Search results for: Arrow’s impossibility theorem

Authors: Serge Provost, Yishan Zang

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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Elvira Lumi, Hans Jazxhi

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In the works of the writer Flutura Açka, the play with these questions is acute, and in almost each of them, the act of loneliness and isolation builds in a completely involuntary way unique and frequent conceptual spaces. Because the object of study is too broad to grasp all the works, this study lays out a rapid paradox of our access to three of the novels in the line of numerous authorial works. The novel "Woman Loneliness" (2001), also marked as the first work in prose by the author, declares in the title the paradigm of what she has decided to confess. The gender segregation proclaimed in the title will be revealed step by step in the work as conventional human segregation without gender. In this novel, the analysis of the state of "loneliness" will require a contemplation beyond man, when the role of the environment and the distance from the center of the narrative base will be extremely visible in the work. The novel "Cross of Oblivion" (2004) has another form of perception of loneliness, which, unlike the one built by the characters themselves in the novel "Woman Loneliness," is imposed and obligatory to live by the circumstances. Its characters are trapped in loneliness, as loneliness that comes from impossibility, from the past, from dependence on fate, from fear of change, and from the obligation to accept it. At the heart of the novel, the plot of the novel game is dictated by the Kanun and its rules and the loneliness of the basis of life in unbroken waves towards the periphery of the event, a periphery that has very large geography and is played in today's Europe. The novel "Where are you?" (2009) has a completely different form of constructing the concept of loneliness and isolation that comes under conditions of repression and political pressure. The loneliness in this novel takes the form of the protective element from the circumstances that actually require a social inclusion; it is personal loneliness that ensures relative mental health of the characters, up to a new trap created by the circumstances, thus building life fragmentary “healthy” in the order of a mentally ill and socially ill society.

Keywords: loneliness, existential, isolation, woman, prose

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Authors: Farshad Ghodoosi

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This article analyzes the effect of supervening events in contracts. Contracts serve an important function: allocation of risks. In spite of its importance, the case law and the doctrine are messy and inconsistent. This article provides a fresh look at excuse doctrines (i.e., force majeure, impracticability, impossibility, and frustration) with a focus on force majeure clauses. The article makes the following contributions: First, it furnishes a new conceptual and theoretical framework of excuse doctrines. By distilling the decisions, it shows that excuse doctrines rests on the triangle of control, foreseeability, and contract language. Second, it analyzes force majeure clauses used by S&P 500 companies to understand the stickiness and similarity of such clauses and the events they cover. Third, using computational and statistical tools, it analyzes US cases since 1810 in order to assess the weight given to the triangle of control, foreseeability, and contract language. It shows that the control factor plays an important role in force majeure analysis, while the contractual interpretation is the least important factor. The Article concludes that it is the standard for control -whether the supervening event is beyond the control of the party- that determines the outcome of cases in the force majeure context and not necessarily the contractual language. This article has important implications on COVID-19-related contractual cases. Unlike the prevailing narrative that it is the language of the force majeure clause that’s determinative, this article shows that the primarily focus of the inquiry will be on whether the effects of COVID-19 have been beyond the control of the promisee. Normatively, the Article suggests that the trifactor of control, foreseeability, and contractual language are not effective for allocation of legal risks in times of crises. It puts forward a novel approach to force majeure clauses whereby that the courts should instead focus on the degree to which parties have relied on (expected) performance, in particular during the time of crisis.

Keywords: contractual risks, force majeure clauses, foreseeability, control, contractual language, computational analysis

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Authors: Selahattin Gultekin

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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: microstretch, deflection, exponential load, Laplace transforms, residue theorem, simply supported

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: David Martínez Rico, Juan Pablo Farid Cuéllar Martínez

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After more than half a century that the first treaty of European cooperation was created, the final result of a difficult and long historical process, which is the current European Union, is facing economical and social challenges. The barriers of policies differences and national sovereignties seem to be being defeated in the last and present decades. However, the last crisis of 2008 brought back problems as xenophobia and nationalism. In this ambit of identity, European Union has made many efforts to reinforce a European identity and leave behind the radical nationalisms which generated World Wars. Nevertheless, these social problems are increasing and becoming more present in the life of many Europeans. Even, in the last Euro Parliamentarian Elections of the present year, 2014, the extreme right parties, in favor of xenophobic and anti European ideals, got more seats and are increasing their presence in Euro Parliament. This essay approaches to this controversial topic of European identity. Taking as start point the nationalist divisions that are causing internal divergences in Europe, the authors of this research study the role and contributions of the Memorials of the fallen soldiers and heroes of World Wars, present in many cities as Amsterdam, Brussels and Paris, to the impossibility to reach an European identity, it means that Europeans feel first part of Europe in place to feel first part of a nation. The objective of this essay is to reaffirm the thesis that establishes that the European Union won´t reach the longed supranational identity with just with the current strategies, because yet there are many cultural elements in its member states societies which exalt the heroes and soldiers of the past wars, increasing nationalism feelings. Besides, in it are promoted some interesting ideas that could change the course in this quest of a European social identity.

Keywords: identity, memorials, European identity, nationalism, proposals

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Ivana R. Moser, Joao C. Souza

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Building fires are random phenomena that can be extremely violent, and safe evacuation of people is the most guaranteed tactic in saving lives. The correct evacuation of buildings, and other spaces occupied by people, means leaving the place in a short time and by the appropriate way. It depends on the perception of spaces by the individual, the architectural layout and the presence of appropriate routing systems. As historical buildings were constructed in other times, when, as in general, the current security requirements were not available yet, it is necessary to adapt these spaces to make them safe. Computer models of evacuation simulation are widely used tools for assessing the safety of people in a building or agglomeration sites and these are associated with the analysis of human behaviour, makes the results of emergency evacuation more correct and conclusive. The objective of this research is the performance evaluation of historical interest buildings, regarding the safe evacuation of people, through computer simulation, using PTV Viswalk software. The buildings objects of study are the Colégio Catarinense, centennial building, located in the city of Florianópolis, Santa Catarina / Brazil. The software used uses the variables of human behaviour, such as: avoid collision with other pedestrians and avoid obstacles. Scenarios were run on the three-dimensional models and the contribution to safety in risk situations was verified as an alternative measure, especially in the impossibility of applying those measures foreseen by the current fire safety codes in Brazil. The simulations verified the evacuation time in situations of normality and emergency situations, as well as indicate the bottlenecks and critical points of the studied buildings, to seek solutions to prevent and correct these undesirable events. It is understood that adopting an advanced computational performance-based approach promotes greater knowledge of the building and how people behave in these specific environments, in emergency situations.

Keywords: computer simulation, escape routes, fire safety, historic buildings, human behavior

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Authors: Daljinder Singh, J.S.Dhillon, Balraj Singh

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According to no free lunch theorem, a single search technique cannot perform best in all conditions. Optimization method can be attractive choice to solve optimization problem that may have exclusive advantages like robust and reliable performance, global search capability, little information requirement, ease of implementation, parallelism, no requirement of differentiable and continuous objective function. In order to synergize between exploration and exploitation and to further enhance the performance of Bat algorithm, the paper proposed a modified bat algorithm that adds additional search procedure based on bat’s previous experience. The proposed algorithm is used for solving the economic load dispatch (ELD) problem. The practical constraint such valve-point loading along with power balance constraints and generator limit are undertaken. To take care of power demand constraint variable elimination method is exploited. The proposed algorithm is tested on various ELD problems. The results obtained show that the proposed algorithm is capable of performing better in majority of ELD problems considered and is at par with existing algorithms for some of problems.

Keywords: bat algorithm, economic load dispatch, penalty method, variable elimination method

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Authors: Nader H. Ghareeb, Mohamed S. Gaith, Sayed M. Soleimani

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In modern engineering, weight optimization has a priority during the design of structures. However, optimizing the weight can result in lower stiffness and less internal damping, causing the structure to become excessively prone to vibration. To overcome this problem, active or smart materials are implemented. The coupled electromechanical properties of smart materials, used in the form of piezoelectric ceramics in this work, make these materials well-suited for being implemented as distributed sensors and actuators to control the structural response. The smart structure proposed in this paper is composed of a cantilevered steel beam, an adhesive or bonding layer, and a piezoelectric actuator. The static deflection of the structure is derived as function of the piezoelectric voltage, and the outcome is compared to theoretical and experimental results from literature. The relation between the voltage and the piezoelectric moment at both ends of the actuator is also investigated and a reduced finite element model of the smart structure is created and verified. Finally, a linear controller is implemented and its ability to attenuate the vibration due to the first natural frequency is demonstrated.

Keywords: active linear control, lyapunov stability theorem, piezoelectricity, smart structure, static deflection

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Authors: A. H. Elkholy, D. M. Almutairi

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The successful and efficient execution of a forging process is dependent upon the correct analysis of loading and metal flow of blanks. This paper investigates the Upper Bound Technique (UBT) and its application in the analysis of open forging process when a possibility of blank bulging exists. The UBT is one of the energy rate minimization methods for the solution of metal forming process based on the upper bound theorem. In this regards, the kinematically admissible velocity field is obtained by minimizing the total forging energy rate. A computer program is developed in this research to implement the UBT. The significant advantages of this method is the speed of execution while maintaining a fairly high degree of accuracy and the wide prediction capability. The information from this analysis is useful for the design of forging processes and dies. Results for the prediction of forging loads and stresses, metal flow and surface profiles with the assured benefits in terms of press selection and blank preform design are outlined in some detail. The obtained predictions are ready for comparison with both laboratory and industrial results.

Keywords: forging, upper bound technique, metal forming, forging energy, forging die/platen

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Authors: M. Uysal, M. Yilmaz, I. Tiryakioğlu

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Digital Terrain Model (DTM) is a digital numerical representation of the Earth's surface. DTMs have been applied to a diverse field of tasks, such as urban planning, military, glacier mapping, disaster management. In the expression of the Earth' surface as a mathematical model, an infinite number of point measurements are needed. Because of the impossibility of this case, the points at regular intervals are measured to characterize the Earth's surface and DTM of the Earth is generated. Hitherto, the classical measurement techniques and photogrammetry method have widespread use in the construction of DTM. At present, RADAR, LiDAR, and stereo satellite images are also used for the construction of DTM. In recent years, especially because of its superiorities, Airborne Light Detection and Ranging (LiDAR) has an increased use in DTM applications. A 3D point cloud is created with LiDAR technology by obtaining numerous point data. However recently, by the development in image mapping methods, the use of unmanned aerial vehicles (UAV) for photogrammetric data acquisition has increased DTM generation from image-based point cloud. The accuracy of the DTM depends on various factors such as data collection method, the distribution of elevation points, the point density, properties of the surface and interpolation methods. In this study, the random data reduction method is compared for DTMs generated from image based point cloud data. The original image based point cloud data set (100%) is reduced to a series of subsets by using random algorithm, representing the 75, 50, 25 and 5% of the original image based point cloud data set. Over the ANS campus of Afyon Kocatepe University as the test area, DTM constructed from the original image based point cloud data set is compared with DTMs interpolated from reduced data sets by Kriging interpolation method. The results show that the random data reduction method can be used to reduce the image based point cloud datasets to 50% density level while still maintaining the quality of DTM.

Keywords: DTM, Unmanned Aerial Vehicle (UAV), uniform, random, kriging

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Authors: Jalal Karam

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The methods of Fourier, Laplace, and Wavelet Transforms provide transfer functions and relationships between the input and the output signals in linear time invariant systems. This paper shows the equivalence among these three methods and in each case presenting an application of the appropriate (Fourier, Laplace or Wavelet) to the convolution theorem. In addition, it is shown that the same holds for a direct integration method. The Biorthogonal wavelets Bior3.5 and Bior3.9 are examined and the zeros distribution of their polynomials associated filters are located. This paper also presents the significance of utilizing wavelets as effective tools in processing speech signals for common multimedia applications in general, and for recognition and compression in particular. Theoretically and practically, wavelets have proved to be effective and competitive. The practical use of the Continuous Wavelet Transform (CWT) in processing and analysis of speech is then presented along with explanations of how the human ear can be thought of as a natural wavelet transformer of speech. This generates a variety of approaches for applying the (CWT) to many paradigms analysing speech, sound and music. For perception, the flexibility of implementation of this transform allows the construction of numerous scales and we include two of them. Results for speech recognition and speech compression are then included.

Keywords: continuous wavelet transform, biorthogonal wavelets, speech perception, recognition and compression

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Authors: Hamdy M. Youssef

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In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of Lord-Shulman thermoelastic theorem, which contains non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations, and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.

Keywords: nanobeam, vibration, constant magnetic field, ramp-type thermal loading, non-Fourier heat conduction law

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Authors: Stepan Papacek, Jiri Jablonsky, Radek Kana, Ctirad Matonoha, Stefan Kindermann

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FRAP (Fluorescence Recovery After Photobleaching) is a widely used measurement technique to determine the mobility of fluorescent molecules within living cells. While the experimental setup and protocol for FRAP experiments are usually fixed, data processing part is still under development. In this paper, we formulate and solve the problem of data selection which enhances the processing of FRAP images. We introduce the concept of the irrelevant data set, i.e., the data which are almost not reducing the confidence interval of the estimated parameters and thus could be neglected. Based on sensitivity analysis, we both solve the problem of the optimal data space selection and we find specific conditions for optimizing an important experimental design factor, e.g., the radius of bleach spot. Finally, a theorem announcing less precision of the integrated data approach compared to the full data case is proven; i.e., we claim that the data set represented by the FRAP recovery curve lead to a larger confidence interval compared to the spatio-temporal (full) data.

Keywords: FRAP, inverse problem, parameter identification, sensitivity analysis, optimal experimental design

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Authors: Serge B. Provost

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Numerous statistical inference and modeling methodologies are based on sample moments rather than the actual observations. A result justifying the validity of this approach is introduced. More specifically, it will be established that given the first n moments of a sample of size n, one can recover the original n sample points. This implies that a sample of size n and its first associated n moments contain precisely the same amount of information. However, it is efficient to make use of a limited number of initial moments as most of the relevant distributional information is included in them. Two types of density estimation techniques that rely on such moments will be discussed. The first one expresses a density estimate as the product of a suitable base density and a polynomial adjustment whose coefficients are determined by equating the moments of the density estimate to the sample moments. The second one assumes that the derivative of the logarithm of a density function can be represented as a rational function. This gives rise to a system of linear equations involving sample moments, the density estimate is then obtained by solving a differential equation. Unlike kernel density estimation, these methodologies are ideally suited to model ‘big data’ as they only require a limited number of moments, irrespective of the sample size. What is more, they produce simple closed form expressions that are amenable to algebraic manipulations. They also turn out to be more accurate as will be shown in several illustrative examples.

Keywords: density estimation, log-density, polynomial adjustments, sample moments

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Authors: Omer Cahana, Ofer Levi, Maya Herman

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Magnetic Resonance Imaging (MRI) is a lengthy medical scan that stems from a long acquisition time. Its length is mainly due to the traditional sampling theorem, which defines a lower boundary for sampling. However, it is still possible to accelerate the scan by using a different approach such as Compress Sensing (CS) or Parallel Imaging (PI). These two complementary methods can be combined to achieve a faster scan with high-fidelity imaging. To achieve that, two conditions must be satisfied: i) the signal must be sparse under a known transform domain, and ii) the sampling method must be incoherent. In addition, a nonlinear reconstruction algorithm must be applied to recover the signal. While the rapid advances in Deep Learning (DL) have had tremendous successes in various computer vision tasks, the field of MRI reconstruction is still in its early stages. In this paper, we present an end-to-end method for MRI reconstruction from k-space to image. Our method contains two parts. The first is sensitivity map estimation (SME), which is a small yet effective network that can easily be extended to a variable number of coils. The second is reconstruction, which is a top-down architecture with lateral connections developed for building high-level refinement at all scales. Our method holds the state-of-art fastMRI benchmark, which is the largest, most diverse benchmark for MRI reconstruction.

Keywords: magnetic resonance imaging, image reconstruction, pyramid network, deep learning

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Authors: Emily S. M. Chow

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The word ‘utopia’ was coined by Thomas More in Utopia (1516). Its Greek roots ‘ou’ means ‘not’ and ‘topos’ means ‘place.’ In other words, it literally refers to ‘no-place.’ However, the possibility of having an alternative and better future society has always been appealing. In fact, at the core of every utopianism is the search for a future alternative state with the anticipation of a better life. Nonetheless, the practicalities of such ideas have never ceased to be questioned. At times, building a utopia presents itself as a divisive act. In addition to the violence that must be employed to sweep away the old regime in order to make space for the new, all utopias carry within them the potential for bringing catastrophic consequences to human life. After all, every utopia seeks to remodel the individual in a very particular way for the benefit of the masses. In this sense, utopian thinking has the potential both to create and destroy the future. While writing during a traumatic transitional period in Zimbabwe’s history, Dambudzo Marechera witnessed an age of upheavals in which different parties battled for power over Zimbabwe. Being aware of the fact that all institutionalized narratives, be they originated from the governance of the UK, Ian Smith’s white minority regime or Zimbabwe’s revolutionary parties, revealed themselves to be nothing more than fiction, Marechera realized the impossibility of determining reality absolutely. As such, this thesis concerns the writing of the Zimbabwean maverick, Dambudzo Marechera. It argues that Marechera writes a unique vision of utopia. In short, for Marechera utopia is not a static entity but a moment of perpetual change. He rethinks utopia in the sense that he phrases it as an event that ceaselessly contests institutionalized and naturalized narratives of a post-colonial self and its relationship to society. Marechera writes towards a vision of an alternative future of the country. Yet, it is a vision that does not constitute a fully rounded sense of utopia. Being cautious about the world and the operation of power upon the people, rather than imposing his own utopian ideals, Marechera chooses to instead peeling away the narrative constitution of the self in relation to society in order to turn towards a truly radical utopian thinking that empowers the individual.

Keywords: African literature, Marechera, post-colonial literature, utopian studies

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Authors: Omer Cahana, Maya Herman, Ofer Levi

Abstract:

Magnetic resonance imaging (MRI) is a long medical scan that stems from a long acquisition time. This length is mainly due to the traditional sampling theorem, which defines a lower boundary for sampling. However, it is still possible to accelerate the scan by using a different approach, such as compress sensing (CS) or parallel imaging (PI). These two complementary methods can be combined to achieve a faster scan with high-fidelity imaging. In order to achieve that, two properties have to exist: i) the signal must be sparse under a known transform domain, ii) the sampling method must be incoherent. In addition, a nonlinear reconstruction algorithm needs to be applied to recover the signal. While the rapid advance in the deep learning (DL) field, which has demonstrated tremendous successes in various computer vision task’s, the field of MRI reconstruction is still in an early stage. In this paper, we present an extension of the state-of-the-art model in MRI reconstruction -VarNet. We utilize VarNet by using dilated convolution in different scales, which extends the receptive field to capture more contextual information. Moreover, we simplified the sensitivity map estimation (SME), for it holds many unnecessary layers for this task. Those improvements have shown significant decreases in computation costs as well as higher accuracy.

Keywords: MRI, deep learning, variational network, computer vision, compress sensing

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Authors: Asma Hanif, A. I. K. Butt, Shabir Ahmad, Rahim Ud Din, Mustafa Inc

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This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.

Keywords: Caputo fractional derivative, existence and uniqueness, gronwall inequality, Lyapunov theory

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Authors: Saimir Heta, Kers Kapaj, Rialda Xhizdari, Ilma Robo

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Despite the existence of different dental specialties, the dentist-patient relationship is unique, in the very fact that the treatment is performed by one doctor and the patient identifies the malpractice presented as part of that doctor's practice; this is in complete contrast to cases of medical treatments where the patient can be presented to a team of doctors, to treat a specific pathology. The rules of dental ethics are almost the same as the rules of medical ethics. The appearance of dental malpractice affects exactly this two-party relationship, created on the basis of professionalism, without deviations in this direction, between the dentist and the patient, but with very narrow individual boundaries, compared to cases of medical malpractice. Main text: Malpractice can have different reasons for its appearance, starting from professional negligence, but also from the lack of professional knowledge of the dentist who undertakes the dental treatment. It should always be seen in perspective that we are not talking about the individual - the dentist who goes to work with the intention of harming their patients. Malpractice can also be a consequence of the impossibility, for anatomical or physiological reasons of the tooth under dental treatment, to realize the predetermined dental treatment plan. On the other hand, the dentist himself is an individual who can be affected by health conditions, or have vices that affect the systemic health of the dentist as an individual, which in these conditions can cause malpractice. So, depending on the reason that led to the appearance of malpractice, the method of treatment from a legal point of view also varies, for the dentist who committed the malpractice, evaluating the latter if the malpractice came under the conditions of applying the rules of dental ethics. Conclusions: The deviation from the predetermined dental plan is the minimum sign of malpractice and the latter should not be definitively related only to cases of difficult dental treatments. The identification of the reason for the appearance of malpractice is the initial element, which makes the difference in the way of its treatment, from a legal point of view, and the involvement of the dentist in the assessment of the malpractice committed, must be based on the legislation in force, which must be said to have their specific changes in different states. Malpractice should be referred to, or included in the lectures or in the continuing education of professionals, because it serves as a method of obtaining professional experience in order not to repeat the same thing several times, by different professionals.

Keywords: dental ethics, malpractice, negligence, legal basis, continuing education, dental treatments

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: equivalent martingale measure, European put option, girsanov theorem, martingales, monte carlo method, option price valuation formula

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Authors: Ankit Kumar, Balram Dubey

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This study proposes a three dimensional prey-predator model with additional food, provided to predator individuals, including gestation delay in predators and delay in supplying the additional food to predators. It is assumed that the interaction between prey and predator is followed by Holling type-II functional response. We discussed the steady states and their local and global asymptotic behavior for the non-delayed system. Hopf-bifurcation phenomenon with respect to different parameters has also been studied. We obtained a range of predator’s tendency factor on provided additional food, in which the periodic solutions occur in the system. We have shown that oscillations can be controlled from the system by increasing the tendency factor. Moreover, the existence of periodic solutions via Hopf-bifurcation is shown with respect to both the delays. Our analysis shows that both delays play an important role in governing the dynamics of the system. It changes the stability behavior into instability behavior. The direction and stability of Hopf-bifurcation are also investigated through the normal form theory and the center manifold theorem. Lastly, some numerical simulations and graphical illustrations have been carried out to validate our analytical findings.

Keywords: additional food, gestation delay, Hopf-bifurcation, prey-predator

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Authors: Muhammad A. Alsubaie

Abstract:

An iterative learning control framework designed in state feedback structure suffers a lack in investigating load disturbance considerations. The presented work discusses the controller previously designed, highlights the disturbance problem, finds new conditions using singular value principle to assure safe operation conditions with error convergence and reference tracking under the influence of load disturbance. It is known that periodic disturbances can be represented by a delay model in a positive feedback loop acting on the system input. This model can be manipulated by isolating the delay model and finding a controller for the overall system around the delay model to remedy the periodic disturbances using the small signal theorem. The overall system is the base for control design and load disturbance investigation. The major finding of this work is the load disturbance condition found which clearly sets safe operation condition under the influence of load disturbances such that the error tends to nearly zero as the system keeps operating trial after trial.

Keywords: iterative learning control, singular values, state feedback, load disturbance

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Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

Abstract:

Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs –Sigmoid, ReLU, and Tanh–have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment with multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLUReLU) combination. Our results show that using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: activation function, universal approximation function, neural networks, convergence

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Authors: F. Amirarfaei, K. Khorasani

Abstract:

In this paper, reconfigurable consensus achievement of a team of agents with marginally stable linear dynamics and single input channel has been considered. The control algorithm is based on a first order linear protocol. After occurrence of a LOE fault in one of the actuators, using the imperfect information of the effectiveness of the actuators from fault detection and identification module, the control gain is redesigned in a way to still reach consensus. The idea is based on the modeling of change in effectiveness as change of Laplacian matrix. Then as special cases of this class of systems, a team of single integrators as well as double integrators are considered and their behavior subject to a LOE fault is considered. The well-known relative measurements consensus protocol is applied to a leaderless team of single integrator as well as double integrator systems, and Gersgorin disk theorem is employed to determine whether fault occurrence has an effect on system stability and team consensus achievement or not. The analyses show that loss of effectiveness fault in actuator(s) of integrator systems affects neither system stability nor consensus achievement.

Keywords: multi-agent system, actuator fault, stability analysis, consensus achievement

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Authors: Erindi Allaj

Abstract:

This paper studies arbitrage pricing theory in financial markets with transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Transaction costs are composed of two terms, one is able to capture the implicit transaction costs and the other the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies which have left and right limit and finite quadratic variation. That is, predictable trading strategies of infinite variation and of finite quadratic variation are allowed in our setting. Within this framework, the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also proved that, when this probability measure is unique, any contingent claim in the market is hedgeable in an L2-sense. The price of any contingent claim is equal to the risk-neutral price. To better understand how to apply the theory proposed we provide an example with linear transaction costs.

Keywords: arbitrage pricing theory,
transaction costs, fundamental theorems of arbitrage, financial markets

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

Abstract:

The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

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Authors: Jorge Gonzalez Camus, Carlos Lizama

Abstract:

In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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