a larger gradient norm. It means that the response value near these points will change rapidly, so they are more valuable for research. Then we use the peak surface in the three-dimensional space to intuitively verify the effect of the above algorithms on response uniformization and response distortion process characterization, and use the simulated annealing algorithm to solve them. The simulation results show that our sequential experiment strategy has a good effect. Finally, we apply the strategy to the practical problem of radar countermeasure experiment, and the obtained results also perform well. [ABSTRACT FROM AUTHOR]

We develop new goodness of fit test for uniform distribution based on a conditional moment characterization. We study the asymptotic properties of the proposed test statistic. We also present a goodness of fit test for uniform distribution to incorporate the right censored observations and studied its properties. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed tests. We illustrate the test procedures using real data sets. [ABSTRACT FROM AUTHOR]

With the wide application of unmanned aerial vehicle (UAV), especially in the military field, the security of inter-aircraft communication has become a critical issue, but the wireless ultraviolet communication can be used as a new communication method to guarantee the communication of UAVs within circular cluster. This paper mainly studies the analytical model for connectivity when UAVs obey random way point (RWP) model based on ultraviolet communication within circular cluster. Connectivity is one of the most important characteristics in network, especially in high-dynamic UAV network. Simulations are made when UAVs in cluster obey uniform distribution and RWP model with modulations of OOK and PPM. The simulation results under different distributions of UAVs indicate that transmitted power required with OOK to achieve same probability of k-connectivity is about 2 times than that required with PPM, whereas the data rate required with OOK is about 0.5 times than PPM. In addition, we compare the approximation method based on the analytical model proposed in this paper with the existing approximation method in three cases, where the number of UAV is 20, 100 and 500, respectively. The simulation results show that the approximation method proposed in this paper converges to 1 much faster. [ABSTRACT FROM AUTHOR]