Search results for: Louisa Smith

Authors: William L. Whitehouse, Louisa H. Y. Lo, Andrew B. Kinghorn, Simon C. C. Shiu, Julian. A. Tanner

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C-reactive protein (CRP) is an acute-phase reactant and sensitive indicator for sepsis and other life-threatening pathologies, including systemic inflammatory response syndrome (SIRS). Currently, clinical turn-around times for established CRP detection methods take between 30 minutes to hours or even days from centralized laboratories. Here, we report the development of an electrochemical biosensor using redox probe-tagged DNA aptamers functionalized onto cheap, commercially available screen-printed electrodes. Binding-induced conformational switching of the CRP-targeting aptamer induces a specific and selective signal-ON event, which enables single-step and reagentless detection of CRP in as little as 1 minute. The aptasensor dynamic range spans 5-1000nM (R=0.97) or 5-500nM (R=0.99) in 50% diluted human serum, with a LOD of 3nM, corresponding to 2-orders of magnitude sensitivity under the clinically relevant cut-off for CRP. The sensor is stable for up to one week and can be reused numerous times, as judged from repeated real-time dosing and dose-response assays. By decoupling binding events from the signal induction mechanism, structure-switching electrochemical aptamer-based sensors (SS-EABs) provide considerable advantages over their adsorption-based counterparts. Our work expands on the retinue of such sensors reported in the literature and is the first instance of an SS-EAB for reagentless CRP detection. We hope this study can inspire further investigations into the suitability of SS-EABs for diagnostics, which will aid translational R&D toward fully realized devices aimed at point-of-care applications or for use more broadly by the public.

Keywords: structure-switching, C-reactive protein, electrochemical, biosensor, aptasensor.

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Authors: Aziz Sezgin, Yuksel Hacioglu, Nurkan Yagiz

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Sliding mode controller for a vehicle active suspension system is designed in this study. The widely used quarter car model is preferred and it is aimed to improve the ride comfort of the passengers. The effect of the actuator time delay, which may arise due to the information processing, sensors or actuator dynamics, is also taken into account during the design of the controller. A sliding mode controller was designed that has taken into account the actuator time delay by using Smith predictor. The successful performance of the designed controller is confirmed via numerical results.

Keywords: sliding mode control, active suspension system, actuator, time delay, vehicle

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Authors: Clifford De Raffaele, Luana Bugeja, Serengul Smith

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The adaptation of social networking sites within higher education has garnered significant interest in the recent years with numerous researches considering it as a possible shift from the traditional classroom based learning paradigm. Notwithstanding this increase in research and conducted studies however, the adaption of SNS based modules have failed to proliferate within Universities. This paper, commences its contribution by analyzing the various models and theories proposed in literature and amalgamates together various effective aspects for the inclusion of social technology within e-Learning. A three phased framework is further proposed which details the necessary considerations for the successful adaptation of SNS in enhancing the students learning experience. This proposal outlines the theoretical foundations which will be analyzed in practical implementation across international university campuses.

Keywords: eLearning, higher education, social network sites, student learning

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Authors: Gregory W. Smith, Paul J. Riccomini

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The goal of this empirical inquiry is to explore the effect of noise reducing headphones on the short-term memory recall of college students. Immediately following the presentation (via PowerPoint) of 12 unrelated and randomly selected one- and two-syllable words, students were asked to recall as many words as possible. Using a linear model with conditions marked with binary indicators, we examined the frequency and accuracy of words that were recalled. The findings indicate that for some students, a reduction of noise has a significant positive impact on their ability to recall information. As classrooms become more aurally distracting due to the implementation of cooperative learning activities, these findings highlight the need for a quiet learning environment for some learners.

Keywords: auditory distraction, education, instruction, noise, working memory

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Authors: Dana S. Smith, Angela Goins, Shahnaz Savani

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Using a mixed-methods approach, this study explored costs to student wellbeing generated by the social work field practicum requirement. The project was conducted by faculty at a medium-sized university in the United States. Social work educators and field practicum instructors participated in interviews. Students and former students completed surveys on the topic. The data analysis revealed emotional burdens as well as threats to student wellbeing in association with the fieldwork required for those in pursuit of a social work degree. The study includes recommendations for anti-oppressive approaches for academic programs and implications for further research.

Keywords: emotional wellbeing, field practicum, mixed-methods, social justice

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Authors: Dana S. Smith, Angela Goins, Shahnaz Savani

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Using a mixed-methods approach, this study explored costs to student wellbeing generated by the social work field practicum requirement. The project was conducted by faculty at a medium sized university in the United States. Social work educators and field practicum instructors participated in interviews. Students and former students completed surveys on the topic. The data analysis revealed emotional burdens as well as threats to student wellbeing in association with the fieldwork required for those in pursuit of a social work degree. The study includes recommendations of anti-oppressive approaches for academic programs and implications for further research.

Keywords: emotional wellbeing, field practicum, mixed-methods, social justice

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Authors: Lukman O. Alimi, Vincent J. Smith, Leonard J. Barbour

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The thermosalient effect is an extremely rare propensity of certain crystalline solids for self-actuation by elastic deformation or a ballistic event1. Thermosalient compounds, colloquially known as ‘jumping crystals’ are promising materials for fabrication of actuators that are also being considered as materials for clean energy conversion because of their capabilities to convert thermal energy into mechanical motion directly. Herein, an organic aminonitrile and its derivatives have been probed by a combination of structural, microscopic and thermoanalytical techniques. Crystals of these compounds were analysed by means of single crystal XRD and hotstage microscopy in the temperature range of 100 to 298 K and found to exhibit the thermosalient effect. We also carried out differential scanning calorimetric analysis at the temperature corresponding to that at which the crystal jumps as observed under a hotstage microscope.

Keywords: aminonitrile, jumping crystal, self actuation, thermosalient effect

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Authors: Arzu K. Kamberli

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This article examines the relationship between economics and physics, starting with Adam Smith, with a new econophysics approach in Economics-Physics with the Gauss Law model proposal using for the Electric Field calculation, which will allow us to anticipate the Global Financial Crisis. For this purpose, the similarities between the Gauss Law using the electric field calculations and the global financial crisis have been explained on the formula, and a model has been suggested to predict the risks of the financial systems from the electricity field calculations. Thus, this study is expected to help for preventing the Global Financial Crisis with the contribution of the science of economics and physics from the aspect of econophysics.

Keywords: econophysics, electric field, financial system, Gauss law, global financial crisis

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Authors: Christopher Spiewak, M. R. Islam, Mohammad Arifur Rahaman, Mohammad H. Rahman, Roger Smith, Maarouf Saad

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For those who have lost the ability to move their hand, going through repetitious motions with the assistance of a therapist is the main method of recovery. We have been developed a robotic assistive device to rehabilitate the hand motions in place of the traditional therapy. The developed assistive device (RAD-HR) is comprised of four degrees of freedom enabling basic movements, hand function, and assists in supporting the hand during rehabilitation. We used a nonlinear computed torque control technique to control the RAD-HR. The accuracy of the controller was evaluated in simulations (MATLAB/Simulink environment). To see the robustness of the controller external disturbance as modelling uncertainty (±10% of joint torques) were added in each joints.

Keywords: biorobotics, rehabilitation, robotic assistive device, exoskeleton, nonlinear control

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Authors: Isaiah Phillip Smith

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It is reported that alcohol consumption accounts for 3 million annual deaths globally, thus, it is a significant public health challenge internationally. The excessive consumption of alcohol is argued in literature to be related to problematic behaviors like crime, accident, fighting, violence, and unprotected sex, among others. Alcohol consumption among university students in South Africa particularly is considered endemic – with a prevalence rate of 25.27%, 32.34%, and 23.34% across universities, colleges, and high schools. Adopting the tenets of social learning and ecological theories, the culture of drinking amongst male university students is critically explored. This study found that age, gender, early exposure to alcohol, and peer pressure are significant factors contributing to alcohol consumption amongst university students. While participants acknowledged that moderate and responsible consumption of alcohol is necessary, they agree that it does not translate to responsible drinking behaviours.

Keywords: alcohol, drinking, university, students

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Authors: Peter Smolianov, Jed Smith, Lisa Chen, Steven Dion, Christopher Schoen, Jaclyn Norberg

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This study compared general conditioning and sport specific fitness tests used in China, European Union (EU), Russia, and the United States. A constant content comparison method was used to identify the differences. Data from the study indicated that there were shared test components, including aerobic fitness, muscular strength, endurance, and flexibility. However, the testing components and items, as well as the cut-off values of the analyzed tests varied by country for the same gender and age. Culturally unique methods of testing and preparing for the tests were identified. Additionally, evidence revealed support for lifelong fitness and long-term sport participation through comprehensive fitness and wellness guidelines for different age groups and through new internet-based technologies.

Keywords: fitness testing, global trends, new developments, worldwide comparison

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Authors: Zeinab Amini Moghaddam, Alireza Dehkhodania

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Nowadays, organizations have found a high status in the cultural and social structures of societies. The purpose of current study is to investigate the relationship between organizational climate with job burnout as well as job satisfaction. The research method is descriptive and correlational. The population of the study includes all employees in Tehran Electric Company, which equals 1984 people in 2018. The sampling was performed in the form of a consensus, and all employees were regarded as samples. The data gathering tools consist of three questionnaires of Smith’s Job Satisfaction Questionnaire, Halpin and Craft's Occupational climate, and Maslach and Jackson's Job burnout. The results showed that there was a direct and positive relationship between organizational climate and job burnout, as well as job satisfaction. The organizational climate variable could successfully predict job satisfaction. It was also able to predict job burnout.

Keywords: organizational climate, job burnout, job satisfaction, descriptive, correlational

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Authors: Om Prakash Keshri, Anand Kumar, Vinod K. Gupta

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In the present study, the effect of gravity modulation on the onset of convection in viscous fluid layer under the influence of induced magnetic field, salted from above on the boundaries, has been investigated. Linear and nonlinear stability analysis has been performed. A linear stability analysis is performed to show that the gravity modulation can significantly affect the stability limits of the system. A method based on small amplitude of the modulation is used to compute the critical value of Rayleigh number and wave number. The effect of Smith number, salute Rayleigh number and magnetic Prandtl number on the stability of the system is investigated.

Keywords: viscous fluid, induced magnetic field, gravity modulation, salute convection

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Authors: Hasan Vural

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In this study, innovation subject is explained firstly. Later the basic concepts of innovation and new food products development in marketing of bee products are investigated. Examples of the application of research results will be presented. Subject will be discussed benefiting from scientific studies based on literature review. Innovation is widely recognised as important to commercial success in the food industry, as both a major source of competitive advantage and the creation of a company’s future. However, the new product development process is described as being fraught with failures, with only approximately 10% of new products remaining on the market within a year of commercialisation. In addition, for every new food product that does reach commercialisation, there are likely to be many concepts that are rejected during the new food product development process. No roadmap exactly describes a route to a goal: exhortations to follow ‘10 Steps to a successful Product’ or use ‘Smith’s Method to Do Successful Products’ are, therefore, all approximations. Roadmaps do not describe the actual journey, only the general direction.

Keywords: innovation, agrofood product development, beekeeping products, honey marketing

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Authors: Sunil Dehipawala, Aregama Sirisumana, stephan Smith, P. Schneider, G. Tremberger Jr, D. Lieberman, Todd Holden, T. Cheung

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The arsenic and iron environments in different growth stages have been studied with EXAFS and XANES using Brookhaven Synchrotron Light Source. Collard Greens plants were grown and tissue samples were harvested. The project studied the EXAFS and XANES of tissue samples using As and Fe K-edges. The Fe absorption and the Fourier transform bond length information were used as a control comparison. The Fourier transform of the XAFS data revealed the coexistence of As (III) and As (V) in the As bonding environment inside the studied plant tissue samples, although the soil only had As (III). The data suggests that Collard Greens has a novel pathway to handle arsenic absorption in soil.

Keywords: EXAFS, fourier transform, metalloproteins, XANES

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Authors: Nurit Carmi

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There are many endangered species that are not popular but whose conservation is, nonetheless, important. The present study deals with sharks who suffer from demonization and, accordingly, from public indifference to the deteriorating state of their conservation. We used the seasonal appearance of sharks in the Israeli coastal zone to study public perceptions and attitudes towards sharks prior to ("control group") and after ("visitors") shark watching during a visit in an information center. We found that shark’s image was significantly more positive among the "visitors" compared to the control group. We found that visiting in the information center was strongly related to a more positive shark image, attitudes toward shark conservation, and willingness to act to preserve them.

Keywords: wildlife tourism, shark conservation, attitudes towards animals, human-animal relationships, Smith's salience index

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Authors: André Smith, Amr Abdel-Dayem

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The stereo matching problem, while having been present for several decades, continues to be an active area of research. The goal of this research is to find correspondences between elements found in a set of stereoscopic images. With these pairings, it is possible to infer the distance of objects within a scene, relative to the observer. Advancements in this field have led to experimentations with various techniques, from graph-cut energy minimization to artificial neural networks. At the basis of these techniques is a cost function, which is used to evaluate the likelihood of a particular match between points in each image. While at its core, the cost is based on comparing the image pixel data; there is a general lack of consistency as to what image data representation to use. This paper presents an experimental analysis to compare the effectiveness of more common image data representations. The goal is to determine the effectiveness of these data representations to reduce the cost for the correct correspondence relative to other possible matches.

Keywords: colour data, local stereo matching, stereo correspondence, disparity map

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Authors: Jovanca Smith, Derek Gay

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All universities possess a standard by which students are assessed and administered into their programs. This paper considers the effect of the educational history of students, as measured by specific subject grades in Caribbean examinations, on overall performance in introductory engineering math and mechanics courses. Results reflect a correlation between the highest grade in the Caribbean examinations with a higher probability of successful advancement in the university courses. Alternatively, lower entrance grades are commensurate with underperformance in the university courses. Results also demonstrate that students matriculating with the Caribbean examinations will not necessarily possess a significant advantage over students entering through an alternative route, and while previous educational background of students is a significant indicator of tentative performance in the University level math and mechanics courses, it is not the sole factor.

Keywords: bimodal distribution, differential learning, engineering education, entrance qualification

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Authors: Christopher Wearmouth, Jacob Smith

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Administration of tranexamic acid (TXA) reduces all-cause mortality in trauma patients when given within 3 hours of injury. Due to geographical distance and lack of emergency medical services patients often present late, following trauma, to our emergency department. Additionally, we found patients that may have benefited from TXA did not receive it, often due to lack of staff awareness, staff shortages out of hours and lack of equipment for delivering infusions. Our objective was to develop a protocol for nurse-led administration of TXA in the emergency department. We developed a protocol using physiological observations along with criteria from the South African Triage Scale to allow nursing staff to identify patients with, or at risk of, significant haemorrhage. We will monitor the use of the protocol to ensure appropriate compliance and for any adverse events reported.

Keywords: emergency department, emergency nursing, rural healthcare, tranexamic acid, trauma, triage

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Authors: Noel Smith

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To achieve professional registration, UK social workers need to complete a programme of education and training which meets standards set down by central government. When it comes to practice, social work in local authorities must fulfil requirements of national legislation but there is considerable local variation in the organisation and delivery of services. This presentation discusses the on-going reform of social work education by central government in the context of research of social work services in a local authority. In doing so it highlights that the ‘direction of travel’ of the national reform of social work education seems at odds with the trajectory of development of local social work services. In terms of education reform, the presentation cites key government initiatives including the knowledge and skills requirements which have been published separately for, respectively, child and family social work and adult social work. Also relevant is the Government’s new ‘teaching partnership’ pilot which focuses exclusively on social work in local government, in isolation from social work in NGOs. In terms of research, the presentation discusses two studies undertaken by Professor Smith in Suffolk County Council, a local authority in the east of England. The first is an equality impact analysis of the introduction of a new model for the delivery of adult and community services in Suffolk. This is based on qualitative research with local government representatives and NGOs involved in social work with older people and people with disabilities. The second study is an on-going, mixed method evaluation of the introduction of a new model of social care for children and young people in Suffolk. This new model is based on the international ‘Signs of Safety’ approach, which is applied in this model to a wide range of services from early intervention to child protection. While both studies are localised, the service models they examine are good illustrations of the way services are developing nationally. Analysis of these studies suggest that, if services continue to develop as they currently are, then social workers will require particular skills which are not be adequately addressed in the Government’s plans for social work education. Two issues arise. First, education reform concentrates on social work within local government while increasingly local authorities are outsourcing service provision to NGOs, expecting greater community involvement in providing care, and integrating social care with health care services. Second, education reform focuses on the different skills required for working with older and disabled adults and working with children and families, to the point where potentially the profession would be fragmented into two different classes of social worker. In contrast, the development of adult and children’s services in local authorities re-asserts the importance of common social work skills relating to personalisation, prevention and community development. The presentation highlights the importance for social work education in the UK to be forward looking, in terms of the changing design of service delivery, and outward looking, in terms of lessons to be drawn from international social work.

Keywords: adult social work, children and families social work, European social work, social work education

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Authors: Paul Okonkwo, Howard Smith

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A study to estimate the size of the cabin and major aircraft components as well as detect and avoid interference between internally placed components and the external surface, during the conceptual design synthesis and optimisation to explore the design space of a BWB, was conducted. Sizing of components follows the Bradley cabin sizing and rubber engine scaling procedures to size the cabin and engine respectively. The interference detection and avoidance algorithm relies on the ability of the Class Shape Transform parameterisation technique to generate polynomial functions of the surfaces of a BWB aircraft configuration from the sizes of the cabin and internal objects using few variables. Interference detection is essential in packaging of non-conventional configuration like the BWB because of the non-uniform airfoil-shaped sections and resultant varying internal space. The unique configuration increases the need for a methodology to prevent objects from being placed in locations that do not sufficiently enclose them within the geometry.

Keywords: packaging, optimisation, BWB, parameterisation, aircraft conceptual design

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Authors: S. Saleem, L. J. Mason, M. Hasan, M. Sagheer, Q. Ali, S. Akhtar, C. M. S. Hanif

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Ozone has been documented as a potential fumigant against major insect pests of stored commodities due to its highly oxidative properties. Present studies were conducted in the Smith Hall (Department of Entomology), Purdue University, USA, to examine the fumigant toxicities of ozone gas (O₃) against stored grain insect pests. Adults of Tribolium castaneum and Cryptolestes ferrugineus were exposed to different concentrations (100, 200, 480, 700, and 800 ppm) of ozone gas. Test insects were fumigated by keeping a constant temperature of 27 ± 2 °C and 75 ± 5% relative humidity, while dead insects were recorded after 6, 12, 18, 24, 30, and 36 hr of treatment. C. ferrugineus was found susceptible, with mean mortality of 90.99% as compared to T. castaneum (53.22%). Fumigation, even with lower concentrations (100 ppm) of ozone gas for 36 hr, exhibited 100% mortality against C. ferrugineus. Mortality increased with the increase in concentration and exposure time. 100% mortality was achieved with 800 ppm concentration after 18hr of treatment against T. castaneum and with 700 ppm after 6 hr of treatment against C. ferrugineus.

Keywords: ozone gas, toxicity, O₃, Tribolium castaneum, Cryptolestes ferrugineus, stored grain insect pests

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Authors: Leonardo Herrera, Shield B. Lin, Stephen J. Montgomery-Smith, Ziraguen O. Williams

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Three control algorithms, proportional-integral-derivative, linear-quadratic-Gaussian, and linear-quadratic-Gaussian with the shift, were applied to the computer simulation of a one-directional dynamic model of a Stewart Platform. The goal was to compare the dynamic system responses under the three control algorithms and to minimize the impact energy when simulating spacecraft docking operations. Equations were derived for the control algorithms and the input and output of the feedback control system. Using MATLAB, Simulink diagrams were created to represent the three control schemes. A switch selector was used for the convenience of changing among different controllers. The simulation demonstrated the controller using the algorithm of Linear-Quadratic-Gaussian with the shift resulting in the lowest impact energy.

Keywords: controller, Stewart platform, docking operation, spacecraft

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Authors: Rosa L. Figueroa, Christopher A. Flores, Qing Zeng-Treitler

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A regular expression consists of sequence characters which allow describing a text path. Usually, in clinical research, regular expressions are manually created by programmers together with domain experts. Lately, there have been several efforts to investigate how to generate them automatically. This article presents a text classification algorithm based on regexes. The algorithm named REX was designed, and then, implemented as a simplified method to create regexes to classify Spanish text automatically. In order to classify ambiguous cases, such as, when multiple labels are assigned to a testing example, REX includes an information gain method Two sets of data were used to evaluate the algorithm’s effectiveness in clinical text classification tasks. The results indicate that the regular expression based classifier proposed in this work performs statically better regarding accuracy and F-measure than Support Vector Machine and Naïve Bayes for both datasets.

Keywords: information gain, regular expressions, smith-waterman algorithm, text classification

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Authors: Leonardo Herrera, Shield B. Lin, Stephen J. Montgomery-Smith, Ziraguen O. Williams

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A one-directional dynamic model of a Stewart Platform was developed to assist NASA in analyzing the dynamic response in spacecraft docking operations. A simplified mechanical drawing was created, capturing the physical structure's main features. A simplified schematic diagram was developed into a lumped mass model from the mechanical drawing. Three differential equations were derived according to the schematic diagram. A Simulink diagram was created using MATLAB to represent the three equations. System parameters, including spring constants and masses, are derived in detail from the physical system. The model can be used for further analysis via computer simulation in predicting dynamic response in its main docking direction, i.e., up-and-down motion.

Keywords: stewart platform, docking operation, spacecraft, spring constant

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Authors: Kevin Smith

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Publicly traded company in the US are legally obligated to host earnings calls that discuss their most recent financial reports. During these calls, investors are able to ask these companies questions about these financial reports and on the future direction of the company. This paper examines whether common institutional owners use these calls as a way to indirectly signal to companies in their portfolio to not take actions that could hurt the common owner's interests. This paper uses transcripts taken from the earnings calls of the six largest health insurance companies in the US from 2014 to 2019. This data is analyzed using text analysis and sentiment analysis to look for patterns in the statements made by common owners. The analysis found that common owners where more likely to recommend against direct price competition and instead redirect the insurance companies towards more passive actions, like investing in new technologies. This result indicates a mechanism that common owners use to reduce competition in the health insurance market.

Keywords: common ownership, text analysis, sentiment analysis, machine learning

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Authors: Edward C. Smith

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Historical narration in literature and film is an act that necessarily develops and deforms history, whether consciously or unconsciously. Such “translation” suffers or thrives depending on its historical context and on the ability of the artist/artists to make choices that enhance or diminish social and political reality. This “translation” and its challenges is examined from within the historical and political context of the 1930 Berlin film premiere of “All Quiet on the Western Front,” a film based on Erich Maria Remarque’s 1928 best-selling novel. Both the film and the novel appeared during a period in which the “aestheticization” of reality predominated. This was an era in early 20th-century European society in which life was conceived of as innately artistic and structured like an art form. The emergence of this modern consciousness, one in which memory and history surrendered their former authority, enabled conservative propaganda of the period to denounce all art that did not adhere conceptually to its political tenets, with “All Quiet” becoming yet another of its “victims.”

Keywords: documentary and propaganda film, film and TV audiences, international literature in film studies, popular culture and film

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Authors: Mohamed T. Faheem Saidahmed, Ahmed M. Attiya Ibrahim, Basma GH. Elkilany

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This paper discusses the application of Time Delay Control (TDC) compensation technique in the juice extraction process in a sugar mill. The objective is to improve the control performance of the process and increase extraction efficiency. The paper presents the mathematical model of the juice extraction process and the design of the TDC compensation controller. Simulation results show that the TDC compensation technique can effectively suppress the time delay effect in the process and improve control performance. The extraction efficiency is also significantly increased with the application of the TDC compensation technique. The proposed approach provides a practical solution for improving the juice extraction process in sugar mills using MATLAB Processes.

Keywords: time delay control (TDC), exact and unique state space model, delay compensation, Smith predictor.

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Authors: Janine Sommer, Mariana Daus, Mariana Simon, Maria Smith, Daniel Luna

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The technologies and communication advances contributed to new tools development which allows patients to have an active role in their own health. In the light of information needs and paradigms changes about health, the patient self-manages their care. This line of care focuses on patients; specific portals come up to people with particular requirements like pregnant women. Thinking of a portal design to this sector of the population, in September 2016 a survey was made to users with the objective to knowing and understanding information’s needs at the moment to use an application for pregnant. Also, prototypes of the portal´s features were designed to try and validate with users, using the methodology of human-centered design. Investigations have made possible the identification of needs of this population and develop a tool who try to satisfy, providing timely information for each part of pregnancy and allowing the patients to make a physical check and the follow up of pregnancy seeking advice from our obstetricians.

Keywords: electronic health record, health personal record, mobile applications, pregnant women

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Authors: Josephine Shamash, Stuart Smith

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We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching

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