Improving the gnomonic approach with the gnomonicM R-package to estimate natural mortality throughout different life stages

Natural mortality (M) is defined as the rate of loss that occurs in a fish stock due to natural (non-fishing) causes and can be influenced by density-dependent or density-independent factors. Different methods have been used to estimate M, one of these is the gnomonic approach. This method estimates M rates by dividing the life cycle of a species into subunits of time that increase as a constant proportion of the time elapsed from birth up to the initiation of each subdivision. In this study, an improved gnomonic approach is proposed to estimate natural mortality throughout different life stages in marine stocks using the gnomonicM package written in R software. This package was built to require data about (i) the number of gnomonic intervals, (ii) egg stage duration, (iii) longevity, and (iv) fecundity. With this information, it is possible to estimate the duration and natural mortality (Mi) of each gnomonic interval. The gnomonicM package uses a deterministic or stochastic approach, the latter of which assesses variability in M by assuming that the mean lifetime fecundity (MLF) is the main source of uncertainty. Additionally, the gnomonicM package allows the incorporation of auxiliary information related to the observed temporal durations of specific gnomonic intervals, which is useful for calibrating estimates of M vectors. The gnomonicM package, tested via deterministic and stochastic functions, was supported by the reproducibility and verification of the results obtained from different reports, thus guaranteeing its functionality, applicability, and performance in estimating M for different ontogenetic developmental stages. Based on the biological information of Pacific chub mackerel (Scomber japonicus), we presented a new case study to provide a comprehensive guide to data collection to obtain results and explain the details of the application of the gnomonicM package and avoid its misuse. This package could provide an alternative approach for estimating M and provide basic input data for ecological models, allowing the option of using estimates of variable natural mortality across different ages, mainly for life stages affected by fishing. The inputs for the gnomonicM packages are composed of numbers, vectors, or characters depending on whether the deterministic or stochastic approach is used, making the package quick, flexible, and easy to use; this allows users to focus on obtaining and interpreting results rather than the calculation process.

sKAdam: An improved scalar extension of KAdam for function optimization

This paper presents an improved extension of the previous algorithm of the authors called KAdam that was proposed as a combination of a first-order gradient-based optimizer of stochastic functions, known as the Adam algorithm and the Kalman filter. In the extension presented here, it is proposed to filter each parameter of the objective function using a 1-D Kalman filter; this allows us to switch from matrix and vector calculations to scalar operations. Moreover, it is reduced the impact of the measurement noise factor from the Kalman filter by using an exponential decay in function of the number of epochs for the training. Therefore in this paper, is introduced our proposed method sKAdam, a straightforward improvement over the original algorithm. This extension of KAdam presents a reduced execution time, a reduced computational complexity, and better accuracy as well as keep the properties from Adam of being well suited for problems with large datasets and/or parameters, non-stationary objectives, noisy and/or sparse gradients.

APLIKASI INTEGRAL DALAM BIDANG EKONOMI DAN FINANSIAL

The characteristics of a function are usually investigated by looking at the continuity of the function. But what happens if a function does not have continuous properties? To what extent can the characteristics of continuous function be maintained for discontinuous cases? The stochastic function that is widely involved in solving problems in the field of average financial mathematics is a discontinuous function. This is reflected by the acquisition of a smooth curve from the modeling drawing obtained. Today, the nature of continuous functions in [a, b] has been widely studied and developed. Some properties of the continuous function can be extended to the appropriate discontinuous function. In this paper, there will be some integral reviews for discontinuous functions which are closely related to stochastic functions.

Models and Algorithms for Optimal Piecewise-Linear Function Approximation

Piecewise-linear functions can approximate nonlinear and unknown functions for which only sample points are available. This paper presents a range of piecewise-linear models and algorithms to aid engineers to find an approximation that fits best their applications. The models include piecewise-linear functions with a fixed and maximum number of linear segments, lower and upper envelopes, strategies to ensure continuity, and a generalization of these models for stochastic functions whose data points are random variables. Derived from recursive formulations, the algorithms are applied to the approximation of the production function of gas-lifted oil wells.