Optimization of Bayesian repetitive group sampling plan for quality determination in Pharmaceutical products and related materials

Sampling plans are extensively used in pharmaceutical industries to test drugs or other related materials to ensure that they are safe and consistent. A sampling plan can help to determine the quality of products, to monitor the goodness of materials and to validate the yields whether it is free from defects or not. If the manufacturing process is precisely aligned, the occurrence of defects will be an unusual occasion and will result in an excess number of zeros (no defects) during the sampling inspection. The Zero Inflated Poisson (ZIP) distribution is studied for the given scenario, which helps the management to take a precise decision about the lot and it can certainly reduce the error rate than the regular Poisson model. The Bayesian methodology is a more appropriate statistical procedure for reaching a good decision if the previous knowledge is available concerning the production process. This article proposed a new design of the Bayesian Repetitive Group Sampling plan based on Zero Inflated Poisson distribution for the quality assurance in pharmaceutical products and related materials. This plan is studied through the Gamma-Zero Inflated Poisson (G-ZIP) model to safeguard both the producer and consumer by minimizing the Average Sample Number. Necessary tables and figures are constructed for the selection of optimal plan parameters and suitable illustrations are provided that are applicable for pharmaceutical industries.

Image segmentation and preserve the boundary of the image using b-spline basis

This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values

Asymptotic vectors of entire curves

We introduce a concept of asymptotic vector of an entire curve with linearly independent components and without common zeros and investigate a relationship between the asymptotic vectors and the Picard exceptional vectors. A non-zero vector $\vec{a}=(a_1,a_2,\ldots,a_p)\in \mathbb{C}^{p}$ is called an asymptotic vector for the entire curve $\vec{G}(z)=(g_1(z),g_2(z),\ldots,g_p(z))$ if there exists a continuous curve $L: \mathbb{R}_+\to \mathbb{C}$ given by an equation $z=z\left(t\right)$, $0\le t<\infty $, $\left|z\left(t\right)\right|<\infty $, $z\left(t\right)\to \infty $ as $t\to \infty $ such that$$\lim\limits_{\stackrel{z\to\infty}{z\in L}} \frac{\vec{G}(z)\vec{a} }{\big\|\vec{G}(z)\big\|}=\lim\limits_{t\to\infty} \frac{\vec{G}(z(t))\vec{a} }{\big\|\vec{G}(z(t))\big\|} =0,$$ where $\big\|\vec{G}(z)\big\|=\big(|g_1(z)|^2+\ldots +|g_p(z)|^2\big)^{1/2}$, $\vec{G}(z)\vec{a}=g_1(z)\cdot\bar{a}_1+g_2(z)\cdot\bar{a}_2+\ldots+g_p(z)\cdot\bar{a}_p$. A non-zero vector $\vec{a}=(a_1,a_2,\ldots,a_p)\in \mathbb{C}^{p}$ is called a Picard exceptional vector of an entire curve $\vec{G}(z)$ if the function $\vec{G}(z)\vec{a}$ has a finite number of zeros in $\left\{\left|z\right|<\infty \right\}$. We prove that any Picard exceptional vector of transcendental entire curve with linearly independent com\-po\-nents and without common zeros is an asymptotic vector.Here we de\-mon\-stra\-te that the exceptional vectors in the sense of Borel or Nevanlina and, moreover, in the sense of Valiron do not have to be asymptotic. For this goal we use an example of meromorphic function of finite positive order, for which $\infty $ is no asymptotic value, but it is the Nevanlinna exceptional value. This function is constructed in known Goldberg and Ostrovskii's monograph``Value Distribution of Meromorphic Functions''.Other our result describes sufficient conditions providing that some vectors are asymptotic for transcendental entire curve of finite order with linearly independent components and without common zeros. In this result, we require that the order of the Nevanlinna counting function for this curve and for each such a vector is less than order of the curve.At the end of paper we formulate three unsolved problems concerning asymptotic vectors of entire curve.

Zeros of a binomial combination of Chebyshev polynomials

For [Formula: see text], we study the zeros of the sequence of polynomials [Formula: see text] generated by the reciprocal of [Formula: see text], expanded as a power series in [Formula: see text]. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of [Formula: see text] outside the interval [Formula: see text] is bounded by a constant independent of [Formula: see text].

Accuracy of Zero Inflated Generalized Poisson Exponentially Moving Average Control Chart

The Zero-Inflated Generalized Poisson (ZIGP) distribution is a case-based distribution where the discrete data has a large number of zeros and an overdispersion occurs, i.e. the variance is greater than the mean value. The purpose of this study is to determine the Exponential Weight Moving Average (EWMA) control chart with the assumption that the data has a Zero-Inflated Generalized Poisson (ZIP) distribution. The results show that the ARL value of the ARL ZIGP EWMA control chart has better accuracy when compared to when using the ZIP EWMA control chart on ZIGP distributed data. This is indicated by the smaller ARL value compared to the ZIP EWMA control chart, namely when φ = 1.4, and φ = 0.6. So that the ARL ZIGP EWMA control chart has a fairly good accuracy in detecting out of control conditions for ZIGP distributed data. In addition, the modified ARL shows the same values ​​before and after the modification for the underdispersion data and shows a larger or negative value for the overdispersion data. This can eliminate or reduce errors in analyzing the accuracy of the control chart.

EXPLICIT DISTRIBUTION OF SELECTED TWO-DIMENSIONAL AND THREE-DIMENSIONAL STATISTICS OF THE (0,1)-SEQUENCE

The joint distributions of the given number of 2-chains and the given number of 3-chains of a fixed form of a random bit sequence are considered, which allow performing a statistical analysis of local sections of this sequence. All configurations consisting of two consecutive zeros or ones of a bit sequence of a given length act as 2-chains. In turn, 3-chains are all configurations consisting of three consecutive either ones (provided that the 2-chains are zero) or zeros (provided that the 2-chains are one), as well as 3-chains all configurations are considered that consist either of three consecutive digits: one, zero and one (provided that the 2- chains are zero), or of three consecutive digits: zero, one and zero (provided that the 2- chains are one). The paper establishes explicit expressions for two-dimensional and three-dimensional joint distributions of events, reflecting the number of some combinations of the indicated chains in a finite random bit sequence. One of the basic assumptions is that zeros and ones in a bit sequence are independent, equally distributed random variables. The proofs of the formulas for the distributions of these events are based on counting the number of corresponding favorable events, provided that the bit sequence contains a fixed number of zeros and ones. As examples of using explicit expressions of joint distributions, tables are given in which the values of the probabilities of the events listed above for a random bit sequence of length 40 (tables 1–3) and length 24 (table 4) are given for some fixed values of the number of 2-chains and the number 3-chains under the assumption that zeros and ones appear independently and uniformly. For clarity, tables 1‑3 are illustrated with bubble charts. The established formulas may be of interest for the problems of testing local sections formed at the output of pseudo-random number generators, for some problems of protecting information from unauthorized access, as well as in other areas where it becomes necessary to analyze bit sequences.

Structural Attack (and Repair) of Diffused-Input-Blocked-Output White-Box Cryptography

In some practical enciphering frameworks, operational constraints may require that a secret key be embedded into the cryptographic algorithm. Such implementations are referred to as White-Box Cryptography (WBC). One technique consists of the algorithm’s tabulation specialized for its key, followed by obfuscating the resulting tables. The obfuscation consists of the application of invertible diffusion and confusion layers at the interface between tables so that the analysis of input/output does not provide exploitable information about the concealed key material.Several such protections have been proposed in the past and already cryptanalyzed thanks to a complete WBC scheme analysis. In this article, we study a particular pattern for local protection (which can be leveraged for robust WBC); we formalize it as DIBO (for Diffused-Input-Blocked-Output). This notion has been explored (albeit without having been nicknamed DIBO) in previous works. However, we notice that guidelines to adequately select the invertible diffusion ∅and the blocked bijections B were missing. Therefore, all choices for ∅ and B were assumed as suitable. Actually, we show that most configurations can be attacked, and we even give mathematical proof for the attack. The cryptanalysis tool is the number of zeros in a Walsh-Hadamard spectrum. This “spectral distinguisher” improves on top of the previously known one (Sasdrich, Moradi, Güneysu, at FSE 2016). However, we show that such an attack does not work always (even if it works most of the time).Therefore, on the defense side, we give a straightforward rationale for the WBC implementations to be secure against such spectral attacks: the random diffusion part ∅ shall be selected such that the rank of each restriction to bytes is full. In AES’s case, this seldom happens if ∅ is selected at random as a linear bijection of F322. Thus, specific care shall be taken. Notice that the entropy of the resulting ∅ (suitable for WBC against spectral attacks) is still sufficient to design acceptable WBC schemes.

DIF Detection With Zero-Inflation Under the Factor Mixture Modeling Framework

Response data containing an excessive number of zeros are referred to as zero-inflated data. When differential item functioning (DIF) detection is of interest, zero-inflation can attenuate DIF effects in the total sample and lead to underdetection of DIF items. The current study presents a DIF detection procedure for response data with excess zeros due to the existence of unobserved heterogeneous subgroups. The suggested procedure utilizes the factor mixture modeling (FMM) with MIMIC (multiple-indicator multiple-cause) to address the compromised DIF detection power via the estimation of latent classes. A Monte Carlo simulation was conducted to evaluate the suggested procedure in comparison to the well-known likelihood ratio (LR) DIF test. Our simulation study results indicated the superiority of FMM over the LR DIF test in terms of detection power and illustrated the importance of accounting for latent heterogeneity in zero-inflated data. The empirical data analysis results further supported the use of FMM by flagging additional DIF items over and above the LR test.