Analysis and Prediction of Graduate Admissions Based on Pre-COVID and post-COVID Scenario

Graduate admissions is one of the events that attracts a lot of attraction from prospective students and universities alike. Be it the university conducting graduate admissions or an aspiring student; both yearn for a prediction system to aid in the process of selecting admits. On one hand, the university can get an insight on the probability of a student's admit thus aiding the graduate admissions office in their workload, and on the other hand the student can get a forecast on the chance of admit and can take preemptive decisions to facilitate the process. However, due to the COVID-19 pandemic, the graduate admissions has seen a slight change in paradigm. This change creates confusion among the related masses. A probing analysis on this change serves as a reference to act upon. In this study, prediction models are built with an extra parameter signifying whether a record in the dataset belongs to the COVID-19 pandemic period. Various models such as Logistic Regression, Decision Tree, Random Forest, Gaussian Naive Bayes and Artificial Neural Networks are used to determine the change in probability of admission due to the effect of the pandemic. All the models provide an accuracy score in the range of about 55% to 80%, with the Neural Network outperforming all the other models with a test accuracy score of 79.03%. The effect of the pandemic has caused an ambiguous response to various factors, but it can be stated the chances of admits of students have generally increased likely due to the lower number of applicants

An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

A continuous switching contact model for virtual environment based teleoperation

Virtual environment (VE), as the proxy of slave contact environment, is the most promising technology to solve the time-delay problems in teleoperation. The accuracy of the predicted force depends not only on the reliability of the contact model but also on the estimation algorithm’s adaptability. A new contact model is proposed to be applicable in various materials, which includes both the Kelvin–Voigt model (KVM) and Hunt–Crossley model (HCM). An extra parameter is set in the model to express the capacity of continuous switching between KVM and HCM, whose rationality is proved based on the energy loss. The energy loss is proportional to a power of impact velocity, and the exponent is bounded at [2,3], which exactly lies between KVM and HCM. Furthermore, to estimate the parameters with a single-stage method, the nonlinear model is linearized approximatively with logarithm function and polynomials. Then, the recursive least squares (RLS) algorithm combining forgetting factor and self-perturbing action is designed to identify the four parameters online. Finally, the model’s continuous switching is verified with ideal simulation, and the model parameters are continuously changed without jumpy switch error. In the experiment, sponge, foam, and human hand represent the complex contact materials of the slave environment where the predicted force is shown to follow the real contact force with enough accuracy. Therefore, the virtual model can be considered the substitution of slave contact environment so that the feedback force in master can be calculated in real-time.

On Methods of Estimation for Generalized Logarithmic Series Distribution and Its Application to Counts of Red Mites on Apple Leaves

The Generalized Logarithmic Series Distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi square and weighted discrepancies. The GLSD was fitted to counts of red mites on apple leaves and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.

$$ T\overline{T} $$ deformations of non-relativistic models

The light-cone gauge approach to $$ T\overline{T} $$ T T ¯ deformed models is used to derive the $$ T\overline{T} $$ T T ¯ deformed matrix nonlinear Schrödinger equation, the Landau-Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $$ T\overline{T} $$ T T ¯ deformed nonlinear Schrödinger and Korteweg-de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the $$ T\overline{T} $$ T T ¯ deformation. However, whether the soliton’s size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. The $$ T\overline{T} $$ T T ¯ deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.

Predicting Fermentation Rates in Ale, Lager and Whisky

Recently there has been an increased interest in characterising the rates of alcoholic fermentations. Sigmoidal models have been used to predict changes such as the rate of density decline. In this study, three published sigmoidal models were assessed and fit to industrial fermentation data. The first is the four-parameter logistic model described in the ASBC Yeast-14 method. The second model is a nested form of the four-parameter logistic function, adding an extra parameter, creating the 5-parameter logistic equation., where an additional parameter was added to allow for asymmetry. The final model is a three-parameter logistic equation which describes the change in the Apparent Degree of Fermentation with time. The three models were compared by fitting them to industrial data from Australian and Canadian lagers, American and Scottish ales and Scotch Whisky fermentations. The model fits were then compared to one another with a technique developed by Akaike and a nested F-test. The Akaike information criterion compares the models and accounts for both the goodness of fit, and the number of parameters in the model. Finally, consideration was given to the establishment of prediction bands (that enclose the area that one can be 99% sure contains the true datapoints). Calculation of these bands was “challenging” but successful as the industrial fermentation data was heteroscedastic.

Conditional t-SNE: more informative t-SNE embeddings

Dimensionality reduction and manifold learning methods such as t-distributed stochastic neighbor embedding (t-SNE) are frequently used to map high-dimensional data into a two-dimensional space to visualize and explore that data. Going beyond the specifics of t-SNE, there are two substantial limitations of any such approach: (1) not all information can be captured in a single two-dimensional embedding, and (2) to well-informed users, the salient structure of such an embedding is often already known, preventing that any real new insights can be obtained. Currently, it is not known how to extract the remaining information in a similarly effective manner. We introduce conditional t-SNE (ct-SNE), a generalization of t-SNE that discounts prior information in the form of labels. This enables obtaining more informative and more relevant embeddings. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining an elegant method with a single integrated objective. We show how to efficiently optimize the objective and study the effects of the extra parameter that ct-SNE has over t-SNE. Qualitative and quantitative empirical results on synthetic and real data show ct-SNE is scalable, effective, and achieves its goal: it allows complementary structure to be captured in the embedding and provided new insights into real data.

On Three Constructions of Nanotori

There are three different approaches for constructing nanotori in the literature: one with three parameters suggested by Altshuler, another with four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks of computer science known under the name generalized honeycomb tori. Altshuler showed that his method gives all non-isomorphic nanotori, but this was not known for the other two constructions. Here, we show that these three approaches are equivalent and give explicit formulas that convert parameters of one construction into the parameters of the other two constructions. As a consequence, we obtain that the other two approaches also construct all nanotori. The four parameters construction is mainly used in chemistry and physics to describe carbon nanotori molecules. Some properties of the nanotori can be predicted from these four parameters. We characterize when two different quadruples define isomorphic nanotori. Even more, we give an explicit form of all isomorphic nanotori (defined with four parameters). As a consequence, infinitely many 4-tuples correspond to each nanotorus; this is due to redundancy of having an “extra” parameter, which is not a case with the other two constructions. This result significantly narrows the realm of search of the molecule with desired properties. The equivalence of these three constructions can be used for evaluating different graph measures as topological indices, etc.

Type II Half Logistic Kumaraswamy Distribution with Applications

In this paper, a new distribution with a unit interval named type II half logistic Kumaraswamy (TIIHLKw) distribution is proposed. Its density and distribution functions are presented using alternate expressions. This distribution is obtained by adding an extra parameter in the existing model to rise its ability fitting complex data sets. Some important statistical properties of TIIHLKw distribution are derived. The estimation of the parameters is obtained by numerous well-recognized approaches and simulation study confirmed the efficiencies of estimates such obtained. We apply the related model to practical datasets, and it is concluded that the proposed model is the best by model selection criteria than other competitive models.

Modified Combined-Step-Size Affine Projection Sign Algorithms for Robust Adaptive Filtering in Impulsive Interference Environments

In this paper, to further improve the filtering performance and enhance the poor tracking capability of the conventional combined step-size affine projection sign algorithm (CSS-APSA) in system identification, we propose a simplified CSS-APSA (SCSS-APSA) by applying the first-order Taylor series expansion to the sigmoidal active function (of which the independent variable is symmetric) of CSS-APSA. SCSS-APSA has lower computational complexity, and can achieve comparable, or even better filtering performance than that of CSS-APSA. In addition, we propose a modification of the sigmoidal active function. The modified sigmoidal active function is a form of scaling transformation based on the conventional one. Applying the modified function to the CSS-APSA, we can obtain the modified CSS-APSA (MCSS-APSA). Moreover, the extra parameter of MCSS-APSA provides the power to accelerate the convergence rate of CSS-APSA. Following the simplification operations of SCSS-APSA, the computational complexity of MCSS-APSA can also be reduced. Therefore, we get the simplified MCSS-APSA (SMCSS-APSA). Simulation results demonstrate that our proposed algorithms are able to achieve a faster convergence speed in system identification.