Search results for: first passage probability theory

Authors: Ruijuan Bi

Abstract:

Discrimination in insurance pricing is a topic of increasing concern, particularly in the context of the rapid development of big data and artificial intelligence. There is a need to explore the various forms of discrimination, such as direct and indirect discrimination, proxy discrimination, algorithmic discrimination, and unfair discrimination, and understand their implications in insurance pricing models. This paper aims to analyze and interpret the definitions of discrimination in insurance pricing and explore measures to reduce discrimination. It utilizes a textual analysis methodology, which involves gathering qualitative data from relevant literature on definitions of discrimination. The research methodology focuses on exploring the various forms of discrimination and their implications in insurance pricing models. Through textual analysis, this paper identifies the specific characteristics and implications of each form of discrimination in the general insurance industry. This research contributes to the theoretical understanding of discrimination in insurance pricing. By analyzing and interpreting relevant literature, this paper provides insights into the definitions of discrimination and the laws and regulations surrounding it. This theoretical foundation can inform future empirical research on discrimination in insurance pricing using relevant theories of probability theory.

Keywords: algorithmic discrimination, direct and indirect discrimination, proxy discrimination, unfair discrimination, insurance pricing

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Authors: Betty Johanna Garzon Rozo, Jonathan Crook, Fernando Moreira

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Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. We propose a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severity distributions, and to calculate the capital for Operational Risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mix distribution (the Lognormal for the body of losses and the Generalized Pareto Distribution for the tail) via extreme value theory using SAS®, (ii) the multivariate skew t-copula applied for the first time for operational losses and (iii) Bayesian theory to estimate new n-dimensional skew t-copula models via Markov chain Monte Carlo (MCMC) simulation. This paper analyses a newly operational loss data set, SAS Global Operational Risk Data [SAS OpRisk], to model operational risk at international financial institutions. All the severity models are constructed in SAS® 9.2. We implement the procedure PROC SEVERITY and PROC NLMIXED. This paper focuses in describing this implementation.

Keywords: operational risk, loss distribution approach, extreme value theory, copulas

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Authors: A. Preetha Priyadharshini, S. B. M. Priya

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In this paper, we consider the MU-MISO downlink scenario, under imperfect channel state information (CSI). The main issue in imperfect CSI is to keep the probability of each user achievable outage rate below the given threshold level. Such a rate outage constraints present significant and analytical challenges. There are many probabilistic methods are used to minimize the transmit optimization problem under imperfect CSI. Here, decomposition based large deviation inequality and Bernstein type inequality convex restriction methods are used to perform the optimization problem under imperfect CSI. These methods are used for achieving improved output quality and lower complexity. They provide a safe tractable approximation of the original rate outage constraints. Based on these method implementations, performance has been evaluated in the terms of feasible rate and average transmission power. The simulation results are shown that all the two methods offer significantly improved outage quality and lower computational complexity.

Keywords: imperfect channel state information, outage probability, multiuser- multi input single output, channel state information

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Authors: Mina Jafari, Kobra Hamraee, Saied Hossein Hosseini

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The prediction of breast cancer disease is one of the challenges in medicine. In this paper we collected 528 records of women’s information who live in Kabul including demographic, life style, diet and pregnancy data. There are many classification algorithm in breast cancer prediction and tried to find the best model with most accurate result and lowest error rate. We evaluated some other common supervised algorithms in data mining to find the best model in prediction of breast cancer disease among afghan women living in Kabul regarding to momography result as target variable. For evaluating these algorithms we used Cross Validation which is an assured method for measuring the performance of models. After comparing error rate and accuracy of three models: Decision Tree, Naive Bays and Rule Induction, Decision Tree with accuracy of 94.06% and error rate of %15 is found the best model to predicting breast cancer disease based on the health care records.

Keywords: decision tree, breast cancer, probability, data mining

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Authors: Magda Cepeda, Frances Hodgson, Ann Jopson

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There are different barriers people face when choosing to cycle for commuting purposes. This study examined the role of psycho-social factors predicting the intention to cycle to commute in Mexico City. An extended version of the theory of planned behaviour was developed and utilized with a simple random sample of 401 road users. We applied exploratory and confirmatory factor analysis and after identifying five factors, a structural equation model was estimated to find the relationships among the variables. The results indicated that cycling attributes, attitudes to cycling, social comparison and social image and prestige were the most important factors influencing intention to cycle. Although the results from this study are specific to Mexico City, they indicate areas of interest to transportation planners in other regions especially in those cities where intention to cycle its linked to its perceived image and there is political ambition to instigate positive cycling cultures. Moreover, this study contributes to the current literature developing applications of the Theory of Planned Behaviour.

Keywords: cycling, latent variable model, perception, theory of planned behaviour

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Samar M. Alqhtani, Suhuai Luo, Brian Regan

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Data fusion technology can be the best way to extract useful information from multiple sources of data. It has been widely applied in various applications. This paper presents a data fusion approach in multimedia data for event detection in twitter by using Dempster-Shafer evidence theory. The methodology applies a mining algorithm to detect the event. There are two types of data in the fusion. The first is features extracted from text by using the bag-ofwords method which is calculated using the term frequency-inverse document frequency (TF-IDF). The second is the visual features extracted by applying scale-invariant feature transform (SIFT). The Dempster - Shafer theory of evidence is applied in order to fuse the information from these two sources. Our experiments have indicated that comparing to the approaches using individual data source, the proposed data fusion approach can increase the prediction accuracy for event detection. The experimental result showed that the proposed method achieved a high accuracy of 0.97, comparing with 0.93 with texts only, and 0.86 with images only.

Keywords: data fusion, Dempster-Shafer theory, data mining, event detection

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Authors: Shittu Akinpelu, Issac Popoola

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The compound NbRhGe has been predicted to be a semiconductor with excellent mechanical properties. It is an indirect band gap material. The potential of NbRhGe for non-volatile data storage via element addition is being studied using the Density Functional Theory (DFT). Preliminary results on the electronic and magnetic properties are suggestive for their application in spintronic.

Keywords: half-metals, Heusler compound, semiconductor, spintronic

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Authors: Sergey Podluzhnyy

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One of the most important tasks of investment and pension fund management is building decision support system which helps to make right decision on corporate bond portfolio formation. Today there are several basic methods of bond portfolio management. They are duration management, immunization and convexity management. Identified methods have serious disadvantage: they do not take into account credit risk or insolvency risk of issuer. So, identified methods can be applied only for management and evaluation of high-quality sovereign bonds. Applying article proposes mathematical model for building an optimal in case of risk and yield corporate bond portfolio. Proposed model takes into account the default probability in formula of assessment of bonds which results to more correct evaluation of bonds prices. Moreover, applied model provides tools for visualization of the efficient frontier of corporate bonds portfolio taking into account the exposure to credit risk, which will increase the quality of the investment decisions of portfolio managers.

Keywords: corporate bond portfolio, default probability, effective boundary, portfolio optimization task

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Authors: Anne Gibbons

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Both inside and outside of academia, people have sought to understand the “sense of place” of various regions, many times over and for many different reasons. The concept of regional identity is highly complex and surrounded by considerable contention. There are multiple bodies of research on regional identity theory in many different disciplines and even across sub-disciplinary classifications. Each discipline takes a slightly different angle or perspective on regional identity, resulting in a fragmented body of work on this topic overall. There is a need to consolidate this body of increasingly fragmented theory through interdisciplinary integration. For the purpose of this study, the province of Saskatchewan will serve as an exemplar for exploring regional identity in a concrete context. Saskatchewan can be thought of as a ‘functional region,’ with clear boundaries and clear residency, from which regional identity can be studied. This thesis shares the outcomes of a qualitative study grounded in a series of group interviews with askatchewan residents, from which it is concluded that the use of interdisciplinary theory is an appropriate approach to the study of regional identity. Regional identity cannot be compartmentalized; it is a web of characteristics, attributes, and feelings that are inextricably linked. The thesis thus concludes by offering lessons learned about how we might better understand regional identity, as illuminated through both interdisciplinary theory and the lived experiences and imaginations of people living in the region of Saskatchewan.

Keywords: interdisciplinary, regional identity, Saskatchewan, tourism studies

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Authors: Pontus Backstrom

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In the educational literature on peer effects, attention has been brought to the fact that the mechanisms creating peer effects are still to a large extent hidden in obscurity. The hypothesis in this study is that the Frame Factor Theory can be used to explain these mechanisms. At heart of the theory is the concept of “time needed” for students to learn a certain curricula unit. The relations between class-aggregated time needed and the actual time available, steers and hinders the actions possible for the teacher. Further, the theory predicts that the timing and pacing of the teachers’ instruction is governed by a “criterion steering group” (CSG), namely the pupils in the 10th-25th percentile of the aptitude distribution in class. The class composition hereby set the possibilities and limitations for instruction, creating peer effects on individual outcomes. To test if the theory can be applied to the issue of peer effects, the study employs multilevel structural equation modelling (M-SEM) on Swedish TIMSS 2015-data (Trends in International Mathematics and Science Study; students N=4090, teachers N=200). Using confirmatory factor analysis (CFA) in the SEM-framework in MPLUS, latent variables are specified according to the theory, such as “limitations of instruction” from TIMSS survey items. The results indicate a good model fit to data of the measurement model. Research is still in progress, but preliminary results from initial M-SEM-models verify a strong relation between the mean level of the CSG and the latent variable of limitations on instruction, a variable which in turn have a great impact on individual students’ test results. Further analysis is required, but so far the analysis indicates a confirmation of the predictions derived from the frame factor theory and reveals that one of the important mechanisms creating peer effects in student outcomes is the effect the class composition has upon the teachers’ instruction in class.

Keywords: compositional effects, frame factor theory, peer effects, structural equation modelling

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Authors: Rawaa El Ayoubi

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Many researchers, academics and practitioners have developed leadership theories during the 20th century. This substantial effort has built more leadership theories, generating considerable organisational research on leadership models in contemporary literature. This paper explores the stages and drivers of leadership theory evolution based on the researcher’s personal conclusions and review of leadership theories. The purpose of this paper is to create a Leadership Process Model (LPM) that can provide guidance in dealing with the key challenges within the organisation. This integrative model of organisational leadership is based on inner meaning, leader values and vision. It further addresses the relationships between leadership theory, practice and development, exploring why challenges exist within the field of leadership theory and how these challenges can be mitigated.

Keywords: leadership challenges, leadership process model, leadership |theories, organisational leadership, paradigm development

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Authors: Saidi Abdelkrim, Hamouine Abdelmadjid, Abdellatif Megnounif

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The study of interaction between vehicles and bridge structures has become extremely important. Large deflections and vibration induced by heavy and high-speed vehicles affect significantly the safety and efficiency of bridge. The vibration of a bridge caused by passage of vehicles is one of the most imperative considerations in the design of a bridge as a common sort of transportation structure. A major goal of this study is to create a simplified model of a vehicle bridge system in MATLAB. The model will then be used to study the influence of parameters to vehicle-bridge vibrations.

Keywords: vehicle-bridge interaction, Newmark-β, MATLAB code

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Authors: Shruti Chopra, Vikas Rao Vadi

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In the era of the digital world, the Internet of Things (IoT) has been receiving significant attention. Its ubiquitous connectivity between humans, machines to machines (M2M) and machines to humans provides it a potential to transform the society and establish an ecosystem to serve new dimensions to the economy of the country. Thereby, this study has attempted to identify the challenges that seem prevalent in IoT adoption in India through the literature survey. Further, the data has been collected by taking the opinions of experts to conduct the foresight analysis and it has been analyzed with the help of scenario planning process – Micmac, Mactor, Multipol, and Smic-Prob. As a methodology, the study has identified the relationship between variables through variable analysis using Micmac and actor analysis using Mactor, this paper has attempted to generate the entire field of possibilities in terms of hypotheses and construct various scenarios through Multipol. And lastly, the findings of the study include final scenarios that are selected using Smic-Prob by assigning the probability to all the scenarios (including the conditional probability). This study may help the practitioners and policymakers to remove the obstacles to successfully implement the IoT in India.

Keywords: Internet of Thing (IoT), foresight analysis, scenario planning, challenges, policymaking

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Authors: S. Zhang, L. Zhang, X. Chen

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Due to the large uncertainty on the mechanical properties of FRP (fibre reinforced plastic), the reliability evaluation of FRP structures are currently receiving much attention in industry. However, possible statistical correlation between ply mechanical properties has been so far overlooked, and they are mostly assumed to be independent random variables. In this study, the statistical correlation between ply mechanical properties of uni-directional and plain weave composite is firstly analyzed by a combination of Monte-Carlo simulation and finite element modeling of the FRP unit cell. Large linear correlation coefficients between the in-plane mechanical properties are observed, and the correlation coefficients are heavily dependent on the uncertainty of the fibre volume ratio. It is also observed that the correlation coefficients related to Poisson’s ratio are negative while others are positive. To experimentally achieve the statistical correlation coefficients between in-plane mechanical properties of FRP, all concerned in-plane mechanical properties of the same specimen needs to be known. In-plane shear modulus of FRP is experimentally derived by the approach suggested in the ASTM standard D5379M. Tensile tests are conducted using the same specimens used for the shear test, and due to non-uniform tensile deformation a modification factor is derived by a finite element modeling. Digital image correlation is adopted to characterize the specimen non-uniform deformation. The preliminary experimental results show a good agreement with the numerical analysis on the statistical correlation. Then, failure probability of laminate plates is calculated in cases considering and not considering the statistical correlation, using the Monte-Carlo and Markov Chain Monte-Carlo methods, respectively. The results highlight the importance of accounting for the statistical correlation between ply mechanical properties to achieve accurate failure probability of laminate plates. Furthermore, it is found that for the multi-layer laminate plate, the statistical correlation between the ply elastic properties significantly affects the laminate reliability while the effect of statistical correlation between the ply strength is minimal.

Keywords: failure probability, FRP, reliability, statistical correlation

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Authors: Ruth Donkoh, Wing On Lee, Solomon A. Boateng, Portia Oware Twerefoo, Josephine Donkor

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In this paper we defend the value of theories and approaches to educational policy and planning in enhancing the educational developments in Ghana. This mission is achieved by enumerating the recent educational developments in Ghana and juxtaposing it with some educational theories, approaches to policy making, and policy planning to see if the educational developments conform with the theory principles as well as policy making and planning processes. Data collection for the research was made through textual analysis of policy documents as well as review of relevant literatures. The findings reveled that educational developments in Ghana are unable to attain its objectives due to the policies not conforming with the policy formation and planning principles. In addition, was that education planning in Ghana does not follow the policy-administration dichotomy theory principles and likewise the distribution of educational needs goes contrary to the equity theory. We recommend that educational policies in Ghana should be in conformity with the principles of theories as well as the approaches to educational policy making and planning to help meet the needs of learners, attain educational quality, and to help in the accomplishment of educational development objectives.

Keywords: Ghana education, equity theories, politics- administration dichotomy theory, educational policies, educational planning

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Authors: Sahar Dehghan, Yeganeh Mousavi Jahromi, Ghahraman Abdoli

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Since tax revenues are one of the most important sources of government revenue, it is essential to consider increasing taxpayers' compliance. One of the factors that can affect the taxpayers' compliance is the structure of the crimes and incentives envisaged in the tax law. In this research, by using the 'prospect theory', the effects of changes in the rate of crimes and the tax incentive in the direct tax law on the taxpayer’s compliance behavior have been investigated. To determine the preferences and preferences of taxpayer’s in the business sector and their degree of sensitivity to fines and incentives, a questionnaire with mixed gamble structure is designed. Estimated results using the Hierarchical Bayesian method indicate that the taxpayer’s that have been tested in this study are more sensitive to the incentives in the direct tax law, and the tax administration can use this to increase the level of collected tax and increase the level of compliance.

Keywords: tax compliance, prospect theory, value function, mixed gamble

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Authors: Flaurence Benjamain, Michel Casperance

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We present in this paper, first, a comparative study of three mathematical theories to achieve the fusion of information sources. This study aims to identify the characteristics inherent in theories of possibilities, belief functions (DST) and plausible and paradoxical reasoning to establish a strategy of choice that allows us to adopt the most appropriate theory to solve a problem of fusion in order, taking into account the acquired information and imperfections that accompany them. Using the new theory of plausible and paradoxical reasoning, also called Dezert-Smarandache Theory (DSmT), to fuse information multi-sources needs, at first step, the generation of the composites events witch is, in general, difficult. Thus, we present in this paper a new approach to construct pertinent paradoxical classes based on gray levels histograms, which also allows to reduce the cardinality of the hyper-powerset. Secondly, we developed a new technique for order and coding generalized focal elements. This method is exploited, in particular, to calculate the cardinality of Dezert and Smarandache. Then, we give an experimentation of classification of a remote sensing image that illustrates the given methods and we compared the result obtained by the DSmT with that resulting from the use of the DST and theory of possibilities.

Keywords: segmentation, image, approach, vision computing

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Authors: Danika Tynes

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Telehealth is a promising advancement in health care, though there are certain conditions under which telehealth has a greater chance of success. This research sought to further the understanding of what conditions compel the success of telehealth adoption at the systems level applying Diffusion of Innovations (DoI) theory (Rogers, 1962). System-level indicators were selected to represent four components of DoI theory (relative advantage, compatibility, complexity, and observability) and regressed on 5 types of telehealth (teleradiology, teledermatology, telepathology, telepsychology, and remote monitoring) using multiple logistic regression. The analyses supported relative advantage and compatibility as the strongest influencers of telehealth adoption, remote monitoring in particular. These findings help to quantitatively clarify the factors influencing the adoption of innovation and advance the ability to make recommendations on the viability of state telehealth adoption. In addition, results indicate when DoI theory is most applicable to the understanding of telehealth diffusion. Ultimately, this research may contribute to more focused allocation of scarce health care resources through consideration of existing state conditions available foster innovation.

Keywords: adoption, diffusion of innovation theory, remote monitoring, system-level indicators

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Authors: Vashti Carissa

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The main objective of this study is to examine whether the life-cycle theory of dividends could explain the determinant of an optimal dividend policy in Indonesia. The sample that was used consists of 1,420 non-financial and non-trade, services, investment firms listed in Indonesian Stock Exchange during the period of 2005-2014. According to this finding using logistic regression, firm life-cycle measured by retained earnings as a proportion of total equity (RETE) significantly has a positive effect on the propensity of a firm pays dividend. The higher company’s earned surplus portion in its capital structure could reflect firm maturity level which will increase the likelihood of dividend payment in mature firms. This result provides an additional empirical evidence about the existence of life-cycle theory of dividends for dividend payout phenomenon in Indonesia. It can be known that dividends tend to be paid by mature firms while retention is more dominating in growth firms. From the testing results, it can also be known that majority of sample firms are being in the growth phase which proves the fact about infrequent dividend distribution in Indonesia during the ten years observation period.

Keywords: dividend, dividend policy, life-cycle theory of dividends, mix of earned and contributed capital

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Authors: M. K. Dce

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The aim of this paper is to investigate the behavior of simply supported beams having rectangular section and subjected to uniformly distributed load (UDL). In this study five beams of span 5m, 6m, 7m and 8m have been considered. The width of all the beams is 400 mm and span to depth ratio has been taken as 12. The superimposed live load has been increased from 10 kN/m to 25 kN/m at the interval of 5 kN/m. The analysis of the beams has been carried out using the elastic beam theory. On the basis of present study it has been concluded that the maximum bending moment as well as deflection occurs at the mid-span of simply supported beam and its magnitude increases in proportion to magnitude of UDL. Moreover, the study suggests that the maximum moment is proportional to square of span and maximum deflection is proportional to fourth power of span.

Keywords: beam, UDL, bending moment, deflection, elastic beam theory

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Authors: Saman R. Khan, Najma Sadiq

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Silencing of opinions is an important aspect of Spiral of Silence theory however its applicability in rape-themed dramas requires investigation. This study focuses on the portrayal of female rape victim protagonists in Pakistani dramas and the factors influencing their behavior after rape. A quantitative content analysis was conducted on two prime-time dramas which directly dealt with female rape victims. Results indicate that the female protagonists who faced rape are shown as silent and submissive characters who are unable to communicate about their ordeal due to fear of social isolation. These findings lend support to the Spiral of Silence theory and indicate that the theory’s basic elements (inability to express opinions and fear of social isolation) exist in these TV dramas.

Keywords: gender stereotyping, rape victims, the spiral of silence, TV dramas

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Authors: Deepshikha Shukla, C. H. Solanki, Mayank K. Desai

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Amongst all the natural hazards, earthquakes have the potential for causing the greatest damages. Since the earthquake forces are random in nature and unpredictable, the quantification of the hazards becomes important in order to assess the hazards. The time and place of a future earthquake are both uncertain. Since earthquakes can neither be prevented nor be predicted, engineers have to design and construct in such a way, that the damage to life and property are minimized. Seismic hazard analysis plays an important role in earthquake design structures by providing a rational value of input parameter. In this paper, both mathematical, as well as computational methods adopted by researchers globally in the past five years, will be discussed. Some mathematical approaches involving the concepts of Poisson’s ratio, Convex Set Theory, Empirical Green’s Function, Bayesian probability estimation applied for seismic hazard and FOSM (first-order second-moment) algorithm methods will be discussed. Computational approaches and numerical model SSIFiBo developed in MATLAB to study dynamic soil-structure interaction problem is discussed in this paper. The GIS-based tool will also be discussed which is predominantly used in the assessment of seismic hazards.

Keywords: computational methods, MATLAB, seismic hazard, seismic measurements

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Muhammad Awais Shafique, Eiji Hato

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Household trip data is of crucial importance for managing present transportation infrastructure as well as to plan and design future facilities. It also provides basis for new policies implemented under Transportation Demand Management. The methods used for household trip data collection have changed with passage of time, starting with the conventional face-to-face interviews or paper-and-pencil interviews and reaching to the recent approach of employing smartphones. This study summarizes the step-wise evolution in the travel data collection methods. It provides a comprehensive review of the topic, for readers interested to know the changing trends in the data collection field.

Keywords: computer, smartphone, telephone, travel survey

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Authors: Juan Manuel Sanchez-Cartas, Gonzalo Leon

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A price competition algorithm for ABMs based on game theory principles is proposed to deal with the simulation of theoretical market models. The algorithm is applied to the classical Hotelling’s model and to a two-sided market model to show it leads to the optimal behavior predicted by theoretical models. However, when theoretical models fail to predict the equilibrium, the algorithm is capable of reaching a feasible outcome. Results highlight that the algorithm can be implemented in other simulation models to guarantee rational users and endogenous optimal behaviors. Also, it can be applied as a tool of verification given that is theoretically based.

Keywords: agent-based models, algorithmic game theory, multi-sided markets, price optimization

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Authors: Sana Ahrar

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Cities are undergoing rapid transformation with the change in lifestyle and technological advancements. These transformations may be experienced or physically visible in the built form. This paper focuses on the relationship between the social, physical environment, change in lifestyle and the interrelated factors influencing the transformation of any historic city. Shahjahanabad as a city has undergone transformation under the various political powers as well as the various policy implementations after independence. These visible traces of transformation diffused throughout the city may be due to socio-economic, historic, political factors and due to the globalization process. This study shall enable evolving a theory for the study of transformation of Historic cities such as Shahjahanabad: which has been plundered, rebuilt, and which still thrives as a ‘living heritage city’. The theory developed will be the process of studying the transformation and can be used by planners, policy makers and researchers in different urban contexts.

Keywords: heritage, historic cities, Shahjahanabad, transformation

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Authors: Valerii Dashuk

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The usage of the confidence intervals in economics and econometrics is widespread. To be able to investigate a random variable more thoroughly, joint tests are applied. One of such examples is joint mean-variance test. A new approach for testing such hypotheses and constructing confidence sets is introduced. Exploring both the value of the random variable and its deviation with the help of this technique allows checking simultaneously the shift and the probability of that shift (i.e., portfolio risks). Another application is based on the normal distribution, which is fully defined by mean and variance, therefore could be tested using the introduced approach. This method is based on the difference of probability density functions. The starting point is two sets of normal distribution parameters that should be compared (whether they may be considered as identical with given significance level). Then the absolute difference in probabilities at each 'point' of the domain of these distributions is calculated. This measure is transformed to a function of cumulative distribution functions and compared to the critical values. Critical values table was designed from the simulations. The approach was compared with the other techniques for the univariate case. It differs qualitatively and quantitatively in easiness of implementation, computation speed, accuracy of the critical region (theoretical vs. real significance level). Stable results when working with outliers and non-normal distributions, as well as scaling possibilities, are also strong sides of the method. The main advantage of this approach is the possibility to extend it to infinite-dimension case, which was not possible in the most of the previous works. At the moment expansion to 2-dimensional state is done and it allows to test jointly up to 5 parameters. Therefore the derived technique is equivalent to classic tests in standard situations but gives more efficient alternatives in nonstandard problems and on big amounts of data.

Keywords: confidence set, cumulative distribution function, hypotheses testing, normal distribution, probability density function

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Authors: Sudaff Mohammed, Wahda Shuker Al-Hinkawi, Nada Abdulmueen Hasan

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The compatibility of the Rhizome and Complex Adaptive system theory as a strategy within the urban context is the essential interest of this paper since there are only a few attempts to establish a hybrid, multi-scalar, and developable strategy based on the concept of the Rhizome and the CAS theory. This paper aims to establish a Rhizomic CAS strategy for different urban contexts by investigating the principles, characteristics, properties, and mechanisms of Rhizome and Complex Adaptive Systems. The research focused mainly on analyzing three properties: aggregation, non-linearity, and flow through the lens of Rhizome, Rhizomatization of CAS properties. The most intriguing result is that the principal and well-investigated characteristics of Complex Adaptive systems can be ‘Rhizomatized’ in two ways; highlighting commonalities between Rhizome and Complex Adaptive systems in addition to using Rhizome-related concepts. This paper attempts to emphasize the potency of the Rhizome as an apparently stochastic and barely anticipatable structure that can be developed to analyze cities of distinctive contexts for formulating better customized urban strategies.

Keywords: rhizome, complex adaptive system (CAS), system Theory, urban system, rhizomatic CAS, assemblage, human occupation impulses (HOI)

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Authors: Iryna Shevchenko

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The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed.

Keywords: illegal operation of division and multiplication by fractions of number, infinity, mathematical row of numbers, theory of number “0”

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