107 resultados para Non-linear multiple regression
Resumo:
As Earth's climate is rapidly changing, the impact of ambient temperature on health outcomes has attracted increasing attention in the recent time. Considerable number of excess deaths has been reported because of exposure to ambient hot and cold temperatures. However, relatively little research has been conducted on the relation between temperature and morbidity. The aim of this study was to characterize the relationship between both hot and cold temperatures and emergency hospital admissions in Brisbane, Australia, and to examine whether the relation varied by age and socioeconomic factors. It aimed to explore lag structures of temperature–morbidity association for respiratory causes, and to estimate the magnitude of emergency hospital admissions for cardiovascular diseases attributable to hot and cold temperatures for the large contribution of both diseases to the total emergency hospital admissions. A time series study design was applied using routinely collected data of daily emergency hospital admissions, weather and air pollution variables in Brisbane during 1996–2005. Poisson regression model with a distributed lag non-linear structure was adopted to assess the impact of temperature on emergency hospital admissions after adjustment for confounding factors. Both hot and cold effects were found, with higher risk of hot temperatures than that of cold temperatures. Increases in mean temperature above 24.2oC were associated with increased morbidity, especially for the elderly ≥ 75 years old with the largest effect. The magnitude of the risk estimates of hot temperature varied by age and socioeconomic factors. High population density, low household income, and unemployment appeared to modify the temperature–morbidity relation. There were different lag structures for hot and cold temperatures, with the acute hot effect within 3 days after hot exposure and about 2-week lagged cold effect on respiratory diseases. A strong harvesting effect after 3 days was evident for respiratory diseases. People suffering from cardiovascular diseases were found to be more vulnerable to hot temperatures than cold temperatures. However, more patients admitted for cardiovascular diseases were attributable to cold temperatures in Brisbane compared with hot temperatures. This study contributes to the knowledge base about the association between temperature and morbidity. It is vitally important in the context of ongoing climate change. The findings of this study may provide useful information for the development and implementation of public health policy and strategic initiatives designed to reduce and prevent the burden of disease due to the impact of climate change.
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Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A primary objective was to produce a comprehensive range of new distributed plasticity analytical benchmark solutions for verification of the concentrated plasticity methods. A distributed plasticity model was developed using shell finite elements to explicitly account for the effects of gradual yielding and spread of plasticity, initial geometric imperfections, residual stresses and local buckling deformations. The model was verified by comparison with large-scale steel frame test results and a variety of existing analytical benchmark solutions. This paper presents a description of the distributed plasticity model and details of the verification study.
Resumo:
Application of `advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.
Resumo:
Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A series of large-scale tests were performed in order to provide experimental results for verification of the new analytical models. Each of the test frames comprised non-compact sections, and exhibited significant local buckling behaviour prior to failure. This paper presents details of the test program including the test specimens, set-up and instrumentation, procedure, and results.
Resumo:
Bangkok Metropolitan Region (BMR) is the centre for various major activities in Thailand including political, industry, agriculture, and commerce. Consequently, the BMR is the highest and most densely populated area in Thailand. Thus, the demand for houses in the BMR is also the largest, especially in subdivision developments. For these reasons, the subdivision development in the BMR has increased substantially in the past 20 years and generated large numbers of subdivision developments (AREA, 2009; Kridakorn Na Ayutthaya & Tochaiwat, 2010). However, this dramatic growth of subdivision development has caused several problems including unsustainable development, especially for subdivision neighbourhoods, in the BMR. There have been rating tools that encourage the sustainability of neighbourhood design in subdivision development, but they still have practical problems. Such rating tools do not cover the scale of the development entirely; and they concentrate more on the social and environmental conservation aspects, which have not been totally accepted by the developers (Boonprakub, 2011; Tongcumpou & Harvey, 1994). These factors strongly confirm the need for an appropriate rating tool for sustainable subdivision neighbourhood design in the BMR. To improve level of acceptance from all stakeholders in subdivision developments industry, the new rating tool should be developed based on an approach that unites the social, environmental, and economic approaches, such as eco-efficiency principle. Eco-efficiency is the sustainability indicator introduced by the World Business Council for Sustainable Development (WBCSD) since 1992. The eco-efficiency is defined as the ratio of the product or service value according to its environmental impact (Lehni & Pepper, 2000; Sorvari et al., 2009). Eco-efficiency indicator is concerned to the business, while simultaneously, is concerned with to social and the environment impact. This study aims to develop a new rating tool named "Rating for sustainable subdivision neighbourhood design (RSSND)". The RSSND methodology is developed by a combination of literature reviews, field surveys, the eco-efficiency model development, trial-and-error technique, and the tool validation process. All required data has been collected by the field surveys from July to November 2010. The ecoefficiency model is a combination of three different mathematical models; the neighbourhood property price (NPP) model, the neighbourhood development cost (NDC) model, and the neighbourhood occupancy cost (NOC) model which are attributable to the neighbourhood subdivision design. The NPP model is formulated by hedonic price model approach, while the NDC model and NOC model are formulated by the multiple regression analysis approach. The trial-and-error technique is adopted for simplifying the complex mathematic eco-efficiency model to a user-friendly rating tool format. Credibility of the RSSND has been validated by using both rated and non-rated of eight subdivisions. It is expected to meet the requirements of all stakeholders which support the social activities of the residents, maintain the environmental condition of the development and surrounding areas, and meet the economic requirements of the developers.
Resumo:
Traditionally, infectious diseases and under-nutrition have been considered major health problems in Sri Lanka with little attention paid to obesity and associated non-communicable diseases (NCDs). However, the recent Sri Lanka Diabetes and Cardiovascular Study (SLDCS) reported the epidemic level of obesity, diabetes and metabolic syndrome. Moreover, obesity-associated NCDs is the leading cause of death in Sri Lanka and there is an exponential increase in hospitalization due to NCDs adversely affecting the development of the country. Despite Sri Lanka having a very high prevalence of NCDs and associated mortality, little is known about the causative factors for this burden. It is widely believed that the global NCD epidemic is associated with recent lifestyle changes, especially dietary factors. In the absence of sufficient data on dietary habits in Sri Lanka, successful interventions to manage these serious health issues would not be possible. In view of the current situation the dietary survey was undertaken to assess the intakes of energy, macro-nutrients and selected other nutrients with respect to socio demographic characteristics and the nutritional status of Sri Lankan adults especially focusing on obesity. Another aim of this study was to develop and validate a culturally specific food frequency questionnaire (FFQ) to assess dietary risk factors of NCDs in Sri Lankan adults. Data were collected from a subset of the national SLDCS using a multi-stage, stratified, random sampling procedure (n=500). However, data collection in the SLDCS was affected by the prevailing civil war which resulted in no data being collected from Northern and Eastern provinces. To obtain a nationally representative sample, additional subjects (n=100) were later recruited from the two provinces using similar selection criteria. Ethical Approval for this study was obtained from the Ethical Review Committee, Faculty of Medicine, University of Colombo, Sri Lanka and informed consent was obtained from the subjects before data were collected. Dietary data were obtained using the 24-h Dietary Recall (24HDR) method. Subjects were asked to recall all foods and beverages, consumed over the previous 24-hour period. Respondents were probed for the types of foods and food preparation methods. For the FFQ validation study, a 7-day weight diet record (7-d WDR) was used as the reference method. All foods recorded in the 24 HDR were converted into grams and then intake of energy and nutrients were analysed using NutriSurvey 2007 (EBISpro, Germany) which was modified for Sri Lankan food recipes. Socio-demographic details and body weight perception were collected from interviewer-administrated questionnaire. BMI was calculated and overweight (BMI ≥23 kg.m-2), obesity (BMI ≥25 kg.m-2) and abdominal obesity (Men: WC ≥ 90 cm; Women: WC ≥ 80 cm) were categorized according to Asia-pacific anthropometric cut-offs. The SPSS v. 16 for Windows and Minitab v10 were used for statistical analysis purposes. From a total of 600 eligible subjects, 491 (81.8%) participated of whom 34.5% (n=169) were males. Subjects were well distributed among different socio-economic parameters. A total of 312 different food items were recorded and nutritionists grouped similar food items which resulted in a total of 178 items. After performing step-wise multiple regression, 93 foods explained 90% of the variance for total energy intake, carbohydrates, protein, total fat and dietary fibre. Finally, 90 food items and 12 photographs were selected. Seventy-seven subjects completed (response rate = 65%) the FFQ and 7-day WDR. Estimated mean energy intake (SD) from FFQ (1794±398 kcal) and 7DWR (1698±333 kcal, P<0.001) was significantly different due to a significant overestimation of carbohydrate (~10 g/d, P<0.001) and to some extent fat (~5 g/d, NS). Significant positive correlations were found between the FFQ and 7DWR for energy (r = 0.39), carbohydrate (r = 0.47), protein (r = 0.26), fat (r =0.17) and dietary fiber (r = 0.32). Bland-Altman graphs indicated fairly good agreement between methods with no relationship between bias and average intake of each nutrient examined. The findings from the nutrition survey showed on average, Sri Lankan adults consumed over 14 portions of starch/d; moreover, males consumed 5 more portions of cereal than females. Sri Lankan adults consumed on average 3.56 portions of added sugars/d. Moreover, mean daily intake of fruit (0.43) and vegetable (1.73) portions was well below minimum dietary recommendations (fruits 2 portions/d; vegetables 3 portions/d). The total fruit and vegetable intake was 2.16 portions/d. Daily consumption of meat or alternatives was 1.75 portions and the sum of meat and pulses was 2.78 portions/d. Starchy foods were consumed by all participants and over 88% met the minimum daily recommendations. Importantly, nearly 70% of adults exceeded the maximum daily recommendation for starch (11portions/d) and a considerable proportion consumed larger numbers of starch servings daily, particularly men. More than 12% of men consumed over 25 starch servings/d. In contrast to their starch consumption, participants reported very low intakes of other food groups. Only 11.6%, 2.1% and 3.5% of adults consumed the minimum daily recommended servings of vegetables, fruits, and fruits and vegetables combined, respectively. Six out of ten adult Sri Lankans sampled did not consume any fruits. Milk and dairy consumption was extremely low; over a third of the population did not consume any dairy products and less than 1% of adults consumed 2 portions of dairy/d. A quarter of Sri Lankans did not report consumption of meat and pulses. Regarding protein consumption, 36.2% attained the minimum Sri Lankan recommendation for protein; and significantly more men than women achieved the recommendation of ≥3 servings of meat or alternatives daily (men 42.6%, women 32.8%; P<0.05). Over 70% of energy was derived from carbohydrates (Male:72.8±6.4%, Female:73.9±6.7%), followed by fat (Male:19.9±6.1%, Female:18.5±5.7%) and proteins (Male:10.6±2.1%, Female:10.9±5.6%). The average intake of dietary fiber was 21.3 g/day and 16.3 g/day for males and females, respectively. There was a significant difference in nutritional intake related to ethnicities, areas of residence, education levels and BMI categories. Similarly, dietary diversity was significantly associated with several socio-economic parameters among Sri Lankan adults. Adults with BMI ≥25 kg.m-2 and abdominally obese Sri Lankan adults had the highest diet diversity values. Age-adjusted prevalence (95% confidence interval) of overweight, obesity, and abdominal obesity among Sri Lankan adults were 17.1% (13.8-20.7), 28.8% (24.8-33.1), and 30.8% (26.8-35.2), respectively. Men, compared with women, were less overweight, 14.2% (9.4-20.5) versus 18.5% (14.4-23.3), P = 0.03, less obese, 21.0% (14.9-27.7) versus 32.7% (27.6-38.2), P < .05; and less abdominally obese, 11.9% (7.4-17.8) versus 40.6% (35.1-46.2), P < .05. Although, prevalence of obesity has reached to epidemic level body weight misperception was common among Sri Lankan adults. Two-thirds of overweight males and 44.7% of females considered themselves as in "about right weight". Over one third of both male and female obese subjects perceived themselves as "about right weight" or "underweight". Nearly 32% of centrally obese men and women perceived that their waist circumference is about right. People who perceived overweight or very overweight (n = 154) only 63.6% tried to lose their body weight (n = 98), and quarter of adults seek advices from professionals (n = 39). A number of important conclusions can be drawn from this research project. Firstly, the newly developed FFQ is an acceptable tool for assessing the nutrient intake of Sri Lankans and will assist proper categorization of individuals by dietary exposure. Secondly, a substantial proportion of the Sri Lankan population does not consume a varied and balanced diet, which is suggestive of a close association between the nutrition-related NCDs in the country and unhealthy eating habits. Moreover, dietary diversity is positively associated with several socio-demographic characteristics and obesity among Sri Lankan adults. Lastly, although obesity is a major health issue among Sri Lankan adults, body weight misperception was common among underweight, healthy weight, overweight, and obese adults in Sri Lanka. Over 2/3 of overweight and 1/3 of obese Sri Lankan adults believe that they are in "right weight" or "under-weight" categories.
Resumo:
Background. In isotropic materials, the speed of acoustic wave propagation is governed by the bulk modulus and density. For tendon, which is a structural composite of fluid and collagen, however, there is some anisotropy requiring an adjustment for Poisson's ratio. This paper explores these relationships using data collected, in vivo, on human Achilles tendon and then compares estimates of elastic modulus and hysteresis against published values from in vitro mechanical tests. Methods. Measurements using conventional B-model ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound in the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates of the elastic modulus and hysteresis of the Achilles tendon derived. Results. Axial speed of sound varied between 1850 and 2090 ms-1 with a non-linear, asymptotic dependency on the level of tensile stress (5-35 MPa) in the tendon. Estimates derived for the elastic modulus of the Achilles tendon ranged between 1-2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3-11%. Discussion. Estimates of elastic modulus agree closely with those previously reported from direct measurements obtained via mechanical tensile tests on major weight bearing tendons in vitro [1,2]. Hysteresis derived from models of the stress-strain relationship is consistent with direct measures from various mamalian tendon (7-10%) but is lower than previous estimates in human tendon (17-26%) [3]. This non-invasive method would appear suitable for monitoring changes in tendon properties during dynamic sporting activities.
Resumo:
Hot spot identification (HSID) aims to identify potential sites—roadway segments, intersections, crosswalks, interchanges, ramps, etc.—with disproportionately high crash risk relative to similar sites. An inefficient HSID methodology might result in either identifying a safe site as high risk (false positive) or a high risk site as safe (false negative), and consequently lead to the misuse the available public funds, to poor investment decisions, and to inefficient risk management practice. Current HSID methods suffer from issues like underreporting of minor injury and property damage only (PDO) crashes, challenges of accounting for crash severity into the methodology, and selection of a proper safety performance function to model crash data that is often heavily skewed by a preponderance of zeros. Addressing these challenges, this paper proposes a combination of a PDO equivalency calculation and quantile regression technique to identify hot spots in a transportation network. In particular, issues related to underreporting and crash severity are tackled by incorporating equivalent PDO crashes, whilst the concerns related to the non-count nature of equivalent PDO crashes and the skewness of crash data are addressed by the non-parametric quantile regression technique. The proposed method identifies covariate effects on various quantiles of a population, rather than the population mean like most methods in practice, which more closely corresponds with how black spots are identified in practice. The proposed methodology is illustrated using rural road segment data from Korea and compared against the traditional EB method with negative binomial regression. Application of a quantile regression model on equivalent PDO crashes enables identification of a set of high-risk sites that reflect the true safety costs to the society, simultaneously reduces the influence of under-reported PDO and minor injury crashes, and overcomes the limitation of traditional NB model in dealing with preponderance of zeros problem or right skewed dataset.
Resumo:
Spatially-explicit modelling of grassland classes is important to site-specific planning for improving grassland and environmental management over large areas. In this study, a climate-based grassland classification model, the Comprehensive and Sequential Classification System (CSCS) was integrated with spatially interpolated climate data to classify grassland in Gansu province, China. The study area is characterized by complex topographic features imposed by plateaus, high mountains, basins and deserts. To improve the quality of the interpolated climate data and the quality of the spatial classification over this complex topography, three linear regression methods, namely an analytic method based on multiple regression and residues (AMMRR), a modification of the AMMRR method through adding the effect of slope and aspect to the interpolation analysis (M-AMMRR) and a method which replaces the IDW approach for residue interpolation in M-AMMRR with an ordinary kriging approach (I-AMMRR), for interpolating climate variables were evaluated. The interpolation outcomes from the best interpolation method were then used in the CSCS model to classify the grassland in the study area. Climate variables interpolated included the annual cumulative temperature and annual total precipitation. The results indicated that the AMMRR and M-AMMRR methods generated acceptable climate surfaces but the best model fit and cross validation result were achieved by the I-AMMRR method. Twenty-six grassland classes were classified for the study area. The four grassland vegetation classes that covered more than half of the total study area were "cool temperate-arid temperate zonal semi-desert", "cool temperate-humid forest steppe and deciduous broad-leaved forest", "temperate-extra-arid temperate zonal desert", and "frigid per-humid rain tundra and alpine meadow". The vegetation classification map generated in this study provides spatial information on the locations and extents of the different grassland classes. This information can be used to facilitate government agencies' decision-making in land-use planning and environmental management, and for vegetation and biodiversity conservation. The information can also be used to assist land managers in the estimation of safe carrying capacities which will help to prevent overgrazing and land degradation.
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Commodity price modeling is normally approached in terms of structural time-series models, in which the different components (states) have a financial interpretation. The parameters of these models can be estimated using maximum likelihood. This approach results in a non-linear parameter estimation problem and thus a key issue is how to obtain reliable initial estimates. In this paper, we focus on the initial parameter estimation problem for the Schwartz-Smith two-factor model commonly used in asset valuation. We propose the use of a two-step method. The first step considers a univariate model based only on the spot price and uses a transfer function model to obtain initial estimates of the fundamental parameters. The second step uses the estimates obtained in the first step to initialize a re-parameterized state-space-innovations based estimator, which includes information related to future prices. The second step refines the estimates obtained in the first step and also gives estimates of the remaining parameters in the model. This paper is part tutorial in nature and gives an introduction to aspects of commodity price modeling and the associated parameter estimation problem.
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Background Heatwaves could cause the population excess death numbers to be ranged from tens to thousands within a couple of weeks in a local area. An excess mortality due to a special event (e.g., a heatwave or an epidemic outbreak) is estimated by subtracting the mortality figure under ‘normal’ conditions from the historical daily mortality records. The calculation of the excess mortality is a scientific challenge because of the stochastic temporal pattern of the daily mortality data which is characterised by (a) the long-term changing mean levels (i.e., non-stationarity); (b) the non-linear temperature-mortality association. The Hilbert-Huang Transform (HHT) algorithm is a novel method originally developed for analysing the non-linear and non-stationary time series data in the field of signal processing, however, it has not been applied in public health research. This paper aimed to demonstrate the applicability and strength of the HHT algorithm in analysing health data. Methods Special R functions were developed to implement the HHT algorithm to decompose the daily mortality time series into trend and non-trend components in terms of the underlying physical mechanism. The excess mortality is calculated directly from the resulting non-trend component series. Results The Brisbane (Queensland, Australia) and the Chicago (United States) daily mortality time series data were utilized for calculating the excess mortality associated with heatwaves. The HHT algorithm estimated 62 excess deaths related to the February 2004 Brisbane heatwave. To calculate the excess mortality associated with the July 1995 Chicago heatwave, the HHT algorithm needed to handle the mode mixing issue. The HHT algorithm estimated 510 excess deaths for the 1995 Chicago heatwave event. To exemplify potential applications, the HHT decomposition results were used as the input data for a subsequent regression analysis, using the Brisbane data, to investigate the association between excess mortality and different risk factors. Conclusions The HHT algorithm is a novel and powerful analytical tool in time series data analysis. It has a real potential to have a wide range of applications in public health research because of its ability to decompose a nonlinear and non-stationary time series into trend and non-trend components consistently and efficiently.
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The paradigm that mangroves are critical for sustaining production in coastal fisheries is widely accepted, but empirical evidence has been tenuous. This study showed that links between mangrove extent and coastal fisheries production could be detected for some species at a broad regional scale (1000s of kilometres) on the east coast of Queensland, Australia. The relationships between catch-per-unit-effort for different commercially caught species in four fisheries (trawl, line, net and pot fisheries) and mangrove characteristics, estimated from Landsat images were examined using multiple regression analyses. The species were categorised into three groups based on information on their life history characteristics, namely mangrove-related species (banana prawns Penaeus merguiensis, mud crabs Scylla serrata and barramundi Lates calcarifer), estuarine species (tiger prawns Penaeus esculentus and Penaeus semisulcatus, blue swimmer crabs Portunus pelagicus and blue threadfin Eleutheronema tetradactylum) and offshore species (coral trout Plectropomus spp.). For the mangrove-related species, mangrove characteristics such as area and perimeter accounted for most of the variation in the model; for the non-mangrove estuarine species, latitude was the dominant parameter but some mangrove characteristics (e.g. mangrove perimeter) also made significant contributions to the models. In contrast, for the offshore species, latitude was the dominant variable, with no contribution from mangrove characteristics. This study also identified that finer scale spatial data for the fisheries, to enable catch information to be attributed to a particular catchment, would help to improve our understanding of relationships between mangroves and fisheries production.
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We present a distinguishing attack against SOBER-128 with linear masking. We found a linear approximation which has a bias of 2^− − 8.8 for the non-linear filter. The attack applies the observation made by Ekdahl and Johansson that there is a sequence of clocks for which the linear combination of some states vanishes. This linear dependency allows that the linear masking method can be applied. We also show that the bias of the distinguisher can be improved (or estimated more precisely) by considering quadratic terms of the approximation. The probability bias of the quadratic approximation used in the distinguisher is estimated to be equal to O(2^− − 51.8), so that we claim that SOBER-128 is distinguishable from truly random cipher by observing O(2^103.6) keystream words.
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In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.
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Firm-customer digital connectedness for effective sensing and responding is a strategic imperative for contemporary competitive firms. This research-in-progress paper conceptualizes and operationalizes the firm-customer mobile digital connectedness of a smart-mobile customer. The empirical investigation focuses on mobile app users and the impact of mobile apps on customer expectations. Based on pilot data collected from 127 customers, we tested hypotheses pertaining to firm-customer mobile digital connectedness and customer expectations. Our test analysis using linear and non-linear postulations reveals those customers raise their expectations as they increase their digital interactions with a firm.