Objectives: Detection of vertical root fractures (VRFs) in their initial stages is a crucial issue, which prevents the propagation of injury to the adjacent supporting structures. Designing a suitable neural network-based model could be a useful method to diagnose the VRFs. The aim of this study was to design a probabilistic neural network (PNN) to diagnose the VRFs in intact and endodontically treated teeth of periapical and CBCT radiographs. Also, we have compared the efficacy of these two imaging techniques in the detection of VRFs. Methods: A total of 240 radiographs of teeth (120 radiographs of teeth with no VRFs and 120 teeth with vertical fractures, with half of the teeth in each category treated endodontically and the remaining half intact, i.e. not endodontically treated) were used in 3 groups for training and testing of the neural network as follows: Group 1, 180/60; Group 2, 120/120; and Group 3, 60/180. First, Daubechies 3 wavelet was applied to acquire the image analysis coefficients on two planes; then Gabor filters were used to extract the image characteristics, which were used to educate the PNN. The designed neural network was able to diagnose and classify teeth with and without VRFs. In addition, in order to determine the best training and test sets in the network, the variance of the function of network changes was manipulated at a range of 0-1 and the results were assessed in terms of the parameters evaluated, including sensitivity, specificity and accuracy. Results: In the periapical radiographs, the maximum accuracy, sensitivity and specificity values in the three groups were 70.00, 97.78 and 67.7%, respectively. These values in the CBCT images were 96.6, 93.3 and 100%, respectively, at the variance change range of 0.1-0.65. Conclusions: The designed neural network can be used as a proper model for the diagnosis of VRFs on CBCT images of endodontically treated and intact teeth; in this context, CBCT images are more effective than similar periapical radiographs. Limitations of this study are the use of sound one-rooted premolar teeth without carious lesions and dental fillings and not simulating the adjacent anatomic structures. Further in vitro work using a full-skull simulation for CBCT and skin/bone simulation is needed.

Abstract-In this paper, an analytical method for management of optimum group velocity dispersion (GVD) for compensation of chromatic dispersion in optical fibers is proposed. The proposed method mathematically is based on the Volterra series as alternative method for solution of the nonlinear Schrödinger equation (NLS). Based on analytical solution of the nonlinear equation in pulse propagation, we propose a differential equation including optimum GVD for complete dispersion compensation for given dispersion coefficient and fiber length. The obtained integro-differential equation is solved for special cases and it is shown that the obtained results are so better than traditional dispersion compensation cases. Also, the proposed technique can be applied to fiber design to introduce an especial GVD profile for dispersion less transmission.

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Abstract-In this paper, analytical relation for pulse width evolution and broadening in fiber systems using the Volterra series transfer function (VSTF) in linear and nonlinear cases are derived. This evaluation is done for traditional and optimum dispersion compensated fibers. Effects of group velocity dispersion (GVD) and self-phase modulation (SPM) are taken into account. It is shown that the analytical formulation can be applied to design and analysis the long hauls practical systems, and is helpful in understanding the pulse distortion caused by the interaction between SPM and GVD. The proposed relations are extracted analytically and for the first time pulse broadening factor in general case is derived.

In this paper we proposed a new structure of two-dimensional photonic crystals with rectangular lattice. After deducing the primitive lattice vectors and first Brillouin zone of the structures, we studied the band gap properties of horizontal and vertical rectangular lattice structures and compared them with conventional square lattice structure. The most excellent characteristic of these structures is their joint band gap regions, which make them suitable for designing polarization-independent devices. The other advantage of these structures is having band gaps at higher normalized frequencies.

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