Search results for: Models of Physics.

Authors: Costin Pribeanu

Abstract:

The model-based approach to user interface design relies on developing separate models capturing various aspects about users, tasks, application domain, presentation and dialog structures. This paper presents a task modeling approach for user interface design and aims at exploring mappings between task, domain and presentation models. The basic idea of our approach is to identify typical configurations in task and domain models and to investigate how they relate each other. A special emphasis is put on applicationspecific functions and mappings between domain objects and operational task structures. In this respect, we will address two layers in task decomposition: a functional (planning) layer and an operational layer.

Keywords: task modeling, user interface design, unit tasks, basic tasks, operational task model.

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

Abstract:

Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: Covariation reasoning, exponential function, modeling, representations.

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Authors: Eugene Kindler

Abstract:

The present paper is oriented to classification and application of agent technique in simulation of anticipatory systems, namely those that use simulation models for the aid of anticipation. The main ideas root in the fact that the best way for description of computer simulation models is the technique of describing the simulated system itself (and the translation into the computer code is provided as automatic), and that the anticipation itself is often nested.

Keywords: Agents, Anticipatory systems, Discrete eventsimulation, Simula, Taxonomy.

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Authors: Sadeep Sasidharan, T. B. Isha

Abstract:

Modern day electric vehicles require compact high torque/power density motors for electric propulsion. This necessitates proper thermal management of the electric motors. The main focus of this paper is to compare the steady state thermal analysis of a conventional 20 kW 8/6 Switched Reluctance Motor (SRM) with that of an Induction Motor and Inset Permanent Magnet (IPM) motor of the same rating. The goal is to develop a proper thermal model of the three types of models for Finite Element Thermal Analysis. JMAG software is used for the development and simulation of the thermal models. The results show that the induction motor is subjected to more heating when used for electric vehicle application constantly, compared to the SRM and IPM.

Keywords: SRM, induction motor, IPM, thermal analysis, loss models, electric vehicles.

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Authors: Alan S. Hoback

Abstract:

Most people see human faces in car front and back ends because of the process of pareidolia. 96 people were surveyed to see how many of them saw a face in the vehicle styling. Participants were aged 18 to 72 years. 94% of the participants saw faces in the front-end design of production models. All participants that recognized faces indicated that most styles showed some degree of an angry expression. It was found that women were more likely to see faces in inanimate objects. However, with respect to whether women were more likely to perceive anger in the vehicle design, the results need further clarification. Survey responses were correlated to the design features of vehicles to determine what cues the respondents were likely looking at when responding. Whether the features looked anthropomorphic was key to anger perception. Features such as the headlights which could represent eyes and the air intake that could represent a mouth had high correlations to trends in scores. Results are compared among models, makers, by groupings of body styles classifications for the top 12 brands sold in the US, and by year for the top 20 models sold in the US in 2016. All of the top models sold increased in perception of an angry expression over the last 20 years or since the model was introduced, but the relative change varied by body style grouping.

Keywords: Aggressive driving, face recognition, road rage, vehicle styling.

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Authors: Jin Zhang, Wing Lon Ng

Abstract:

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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Authors: Ioannis P. Panapakidis, Marios N. Moschakis

Abstract:

The Greek Energy Market is structured as a mandatory pool where the producers make their bid offers in day-ahead basis. The System Operator solves an optimization routine aiming at the minimization of the cost of produced electricity. The solution of the optimization problem leads to the calculation of the System Marginal Price (SMP). Accurate forecasts of the SMP can lead to increased profits and more efficient portfolio management from the producer`s perspective. Aim of this study is to provide a comparative analysis of various machine learning models such as artificial neural networks and neuro-fuzzy models for the prediction of the SMP of the Greek market. Machine learning algorithms are favored in predictions problems since they can capture and simulate the volatilities of complex time series.

Keywords: Deregulated energy market, forecasting, machine learning, system marginal price, energy efficiency and quality.

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Authors: Zhihan Li

Abstract:

Nowadays, most universities use the course enrollment system considering students’ registration orders. However, the students’ preference level to certain courses is also one important factor to consider. In this research, the possibility of applying a preference-first system has been discussed and analyzed compared to the order-first system. A bipartite graph is applied to resemble the relationship between students and courses they tend to register. With the graph set up, we apply Ford-Fulkerson (F.F.) Algorithm to maximize parings between two sets of nodes, in our case, students and courses. Two models are proposed in this paper: the one considered students’ order first, and the one considered students’ preference first. By comparing and contrasting the two models, we highlight the usability of models which potentially leads to better designs for school course registration systems.

Keywords: Bipartite graph, Ford-Fulkerson Algorithm, graph theory, maximum matching.

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Authors: Mohammed H. Mohammed, Mats Emborg, Roland Pusch, Sven Knutsson

Abstract:

Concrete performance is strongly affected by the particle packing degree since it determines the distribution of the cementitious component and the interaction of mineral particles. By using packing theory designers will be able to select optimal aggregate materials for preparing concrete with low cement content, which is beneficial from the point of cost. Optimum particle packing implies minimizing porosity and thereby reducing the amount of cement paste needed to fill the voids between the aggregate particles, taking also the rheology of the concrete into consideration. For reaching good fluidity superplasticizers are required. The results from pilot tests at Luleå University of Technology (LTU) show various forms of the proposed theoretical models, and the empirical approach taken in the study seems to provide a safer basis for developing new, improved packing models.

Keywords: Aggregate mix, Computer program, Concrete mix design, Models of packing.

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Authors: V. B. Bastos, M. P. Lima, P. R. G. Kurka

Abstract:

This paper applies to the creation of virtual 3D environments for the study and development of mobile robot image based navigation algorithms and techniques, which need to operate robustly and efficiently. The test of these algorithms can be performed in a physical way, from conducting experiments on a prototype, or by numerical simulations. Current simulation platforms for robotic applications do not have flexible and updated models for image rendering, being unable to reproduce complex light effects and materials. Thus, it is necessary to create a test platform that integrates sophisticated simulated applications of real environments for navigation, with data and image processing. This work proposes the development of a high-level platform for building 3D model’s environments and the test of image-based navigation algorithms for mobile robots. Techniques were used for applying texture and lighting effects in order to accurately represent the generation of rendered images regarding the real world version. The application will integrate image processing scripts, trajectory control, dynamic modeling and simulation techniques for physics representation and picture rendering with the open source 3D creation suite - Blender.

Keywords: Simulation, visual navigation, mobile robot, data visualization.

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Authors: Philip Symonds, Jon Taylor, Zaid Chalabi, Michael Davies

Abstract:

Average temperatures worldwide are expected to continue to rise. At the same time, major cities in developing countries are becoming increasingly populated and polluted. Governments are tasked with the problem of overheating and air quality in residential buildings. This paper presents the development of a model, which is able to estimate the occupant exposure to extreme temperatures and high air pollution within domestic buildings. Building physics simulations were performed using the EnergyPlus building physics software. An accurate metamodel is then formed by randomly sampling building input parameters and training on the outputs of EnergyPlus simulations. Metamodels are used to vastly reduce the amount of computation time required when performing optimisation and sensitivity analyses. Neural Networks (NNs) have been compared to a Radial Basis Function (RBF) algorithm when forming a metamodel. These techniques were implemented using the PyBrain and scikit-learn python libraries, respectively. NNs are shown to perform around 15% better than RBFs when estimating overheating and air pollution metrics modelled by EnergyPlus.

Keywords: Neural Networks, Radial Basis Functions, Metamodelling, Python machine learning libraries.

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Authors: Vu Ngoc Pi

Abstract:

In this paper, a study on the applications of the optimization and regression techniques for optimal calculation of partial ratios of helical gearboxes with second-step double gear-sets for minimal cross section dimension is introduced. From the condition of the moment equilibrium of a mechanic system including three gear units and their regular resistance condition, models for calculation of the partial ratios of helical gearboxes with second-step double gear-sets were given. Especially, by regression analysis, explicit models for calculation of the partial ratios are introduced. These models allow determining the partial ratios accurately and simply.

Keywords: Gearbox design, optimal design, helical gearbox, transmission ratio.

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Authors: Baeza S. Roberto

Abstract:

The knitted fabric suffers a deformation in its dimensions due to stretching and tension factors, transverse and longitudinal respectively, during the process in rectilinear knitting machines so it performs a dry relaxation shrinkage procedure and thermal action of prefixed to obtain stable conditions in the knitting. This paper presents a dry relaxation shrinkage prediction of Bordeaux fiber using a feed forward neural network and linear regression models. Six operational alternatives of shrinkage were predicted. A comparison of the results was performed finding neural network models with higher levels of explanation of the variability and prediction. The presence of different reposes is included. The models were obtained through a neural toolbox of Matlab and Minitab software with real data in a knitting company of Southern Guanajuato. The results allow predicting dry relaxation shrinkage of each alternative operation.

Keywords: Neural network, dry relaxation, knitting, linear regression.

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Authors: G. R. Boroun, R. Harami

Abstract:

Using form factors of the proton and the neutron for different of Q2, bag radius of the proton and the neutron can be obtained based on bag models. Then using static bag radius, magnetic moments of the proton and the neutron can be obtained and compared with other results.

Keywords: MIT bag model, proton and neutron, magnetic moment.

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Authors: Avellino I. Mondlane, Karin Hansson, Oliver Popov

Abstract:

This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes based on these three main distributions.

Keywords: Catastrophes, extreme event, disasters, mathematical models, simulation.

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Authors: Mohamed S. Sasi, Adel M. Mlitan, Abdulfattah M. Alkherraz

Abstract:

This research project aims to investigate difference in relative rates concerning phosphoryl transfer relevant to biological catalysis of DNA and RNA in the pH-independent reactions. Activated Models of DNA and RNA for alkyl-aryl phosphate diesters (with 4-nitrophenyl as a good leaving group) have successfully been prepared to gather kinetic parameters. Eyring plots for the pH– independent hydrolysis of 1 and 2 were established at different temperatures in the range 100–160 °C. These measurements have been used to provide a better estimate for the difference in relative rates between the reactivity of DNA and RNA cleavage. Eyring plot gave an extrapolated rate of kH2O = 1 × 10-10 s -1 for 1 (RNA model) and 2 (DNA model) at 25°C. Comparing the reactivity of RNA model and DNA model shows that the difference in relative rates in the pH-independent reactions is surprisingly very similar at 25°. This allows us to obtain chemical insights into how biological catalysts such as enzymes may have evolved to perform their current functions.

Keywords: DNA & RNA Models, Relative Rates, Reactivity.

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Authors: Khine Phyu, Aung Myint Aye

Abstract:

This paper presents results of measurements campaign carried out at a carrier frequency of 24GHz with the help of TPLINK router in indoor line-of-sight (LOS) scenarios. Firstly, the radio wave propagation strategies are analyzed in some rooms with router of point to point Ad hoc network. Then floor attenuation is defined for 3 floors in experimental region. The free space model and dual slope models are modified by considering the influence of corridor conditions on each floor. Using these models, indoor signal attenuation can be estimated in modeling of indoor radio wave propagation. These results and modified models can also be used in planning the networks of future personal communications services.

Keywords: radio wave signal analyzing, LOS radio wavepropagation, indoor radio wave propagation, free space model, tworay model and indoor attenuation.

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Authors: Abhishek Soni, A. Kumaraswamy, M. S. Mahesh

Abstract:

Bullet penetration in steel plate is investigated with the help of three-dimensional, non-linear, transient, dynamic, finite elements analysis using explicit time integration code LSDYNA. The effect of large strain, strain-rate and temperature at very high velocity regime was studied from number of simulations of semi-spherical nose shape bullet penetration through single layered circular plate with 2 mm thickness at impact velocities of 500, 1000, and 1500 m/s with the help of Johnson Cook material model. Mie-Gruneisen equation of state is used in conjunction with Johnson Cook material model to determine pressure-volume relationship at various points of interests. Two material models viz. Plastic-Kinematic and Johnson- Cook resulted in different deformation patterns in steel plate. It is observed from the simulation results that the velocity drop and loss of kinetic energy occurred very quickly up to perforation of plate, after that the change in velocity and changes in kinetic energy are negligibly small. The physics behind this kind of behaviour is presented in the paper.

Keywords: AISI 4340 steel, ballistic impact simulation, bullet penetration, non-linear FEM.

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Authors: Costin Pribeanu

Abstract:

The model-based approach to user interface design relies on developing separate models that are capturing various aspects about users, tasks, application domain, presentation and dialog representations. This paper presents a task modeling approach for user interface design and aims at exploring the mappings between task, domain and presentation models. The basic idea of our approach is to identify typical configurations in task and domain models and to investigate how they relate each other. A special emphasis is put on application-specific functions and mappings between domain objects and operational task structures. In this respect, we will distinguish between three layers in the task decomposition: a functional layer, a planning layer, and an operational layer.

Keywords: task modeling, user interface design, unit tasks, basic tasks, operational task model

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Authors: M. A. S. Fahim, J. Sužiedelytė Visockienė

Abstract:

With the growing concern over air pollution (AP), it is clear that this has gained more prominence than ever before. The level of consciousness has increased and a sense of knowledge now has to be forwarded as a duty by those enlightened enough to disseminate it to others. This realization often comes after an understanding of how poor air quality indices (AQI) damage human health. The study focuses on assessing air pollution prediction models specifically for Lithuania, addressing a substantial need for empirical research within the region. Concentrating on Vilnius, it specifically examines particulate matter concentrations 10 micrometers or less in diameter (PM10). Utilizing Gaussian Process Regression (GPR) and Regression Tree Ensemble, and Regression Tree methodologies, predictive forecasting models are validated and tested using hourly data from January 2020 to December 2022. The study explores the classification of AP data into anthropogenic and natural sources, the impact of AP on human health, and its connection to cardiovascular diseases. The study revealed varying levels of accuracy among the models, with GPR achieving the highest accuracy, indicated by an RMSE of 4.14 in validation and 3.89 in testing.

Keywords: Air pollution, anthropogenic and natural sources, machine learning, Gaussian process regression, tree ensemble, forecasting models, particulate matter.

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Authors: M. O. Oke, T. S. Workneh

Abstract:

Drying behavior of blanched sweet potato in a cabinet dryer using different five air temperatures (40-80°C) and ten sweet potato varieties sliced to 5mm thickness were investigated. The drying data were fitted to eight models. The Modified Henderson and Pabis model gave the best fit to the experimental moisture ratio data obtained during the drying of all the varieties while Newton (Lewis) and Wang and Singh models gave the least fit. The values of Deff obtained for Bophelo variety (1.27 x 10-9 to 1.77 x 10-9 m2/s) was the least while that of S191 (1.93 x 10-9 to 2.47 x 10-9 m2/s) was the highest which indicates that moisture diffusivity in sweet potato is affected by the genetic factor. Activation energy values ranged from 0.27-6.54 kJ/mol. The lower activation energy indicates that drying of sweet potato slices requires less energy and is hence a cost and energy saving method. The drying behavior of blanched sweet potato was investigated in a cabinet dryer. Drying time decreased considerably with increase in hot air temperature. Out of the eight models fitted, the Modified Henderson and Pabis model gave the best fit to the experimental moisture ratio data on all the varieties while Newton, Wang and Singh models gave the least. The lower activation energy (0.27 - 6.54 kJ/mol) obtained indicates that drying of sweet potato slices requires less energy and is hence a cost and energy saving method.

Keywords: Sweet Potato Slice, Drying Models, Moisture Ratio, Moisture Diffusivity, Activation Energy.

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Authors: Konstantinos Perifanos, Eirini Florou, Dionysis Goutsos

Abstract:

This paper presents and benchmarks a number of end-to-end Deep Learning based models for metaphor detection in Greek. We combine Convolutional Neural Networks and Recurrent Neural Networks with representation learning to bear on the metaphor detection problem for the Greek language. The models presented achieve exceptional accuracy scores, significantly improving the previous state-of-the-art results, which had already achieved accuracy 0.82. Furthermore, no special preprocessing, feature engineering or linguistic knowledge is used in this work. The methods presented achieve accuracy of 0.92 and F-score 0.92 with Convolutional Neural Networks (CNNs) and bidirectional Long Short Term Memory networks (LSTMs). Comparable results of 0.91 accuracy and 0.91 F-score are also achieved with bidirectional Gated Recurrent Units (GRUs) and Convolutional Recurrent Neural Nets (CRNNs). The models are trained and evaluated only on the basis of training tuples, the related sentences and their labels. The outcome is a state-of-the-art collection of metaphor detection models, trained on limited labelled resources, which can be extended to other languages and similar tasks.

Keywords: Metaphor detection, deep learning, representation learning, embeddings.

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Authors: Iliana Marinova, Valentin Mateev

Abstract:

For investigations of electromagnetic field distributions in biological structures by Finite Element Method (FEM), a method for automatic 3D model building of human anatomical objects is developed. Models are made by meshed structures and specific electromagnetic material properties for each tissue type. Mesh is built according to specific FEM criteria for achieving good solution accuracy. Several FEM models of anatomical objects are built. Formulation using magnetic vector potential and scalar electric potential (A-V, A) is used for modeling of electromagnetic fields in human tissue objects. The developed models are suitable for investigations of electromagnetic field distributions in human tissues exposed in external fields during magnetic stimulation, defibrillation, impedance tomography etc.

Keywords: electromagnetic field, finite element method, humantissue.

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Authors: Valerio D’Andrea

Abstract:

The GERmanium Detector Array (GERDA) experiment, located at the Laboratori Nazionali del Gran Sasso (LNGS) of INFN, searches for 0νββ of 76Ge. Germanium diodes enriched to ∼ 86 % in the double beta emitter 76Ge(enrGe) are exposed being both source and detectors of 0νββ decay. Neutrinoless double beta decay is considered a powerful probe to address still open issues in the neutrino sector of the (beyond) Standard Model of particle Physics. Since 2013, just after the completion of the first part of its experimental program (Phase I), the GERDA setup has been upgraded to perform its next step in the 0νββ searches (Phase II). Phase II aims to reach a sensitivity to the 0νββ decay half-life larger than 1026 yr in about 3 years of physics data taking. This exposing a detector mass of about 35 kg of enrGe and with a background index of about 10^−3 cts/(keV·kg·yr). One of the main new implementations is the liquid argon scintillation light read-out, to veto those events that only partially deposit their energy both in Ge and in the surrounding LAr. In this paper, the GERDA Phase II expected goals, the upgrade work and few selected features from the 2015 commissioning and 2016 calibration runs will be presented. The main Phase I achievements will be also reviewed.

Keywords: Gerda, double beta decay, germanium, LNGS.

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Authors: A. Rouili

Abstract:

In the present paper the results of a numerical study are presented, numerical models were developed to simulate the behaviour of vertical massive dikes. The proposed models were developed according to the geometry, boundary conditions, loading conditions and initial conditions of a physical model taken as reference. The results obtained were compared to the experimental data. As far as the overall behaviour, the displacements and the failure mechanisms of the dikes is concerned, the numerical results were in good agreement with the experimental results, which clearly indicates a good quality of numerical modelling. The validated numerical models were used in a parametric study were the displacements and failure mechanisms were fully investigated. Out of the results obtained, some conclusions and recommendations related to the design of massive dikes are proposed.

Keywords: Water conservation, dikes, risk assessment and numerical modelling.

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Authors: Donglan Zha, Jiansong Si

Abstract:

Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: Bias of technical change, CES production function, elasticity of substitution, energy input.

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Authors: Amir Hadi Ziaie

Abstract:

In the present work, we revisit the collapse process of a spherically symmetric homogeneous scalar field (in FRW background) minimally coupled to gravity, when the phase-space deformations are taken into account. Such a deformation is mathematically introduced as a particular type of noncommutativity between the canonical momenta of the scale factor and of the scalar field. In the absence of such deformation, the collapse culminates in a spacetime singularity. However, when the phase-space is deformed, we find that the singularity is removed by a non-singular bounce, beyond which the collapsing cloud re-expands to infinity. More precisely, for negative values of the deformation parameter, we identify the appearance of a negative pressure, which decelerates the collapse to finally avoid the singularity formation. While in the un-deformed case, the horizon curve monotonically decreases to finally cover the singularity, in the deformed case the horizon has a minimum value that this value depends on deformation parameter and initial configuration of the collapse. Such a setting predicts a threshold mass for black hole formation in stellar collapse and manifests the role of non-commutative geometry in physics and especially in stellar collapse and supernova explosion.

Keywords: Gravitational collapse, non-commutative geometry, spacetime singularity, black hole physics.

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Authors: Mingren Shi, Michael Renton

Abstract:

There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.

Keywords: mortality estimation, probit models, logistic model, generalized inverse matrix approach, pest control simulation

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Authors: Hossein Zeinivand, Florimond De Smedt

Abstract:

Snow cover is an important phenomenon in hydrology, hence modeling the snow accumulation and melting is an important issue in places where snowmelt significantly contributes to runoff and has significant effect on water balance. The physics-based models are invariably distributed, with the basin disaggregated into zones or grid cells. Satellites images provide valuable data to verify the accuracy of spatially distributed model outputs. In this study a spatially distributed physically based model (WetSpa) was applied to predict snow cover and melting in the Latyan dam watershed in Iran. Snowmelt is simulated based on an energy balance approach. The model is applied and calibrated with one year of observed daily precipitation, air temperature, windspeed, and daily potential evaporation. The predicted snow-covered area is compared with remotely sensed images (MODIS). The results show that simulated snow cover area SCA has a good agreement with satellite image snow cover area SCA from MODIS images. The model performance is also tested by statistical and graphical comparison of simulated and measured discharges entering the Latyan dam reservoir.

Keywords: Physical based model, Satellite image, Snow covers.

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Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, L-stable methods, pricing European options, Jump–diffusion model.

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