Probability Density Function Analysis Based on Logistic Regression Model

The data fitting level in probability density function analysis has great influence on the analysis results, so it is of great significance to improve the data fitting level. Therefore, a probability density function analysis method based on logistic regression model is proposed. The logistic regression model with kernel function is established, and the optimal window width and mean square integral error are selected to limit the solution accuracy of probability density function. Using the real probability density function, the probability density function with the smallest error is obtained. The estimated probability density function is analyzed from two aspects of consistency and convergence speed. The experimental results show that compared with the traditional probability density function analysis method, the probability density function analysis method based on logistics regression model has a higher fitting level, which is more suitable for practical research projects.

Extended Fractional Singular Kalman Filter

Effective and accurate state estimation is a staple of modern modeling. On the other hand, nonlinear fractional-order singular (FOS) systems are an attractive modeling tool as well since they can provide accurate descriptions of systems with complex dynamics. Consequently, developing accurate state estimation methods for such systems is highly relevant since it provides vital information about the system including related memory effects and long interconnection properties with constraint elements. However, missing features in transforming structures such as violation of constraints in non-singular versions of such systems may affect the performance of the estimation result. This paper proposes the state estimation algorithm design for the original and non-transformed stochastic nonlinear FOS system. We introduce a deterministic data-fitting based framework which helps us to take steps directly towards Kalman filter (KF) derivation of the system, called extended fractional singular KF (EFSKF). Using stochastic reasoning, we demonstrate how to construct recursive form of the filter. Analysis of the filter shows how the proposed algorithm reduces to the nominal nonlinear filters when the system is in its usual state-space form making said algorithm highly flexible. Finally, simulation results verify that the estimation of nonlinear states can be accomplished with the proposed EFSKF algorithm with a reasonable performance.

US Nobel laureates: Logistic growth versus Volterra–Lotka

The logistic-growth equation is a special case of the Volterra-Lotka equations. The former describes competition only between members of the same species whereas the latter describes competition also with other species. In the study of US Nobel laureates considering laureates per population improves the quality of the logistic fit but the Volterra-Lotka approach suggests that a logistic description would be a good approximation for data per unit of time rather than cumulative data. Fitting logistic S curves on cumulative data — although proven successful in many business and other applications — constitutes treacherous terrain for inexperienced S-curve enthusiasts. The Volterra-Lotka analysis of Nobel laureates reveals other insights such as that Americans and other nationalities are locked in a win-win struggle with Americans drawing more of a benefit, and also that American Nobel laureates “incubate” new Nobel laureates to a lesser extent than other nationalities.

Estimation of Sine Inverse Exponential Model under Censored Schemes

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

Artificial Neural Networks and Response Surface Methodology Approach for Optimization of an Eco-Friendly and Detergent-Stable Lipase Production from Actinomadura Keratinilytica Strain Cpt29

This work mainly focused on the production of an efficient, economical, and eco-friendly lipase (AKL29) from Actinomadura keratinilytica strain Cpt29 isolated from poultry compost in north east of Algeria, for use in detergent industries. AKL29 shows a significant lipase activity (45 U/mL) towards hydrolyzed triacylglycerols, indicating that it is a true lipase. For maximum lipase production the modeling and optimization of potential culture parameters such as incubation temperature, cultivation time, and Tween 80 (v/v) were built using RSM and ANN approaches. The results show that both the two models provided good quality predictions, yet the ANN showed a clear superiority over RSM for both data fitting and estimation capabilities. A 4.1-fold increase in lipase production was recorded under the following optimal condition: incubation temperature (37.9 °C), cultivation time (111 h), and Tween 80 (3.27%, v/v). Furthermore, the partially purified lipase showed good stability, high compatibility, and significant wash performance with various commercial laundry detergents, making this novel lipase a promising potential candidate for detergent industries.

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. In this study, a new Weibull-generated-type class is presented, called the weighted odd Weibull generated class. Its definition is based on a cumulative distribution function, which combines a specific weighted odd function with the cumulative distribution function of the Weibull distribution. This weighted function was chosen to make the new class a real alternative in the first-order stochastic sense to two of the most famous existing Weibull generated classes: the Weibull-G and Weibull-H classes. Its mathematical properties are provided, leading to the study of various probabilistic functions and measures of interest. In a consequent part of the study, the focus is on a special three-parameter survival distribution of the new class defined with the standard exponential distribution as a reference. The exploratory analysis reveals a high level of adaptability of the corresponding probability density and hazard rate functions; the curves of the probability density function can be decreasing, reversed N shaped, and unimodal with heterogeneous skewness and tail weight properties, and the curves of the hazard rate function demonstrate increasing, decreasing, almost constant, and bathtub shapes. These qualities are often required for diverse data fitting purposes. In light of the above, the corresponding data fitting methodology has been developed; we estimate the model parameters via the likelihood function maximization method, the efficiency of which is proven by a detailed simulation study. Then, the new model is applied to engineering and environmental data, surpassing several generalizations or extensions of the exponential model, including some derived from established Weibull-generated classes; the Weibull-G and Weibull-H classes are considered. Standard criteria give credit to the proposed model; for the considered data, it is considered the best.

Design of time-delayed safety switches for CRISPR gene therapy

CRISPR system is a powerful gene editing tool which has already been reported to address a variety of gene relevant diseases in different cell lines. However, off-target effect and immune response caused by Cas9 remain two fundamental problems. Inspired by previously reported Cas9 self-elimination systems, time-delayed safety switches are designed in this work. Firstly, ultrasensitive relationship is constructed between Cas9-sgRNA (enzyme) and Cas9 plasmids (substrate), which generates the artificial time delay. Then intrinsic time delay in biomolecular activities is revealed by data fitting and utilized in constructing safety switches. The time-delayed safety switches function by separating the gene editing process and self-elimination process, and the tunable delay time may ensure a good balance between gene editing efficiency and side effect minimization. By addressing gene therapy efficiency, off-target effect, immune response and drug accumulation, we hope our safety switches may offer inspiration in realizing safe and efficient gene therapy in humans.