Search results for: Central limit theorem

Authors: D. Del Corso, A. Tartaglia, E. Tresso, M. Cambiolo, L. Forno, G. Morrone

Abstract:

A key requirement for e-learning materials is reusability and interoperability, that is the possibility to use at least part of the contents in different courses, and to deliver them trough different platforms. These features make possible to limit the cost of new packages, but require the development of material according to proper specifications. SCORM (Sharable Content Object Reference Model) is a set of guidelines suitable for this purpose. A specific adaptation project has been started to make possible to reuse existing materials. The paper describes the main characteristics of SCORM specification, and the procedure used to modify the existing material.

Keywords: SCORM, e-learning, standard, educational effectiveness, assessment, methodology, open access.

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Authors: A. Zemirline, M. Ouali, A. Mahieddine

Abstract:

The FOSDT (the First Order Shear Deformation Theory) is taking into consideration to study the static behavior of a bimorph beam, with a delamination zone between the upper and the lower layer. The effect of limit conditions and lengths of the delamination zone are presented in this paper, with a PVDF piezoelectric material application. A FEM “Finite Element Method” is used to discretize the beam. In the axial displacement, a displacement field appears in the debonded zone with inverse effect between the upper and the lower layer was observed.

Keywords: Beam, Delamination, Piezoelectricity, Static.

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Authors: Yue Sun, Yuan Wang

Abstract:

The Grand Canal of China has been in use for more than two thousand years. It runs through the central and eastern regions of China and communicates with the five major river systems of Haihe River, Yellow River, Huaihe River, Yangtze River and Qiantang River from north to south. It is a complex, systematic and comprehensive water conservancy project in the period of agricultural civilization and includes the three parts of the Beijing-Hangzhou Canal, the Sui and Tang Dynasties Canal and the Eastern Zhejiang Canal. It covers eight provinces and cities including Beijing, Tianjin, Hebei, Shandong, Jiangsu, Zhejiang, Henan and Anhui. The Grand Canal is an important channel connecting the Central Plains and the Beijing-Hangzhou Canal, and it is also an important waterway trade channel. Nowadays, although the Grand Canal no longer bears the burden of communicating water transportation between the north and the south, the site of the Grand Canal is still a “historical museum” of the lifestyle of people who lived on the canal from the Ming and Qing Dynasties to the Republic of China. By means of literature reading and field investigation, this paper compares the different protection strategies of the Grand Canal in the region between the ancient villages of Huaxian and Xunxian, which witness the vicissitudes of canal water transport, to explore whether the protective renovation of historical and cultural routes is “protection” or “destruction”, and puts forward some protection suggestions.

Keywords: The Grand Canal, heritage conservation, cultural route, ancient villages, strategies.

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Authors: Yu-Sheng Lee, Qi An

Abstract:

Offset mismatch, gain mismatch, and time-skew error between time-interleaved channels limit the performance of time-interleaved analog-to-digital converters (TIADC). This paper focused on the time-skew error. A new technique for calibrating time-skew error in M-channels TIADC is described, and simulation results are also presented.

Keywords: Calibration, time-skew error, time-interleavedanalog-to-digital converters.

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Authors: Sami W. Tabsh

Abstract:

The strength of reinforced concrete depends on the member dimensions and material properties. The properties of concrete and steel materials are not constant but random variables. The variability of concrete strength is due to batching errors, variations in mixing, cement quality uncertainties, differences in the degree of compaction and disparity in curing. Similarly, the variability of steel strength is attributed to the manufacturing process, rolling conditions, characteristics of base material, uncertainties in chemical composition, and the microstructure-property relationships. To account for such uncertainties, codes of practice for reinforced concrete design impose resistance factors to ensure structural reliability over the useful life of the structure. In this investigation, the effects of reductions in concrete and reinforcing steel strengths from the nominal values, beyond those accounted for in the structural design codes, on the structural reliability are assessed. The considered limit states are flexure, shear and axial compression based on the ACI 318-11 structural concrete building code. Structural safety is measured in terms of a reliability index. Probabilistic resistance and load models are compiled from the available literature. The study showed that there is a wide variation in the reliability index for reinforced concrete members designed for flexure, shear or axial compression, especially when the live-to-dead load ratio is low. Furthermore, variations in concrete strength have minor effect on the reliability of beams in flexure, moderate effect on the reliability of beams in shear, and sever effect on the reliability of columns in axial compression. On the other hand, changes in steel yield strength have great effect on the reliability of beams in flexure, moderate effect on the reliability of beams in shear, and mild effect on the reliability of columns in axial compression. Based on the outcome, it can be concluded that the reliability of beams is sensitive to changes in the yield strength of the steel reinforcement, whereas the reliability of columns is sensitive to variations in the concrete strength. Since the embedded target reliability in structural design codes results in lower structural safety in beams than in columns, large reductions in material strengths compromise the structural safety of beams much more than they affect columns.

Keywords: Code, flexure, limit states, random variables, reinforced concrete, reliability, reliability index, shear, structural safety.

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Authors: Timothy E. Frank, Peter J. Amaddio, Elizabeth D. Decko, Alexis M. Tri, Darcy A. Farrell, Cole M. Landes

Abstract:

Ultra-high performance concrete (UHPC) is a class of cementitious composites with a relatively large percentage of cement generating high compressive strength. Additionally, UHPC contains disbursed fibers, which control crack width, carry the tensile load across narrow cracks, and limit spalling. These characteristics lend themselves to a wide range of structural applications when UHPC members are reinforced with longitudinal steel. Efficient use of fibers and longitudinal steel is required to keep lifecycle cost competitive in reinforced UHPC members; this requires full utilization of both the compressive and tensile qualities of the reinforced cementitious composite. The objective of this study is to investigate the shear response of steel-reinforced UHPC beams to guide design decisions that keep initial costs reasonable, limit serviceability crack widths, and ensure a ductile structural response and failure path. Five small-scale, reinforced UHPC beams were experimentally tested. Longitudinal steel, transverse steel, and casting direction were varied. Results indicate that an increase in transverse steel in short-spanned reinforced UHPC beams provided additional shear capacity and increased the peak load achieved. Beams with very large longitudinal steel reinforcement ratios did not achieve yield and fully utilized the tension properties of the longitudinal steel. Casting the UHPC beams from the end or from the middle affected load-carrying capacity and ductility, but image analysis determined that the fiber orientation was not significantly different. It is believed that the presence of transverse and longitudinal steel reinforcement minimized the effect of different UHPC casting directions. Results support recent recommendations in the literature suggesting that a 1% fiber volume fraction is sufficient within UHPC to prevent spalling and provide compressive fracture toughness under extreme loading conditions.

Keywords: Fiber orientation, reinforced ultra-high performance concrete beams, shear, transverse steel.

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Authors: M.J. Sharifi

Abstract:

Several models have been introduced so far for single electron box, SEB, which all of them were restricted to DC response and or low temperature limit. In this paper we introduce a new time dependent, high temperature analytical model for SEB for the first time. DC behavior of the introduced model will be verified against SIMON software and its time behavior will be verified against a newly published paper regarding step response of SEB.

Keywords: Single electron box, SPICE, SIMON, Timedependent, Circuit model.

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Authors: Gizem Intepe, Tufan Koc

Abstract:

S-Curves are commonly used in technology forecasting. They show the paths of product performance in relation to time or investment in R&D. It is a useful tool to describe the inflection points and the limit of improvement of a technology. Companies use this information to base their innovation strategies. However inadequate use and some limitations of this technique lead to problems in decision making. In this paper first technology forecasting and its importance for company level strategies will be discussed. Secondly the S-Curve and its place among other forecasting techniques will be introduced. Thirdly its use in technology forecasting will be discussed based on its advantages, disadvantages and limitations. Finally an application of S-curve on 3D TV technology using patent data will also be presented and the results will be discussed.

Keywords: Patent analysis, Technological forecasting. S curves, 3D TV

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Authors: M. Paseková, L. Müllerová, J. Strouhal, L. Chyzhevska

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Increase in globalization of capital markets brings the higher requirements on financial information provided for investors who look for a highly comparable information. Paper deals with the advantages and limitations of applying International Financial Reporting Standards (IFRS) in the Czech Republic and Ukraine. As a greatest limit for full adoption of IFRS shall be acknowledged the strong connection of continental accounting to tax system and enormous high administrative burden for IFRS appliers.

Keywords: International Financial Reporting Standards (IFRS), Small and Medium-sized Enterprises (SMEs), Czech Republic, Ukraine.

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Authors: Pavel Psota, Vít Lédl, Jan Václavík, Roman Doleček, Pavel Mokrý, Petr Vojtíšek

Abstract:

This paper presents advanced time average digital holography by means of frequency shift and phase modulation. This technique can measure amplitudes of vibrations at ultimate dynamic range while the amplitude distribution evaluation is done independently in every pixel. The main focus of the paper is to gain insight into behavior of the method at low amplitudes of vibrations. In order to reach that, a set of experiments was performed. Results of the experiments together with novel noise suppression show the limit of the method to be below 0.1 nm.

Keywords: Acousto-optical modulator, digital holography, low amplitudes, vibrometry.

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Authors: Asuman Baldiran, Erdener Pehlivan

Abstract:

In this study, the root of the name Lykaonia and the geographical area defined as Lykaonia Region are mentioned. In this context, information concerning the settlements of Paleolithic Age, Neolithic Age and Chalcolithic Age are given place. Particularly the settlements belonging to Classical Age are localized and brief information about the history of these settlements is provided. In the light of this information, roads of Antique period in the region are evaluated.

Keywords: Ancient Cities, Central Anatolia, Historical Geography, Lykaonia Region.

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Authors: Amaraja Taur, Pankaj Doshi, Hak Koon Yeoh

Abstract:

The dripping modes for a Newtonian liquid of viscosity µ emanating from an inclined nozzle at flow rate Q is investigated experimentally. As the liquid flow rate Q increases, starting with period-1 with satellite drops, the system transitions to period-1 dripping without satellite, then to limit cycle before showing chaotic responses. Phase diagrams showing the changes in the transitions between the different dripping modes for different nozzle inclination angle q is constructed in the dimensionless (Q, µ) space.

Keywords: Dripping, inclined nozzle, phase diagram.

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Authors: R. Pääkkönen, L. Korpinen, F. Gobba

Abstract:

The objective of our study is to investigate UV exposure in Finland through sample measurements as a typical case study in summer and winter. We measured UV-BC weighted radiation and calculated a daily dose, which is about 100–150 times the Finnish exposure limit value in summer and 1–6 times in winter. The measured ultraviolet indices varied from 0 to 7 (scale 0–18), which is less than the values obtained in countries that are located farther south from Tampere latitude of 61 degrees. In wintertime, the UV exposure was modest compared to summertime, 50–150 mW/m² and about 1–5 mW/m² in summer and winter, respectively. However, technical means to manage UV exposure in Scandinavia are also needed in summer- and springtime.

Keywords: Ultraviolet radiation, measurement, winter, summer.

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Authors: N. Olarte L, A. Rubiano F, A. Mejía F.

Abstract:

This comparison of valuation techniques for bone age assessment is a work carried out by the Telemedicine Research Group of the Military University - TIGUM, as a preliminary to the Design and development a treatment system of hand and wrist radiological images for children aged 0-6 years to bone age assessment . In this paper the techniques mentioned for decades have been the most widely used and the statistically significant. Althought, initially with the current project, it wants to work with children who have limit age, this comparison and evaluation techniques work will help in the future to expand the study subject in the system to bone age assessment, implementing more techniques, tools and deeper analysis to accomplish this purpose.

Keywords: Atlas, Bone Age Assessment, Hand and Wrist Radiograph, Image Processing

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Authors: S. Forkapic, J. Nikolov, N. Todorovic, D. Mrdja, I. Bikit

Abstract:

Tritium activity concentration in Danube river water in Serbia has been determinate using a liquid scintillation counter Quantulus 1220. During December 2010, water samples were taken along the entire course of Danube through Serbia, from Hungarian- Serbian to Romanian-Serbian border. This investigation is very important because of the nearness of nuclear reactor Paks in Hungary. Sample preparation was performed by standard test method using Optiphase HiSafe 3 scintillation cocktail. We used a rapid method for the preparation of environmental samples, without electrolytic enrichment.

Keywords: detection limit, liquid scintillation counter, low-leveltritium analysis, monitoring.

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Authors: Driss Guerchi, Fatiha Djebbar

Abstract:

In this work we introduce an efficient method to limit the impact of the hiding process on the quality of the cover speech. Vector quantization of the speech spectral information reduces drastically the number of the secret speech parameters to be embedded in the cover signal. Compared to scalar hiding, vector quantization hiding technique provides a stego signal that is indistinguishable from the cover speech. The objective and subjective performance measures reveal that the current hiding technique attracts no suspicion about the presence of the secret message in the stego speech, while being able to recover an intelligible copy of the secret message at the receiver side.

Keywords: Speech steganography, LSF vector quantization, fast Fourier transform

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Authors: Md. Royhanur Islam, Thomas Cansse, Md. Sahidul Islam, Atiqur Rahman Sunny

Abstract:

The geographical location of Bangladesh makes it one of the most vulnerable countries to climate change. Climate-induced phenomena mainly affect the south-central region of Bangladesh (Laxmipur district) where they have begun to occur more frequently. The aim of the study was to identify the hydro-climatic factors that lead to weather-related disasters in the coastal areas and analyse the consequences of these factors on coastal livelihoods, with possible adaptation options using participatory rural appraisal (PRA) tools. The present study showed several disasters such as land erosion, depressions and cyclones, coastal flooding, storm surge, and precipitation. The frequency of these disasters is of a noticeable rate. Surveys have also discovered that land erosion is ongoing. Tidal water is being introduced directly into the mainland, and as a result of the salt intrusion, production capacity is declining. The coastal belt is an important area for fishing activities, but due to changed fishing times and a lack of Alternative Income Generating Activities (AIGAs), people have been forced to search for alternative livelihood options by taking both short-term and long-term adaptation options. Therefore, in order to increase awareness and minimize the losses, vulnerable communities must be fully incorporated into disaster response strategies. The government as well as national and international donor organizations should come forward and resolve the present situation of these vulnerable groups since otherwise, they will have to endure endless and miserable suffering due to the effects of climate change ahead in their lives.

Keywords: Adaptation, community, fishery development, livelihood.

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Authors: Burak Yildirim, Muhsin Tunay Gençoğlu

Abstract:

A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

Keywords: Eigenvalue analysis, microgrid, modal analysis, voltage stability.

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Authors: P. R. Prabhu, S. M. Kulkarni, S. S. Sharma, K. Jagannath, Achutha Kini U.

Abstract:

In the present study, response surface methodology has been used to optimize turn-assisted deep cold rolling process of AISI 4140 steel. A regression model is developed to predict surface hardness and surface roughness using response surface methodology and central composite design. In the development of predictive model, deep cold rolling force, ball diameter, initial roughness of the workpiece, and number of tool passes are considered as model variables. The rolling force and the ball diameter are the significant factors on the surface hardness and ball diameter and numbers of tool passes are found to be significant for surface roughness. The predicted surface hardness and surface roughness values and the subsequent verification experiments under the optimal operating conditions confirmed the validity of the predicted model. The absolute average error between the experimental and predicted values at the optimal combination of parameter settings for surface hardness and surface roughness is calculated as 0.16% and 1.58% respectively. Using the optimal processing parameters, the surface hardness is improved from 225 to 306 HV, which resulted in an increase in the near surface hardness by about 36% and the surface roughness is improved from 4.84µm to 0.252 µm, which resulted in decrease in the surface roughness by about 95%. The depth of compression is found to be more than 300µm from the microstructure analysis and this is in correlation with the results obtained from the microhardness measurements. Taylor hobson talysurf tester, micro vickers hardness tester, optical microscopy and X-ray diffractometer are used to characterize the modified surface layer. 

Keywords: Surface hardness, response surface methodology, microstructure, central composite design, deep cold rolling, surface roughness.

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Authors: Vladimir I. Ponomarenko, Mikhail D. Prokhorov, Anatoly S. Karavaev

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The interaction between respiration and low-frequency rhythms of the cardiovascular system is studied. The obtained results count in favor of the hypothesis that low-frequency rhythms in blood pressure and R-R intervals are generated in different central neural structures involved in the autonomic control of the cardiovascular systems.

Keywords: Cardiovascular system, R-R intervals, blood pressure, synchronization.

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Authors: J. Kala, J. Melcher, M. Škaloud, Z. Kala

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In the paper, the results of sensitivity analysis of the influence of initial imperfections on the web stress state of a thinwalled girder are presented. The results of the study corroborate a very good and effective agreement of experiments with theory. Most input random quantities were found experimentally. The change of sensitivity coefficients in dependence on working load value is analysed. The stress was analysed by means of a geometrically and materially non-linear solution by applying the program ANSYS. This research study offers important background for theoretical studies of stability problems, post-critical effects and limit states of thin-walled steel structures.

Keywords: Buckling, Fatigue, Imperfection, Steel, Sensitivity analysis.

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Authors: Tze Sian Pui, Tushar Bansal, Patthara Kongsuphol, Sunil K. Arya

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We present a label-free biosensor based on electrochemical impedance spectroscopy for the detection of proinflammatory cytokine Tumor Necrosis Factor (TNF-α). Secretion of TNF-α has been correlated to the onset of various diseases including rheumatoid arthritis, Crohn-s disease etc. Gold electrodes were patterned on a silicon substrate and self assembled monolayer of dithiobis-succinimidyl propionate was used to develop the biosensor which achieved a detection limit of ~57fM. A linear relationship was also observed between increasing TNF-α concentrations and chargetransfer resistance within a dynamic range of 1pg/ml – 1ng/ml.

Keywords: Tumor necrosis factor, electrochemical impedance spectroscopy, label free, self assembled monolayer

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Authors: Maitham Al-Safwani

Abstract:

Motor vibration issues were analyzed and correlated to poor equipment installation. We had a water injection pump tested in the factory and exceeded the pump vibration limit. Once the pump was brought to the site, its half-size shim plates were replaced with full-size shims plate that drastically reduced the vibration. In this study, vibration data were recorded for several and similar motors run at the same and different speeds. The vibration values were recorded — for two and a half hours — and the vibration readings analyzed to determine when the readings become consistent. This was as well supported by recording the audio noises produced by some machines seeking a relationship between changes in machine noises and machine abnormalities, such as vibration.

Keywords: Vibration, noise, shaft unbalance, shaft misalignment.

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Authors: Sadovska V.

Abstract:

The progress of concentrations of particular heavy metals was assessed in chosen localities in region Moravia, the Czech Republic, from 2007 to 2009. Particular metals were observed in localities with various types and characterization of zone. Pb, Ni, As and Cd were emphasized as a result of their toxicity and potential adverse health effect to the exposed population. The progress of metal concentrations and their health effects in the most polluted localities were examined. According to the results, the air pollution limit values were not exceeded. Based on the health risk assessment, the probability of developing tumorous diseases is acceptable, except for the increased probability of cancer risk from long-term exposure to As.

Keywords: Air pollution, heavy metals, health risk assessment, individual lifetime cancer risk

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Authors: Abdulraaof H. Alqaili, Hamad A. Alsoliman

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Through progress in pavement design developments, a pavement design method was developed, which is titled the Mechanistic Empirical Pavement Design Guide (MEPDG). Nowadays, the evolution in roads network and highways is observed in Saudi Arabia as a result of increasing in traffic volume. Therefore, the MEPDG currently is implemented for flexible pavement design by the Saudi Ministry of Transportation. Implementation of MEPDG for local pavement design requires the calibration of distress models under the local conditions (traffic, climate, and materials). This paper aims to prepare data for calibration of MEPDG in Central Saudi Arabia. Thus, the first goal is data collection for the design of flexible pavement from the local conditions of the Riyadh region. Since, the modifying of collected data to input data is needed; the main goal of this paper is the analysis of collected data. The data analysis in this paper includes processing each: Trucks Classification, Traffic Growth Factor, Annual Average Daily Truck Traffic (AADTT), Monthly Adjustment Factors (MAFi), Vehicle Class Distribution (VCD), Truck Hourly Distribution Factors, Axle Load Distribution Factors (ALDF), Number of axle types (single, tandem, and tridem) per truck class, cloud cover percent, and road sections selected for the local calibration. Detailed descriptions of input parameters are explained in this paper, which leads to providing of an approach for successful implementation of MEPDG. Local calibration of MEPDG to the conditions of Riyadh region can be performed based on the findings in this paper.

Keywords: Mechanistic-empirical pavement design guide, traffic characteristics, materials properties, climate, Riyadh.

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Authors: Mehrdad Ahmadi Kamarposhti, Mostafa Alinezhad

Abstract:

One of the major causes of voltage instability is the reactive power limit of the system. Improving the system's reactive power handling capacity via Flexible AC transmission System (FACTS) devices is a remedy for prevention of voltage instability and hence voltage collapse. In this paper, the effects of SVC and STATCOM in Static Voltage Stability Margin Enhancement will be studied. AC and DC representations of SVC and STATCOM are used in the continuation power flow process in static voltage stability study. The IEEE-14 bus system is simulated to test the increasing loadability. It is found that these controllers significantly increase the loadability margin of power systems.

Keywords: SVC, STATCOM, Voltage Collapse, Maximum Loading Point.

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Authors: Yilun Shang

Abstract:

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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Authors: Jefri Marzal, Hong Xie, Chun Che Fung

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Visibility problems are central to many computational geometry applications. One of the typical visibility problems is computing the view from a given point. In this paper, a linear time procedure is proposed to compute the visibility subsets from a corner of a rectangular prism in an orthogonal polyhedron. The proposed algorithm could be useful to solve classic 3D problems.

Keywords: Visibility, rectangular prism, orthogonal polyhedron.

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Authors: F.Katlane, M.S.Naceur, M.A.Loghmari

Abstract:

Automatic methods of detecting changes through satellite imaging are the object of growing interest, especially beca²use of numerous applications linked to analysis of the Earth’s surface or the environment (monitoring vegetation, updating maps, risk management, etc...). This work implemented spatial analysis techniques by using images with different spatial and spectral resolutions on different dates. The work was based on the principle of control charts in order to set the upper and lower limits beyond which a change would be noted. Later, the a contrario approach was used. This was done by testing different thresholds for which the difference calculated between two pixels was significant. Finally, labeled images were considered, giving a particularly low difference which meant that the number of “false changes” could be estimated according to a given limit.

Keywords: multi-scale, a contrario approach, significantthresholds, change detection.

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Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

Abstract:

Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: Diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion equation, trends functions, bi-parameters Weibull density function.

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