exponential regression model
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To predict the spread of the new coronavirus infection COVID-19, the critical values of spread indicators have been determined for deciding on the introduction of restrictive measures using the city of Moscow as an example. A model was developed using classical methods of mathematical modeling based on exponential regression, the accuracy of the forecast was estimated, and the shortcomings of mathematical methods for predicting the spread of infection for more than two weeks. As a solution to the problem of the accuracy of long-term forecasts for more than two weeks, two models based on machine learning methods are proposed: a recurrent neural network with two layers of long short-term memory (LSTM) blocks and a 1-D convolutional neural network with a description of the choice of an optimization algorithm. The forecast accuracy of ML models was evaluated in comparison with the exponential regression model and one another using the example of data on the number of COVID-19 cases in the city of Moscow.

Cerebrovascular reactivity (CVR) to changes in the partial pressure of arterial carbon dioxide (PaCO2) is an important mechanism that maintains CO2 or pH homeostasis in the brain. To what extent this is influenced by gravitational stress and corresponding implications for the regulation of cerebral blood flow (CBF) remain unclear. The present study examined the onset responses of pulmonary ventilation (V̇E) and anterior middle (MCA) and posterior (PCA) cerebral artery mean blood velocity (Vmean) responses to acute hypercapnia (5% CO2) to infer dynamic changes in the central respiratory chemoreflex and cerebrovascular reactivity (CVR), in supine and 50° head-up tilt (HUT) positions. Each onset response was evaluated using a single-exponential regression model consisting of the response time latency [CO2-response delay (t0)] and time constant (τ). Onset response of V̇E and PCA Vmean to changes in CO2 was unchanged during 50° HUT compared with supine (τ: V̇E, p = 0.707; PCA Vmean, p = 0.071 vs. supine) but the MCA Vmean onset response was faster during supine than during 50° HUT (τ: p = 0.003 vs. supine). These data indicate that gravitational stress selectively impaired dynamic CVR in the anterior cerebral circulation, whereas the posterior circulation was preserved, independent of any changes to the central respiratory chemoreflex. Collectively, our findings highlight the regional heterogeneity underlying CBF regulation that may have translational implications for the microgravity (and hypercapnia) associated with deep-space flight notwithstanding terrestrial orthostatic diseases that have been linked to accelerated cognitive decline and neurodegeneration.

This observational study aims to investigate the early disease patterns of coronavirus disease 2019 (COVID-19) in Southeast Asia, consequently providing historical experience for further interventions. Data were extracted from official websites of the WHO and health authorities of relevant countries. A total of 1346 confirmed cases of COVID-19, with 217 recoveries and 18 deaths, were reported in Southeast Asia as of 16 March 2020. The basic reproductive number (R0) of COVID-19 in the region was estimated as 2.51 (95% CI:2.31 to 2.73), and there were significant geographical variations at the subregional level. Early transmission dynamics were examined with an exponential regression model: y = 0.30e0.13x (p < 0.01, R2 = 0.96), which could help predict short-term incidence. Country-level disease burden was positively correlated with Human Development Index (r = 0.86, p < 0.01). A potential early shift in spatial diffusion patterns and a spatiotemporal cluster occurring in Malaysia and Singapore were detected. Demographic analyses of 925 confirmed cases indicated a median age of 44 years and a sex ratio (male/female) of 1.25. Age may play a significant role in both susceptibilities and outcomes. The COVID-19 situation in Southeast Asia is challenging and unevenly geographically distributed. Hence, enhanced real-time surveillance and more efficient resource allocation are urgently needed.

The introduction specifies the object of the study - hydrogenated fat subjected to purification from suspended nickel-containing catalyst in a high-gradient magnetic field. The nickel-containing catalyst, due to the presence of nickel salts in it, is paramagnetic and can be effectively extracted from hydrated fat in the magnetic field by a method of highly gradient magnetic separation. In the experiment technique the magnetic field strength was not less than 600 kA/m, the gradient not less than (20-30)∙104 kA/m2. Based on the results and their discussion, the analysis of empirical dependencies on each factor basis is carried out separately, as well as the construction of classical types of one-dimensional non-linear regression models for each of them.  It is shown that the most statistically reliable are the exponential models. It was found that after purification the content of suspended nickel-containing catalyst in the hydrogenated fat has an inverse proportional dependence on the magnetic field strength, height (length) of the filtration zone and filtration rate. A two-dimensional exponential regression model of the content of the nickel-containing catalyst in the hydrogenated fat in the complex dependence on the rate and height of the filtration zone is built. Based on the experimental data at a certain height of the filtration zone and the selected filtration rate, a mathematical-statistical model of change in the concentration of nickel-containing catalyst depending on the magnetic field strength is made. Using the resulting two-dimensional exponential regression model, it is possible to predict the degree of purification of the salomas from the suspended catalyst depending on the specific tension of the magnetic field and to determine the tension of the magnetic field, at which the concentration of nickel as a result of cleaning will reach an advance value.

Gunung Anyar is one of the districts in the city of Surabaya. This district has a height of approximately 3 meters above sea level. Based on data from the Central Statistics Agency (BPS) for the City of Surabaya 2019, Gunung Anyar District has an area of ​​9.2 square kilometers and is divided into four sub-districts. These include the Kelurahan Rungkut Menanggal, Rungkut Tengah, Mount Anyar and Mount Anyar Tambak (AyoSurabaya.com by Rizma Riyandi). The mangrove's robust root system helps form a natural barrier against storm surges and flooding. River and land sediments are trapped by roots, which protect shorelines and slow erosion. This filtering process also prevents harmful sediments from reaching coral reefs and seagrass beds (Anugerah Ayu Sundari 2019). The method used by remote sensing with Landsat 8 satellite imagery was analyzed using SeaDAS software, it was obtained that the comparison value in each band 2,3,4 and band 5 had differences in each reflectance value. The 2015 satellite image map has the largest value in band_4 with the exponential regression model y = 125.06e-22.13x with R2 = 0.0732, while the 2019 satellite image map which has the largest value is band_4 with the logarithmic regression model y = 141.72ln (x) + 326.3 where R2 = 0.0281. Using the Wilcoxon H1 Test Statistics it is accepted that there is a significant difference between the diameter of mangroves from satellite imagery in 2015 and the diameter of mangroves from satellite images in 2019. Because the number of positive rankings from the diameter of mangrove satellite imagery in 2015 is greater than the diameter of mangroves from satellite imagery in 2019. , it can be concluded that the mangrove area of ​​Wonorejo Surabaya is experiencing fertility.

In this paper, we reparameterized the extended exponential model based on the mean in order to include covariates and facilitate the interpretation of the coefficients. The model is compared with common models defined in the positive line also reparametrized in the mean. Parameter estimation is approached based on the expectation–maximization algorithm. Furthermore, we discuss residuals and influence diagnostic tools. A simulation study for recovered parameters is presented. Finally, an application illustrating the advantages of the model in a real data set is presented.

Over 44.7 million Americans carry student loan debt, with the total amount valued at approximately $1.31 trillion (Quarterly Report, 2019). Ergo, consumer spending, a factor of GDP, is stifled and negatively impacts the economy (Frizell, 2014, p. 22). This study examined the relationship between student loan debt and the probability of a recession in the near future, as well as the effects of proposed student loan forgiveness policies through the use of a created model. The Federal Reserve Bank of St. Louis’s website (FRED) was used to extract data regarding total GDP per quarter and student loan debt per quarter ("Federal Reserve Economic Data," 2019). Through the combination of the student loan debt per quarter and total GDP per quarter datasets, the percentage of total GDP composed of student loan debt per quarter was calculated and fitted to a logistic curve. Future quarterly values for total GDP and the percentage of total GDP composed by student loan debt per quarter were found through Long Short Term Models and Euler’s Method, respectively. Through the creation of a probability of recession index, the probability of recession per quarter was compared to the percentage of total GDP composed by student loan debt per quarter to construct an exponential regression model. Utilizing a primarily quantitative method of analysis, the percentage of total GDP composed by student loan debt per quarter was found to be strongly associated[p &lt; 1.26696* 10-8]with the probability of recession per quarter(p(R)), with the p(R) tending to peak as the percentage of total GDP composed of student loan debt per quarter strayed away from the carrying capacity of the logistic curve. Inputting the student loan debt forgiveness policies of potential congressional bills proposed by lawmakers found that eliminating 49.7 % and 36.7% of student loan debt would reduce the recession probabilities to be 1.73545*10-29% and 9.74474*10-25%, respectively.

Over 44.7 million Americans carry student loan debt, with the total amount valued at approximately $1.31 trillion (Quarterly Report, 2019). Ergo, consumer spending, a factor of GDP, is stifled and negatively impacts the economy (Frizell, 2014, p. 22). This study examined the relationship between student loan debt and the probability of a recession in the near future, as well as the effects of proposed student loan forgiveness policies through the use of a created model. The Federal Reserve Bank of St. Louis’s website (FRED) was used to extract data regarding total GDP per quarter and student loan debt per quarter ("Federal Reserve Economic Data," 2019). Through the combination of the student loan debt per quarter and total GDP per quarter datasets, the percentage of total GDP composed of student loan debt per quarter was calculated and fitted to a logistic curve. Future quarterly values for total GDP and the percentage of total GDP composed by student loan debt per quarter were found through Long Short Term Models and Euler’s Method, respectively. Through the creation of a probability of recession index, the probability of recession per quarter was compared to the percentage of total GDP composed by student loan debt per quarter to construct an exponential regression model. Utilizing a primarily quantitative method of analysis, the percentage of total GDP composed by student loan debt per quarter was found to be strongly associated[p &lt; 1.26696* 10-8]with the probability of recession per quarter(p(R)), with the p(R) tending to peak as the percentage of total GDP composed of student loan debt per quarter strayed away from the carrying capacity of the logistic curve. Inputting the student loan debt forgiveness policies of potential congressional bills proposed by lawmakers found that eliminating 49.7 % and 36.7% of student loan debt would reduce the recession probabilities to be 1.73545*10-29% and 9.74474*10-25%, respectively.