Search results for: weighted approximation

Authors: Mekdelawit Teferi Alamirew

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As a practical tool, the Geographical information system (GIS) was used for data integration, collection, management, analysis, and output presentation in pavement mangement systems . There are many GIS techniques to improve the maintenance activities like Dynamic segmentation and weighted overlay analysis which considers Multi Criteria Decision Making process. The results indicated that the developed MPI model works sufficiently and yields adequate output for providing accurate decisions. Hence considering multi criteria to prioritize the pavement sections for maintenance, as a result of the fact that GIS maps can express position, extent, and severity of pavement distress features more effectively than manual approaches, lastly the paper also offers digitized distress maps that can help agencies in their decision-making processes.

Keywords: pavement, flexible, maintenance, index

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

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The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: job-shop scheduling, classification, constraints, objective functions

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Authors: Ahmad Sarfaraz, Raiyad Herwies

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In this paper, a multi-criteria decision making analysis is used to help any organization selects the best KM tool that fits and serves its needs. The AHP model is used based on a previous study to highlight and identify the main criteria and sub-criteria that are incorporated in the selection process. Different KM tools alternatives with different criteria are compared and weighted accurately to be incorporated in the GP model. The main goal is to combine the GP model with the AHP model to ensure that selecting the KM tool considers the resource constraints. Two important issues are discussed in this paper: how different factors could be taken into consideration in forming the AHP model, and how to incorporate the AHP results into the GP model for better results.

Keywords: knowledge management, analytical hierarchy process, goal programming, multi-criteria decision making

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Authors: Iftikhar U. Sikder

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This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.

Keywords: concept approximation, granular computing, reducts, rough set theory, rule induction

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Aries Nawel, Bentarzi Mohamed

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This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model (PINMA_{S}(q)). The closed forms of the mean, the second moment and the periodic autocovariance function are obtained. Furthermore, the time reversibility of the model is discussed in details. Moreover, the estimation of the underlying parameters are obtained by the Yule-Walker method, the Conditional Least Square method (CLS) and the Weighted Conditional Least Square method (WCLS). A simulation study is carried out to evaluate the performance of the estimation method. Moreover, an application on real data set is provided.

Keywords: periodic integer-valued moving average, periodically correlated process, time reversibility, count data

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Authors: Hassan Eshkiki, Benjamin Mora

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The Neighbor Migrating Generator is a simple and efficient approach to finding the closest potential neighbor(s) with a different label for a given instance and so without the need to calibrate any kernel settings at all. This allows determining and explaining the most important features that will influence an AI model. It can be used to either migrate a specific sample to the class decision boundary of the original model within a close neighborhood of that sample or identify global features that can help localising neighbor classes. The proposed technique works by minimizing a loss function that is divided into two components which are independently weighted according to three parameters α, β, and ω, α being self-adjusting. Results show that this approach is superior to past techniques when detecting the smallest changes in the feature space and may also point out issues in models like over-fitting.

Keywords: explainable AI, EX AI, feature importance, counterfactual explanations

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Authors: Takuya Suzuki, Atsushi Shirai, Takashi Seki

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Acupuncture therapy is one of the treatments in traditional Chinese medicine. Recently, some reports have shown the effectiveness of acupuncture. However, its full acceptance has been hindered by the lack of understanding on mechanism of the therapy. Acupuncture applied to Zusanli (ST-36) enhances blood flow volume in superior mesenteric artery (SMA), yielding peripheral vascular resistance – regulated blood flow of SMA dominated by the parasympathetic system and inhibition of sympathetic system. In this study, a lumped-parameter approximation model of blood flow in the systemic arteries was developed. This model was extremely simple, consisting of the aorta, carotid arteries, arteries of the four limbs and SMA, and their peripheral vascular resistances. Here, the individual artery was simplified to a tapered tube and the resistances were modelled by a linear resistance. We numerically investigated contribution of the peripheral vascular resistance of SMA to the systemic blood distribution using this model. In addition to the upstream end of the model, which correlates with the left ventricle, two types of boundary condition were applied; mean left ventricular pressure which correlates with blood pressure (BP) and mean cardiac output which corresponds to cardiac index (CI). We examined it to reproduce the experimentally obtained hemodynamic change, in terms of the ratio of the aforementioned hemodynamic parameters from their initial values before the acupuncture, by regulating the peripheral vascular resistances and the upstream boundary condition. First, only the peripheral vascular resistance of SMA was changed to show contribution of the resistance to the change in blood flow volume in SMA, expecting reproduction of the experimentally obtained change. It was found, however, this was not enough to reproduce the experimental result. Then, we also changed the resistances of the other arteries together with the value given at upstream boundary. Here, the resistances of the other arteries were changed simultaneously in the same amount. Consequently, we successfully reproduced the hemodynamic change to find that regulation of the upstream boundary condition to the value experimentally obtained after the stimulation is necessary for the reproduction, though statistically significant changes in BP and CI were not observed in the experiment. It is generally known that sympathetic and parasympathetic tones take part in regulation of whole the systemic circulation including the cardiac function. The present result indicates that stimulation to ST-36 could induce vasodilation of peripheral circulation of SMA and vasoconstriction of that of other arteries. In addition, it implies that experimentally obtained small changes in BP and CI induced by the acupuncture may be involved in the therapeutic response.

Keywords: acupuncture, hemodynamics, lumped-parameter approximation, modeling, systemic vascular resistance

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Jing Zhang, Daniel Nikovski

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We propose an approximation algorithm called LINKUMP to compute the Pan Matrix Profile (PMP) under the unnormalized l∞ distance (useful for value-based similarity search) using double-ended queue and linear interpolation. The algorithm has comparable time/space complexities as the state-of-the-art algorithm for typical PMP computation under the normalized l₂ distance (useful for shape-based similarity search). We validate its efficiency and effectiveness through extensive numerical experiments and a real-world anomaly detection application.

Keywords: pan matrix profile, unnormalized euclidean distance, double-ended queue, discord discovery, anomaly detection

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Abbas Hani, Maryam Jassasizadeh

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The concentrations of Cd, Pb, and Ni were determined from 40 soil samples collected in surface soils of Khark Island. Geostatistic methods and GIS were used to identify heavy metal sources and their spatial pattern. Principal component analysis coupled with correlation between heavy metals showed that level of mentioned heavy metal was lower than the standard level. Then the data obtained from the soil analyzing were studied for the purposes of normal distribution. The best way of interior finding for cadmium and nickel was ordinary kriging and the best way of interpolation of lead was inverse distance weighted. The result of this study help us to understand heavy metals distribution and make decision for remediation of soil pollution.

Keywords: geostatistics, ordinary kriging, heavy metals, GIS, Khark

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Danni Cheng

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Background: Preclinical and epidemiological studies have reported potential protective effects of low-density lipoprotein cholesterol (LDL-C) lowering drugs on head and neck squamous cell cancer (HNSCC) survival, but the causality was not consistent. Genetic variants associated with LDL-C lowering drug targets can predict the effects of their therapeutic inhibition on disease outcomes. Objective: We aimed to evaluate the causal association of genetically proxied cholesterol-lowering drug targets and circulating lipid traits with cancer survival in HNSCC patients stratified by human papillomavirus (HPV) status using two-sample Mendelian randomization (MR) analyses. Method: Single-nucleotide polymorphisms (SNPs) in gene region of LDL-C lowering drug targets (HMGCR, NPC1L1, CETP, PCSK9, and LDLR) associated with LDL-C levels in genome-wide association study (GWAS) from the Global Lipids Genetics Consortium (GLGC) were used to proxy LDL-C lowering drug action. SNPs proxy circulating lipids (LDL-C, HDL-C, total cholesterol, triglycerides, apoprotein A and apoprotein B) were also derived from the GLGC data. Genetic associations of these SNPs and cancer survivals were derived from 1,120 HPV-positive oropharyngeal squamous cell carcinoma (OPSCC) and 2,570 non-HPV-driven HNSCC patients in VOYAGER program. We estimated the causal associations of LDL-C lowering drugs and circulating lipids with HNSCC survival using the inverse-variance weighted method. Results: Genetically proxied HMGCR inhibition was significantly associated with worse overall survival (OS) in non-HPV-drive HNSCC patients (inverse variance-weighted hazard ratio (HR IVW), 2.64[95%CI,1.28-5.43]; P = 0.01) but better OS in HPV-positive OPSCC patients (HR IVW,0.11[95%CI,0.02-0.56]; P = 0.01). Estimates for NPC1L1 were strongly associated with worse OS in both total HNSCC (HR IVW,4.17[95%CI,1.06-16.36]; P = 0.04) and non-HPV-driven HNSCC patients (HR IVW,7.33[95%CI,1.63-32.97]; P = 0.01). A similar result was found that genetically proxied PSCK9 inhibitors were significantly associated with poor OS in non-HPV-driven HNSCC (HR IVW,1.56[95%CI,1.02 to 2.39]). Conclusion: Genetically proxied long-term HMGCR inhibition was significantly associated with decreased OS in non-HPV-driven HNSCC and increased OS in HPV-positive OPSCC. While genetically proxied NPC1L1 and PCSK9 had associations with worse OS in total and non-HPV-driven HNSCC patients. Further research is needed to understand whether these drugs have consistent associations with head and neck tumor outcomes.

Keywords: Mendelian randomization analysis, head and neck cancer, cancer survival, cholesterol, statin

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Authors: Stefan Peters, Phillip Roetman

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The global loss of biodiversity is threatening the benefits nature provides to human populations and has become a more pressing issue than climate change and requires immediate attention. While there have been successful global agreements for environmental protection, such as the Montreal Protocol, these are rare, and we cannot rely on them solely. Thus, it is crucial to take national and local actions to support biodiversity. Australia is one of the 17 countries in the world with a high level of biodiversity, and its cities are vital habitats for endangered species, with more of them found in urban areas than in non-urban ones. However, the protection of biodiversity in metropolitan Adelaide has been inadequate, with over 130 species disappearing since European colonization in 1836. In this research project we conceptualized, developed and implemented a framework for wildlife Habitat Hotspots and Habitat Corridor modelling in an urban context using geographic data and GIS modelling and analysis. We used detailed topographic and other geographic data provided by a local council, including spatial and attributive properties of trees, parcels, water features, vegetated areas, roads, verges, traffic, and census data. Weighted factors considered in our raster-based Habitat Hotspot model include parcel size, parcel shape, population density, canopy cover, habitat quality and proximity to habitats and water features. Weighted factors considered in our raster-based Habitat Corridor model include habitat potential (resulting from the Habitat Hotspot model), verge size, road hierarchy, road widths, human density, and presence of remnant indigenous vegetation species. We developed a GIS model, using Python scripting and ArcGIS-Pro Model-Builder, to establish an automated reproducible and adjustable geoprocessing workflow, adaptable to any study area of interest. Our habitat hotspot and corridor modelling framework allow to determine and map existing habitat hotspots and wildlife habitat corridors. Our research had been applied to the study case of Burnside, a local council in Adelaide, Australia, which encompass an area of 30 km2. We applied end-user expertise-based category weightings to refine our models and optimize the use of our habitat map outputs towards informing local strategic decision-making.

Keywords: biodiversity, GIS modeling, habitat hotspot, wildlife corridor

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Authors: Adnan A. Y. Mustafa

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In this paper we present a quick technique to measure the similarity between binary images. The technique is based on a probabilistic mapping approach and is fast because only a minute percentage of the image pixels need to be compared to measure the similarity, and not the whole image. We exploit the power of the Probabilistic Matching Model for Binary Images (PMMBI) to arrive at an estimate of the similarity. We show that the estimate is a good approximation of the actual value, and the quality of the estimate can be improved further with increased image mappings. Furthermore, the technique is image size invariant; the similarity between big images can be measured as fast as that for small images. Examples of trials conducted on real images are presented.

Keywords: big images, binary images, image matching, image similarity

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: Dimitra Alexiou, Stefanos Katsavounis, Ria Kalfakakou

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In an urban area the determination of transportation routes should be planned so as to minimize the provoked pollution taking into account the cost of such routes. In the sequel these routes are cited as pollution routes. The transportation network is expressed by a weighted graph G= (V, E, D, P) where every vertex represents a location to be served and E contains unordered pairs (edges) of elements in V that indicate a simple road. The distances/cost and a weight that depict the provoked air pollution by a vehicle transition at every road are assigned to each road as well. These are the items of set D and P respectively. Furthermore the investigated pollution routes must not exceed predefined corresponding values concerning the route cost and the route pollution level during the vehicle transition. In this paper we present an algorithm that generates such routes in order that the decision maker selects the most appropriate one.

Keywords: bi-criteria, pollution, shortest paths, computation

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Authors: Yuzhi Cai

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In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: combining forecasts, MCMC, predictive density functions, quantile forecasting, quantile modelling

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Authors: Yisau Adelaja Odusote, Olakanmi Felix Akinto

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The associative tendency between like atoms in molten Cd-Ga and Cd-In alloy systems has been studied by using the Quasi-Chemical Approximation Model (QCAM). The concentration dependence of the microscopic functions (the concentration-concentration fluctuations in the long-wavelength limits, Scc(0), the chemical short-range order (CSRO) parameter α1 as well as the chemical diffusion) and the mixing properties as the free energy of mixing, GM, enthalpy of mixing and entropy of mixing of the two molten alloys have been determined. Thermodynamic properties of both systems deviate positively from Raoult's law, while the systems are characterized by positive interaction energy. The role of atomic size ratio on the alloying properties was discussed.

Keywords: homo-pairs, interchange energy, enthalpy, entropy, Cd-Ga, Cd-In

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Authors: Punnoose A. K.

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This paper presents an approach for identifying noisy speech recording using a multi-layer perception (MLP) trained to predict phonemes from acoustic features. Characteristics of the MLP posteriors are explored for clean speech and noisy speech at the frame level. Appropriate density functions are used to fit the softmax probability of the clean and noisy speech. A function that takes into account the ratio of the softmax probability density of noisy speech to clean speech is formulated. These phoneme independent scoring is weighted using a phoneme-specific weightage to make the scoring more robust. Simple thresholding is used to identify the noisy speech recording from the clean speech recordings. The approach is benchmarked on standard databases, with a focus on precision.

Keywords: noisy speech identification, speech pre-processing, noise robustness, feature engineering

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Authors: Dercan Gencbas, Hatice Bebis, Sue Moorhead

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In the nursing process, many of the nursing classification systems were created to be used in international. From these, NANDA-I, Nursing Outcomes Classification (NOC) and Nursing Interventions Classification (NIC). In this direction, the main objective of this study is to establish a model for caregivers in hospitals and communities in Turkey and to ensure that nursing outputs are assessed by NOC-based measures. There are many scales to measure Urinary Incontinence (UI), which is very common in children, in old age, vaginal birth, NOC scales are ideal for use in the nursing process for comprehensive and holistic assessment, with surveys available. For this reason, the purpose of this study is to evaluate the validity of the NOC outputs and indicators used for UI NANDA-I. This research is a methodological study. In addition to the validity of scale indicators in the study, how much they will contribute to recovery after the nursing intervention was assessed by experts. Scope validations have been applied and calculated according to Fehring 1987 work model. According to this, nursing inclusion criteria and scores were determined. For example, if experts have at least four years of clinical experience, their score was 4 points or have at least one year of the nursing classification system, their score was 1 point. The experts were a publication experience about nursing classification, their score was 1 point, or have a doctoral degree in nursing, their score was 2 points. If the expert has a master degree, their score was 1 point. Total of 55 experts rated Fehring as a “senior degree” with a score of 90 according to the expert scoring. The nursing interventions to be applied were asked to what extent these indicators would contribute to recovery. For coverage validity tailored to Fehring's model, each NOC and NOC indicator from specialists was asked to score between 1-5. Score for the significance of indicators was from 1=no precaution to 5=very important. After the expert opinion, these weighted scores obtained for each NOC and NOC indicator were classified as 0.8 critical, 0.8 > 0.5 complements, > 0.5 are excluded. In the NANDA-I / NOC / NIC system (guideline), 5 NOCs proposed for nursing diagnoses for UI were proposed. These outputs are; Urinary Continence, Urinary Elimination, Tissue Integrity, Self CareToileting, Medication Response. After the scales are translated into Turkish, the weighted average of the scores obtained from specialists for the coverage of all 5 NOCs and the contribution of nursing initiatives exceeded 0.8. After the opinions of the experts, 79 of the 82 indicators were calculated as critical, 3 of the indicators were calculated as supplemental. Because of 0.5 > was not obtained, no substance was removed. All NOC outputs were identified as valid and usable scales in Turkey. In this study, five NOC outcomes were verified for the evaluation of the output of individuals who have received nursing knowledge of UI and variant types. Nurses in Turkey can benefit from the outputs of the NOC scale to perform the care of the elderly incontinence.

Keywords: nursing outcomes, content validity, nursing diagnosis, urinary incontinence

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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Authors: Shiva Ebrahimian Dehaghani, Afsaneh Doosti, Morteza Zare

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Background: There is no consensus regarding the association between dysphagia and cognition. Purpose: The aim of this study was to quantitatively and qualitatively analyze the available evidence on the direction and strength of association between dysphagia and cognition. Methodology: PubMed, Scopus, Embase and Web of Science were searched about the association between dysphagia and cognition. A random-effects model was used to determine weighted odds ratios (OR) and 95% confidence intervals (CI). Sensitivity analysis was performed to determine the impact of each individual study on the pooled results. Results: A total of 1427 participants showed that some cognitive disorders were significantly associated with dysphagia (OR = 3.23; 95% CI, 2.33–4.48). Conclusion: The association between cognition and swallowing disorders suggests that multiple neuroanatomical systems are involved in these two functions.

Keywords: adult, association, cognitive impairment, dysphagia, systematic review

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Shuhua Lai, Kairui Chen

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In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.

Keywords: coarsening, mesh clustering, shape approximation, mesh simplification

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Christoph Opperer

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Space syntax is a theory and method for analyzing the spatial layout of buildings and urban environments to understand how they can influence patterns of human movement, social interaction, and behavior. While direct visibility is a key factor in space syntax research, important visual information such as light, color, texture, etc., are typically not considered, even though psychological studies have shown a strong correlation to the human perceptual experience within physical space – with light and color, for example, playing a crucial role in shaping the perception of spaciousness. Furthermore, these surface properties are often the visual features that are most salient and responsible for drawing attention to certain elements within the environment. This paper explores the potential of integrating these factors into general space syntax methods and visibility-based analysis of space, particularly for architectural spatial layouts. To this end, we use a combination of geometric (isovist) and topological (visibility graph) approaches together with image-based methods, allowing a comprehensive exploration of the relationship between spatial geometry, visual aesthetics, and human experience. Custom-coded ray-tracing techniques are employed to generate spherical panorama images, encoding three-dimensional spatial data in the form of two-dimensional images. These images are then processed through computer vision algorithms to generate saliency-maps, which serve as a visual representation of areas most likely to attract human attention based on their visual properties. The maps are subsequently used to weight the vertices of isovists and the visibility graph, placing greater emphasis on areas with high saliency. Compared to traditional methods, our weighted visibility analysis introduces an additional layer of information density by assigning different weights or importance levels to various aspects within the field of view. This extends general space syntax measures to provide a more nuanced understanding of visibility patterns that better reflect the dynamics of human attention and perception. Furthermore, by drawing parallels to traditional isovist and VGA analysis, our weighted approach emphasizes a crucial distinction, which has been pointed out by Ervin and Steinitz: the difference between what is possible to see and what is likely to be seen. Therefore, this paper emphasizes the importance of including surface properties in visibility-based analysis to gain deeper insights into how people interact with their surroundings and to establish a stronger connection with human attention and perception.

Keywords: space syntax, visibility analysis, isovist, visibility graph, visual features, human perception, saliency detection, raytracing, spherical images

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