Machine Learning Algorithms Analysis of Synthetic Minority Oversampling Technique (SMOTE): Application to Credit Default Prediction

Credit default prediction is an important problem in financial risk management. It aims to determine the possibility of borrowers failing on their loan commitments. However, dataset to guide Machine Learning modeling procedure for data driven support suffers from class imbalance. Class imbalance in Machine Learning is an unbalanced distribution of classes within a dataset. This problem often arises in classification jobs if the distribution of classes or labels in a dataset is not uniform. To overcome this issue, just resample by adding or removing entries from the minority or majority classes. The present study looks on the efficacy of classification algorithms employing various data balancing approaches. The dataset was collected from a well-known commercial bank in Ghana. To resolve the imbalance, three data balancing approaches were used: under-sampling, oversampling, and the synthetic minority oversampling technique (SMOTE). Findings, with the exception of the SMOTE dataset, XGBoost consistently beat the other classifiers across the other datasets in terms of AUC. Random forest, decision tree, and logistic regression all performed well and might be utilized as alternatives to XGBoost classifiers for developing credit scoring models. The findings demonstrate that classifiers trained on balanced datasets have higher sensitivity scores than those trained on the original skewed dataset, while maintaining their capacity to differentiate between defaulters and non-defaulters. This demonstrates the value of data balancing strategies in increasing models' ability to anticipate minority class occurrences, Hence, the major discovery is that oversampling outperforms under-sampling across classifiers and evaluation measures is affirmed

Common fixed points for two pairs of selfmaps satisfying certain contraction condition in bb-metric spaces

This study introduces generalized contraction for two pairs of selfmaps in complete $b$-metric spaces, and it then establishes the existence of common fixed points under the presumptions that these two pairs of maps are weakly compatible and satisfy the condition for generalized contraction.  A sequence of selfmaps is added as an extension of the same.  Additionally, we demonstrate the same using various hypotheses on two pairs of selfmaps that satisfy the $b$-(E.A)-property.  Some of the conclusions in the literature are extended /generalized to two pairs of self maps by our theorems

Some special cases on Stolarsky’s means

In this paper we observe that one-parameter Stolarsky’s means (SM) are deduced from both the Mean Value Theorem for derivatives (MVTD) and the Mean Value Theorem for definite integrals (MVTI), and we study their elementary properties as the parameter varies. In the subfamily of SM having a natural number as parameter, we geometrically interpret one of them in particular as a real elliptic cone. We link SM having the integer power of a prime number as a parameter to classical means (i.e., harmonic mean, geometric mean, arithmetic mean, power mean). Finally, from an extension of Flett's Theorem (FT), we derive the expression of a new mean that is a upper bound of the arithmetic mean

Lie-Santilli admissible hyper-structures, from numbers to Hv-numbers

The class of Hv-structures defined on a set is very big and admits a partial order. For this reason, it has a numerous of applications in mathematics and other sciences as physics, biology, linguistics, to mention but a few. Here, we focus on the Lie-Santilli’s admissible case, where the hyper-numbers, called Hv-numbers, are used. In order to verify all needed axioms for Lie-Santilli’s admissibility, as the irreversibility and uniqueness of living organisms and time, on the one side and small results on the other side, we use the verythin Hv-fields. Therefore, we take rings and we enlarge only one result by adding only one element in order to obtain an Hv-field. This means that, we use only the associativity on the product and we transfer this to the weak-associativity on the hyper-product. Thus, from a semigroup on the product, we construct an Hv-group on the hyper-product

La disputa fra Federigo Enriques e i neoidealisti italiani: una disfatta dell’Enriques? (The dispute between Federigo Enriques and the Italian neo-idealists: a defeat for Enriques?)

AbstractThe controversy that between 1908 and 1912 saw Benedetto Croce and Giovanni Gentile opposed, on one side, and Federigo Enriques, on the other, did not actually have a conclusive episode, but its end was perceived, for its results on culture, on society and teaching in Italy, as a "defeat" of Enriques. A more careful examination of the events and of the historical context in which it took place seems, however, to clearly demonstrate that we can speak not of a personal defeat of the great mathematician from Livorno, but rather of a defeat of the commendable attempts at cultural and social modernization of Italy in an international perspective, of which Enriques was not the only actor but certainly the most exposed. Such intentions were crushed by the myopic provincial conservatism of the Italian neo-idealism, favored by the fascist regime, concerned only with affirming in the world an alleged autarkic national cultural superiority, based on the traditional literary-humanistic culture, ignoring the progress of the new technical-scientific thought, placed in an international context. Keywords: Federigo Enriques, Italian neo.idealists, Benedetto Croce, Giovanni Gentile.[1] SuntoLa polemica che dal 1908 al 1912 vide contrapposti da una parte Benedetto Croce e Giovanni Gentile e dall’altra Federigo Enriques non ebbe, in realtà, un episodio conclusivo, ma la sua fine è stata percepita, per i suoi esiti sulla cultura, sulla società e sull’insegnamento in Italia, come una “sconfitta” dell’Enriques. Un esame più attento delle vicende e del contesto storico nel quale si svolse sembra, invece, dimostrare chiaramente di poter parlare non di una sconfitta personale del grande matematico livornese, quanto piuttosto di una sconfitta dei lodevoli tentativi di ammodernamento culturale e sociale dell’Italia in una prospettiva internazionale, di cui Enriques non fu l’unico attore ma sicuramente quello più esposto. Tali propositi furono schiacciati dal miope conservatorismo provinciale del neoidealismo italiano, favorito dal regime fascista, preoccupato unicamente di affermare nel mondo una pretesa superiorità culturale nazionale autarchica, basata sulla tradizionale cultura letterario-umanistica, ignorando il progresso del nuovo pensiero tecnico-scientifico, per sua natura, invece, inserito in un contesto internazionale.Parole chiave: Federigo Enriques, Neo-idealisti italiani, Benedetto Croce, Giovanni Gentile.[1] Received on February 28th, 2024. Accepted on ….. Published on ….. doi: …….. ISSN 2282-7757; eISSN  2282-7765. ©The Authors. This paper is published under the CC-BY licence agreement

Unicity Results Concerning of difference monomials of L-function and a meromorphic function

In this paper, we study the value distribution of $\mathcal{L}$-function in the extend Selberg class and a non-constant transcendental meromorphic $\mathsf{f}$ function with finitely many zeros of finite order, sharing a polynomial with its difference monomial. Meromorphic functions and $L$-functions are central to Nevanlinna theory, a branch of complex analysis focusing on the distribution of zeros and poles of analytic functions. The  Meromorphic functions are unique due to their combination of meromorphicity and analyticity. They are defined on the entire complex plane except for isolated poles in the complex analysis. On the other hand, $L$-functions, arising notably in number theory and automorphic forms, exhibit unique properties related to their zeros and poles. One classic example of a prime number distribution is the Riemann $\zeta$-function. In this paper, we analyse the uniqueness results between a non-constant meromorphic function $\mathsf{f}$ having finitely many zeros and $L$-function, when their difference monomial $\mathsf{f}^{n}\prod\limits_{j=1}^{s}\mathsf{f}(z+c_{j})^{\mu_{j}}$ and $\mathcal{L}^{n}\prod\limits_{j=1}^{s}\mathcal{L}(z+c_{j})^{\mu_{j}}$ share a non-zero polynomial $p$. Our results extends and improves the earlier results of Harina P. Waghamore and Manjunatha B E\cite{bib6}

Small weak hyperfields in hadronic mechanics

It was in mid 90es when Professor R. M. Santilli realized, for the first time, that his innovating theories can be appropriate expressed by multi-valued systems. At that time the largest class of hyper-structures, the Hv-structures, based on the weak properties, were introduced and studied deeply. The extremely large number of weak hyper-structures defined on the same set can be reduced by demanding a lot of properties. Therefore, whenever the Santilli’s Hadronic Mechanics need special elements satisfying a number of properties then the class of the Hv-structures is the appropriate one. The first Hv-structures in Hadronic Mechanics, introduced in 1996, are called e-hyper-structures. The main question in this theory proposed by Santilli is: What are the hyper-numbers? Hyper-numbers or Hv-numbers are called the elements of any Hv-field and they are important in representation theory, as well. In this presentation we give some constructions and properties on minimal Hv-fields

Second Kind Chebyshev Wavelet Analysis of Abel’s Integral Equations

This paper presents two approximations of the solution functions of Abel’s integral equations belong ing to classes Hα[0,1), Hϕ[0,1) by (λk+1 −1,M)th partial sums of their second kind Chebyshev wavelet expansion in the interval [0,1), for λ > 1. These approximations are E(1) λk+1−1,M (f), E(2) λk+1−1,M (f). Chebyshev wavelets of the second kind were used to solve Abel’s integral equations. The Chebyshev wavelet of the second kind leads to a solution that is almost identical to their exact solution. This research paper’s accomplishment in wavelet analysis is noteworthy

Il latino della scienza Galilei e i fratelli Bernoulli in uno studio interdisciplinare sulla brachistocrona (Latin in Science, Galilei and the Bernoulli brothers in interdisciplinary study over the Brachistochrone)

In this paper, we describe an interdisciplinary study between Latin and Mathematics, where Latin serves as a tool for inquiry, facilitating access to and reflection on the new mathematical concepts that emerged during the Scientific Revolution of the 17th and 18th centuries. By examining original texts in Latin, we trace the genesis of these concepts and their development through the creation of a new Latin lexicon tailored to express them.We analyze texts by Galileo and the Bernoulli brothers concerning the brachistochrone problem, which marks the transition from classical mathematics to the new infinitesimal calculus that laid the groundwork for the Scientific Revolution. From an epistemological perspective, solving this problem—which requires the new tools of differential calculus—offers a significant example of the limitations of classical mathematics. The analysis of primary sources allows us to reconstruct the original thinking that led scientists to propose solutions, while also encountering an epistemological obstacle: the concept of the limit. Furthermore, analyzing the Latin texts reveals the construction and evolution of scientific language as it developed alongside the new mathematics.

Best proximity point for weak cyclic Kannan type F−F-contraction map and cyclic Chatterjea type F−F-contraction map

In this paper, we introduce an innovative category of contractions termed "cyclic Chatterjea type $F-$contraction" and "weak cyclic Kannan type $F-$contraction." Subsequently, we establish a theorem for determining the best proximity point in a uniformly convex Banach space, specifically focusing on weak cyclic Kannan type $F-$contractions. Furthermore, we extend our investigation to include cyclic Chatterjea type $F-$contractions in uniformly convex Banach spaces. To support our findings, we present illustrative examples