Search results for: fractional order analysis

Authors: B. Arend, P. Sunnen, P. Caire

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In a single case study, we show how a conversation analysis (CA) approach can shed light onto the sequential unfolding of human-robot interaction. Relying on video data, we are able to show that CA allows us to investigate the respective turn-taking systems of humans and a NAO robot in their dialogical dynamics, thus pointing out relevant differences. Our fine grained video analysis points out occurring breakdowns and their overcoming, when humans and a NAO-robot engage in a multimodally uttered multi-party communication during a sports guessing game. Our findings suggest that interdisciplinary work opens up the opportunity to gain new insights into the challenging issues of human robot communication in order to provide resources for developing mechanisms that enable complex human-robot interaction (HRI).

Keywords: human robot interaction, conversation analysis, dialogism, breakdown, museum

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Authors: A. Boateng, La Gil-Alana, M. Lesaoana; Hj. Siweya, A. Belete

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This study examines long memory or long-range dependence in the CPI inflation rates of Ghana and South Africa using Whittle methods and autoregressive fractionally integrated moving average (ARFIMA) models. Standard I(0)/I(1) methods such as Augmented Dickey-Fuller (ADF), Philips-Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests were also employed. Our findings indicate that long memory exists in the CPI inflation rates of both countries. After processing fractional differencing and determining the short memory components, the models were specified as ARFIMA (4,0.35,2) and ARFIMA (3,0.49,3) respectively for Ghana and South Africa. Consequently, the CPI inflation rates of both countries are fractionally integrated and mean reverting. The implication of this result will assist in policy formulation and identification of inflationary pressures in an economy.

Keywords: Consumer Price Index (CPI) inflation rates, Whittle method, long memory, ARFIMA model

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Authors: Rodrigo Zepeda

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Transaction cost analysis (TCA) is a way of analyzing the relative performance of different intermediaries and different trading strategies for trades undertaken in financial instruments. It is a way for an investor to determine the overall quality of execution of a particular trade, and there are many different approaches to undertaking TCA. Under the updated Markets in Financial Instruments Directive (2014/65/EU) (MiFID II), investment firms are required when executing orders, to take all sufficient steps to obtain the best possible result for their clients. This requirement for 'Best Execution' must take into account price, costs, speed, likelihood of execution and settlement, size, nature or any other consideration relevant to the execution of the order. The new regulatory compliance framework under MiFID II will now also apply across a very broad range of financial instruments. This article will provide a comprehensive technical analysis of how TCA and Best Execution will significantly change under MiFID II. It will also explain why harmonization of post-trade reporting requirements under MiFID II could potentially support the development of peer group analysis, which in turn could provide a new and highly advanced framework for TCA that could more effectively support Best Execution requirements under MiFID II. The study is significant because there are no studies that have dealt with TCA and Best Execution under MiFID II in the literature.

Keywords: transaction cost analysis, execution quality, best execution, MiFID II, financial instruments

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Authors: Moh'd Alodat

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In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

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Authors: Justyna Żywiołek, Marek Matulewski

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Data, is information processed by enterprises for primary and secondary purposes as processes. Thanks to processing, the sales process takes place; in the case of the surveyed companies, sales take place online. However, this indirect form of contact with the customer causes many problems for both customers and furniture manufacturers. The article presents solutions that would solve problems related to the analysis of data and information in the order fulfillment process sent to post-warranty service. The article also presents an analysis of threats to the security of this information, both for customers and the enterprise.

Keywords: ordering furniture online, information security, furniture industry, enterprise security, risk analysis

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Authors: Marwah Mohsin, Thomas Beach, Alan Kwan, Mahdi Ismail

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This paper describes the differences in views on sustainable development between the general public and experts in a developing country, Iraq. This paper will answer the question: How do the views of the public differ from the generally accepted view of experts in the context of sustainable urban development in Iraq? In order to answer this question, the views of both the public and the experts will be analysed. These results are taken from a public survey and a Delphi questionnaire. These will be analysed using statistical methods in order to identify the significant differences. This will enable investigation of the different perceptions between the public perceptions and the experts’ views towards urban sustainable development factors. This is important due to the fact that different viewpoints between policy-makers and the public will impact on the acceptance by the public of any future sustainable development work that is undertaken. The brief findings of the statistical analysis show that the views of both the public and the experts are considered different in most of the variables except six variables show no differences. Those variables are ‘The importance of establishing sustainable cities in Iraq’, ‘Mitigate traffic congestion’, ‘Waste recycling and separating’, ‘Use wastewater recycling’, ‘Parks and green spaces’, and ‘Promote investment’.

Keywords: urban sustainability, experts views, public views, principle component analysis, PCA

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Authors: Gyongyver Csapo, Andrea Czibor

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Machiavellianism is a personality trait based on the exploitation and deception of others. Machiavellian individuals are motivated to gain and to maintain power with the help of their strategic thinking, manipulation tactics, and interpersonal skills. Consequently, Machiavellianism is treated as a personality trait that can affect an individual’s career and work-related behavior. The aim of our research is to provide a narrative psychological approach to Machiavellianism in order to get a more comprehensive picture about the attitudes, values, and work-related behaviors of Machiavellian individuals. In this study, semi-structured interviews were made with employees (N=275) about their work-related experiences. Additionally, participants completed questionnaires about their turnover intention and perceived stress. The interviews were examined with narrative psychological content analysis and thematic analyzes. Based on the thematic analysis, mentioning of two topics (recognition at work and control) were associated with Machiavellianism. Scientific narrative psychological content analysis showed a negative association between Machiavellianism and positive emotions. Turnover intention and the magnitude of perceived work-related stress showed a significant positive correlation with Machiavellianism. In this study, qualitative and quantitative methodologies were combined in order to get a deeper insight of Machiavellianism from an organizational psychological perspective. Our research can contribute to a better understanding of this personality trait and provides an excellent basis for further investigations.

Keywords: machiavellianism, narrative psychology, turnover intention, work-related stress

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Hanan Alshaher, Jinsheng Xu

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Large amounts of data on the web can provide valuable information. For example, product reviews help business owners measure customer satisfaction. Sentiment analysis classifies texts into two polarities: positive and negative. This paper examines movie reviews and tweets using a new term weighting scheme, called one-over-sigma (1/sigma), on benchmark datasets for sentiment classification. The proposed method aims to improve the performance of sentiment classification. The results show that 1/sigma is more accurate than the popular term weighting schemes. In order to verify if the entropy reflects the discriminating power of terms, we report a comparison of entropy values for different term weighting schemes.

Keywords: 1/sigma, natural language processing, sentiment analysis, term weighting scheme, text classification

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Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja

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This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are, therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.

Keywords: performance modeling, markov process, steady state availability, availability analysis

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Authors: Abdellatif Baba

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In order to facilitate medical images analysis by improving their quality and readability, we present in this paper a new dynamic band pass filter as a general and suitable operator for different types of medical images. Our objective is to enrich the details of any treated medical image to make it sufficiently clear enough to give an understood and simplified meaning even for unspecialized people in the medical domain.

Keywords: medical image enhancement, dynamic band pass filter, analysis improvement

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Authors: F. Majeed, D. V. Thiel, M. Shahpari

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An electrically small meander line antenna is designed for impedance matching with RF transceiver chip CC1101. The design provides the flexibility of tuning the reactance of the antenna over a wide range of values: highly capacitive to highly inductive. The antenna was printed with silver ink on FR4 substrate using the screen printing design process. The antenna impedance was perfectly matched to CC1101 at 433 MHz. The measured radiation efficiency of the antenna was 81.3% at resonance. The 3 dB and 10 dB fractional bandwidth of the antenna was 14.5% and 4.78%, respectively. The read range of the antenna was compared with a copper wire monopole antenna over a distance of five meters. The antenna, with a perfect impedance match with RF transceiver chip CC1101, shows improvement in the read range compared to a monopole antenna over the specified distance.

Keywords: meander line antenna, RFID, silver ink printing, impedance matching

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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Authors: Shilpa Kapoor, Namrata Yaduvanshi, Pooja Pawar, Sadhna Singh

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A Three Body Interaction Potential (TBIP) model is developed to study the high pressure phase transition of SrS having NaCl (B1) structure at room temperature. This model includes the long range Columbic, three body interaction forces, short range overlap forces operative up to next nearest neighbors and zero point energy effects. We have investigated the phase transition with pressure, volume collapse and second order elastic constants and found results well suited with available experimental data.

Keywords: phase transition, second order elastic constants, three body interaction forces, volume collapses

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Authors: Sangdeok Lee, Sangwon Han, Changtaek Hyun

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Construction defects are major components that result in negative impacts on project performance including schedule delays and cost overruns. Since construction defects generally occur when a few associated causes combine, a thorough understanding of defect causality is required in order to more systematically prevent construction defects. To address this issue, this paper uses association rule mining (ARM) to quantify the causality between defect causes, and social network analysis (SNA) to find indirect causality among them. The suggested approach is validated with 350 defect instances from concrete works in 32 projects in Korea. The results show that the interrelationships revealed by the approach reflect the characteristics of the concrete task and the important causes that should be prevented.

Keywords: causality, defect causes, social network analysis, association rule mining

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Authors: Abdelsalam Omar

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This paper presents simulation-based case study that indicate the need for accurate dynamic modeling of distance protection relay. In many cases, a static analysis based on current and voltage phasors may be sufficient to assess the performance of distance protection. There are several circumstances under which such a simplified study does not provide the depth of analysis necessary to obtain accurate results, however. This letter present study of the influences of magnetizing inrush and power swing on the performance of distance protection relay. One type of numerical distance protection relay has been investigated: 7SA511. The study has been performed in order to demonstrate the relay response when dynamic model of distance relay is utilized.

Keywords: distance protection, magnitizing inrush, power swing, dynamic model of protection relays, simulatio

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Authors: Yeliz Ekinci, Raife Merve Ön

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Nowadays, technological progress is one of the most important components of economic growth and the efficiency of R&D activities is particularly essential for countries. This study is an attempt to analyze the R&D efficiencies of EU countries. The indicators related to R&D efficiencies should be determined in advance in order to use DEA. For this reason a list of input and output indicators are derived from the literature review. Considering the data availability, a final list is given for the numerical analysis for future research.

Keywords: data envelopment analysis, economic growth, EU countries, R&D efficiency

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Authors: Boris M. Fedorov, Liudmila P. Goncharenko, Sergey A. Sybachin, Natalia A. Mamedova, Ekaterina V. Makarenkova, Saule Rakhimova

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In modern economic conditions, the question of the possibility of correct recognition of a signature on digital documents in order to verify the expression of will or confirm a certain operation is relevant. The additional complexity of processing lies in the dynamic variability of the signature for each individual, as well as in the way information is processed because the signature refers to biometric data. The article discusses the issues of using artificial intelligence models in order to improve the quality of signature confirmation in document recognition. The analysis of several possible options for using the model is carried out. The results of the study are given, in which it is possible to correctly determine the authenticity of the signature on small samples.

Keywords: signature recognition, biometric data, artificial intelligence, neural networks

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Authors: Gideon Baffoe

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The concept of neighbourhood remains highly relevant in urban studies. However, until now, no attempt has been made to statistically chart the field. This study aims to provide a macroscopic overview using bibliometric analysis of the main characteristics of neighbourhood research in order to understand the academic landscape. The study analyses the emergence and evolution of the concept of neighbourhood in published research, conceptual and intellectual structures as well as scholarship collaboration. It is found that topics related to the local economy of neighbourhoods are sparse, suggesting a major gap in the literature.

Keywords: neighbourhood, global south, bibliometric analysis, scholarship

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Authors: Jian Wang, Lu Yang, Jiong Peng

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Internal circulation two-platen clamping system for injection molding machine (IMM) has many potential advantages on energy-saving. In order to estimate its properties, experiments in this paper were carried out. Displacement and pressure of the components were measured. In comparison, the model of hydraulic clamping system was established by using AMESim. The related parameters as well as the energy consumption could be calculated. According to the analysis, the hydraulic system was optimized in order to reduce the energy consumption.

Keywords: AMESim, energy-saving, injection molding machine, internal circulation

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Authors: Roikhan Mochamad Aziz

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This study aims to analze the interdependence of several variables simultaneously in order to simplify the form of the relationship between some of the variables studied a number of factors less than the variable studied which means it can also describe the data structure of a research. Based 100 respondents from the public, such as the people of South Tangerang, this study used factor analysis tool. The results of this study indicate that the studied variables being formed into nine factors, namely faith factors, community factors, factors of social care, confidence factor, factor income, educational factors, self-satisfaction factors, factors work, and knowledge factor. Total variance of the 9 factors is 67,30% means that all nine of these factors are factors that can contribute too paying zakat of muzakki consciousness of 67,30% while the remaining 32,70% is supported by other factors outside the 9 factors.

Keywords: zakat, analysis factor, faith, education, knowledge

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Authors: Stewart A. Keir, Faik A. Hamad

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This study aims to use both analytical and experimental methods of analysis to examine the accuracy of Computational Fluid Dynamics (CFD) models that can then be used for more complex analyses, accurately representing more elaborate flow phenomena such as internal shockwaves and boundary layers. The geometry used in the analytical study and CFD model is taken from the experimental rig. The analytical study is undertaken using isentropic and adiabatic relationships and the output of the analytical study, the 'shockwave location tool', is created. The results from the analytical study are then used to optimize the redesign an experimental rig for more favorable placement of pressure taps and gain a much better representation of the shockwaves occurring in the divergent section of the nozzle. The CFD model is then optimized through the selection of different parameters, e.g. turbulence models (Spalart-Almaras, Realizable k-epsilon & Standard k-omega) in order to develop an accurate, robust model. The results from the CFD model can then be directly compared to experimental and analytical results in order to gauge the accuracy of each method of analysis. The CFD model will be used to visualize the variation of various parameters such as velocity/Mach number, pressure and turbulence across the shock. The CFD results will be used to investigate the interaction between the shock wave and the boundary layer. The validated model can then be used to modify the nozzle designs which may offer better performance and ease of manufacture and may present feasible improvements to existing high-speed flow applications.

Keywords: CFD, nozzle, fluent, gas dynamics, shock-wave

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Authors: J. Sánchez-Beaskoetxea

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The analysis of accidents, such as marine accidents, is one of the most useful instruments to avoid future accidents. In the case of marine accidents, from a simple collision of a small boat in a port to the wreck of a gigantic tanker ship, the study of the causes of the accidents is the basis of a great part of the marine international legislation. Some countries have official institutions who investigate all the accidents in which a ship with their flag is involved. In the case of the USA, the National Transportation Safety Board (NTSB) is responsible for these researches. The NTSB, after a deep investigation into each accident, publishes a Marine Accident Report with the possible cause of the accident. This paper analyses all the Marine Accident Reports published by the NTBS and focuses its attention especially in the Human Errors that led to reported accidents. In this research, the different Human Errors made by crew members are cataloged in 10 different groups. After a complete analysis of all the reports, the statistical analysis on the Human Errors typology in marine accidents is presented in order to use it as a tool to avoid the same errors in the future.

Keywords: human error, marine accidents, ship crew, USA

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Authors: Nishant Parashar, Sawan S. Sinha, Balaji Srinivasan

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We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors.

Keywords: compressible turbulence, neural network, velocity gradient tensor, direct numerical simulation

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Authors: Marina Sartor Hoffer

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The multicultural composition of today's societies poses new challenges to educational contexts. Schools are therefore called first to develop dialogic aptitudes and communicative skills adapted to the complex reality of post-modern societies. It is indispensable for educators and for young people to learn theoretical and practical tools during their scholastic path, in order to allow the knowledge of themselves and of the others with the aim of recognizing the value of the others regardless of their culture. Dialogic Skills help to understand and manage individual differences by allowing the solution of problems and preventing conflicts. The Educational Sector of Eric Berne’s Transactional Analysis offers a range of methods and techniques for this purpose. Educational Transactional Analysis is firmly anchored in the Personalist Philosophy and deserves to be promoted as a theoretical frame suitable to face the challenges of contemporary education. The goal of this paper is therefore to outline some conceptual and methodological signposts for the education to dialogue by drawing concepts and methodologies from educational transactional analysis.

Keywords: dialogic process, education to dialogue, educational transactional analysis, personalism, the good of the relationship

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Authors: Omar Khan, Shana Krstevska, Edwin George, Veronica Gorden, Fen Bao, Christina Caon, NP-C, Carla Santiago, Imad Zak, Navid Seraji-Bozorgzad

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Objective: To quantify cellular injury in the substantia nigra (SN) in patients with Parkinson's disease (PD) and to examine the effect of rasagiline of tissue injury in the SN in patients with PD. Background: N-acetylaspartate (NAA) quantified with MRS is a reliable marker of neuronal metabolic function. Fractional anisotropy (FA) and mean diffusivity (MD) obtained with DTI, characterize tissue alignment and integrity. Rasagline, has been shown to exert anti-apototic effect. We applied these advanced MRI techniques to examine: (i) the effect of rasagiline on cellular injury and metabolism in patients with early PD, and (ii) longitudinal changes seen over time in PD. Methods: We conducted a prospective longitudinal study in patients with mild PD, naive to dopaminergic treatment. The imaging protocol included multi-voxel proton-MRS and DTI of the SN, acquired on a 3T scanner. Scans were performed at baseline and month 3, during which the patient was on no treatment. At that point, rasagiline 1 mg orally daily was initiated and MRI scans are were obtained at 6 and 12 months after starting rasagiline. The primary objective was to compare changes during the 3-month period of “no treatment” to the changes observed “on treatment” with rasagiline at month 12. Age-matched healthy controls were also imaged. Image analysis was performed blinded to treatment allocation and period. Results: 25 patients were enrolled in this study. Compared to the period of “no treatment”, there was significant increase in the NAA “on treatment” period (-3.04 % vs +10.95 %, p= 0.0006). Compared to the period of “no treatment”, there was significant increase in following 12 month in the FA “on treatment” (-4.8% vs +15.3%, p<0.0001). The MD increased during “no treatment” and decreased in “on treatment” (+2.8% vs -7.5%, p=0.0056). Further analysis and clinical correlation are ongoing. Conclusions: Advanced MRI techniques quantifying cellular injury in the SN in PD is a feasible approach to investigate dopaminergic neuronal injury and could be developed as an outcome in exploratory studies. Rasagiline appears to have a stabilizing effect on dopaminergic cell loss and metabolism in the SN in PD, that warrants further investigation in long-term studies.

Keywords: substantia nigra, Parkinson's disease, MRI, neuronal loss, biomarker

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Authors: Mahdieh Khalilinezhad, Silvana Dellepiane, Gianni Vernazza

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The aim of the present work is to build a model based on tissue characterization that is able to discriminate pathological and non-pathological regions from three-phasic CT images. Based on feature selection in different phases, in this research, we design a neural network system that has optimal neuron number in a hidden layer. Our approach consists of three steps: feature selection, feature reduction, and classification. For each ROI, 6 distinct set of texture features are extracted such as first order histogram parameters, absolute gradient, run-length matrix, co-occurrence matrix, autoregressive model, and wavelet, for a total of 270 texture features. We show that with the injection of liquid and the analysis of more phases the high relevant features in each region changed. Our results show that for detecting HCC tumor phase3 is the best one in most of the features that we apply to the classification algorithm. The percentage of detection between these two classes according to our method, relates to first order histogram parameters with the accuracy of 85% in phase 1, 95% phase 2, and 95% in phase 3.

Keywords: multi-phasic liver images, texture analysis, neural network, hidden layer

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Authors: F. Chigondo, G. Chitabati

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Hexavalent chromium is toxic and is widely used in many industries hence efficient and economical methods must be explored to remove the chromium(VI) from the environment. The removal of Cr (VI) from aqueous solutions onto polyaniline coated maize tassel was studied in batch mode at varying initial metal concentrations, adsorbent doses, pH and contact times. The residual Cr (VI) concentrations before and after adsorption were analyzed by Ultraviolet–visible spectroscopy. FTIR analysis of the polyaniline coated maize tassel showed the presence of C=C, C=N, C-H, C-N and N-H groups. Adsorption conditions were deduced to be pH of 2, adsorbent dosage 1g/L, Cr(VI) initial concentration of 40mg/L contact time of 150 minutes and agitation speed of 140rpm. Data obtained fitted best to the Langmuir isotherm (R2 = 0.972) compared to the Freundlich isotherm (R2 0.671. The maximum adsorption capacity was found to be 125mg/L. Correlation coefficients for pseudo first order and pseudo second order were 0.952 and 0.971 respectively. The adsorption process followed the pseudo-second order kinetic model. The studied polyaniline coated maize tassel can therefore be used as a promising adsorbent for the removal of Cr (VI) ion from aqueous solution.

Keywords: polyaniline-coated, maize tassels, adsorption, hexavalent chromium

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Authors: Susana Sousa Machado

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The debate on the use of religious symbols has been highlighted in modern societies, especially in the field of labour relationships. As litigiousness appears to be growing, the matter requires a careful study from a legal perspective. In this context, a description and critical analysis of the most recent case law is conducted regarding the use of symbols by the employee in the workplace, delivered both by the European Court of Human Rights and by the Court of Justice of the European Union. From this comparative analysis we highlight the most relevant aspects in order to seek a common core regarding the juridical-argumentative approach of case law.

Keywords: religion, religious symbols, workplace, discrimination

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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