An Optimal Estimate for the Anisotropic Logarithmic Potential

This paper introduces the new annulus body to establish the optimal lower bound for the anisotropic logarithmic potential as the complement to the theory of its upper bound estimate which has already been investigated. The connections with convex geometry analysis and some metric properties are also established. For the application, a polynomial dual log-mixed volume difference law is deduced from the optimal estimate.

Stretching and Rotation of Planar Quasiconformal Mappings on a Line

In this article, we examine stretching and rotation of planar quasiconformal mappings on a line. We show that for almost every point on the line, the set of complex stretching exponents (describing stretching and rotation jointly) is contained in the disk $ \overline {B}(1/(1-k^{4}),k^{2}/(1-k^{4}))$ B ¯ ( 1 / ( 1 − k 4 ) , k 2 / ( 1 − k 4 ) ) . This yields a quadratic improvement over the known optimal estimate for general sets of Hausdorff dimension 1. Our proof is based on holomorphic motions and estimates for dimensions of quasicircles. We also give a lower bound for the dimension of the image of a 1-dimensional subset of a line under a quasiconformal mapping.

On the Estimation of the Initial Stock in the Problem of Resource Extraction

We consider a differential game of non-renewable resource extraction, in which the players do not know the precise value of the resource stock and, thus, have to make an estimate. We define the value of information about the initial stock and give recommendations for the choice of the estimate depending on the parameters of the problem. Further, we consider the situation where the players only know the bounds for the stock of the resource and solve the problem of computing the optimal estimate, such that it minimizes the players’ losses in the worst-case scenario. The analysis allows us to give a simple rule for the choice of the optimal estimate of the resource stock.

Pengendalian Stok Spareparts Mobil Dengan Metode EOQ dan Min-Max Inventory

This research was conducted in the distributor of car spare parts and the object studied was car glass glue. This item is a product that experiences a stacking stock in the warehouse, so it needs inventory control to reduce the stacking stock. The character of the product which does not have expired date as long as it is not used and small size, the company never make an optimal estimate of the order, so the activity of ordering goods is only based on its own estimates. The method used in this research is EOQ to obtain the economical amount of the product to be ordered. The calculation process using EOQ method is done against 2019 sales data predicted to 2021 using Trend Linear forecasting method, with function form is Y=1,8776x+256,21. Furthermore, the minimum and maximum stock quantity is determined using the Min-Max Inventory method. From the result of the study found that the economic Q per ordered is 386 pcs with the frequency of bookings 8 times a year. The minimum inventory is 108 pcs and the maximum is 144 pcs with the amount of safety stock is 72 pcs and ROP is 108 pcs. By using EOQ method, the company can make savings of Rp3,939,330 per year and reduce storage cost by Rp10,119,635 per year.

The Role of Spectral Complexity in Connectivity Estimation

The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.

Assessment of the impact of non-architectural changes in the predictive model on the quality of ECG classification

Recording and analyzing 12-lead electrocardiograms is the most common procedure for detecting heart disease. Recently, various deep learning methods have been proposed for the automatic diagnosis by an electrocardiogram. The proposed methods can provide a second opinion for the doctor and help detect pathologies at an early stage. Various methods are proposed in the paper to improve the quality of prediction of ECG recording pathologies. Techniques include adding patient metadata, ECG noise reduction, and self-adaptive learning. The significance of data parameters in training a classification model is also explored. Among the considered parameters, the influence of various ECG leads, the length of the electrocardiogram and the volume of the training sample is studied. The experiments carried out show the relevance of the described approaches and offer an optimal estimate of the input data parameters.

Measurement Error and Our Data

This chapter introduces the idea that all data are measured with error. It then uses a standard normally distributed error formulation within a state and measurement context to derive the optimal estimate of the measurement error given a data measurement.