Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. In this paper, we analyze Taylor model based integration of ODEs and compare Taylor model with traditional enclosure methods for IVPs for ODEs. More advanced Taylor model integration methods are discussed in the algorithm (1). For clarity, we summarize the major steps of the naive Taylor model method as algorithm 1.
Obtaining the computational models for the functioning of the brain gives us a chance to understand the brain functionality thoroughly. This would help the development of better treatments for neurological illnesses and disorders. We created a cortical model using Python language using the Brian simulator. The Brian simulator is specialized in simulating the neuronal connections and synaptic interconnections. The dynamic connection model has multiple parameters in order to ensure an accurate simulation (Bowman, 2016). We concentrated on the connection weights and studied their effect on the interactivity and connectivity of the cortical neurons in the same cortical layer and across multiple layers. As synchronization helps us to mea
... Show MoreAcquisition provisions in Islamic jurisprudence
The construction of embankment for roadway interchange system at urban area is restricted due to the large geometry requirements, since the value of land required for such construction is high, and the area available is limited as compared to rural area. One of the optimum solutions to such problem is the earth reinforcement technique which requires a limited area for embankment construction. Gypseous soil from Al-Anbar governorate area was obtained and subjected to various physical and chemical analysis to determine it is properties. A laboratory model box of 50x50x25 cm was used as a representative embankment; soil has been compacted in five layers at maximum dry density (modified compaction) and an aluminum reinforcement strips we
... Show MoreThis work represents development and implementation a programmable model for evaluating pumping technique and spectroscopic properties of solid state laser, as well as designing and constructing a suitable software program to simulate this techniques . A study of a new approach for Diode Pumped Solid State Laser systems (DPSSL), to build the optimum path technology and to manufacture a new solid state laser gain medium. From this model the threshold input power, output power optimum transmission, slop efficiency and available power were predicted. different systems configuration of diode pumped solid state laser for side pumping, end pump method using different shape type (rod,slab,disk) three main parameters are (energy transfer efficie
... Show MoreAs the bit rate of fiber optic transmission systems is increased to more than , the system will suffer from an important random phenomena, which is called polarization mode dispersion. This phenomenon contributes effectively to: increasing pulse width, power decreasing, time jittering, and shape distortion. The time jittering means that the pulse center will shift to left or right. So that, time jittering leads to interference between neighboring pulses. On the other hand, increasing bit period will prevent the possibility of sending high rates. In this paper, an accurate mathematical analysis to increase the rates of transmission, which contain all physical random variables that contribute to determine the transmission rates, is presen
... Show MoreWastewater projects are one of the most important infrastructure projects, which require developing strategic plans to manage these projects. Most of the wastewater projects in Iraq don’t have a maintenance plan. This research aims to prepare the maintenance management plan (MMP) for wastewater projects. The objective of the research is to predict the cost and time of maintenance projects by building a model using ANN. The research sample included (15) completed projects in Wasit Governorate, where the researcher was able to obtain the data of these projects through the historical information of the Wasit Sewage Directorate. In this research artificial neural networks (ANN) technique was used to build two models (cost
... Show MoreThe convolutional neural networks (CNN) are among the most utilized neural networks in various applications, including deep learning. In recent years, the continuing extension of CNN into increasingly complicated domains has made its training process more difficult. Thus, researchers adopted optimized hybrid algorithms to address this problem. In this work, a novel chaotic black hole algorithm-based approach was created for the training of CNN to optimize its performance via avoidance of entrapment in the local minima. The logistic chaotic map was used to initialize the population instead of using the uniform distribution. The proposed training algorithm was developed based on a specific benchmark problem for optical character recog
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In this research we discussed the parameter estimation and variable selection in Tobit quantile regression model in present of multicollinearity problem. We used elastic net technique as an important technique for dealing with both multicollinearity and variable selection. Depending on the data we proposed Bayesian Tobit hierarchical model with four level prior distributions . We assumed both tuning parameter are random variable and estimated them with the other unknown parameter in the model .Simulation study was used for explain the efficiency of the proposed method and then we compared our approach with (Alhamzwi 2014 & standard QR) .The result illustrated that our approach
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