Analytical Form Research Articles

Evolving Transparent Credit Risk Models: A Symbolic Regression Approach Using Genetic Programming

Credit scoring is a cornerstone of financial risk management, enabling financial institutions to assess the likelihood of loan default. However, widely recognized contemporary credit risk metrics, like FICO (Fair Isaac Corporation) or Vantage scores, remain proprietary and inaccessible to the public. This study aims to devise an alternative credit scoring metric that mirrors the FICO score, using an extensive dataset from Lending Club. The challenge lies in the limited available insights into both the precise analytical formula and the comprehensive suite of credit-specific attributes integral to the FICO score’s calculation. Our proposed metric leverages basic information provided by potential borrowers, eliminating the need for extensive historical credit data. We aim to articulate this credit risk metric in a closed analytical form with variable complexity. To achieve this, we employ a symbolic regression method anchored in genetic programming (GP). Here, the Occam’s razor principle guides evolutionary bias toward simpler, more interpretable models. To ascertain our method’s efficacy, we juxtapose the approximation capabilities of GP-based symbolic regression with established machine learning regression models, such as Gaussian Support Vector Machines (GSVMs), Multilayer Perceptrons (MLPs), Regression Trees, and Radial Basis Function Networks (RBFNs). Our experiments indicate that GP-based symbolic regression offers accuracy comparable to these benchmark methodologies. Moreover, the resultant analytical model offers invaluable insights into credit risk evaluation mechanisms, enabling stakeholders to make informed credit risk assessments. This study contributes to the growing demand for transparent machine learning models by demonstrating the value of interpretable, data-driven credit scoring models.

Analysis of the third class mechanism using the modeling method in the Mathcad software environment

Purpose. To carry out a kinematic analysis of a flat twelve-link hinged mechanism with three leading links, the basis of which is a structural group of links of the third class of the fourth order with rotational kinematic pairs, which is used in technological equipment. Methodology. The kinematic study of a flat complex mechanism of the third class with three leading links was performed using the mathematical modeling method in the Mathcad software environment. Findings. Using the method of mathematical modeling, the mechanism was presented in the form of free vectors built on its links, for which, taking into account the presence of three leading links, three vector contours were selected, which made it possible to draw up a system of vector equations of their closedness with further solving by a numerical method in the Mathcad software environment. The functions of the rotation angles of the mechanism links, their angular velocities and accelerations were obtained in analytical and graphical form depending on the rotation angle of the first driving crank of the mechanism, the calculation of the angular velocities and accelerations of all the driven links of the mechanism was performed. Originality. A sequence was developed and a kinematic study of a complex planar mechanism of the third class with three leading links was done, the basis of which is a structural group of links of the third class of the fourth order. Schematic modeling of the mechanism with three leading links was performed, a visualization schedule of its kinematic scheme was built, and a valid version of its assembly was obtained from many possible ones, for which the values of kinematic parameters of all its links were determined. Practical value. An analysis of the effect of the kinematic parameters of the three leading links of the third-class mechanism on the movement of the working body of the technological equipment was carried out. From the analysis of the obtained research results for the cycle of the mechanism the reason was found for the incomplete technological stoppage of the link, which should provide the working body of the machine for the required period of time. Recommendations of the elimination were made to identify the deficiency and proposals for the need to improve the drive of this equipment.

Identification of moment equations via data-driven approaches in nonlinear Schrödinger models

IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments.MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically.Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.

On the issue of the development of adjective degree forms in the Western Lithuanian and Latvian dialects

Abstract In the Lithuanian and Latvian languages, forms of adjective degrees do not have a common etymological basis. The New Curonian (Kuresnieku) language which is a relatively new Baltic geolect has preserved a fairly distinct archaic layer of phonetics and grammar, where one can look not only for the archaisms of the western dialects of the Latvian language but also for traces of the substrate of Old Curonian. Although synthetic forms of the degrees of adjectives with the suffix -āk- are used in the current Latvian language area they are almost unknown in New Curonian. The forms of the comparative degree are made with the particle juo and an adjective of the positive degree. Analytical forms with the pronoun visu and the pronominal form of an adjective express the superlative degree. In the western Latvian and Lithuanian dialects and the Livonian language in Latvia, the relics of the analytical forms of the comparative and superlative degree are recorded in written sources and rarely in modern spoken language. Since a large part of the western dialects of the Lithuanian and Latvian languages take up the former territory of the old tribe, it may be assumed that the analytical forms of adjective degrees are possibly a sign of the substrate of Old Curonian.

On the Implementation of Iterative Methods Without Inverse Updating for Solving Equations in Banach Spaces

The implementation of iterative methods using inverses to solve equations is a computationally expensive or impossible task in general. This is the case, since the analytical form of the inverse is difficult to find in practice. That is why, we replace the inverse by a sum of linear operators which is well defined. The convergence of the resulting hybrid methods is studied based on majorizing sequences under generalized continuity assumptions on the operators involved and in the setting of a Banach space. It is demonstrated by numerical experimentations that the convergence order as well as the number of iterations required to obtain a predetermined error tolerance when comparing the original to the hybrid method is essentially the same.

Method for Increasing the Energy Efficiency of the Gear Teeth Cutting Process by Smoothing the Cutting Force Variation

The energy efficiency in metal cutting is, sometimes, very low. Recent studies show that the energy consumed for detaching chips represents only about 15% of the total energy involved in material machining. The available solutions for energy optimization in cutting processes mentioned are the improvement of manufacturing equipment, the optimization of processes, and appropriate production scheduling. Already-performed research shows that to increase energy efficiency, the cutting force must be reduced, for example, by reducing the depth of the cut and by increasing the feed rate. However, this is applicable when the cutting force is quasi-constant during the process, which is not the case for gear teeth cutting when the cutting force significantly varies. The present paper proposes a new solution for energy efficiency increase in gear teeth cutting, namely, the smoothing of the cutting force variation during the machining process, by keeping the area of the detached chip section quasi-constant during the cutting process. This can be reached by replacing the constant rolling feed, currently used in gear teeth cutting, with a rolling feed that varies after an appropriate law. An algorithm dedicated to implementing this solution has been developed. It uses graphical modeling in CATIA to find the variation in the detached chip area. Original MatLab R2018a applications were developed (i) to identify the analytical form of the law that approximates this variation and (ii) to find the variation law of the feed during the rolling motion, if imposing a constant area of the detached chip. The algorithm was successfully applied in the cases of toothing with a rack tool (by slotting) and with a pinion cutter (by slotting and turning). A technical solution for method implementation in practice is also presented.

Analytical Survival Analysis of the Non-autonomous Ornstein–Uhlenbeck Process

The survival probability for a periodic non-autonomous Ornstein–Uhlenbeck process is calculated analytically using two different methods. The first uses an asymptotic approach. We treat the associated Kolmogorov Backward Equation with an absorbing boundary by dividing the domain into an interior region, centered around the origin, and a “boundary layer” near the absorbing boundary. In each region we determine the leading-order analytical solutions, and construct a uniformly valid solution over the entire domain using asymptotic matching. In the second method we examine the integral relationship between the probability density function and the mean first passage time probability density function. These allow us to determine approximate analytical forms for the exit rate. The validity of the solutions derived from both methods is assessed numerically, and we find the asymptotic method to be superior.

High-temperature transport properties of a two-dimensional weakly doped parabolic semiconductor

A version of the Mexican-hat Hamiltonian is used to study high-temperature transport properties of a two-dimensional weakly doped semiconductor with electron-hole symmetric bands. For a finite doping level and a temperature-dependent band gap, we find a closed analytical form of the temperature-dependent chemical potential. The effective concentrations of charge carriers participating in transport coefficients are analyzed in the space spanned by the total electron concentration and temperature. It is shown that these concentrations are the sum of a residual contribution and two thermally activated contributions, with a complicated dependence on temperature. The analytical expression for the Hall coefficient RHis also found. It is argued that it is a non-monotonic function of the doping level with the maximum at the doping nmax that is a linear function of temperature at high enough temperatures. The analysis of the real part of the interband conductivity shows that it is inversely proportional to incoming photon energy at low temperatures and that it is nearly constant over a wide energy range at high temperatures. This results are expected to be of significant importance in understanding transport and optical properties of weakly doped two-dimensional semiconductors with nearly symmetric parabolic bands.&#xD.

Modified method of round Gaussian rings. Application to the two-planetary problem

A scheme of the modified method of round Gaussian rings, designed to study the secular evolution of orbits in systems consisting of a central star and two planets, is presented. The reason for the secular evolution of the nodes and inclinations of the orbits of the planets is their mutual gravitational attraction. The orbits of the planets are modeled by homogeneous round Gaussian rings, to which the masses, sizes and angles of inclination of the orbits, as well as orbital angular momenta of the planets, are transferred. The method takes into account the fact that, in general, the ascending nodes of the orbits may not coincide. The mutual gravitational energy of the rings 𝑊𝑚𝑢𝑡 is represented as a series in the quadratic approximation in powers of small inclination angles. Using this function 𝑊𝑚𝑢𝑡, a closed system of four differential equations describing the secular evolution of the planets’ orbits is composed. The solution to the equations is obtained in finite analytic form, which simplifies the interpretation of the investigated planetary motions. The method was tested on the example of the Sun-Jupiter-Saturn system; for it, in particular, the difference in the longitudes of the nodes of the orbits of Jupiter and Saturn was calculated as a function of time. New approach is also used to study the precession of nodes in the exoplanetary system K2-36; graphs of all unknown quantities are obtained. It has been established that in the course of evolution the mutual inclination angle of the orbits remains constant, and the librations of the orbits in the inclination angle and in the motion of the nodes occur synchronously.

Effective diffusion along the backbone of combs with finite-span 1D and 2D fingers.

Diffusion in complex heterogeneous media, such as biological tissues or porous materials, typically involves constrained displacements in tortuous structures and sticky environments. Therefore, diffusing particles experience both entropic (excluded-volume) forces and the presence of complex energy landscapes. In this situation, one may describe transport through an effective diffusion coefficient. In this paper, we examine comb structures with finite-length 1D and finite-area 2D fingers, which act as purely diffusive traps. We find that there exists a critical width of 2D fingers, above which the effective diffusion along the backbone is faster than for an equivalent arrangement of 1D fingers. Moreover, we show that the effective diffusion coefficient is described by a general analytical form for both 1D and 2D fingers, provided the correct scaling variable is identified as a function of the structural parameters. Interestingly, this formula corresponds to the well-known general situation of diffusion in a medium with fast reversible adsorption. Finally, we show that the same formula describes diffusion in the presence of dilute potential energy traps, e.g., through a landscape of square wells. While diffusion is ultimately always the result of microscopic interactions (with particles in the fluid, other solutes, and the environment), effective representations are often of great practical use. The results reported in this paper help clarify the microscopic origins and the applicability of global, integrated descriptions of diffusion in complex media.

Bouncing universe scenarios in an extended gravitational framework involving curvature-matter coupling

Exploration of bouncing cosmic models in modified theories has gained much popularity in modern cosmology. This paper explores the Lagrangian function of a new theory namely F(R,Lm,T) framework by taking four renowned cosmic bouncing models, i.e., the exponential bounce, oscillatory bounce scenario, power law, and matter bouncing. Our primary objective is to fix the form of F(R,Lm,T) function for each model and investigate which kinds of reconstructed Lagrangian function have potential of regenerating bouncing scenario in terms of analytical form. It is seen that except power law model, the analytical solutions are conceivable only for certain cases of these bouncing models. For power law bounce, different cases of Lagrangian function may be rebuilt analytically while for some other bouncing scenarios, it is found that particular solutions are not always attainable and hence only the complimentary solutions can be explored. Further, we examine the behavior of energy constraints and stability of these analytically formed bouncing solutions. Additionally, we determine that the dark energy phase in F(R,Lm,T) gravity is compatible with the experimental data of BAO+Sne-Ia+CMB+H(z) and it is shown that cosmic bounce can be produced with dark energy eras in this gravity. We also present some constraints on the model parameters with Hubble parameter values and ΛCDM to determine the best-fit values of model via least square and reduced chi-squares methods. It is concluded that matter bounce model is the best fitted with the observational data set as well as ΛCDM model because it has least value of χm2.

Simplified approach to retention times of narrow binary pulses in the case of ideal chromatography model and Langmuir isotherm

Analytical solution to ideal chromatography model has been established for binary Langmuir isotherm and rectangular injections. However, retention time of the less adsorbed species, which is of great theoretical and practical significance, cannot be given in a closed form and is conventionally solved by numerical integration with a floating boundary. A simplified approach is provided in this article. A 4th order algebraic equation was derived and used to solve the maximum concentration that can be further used to explicitly calculate retention time. Under most practical conditions, reliable initial guess can be easily acquired, allowing for the application of Newton-Raphson method for rapid determination of the root of the 4th order equation. In addition, derivatives of retention time with respective to isotherm parameters can be given in analytical forms.

Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: application to T-models

We develop a method to compute the slow-roll expansion for the Hubble parameter in inflationary models in a flat Friedmann-Lemaître-Robertson-Walker spacetime that is applicable to a wide class of potentials including monomial, polynomial, or rational functions of the inflaton, as well as polynomial or rational functions of the exponential of the inflaton. The method, formulated within the Hamilton-Jacobi formalism, adapts the form of the slow-roll expansion to the analytic form of the inflationary potential, thus allowing a consistent order-by-order computation amenable to Padé summation. Using T-models as an example, we show that Padé summation extends the domain of validity of this adapted slow-roll expansion to the end of inflation. Likewise, Padé summation extends the domain of validity of kinetic-dominance asymptotic expansions of the Hubble parameter into the fast-roll regime, where they can be matched to the aforesaid Padé-summed slow-roll expansions. This matching in turn determines the relation between the expansions for the number N of e-folds and allows us to compute the total amount of inflation as a function of the initial data or, conversely, to select initial data that correspond to a fixed total amount of inflation. Using the slow-roll stage expansions, we also derive expansions for the corresponding spectral index ns accurate to order 1/N2, and tensor-to-scalar ratio r accurate to order 1/N3 for these T-models.

LINGUISTIC UNITS FORMING CAUSATIVE MEANING

The article deals with comparative study of linguistic units that express causative meaning in English and Karakalpak languages. It is noted that there are similarities and differences of causative structures that can be formed morphologically and syntactically. Moreover, some scholars’ views were stated and examples of causative verbs were taken from literary texts in order to reveal causative meaning used in the text. Due to the study, analytical form is used to express causative meaning in English while it is mostly formed morphologically in Karakalpak language.

Statistical distribution of surface elevation by using quadratic forms of normal random variables

This paper is concerned with the statistical properties of surface elevation, which is crucial for the design and operation of marine and coastal structures and is helpful to the prediction of rogue waves. A semi-analytic quadratic model is proposed to describe the statistical distribution of surface elevation by using the theory of quadratic forms of normal random variables, in which the characteristic function and cumulants are given in analytical form, and the probability density is obtained by the numerical inversion of the characteristic function using the fast Fourier transform algorithm. Compared with Monte Carlo simulations, the quadratic model presents excellent performance in describing the probability density function of surface elevation, especially at the tails, for varying degrees of steepness, bandwidth, and directional spreading in both finite and infinite water depth. The effect of these parameters that characterize sea states on the statistical properties of surface elevation is also investigated. Through a comparative study, the quadratic model is superior to previously existing theoretical models.

A dictionary-based Bayesian approach to optimizing left-turn restriction locations in grid networks

Left-turn movements at signalized intersections pose significant safety risks for the drivers and efficiency concerns for the traffic operations in urban networks. Restricting left-turn movements at selected locations has been shown to be effective at improving operational efficiency and mitigating safety concerns. However, determining optimal locations to restrict left-turns is a complex combinatorial optimization problem that is compounded by the lack of analytical forms for the objective function and constraints, as well as potential interdependencies between the decision variables. Following the common solution paradigm for this type of optimization problems, this paper presents a novel Bayesian approach that utilizes dictionary-based embeddings and is tailored for high-dimensional combinatorial (or even mixed) spaces. Simulation studies conducted using the Aimsun software under perfect or imperfect grid networks demonstrate that the presented method can consistently find promising left-turn restriction configurations that outperform the all-or-nothing strategies (to restrict all or none left-turn movements at all intersections), as well as the population based incremental learning algorithm. In addition, the presented method often does so with less simulation cost, thus showcasing its potential for efficient solution of more general traffic optimization problems.

Event-triggered nonlinear state estimation with quantized innovations

This paper proposes an event-triggered (ET) estimator with quantization mechanism to relieve the bandwidth and energy limitations of wireless sensors, where the ET strategy reduces the overall communication rate of the system, and the quantization mechanism mitigates the instantaneous bit rate constraint. Then, Gaussian approximation is applied to derive the analytical form of the minimum mean squared error (MMSE) estimator under the event-triggered strategy and quantization mechanism. Furthermore, the relationship between event-triggered parameter and communication rate is explicitly established. Finally, theoretical results are validated through some simulations on a target tracking system.

The integration of Artificial Intelligence in demand forecasting and inventory management in the United States

The integration of Artificial Intelligence in demand forecasting and inventory management in the United States has been examined in this paper. Demand forecasting and inventory management are two of critical areas in supply chain management, which is a veritable tool for promoting industrialization, manufacturing capabilities, and customers satisfaction. The use of AI in form of robotics, machine learning, deep learning, and predictive analytics, among others in all aspects of supply chain operations is gaining ground by the day. The integration of AI into the supply chain process can sustain multi-billion dollars trades in the United States, by reducing the cost of production and distribution, reducing human errors causing inaccurate demand forecasts, return shipment and cancellations of orders, etc. The challenges relating to the use of AI in demand forecasting and inventory management such as high cost of installation and maintenance, data privacy violations, requirement of skilled personnel, which are limited in global supply, and employees’ resistance to change were also identified. The outlook of relationship between Artificial Intelligence and supply chain management looks hopeful, brighter, and encouraging. This will be made possible by continuous development of AI capabilities and reducing the challenges of its widespread integration.

Multipath Characteristics of Orbital Angular Momentum Vortex Electromagnetic Radio Waves Over an Infinite Ground Plane

In this paper, the effect of an infinitely sized ground plane on the orbital angular momentum (OAM) vortex electromagnetic (EM) radio waves is investigated. Although the effect of an infinite ground on OAM wave propagation and communication has already been numerically examined in the literature using the method of moments (MoM), this situation needs to be examined analytically and theoretically derived final form expressions need to be obtained. The multipath characteristics of OAM waves in a superconducting ground plane are theoretically presented considering both horizontal and vertical polarization conditions. In addition to direct radiation to an observation point in the far-field from the array antenna, many reflected radiations from the ground plane are also transmitted. The most fundamental reflected radiation is analyzed over a uniform circular array (UCA), adopting electromagnetic image theory. Furthermore, the transmitted field expressions obtained by considering both the circular array parallel to the ground plane and the circular array upright to the ground plane are formulated in a general analytical form for an OAM wave on a superconducting ground plane. In addition, numerical simulations are applied to exemplify the properties of OAM waves in the superconducting ground plane, unlike the isolated medium.

Analysis of 11B + 13,14C scattering and 13C(11B, 10B)14C reaction data at E lab(11B) = 45 MeV using energy dependent optical model systematics for carbon isotopes

Existing data for 11B + 13,14C elastic and inelastic scattering at E lab(11B) = 45 MeV, as well as new data for the 13C(11B, 10B)14C reaction for transitions populating the ground state of 14C and the ground plus first four excited states of 10B, were analysed using the coupled-channels (CC) and coupled-reaction-channels (CRC) methods. A recently proposed energy dependent optical model (OM) potential for carbon isotopes, consisting of Woods-Saxon (WS) volume real and WS volume plus surface imaginary components, applied successfully to OM analyses of scattering from mid-mass (A > 27) and heavy target nuclei, was used to generate the distorted waves in the entrance and exit channels. The data analysed in this work cover the whole angular range, enabling the most important reaction mechanisms leading to the production of nuclei in the exit reaction channels to be established. For these light boron + carbon systems, a reasonable fit to both scattering and reaction data over the full angular range required some modification of the parameters of the OM potential extracted from the energy-dependent carbon systematics: omission of the surface imaginary part and a slight increase in the radius of the real part. Inclusion of a sufficient number of inelastic channels in a CC analysis of the 11B + 13,14C elastic scattering was shown to be important at mid-range scattering angles, while for the 13C(11B, 10B)14C reaction inclusion of two-step neutron transfers via low-lying excited states of 11B was required to give good overall agreement between the CRC calculations and the data. We suggest the analytical form of the global carbon OM potential may benefit from an additional parameterization of the radius of the real part and the depth of the surface imaginary part, dependent on the target mass number, to give better applicability to the analysis of scattering from light target nuclei.