DNMT3B (DNA (cytosine-5-)-methyltransferase 3 beta)

Review on DNMT3B (DNA (cytosine-5-)-methyltransferase 3 beta), with data on DNA, on the protein encoded, and where the gene is implicated

Wave polynomials, transmutations and Cauchy's problem for the Klein-Gordon equation

We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein-Gordon equation with a variable coefficient. Using the transmutation (transformation) operators and their recently discovered mapping properties we prove the completeness of the generalized wave polynomials and use them for an explicit construction of the solution of the Cauchy problem for the Klein-Gordon equation. Based on this result we develop a numerical method for solving the Cauchy problem and test its performance.Comment: 31 pages, 8 figures (16 graphs

Transmutations, L-bases and complete families of solutions of the stationary Schr\"odinger equation in the plane

An L-basis associated to a linear second-order ordinary differential operator L is an infinite sequence of functions {\phi_k}_{k=0}^{\infty} such that L\phi_k=0 for k=0,1, L\phi_k=k(k-1)\phi_{k-2}, for k=2,3,... and all \phi_k satisfy certain prescribed initial conditions. We study the transmutation operators related to L in terms of the transformation of powers of the independent variable {(x-x_{0})^k}_{k=0}^{\infty} to the elements of the L-basis and establish a precise form of the transmutation operator realizing this transformation. We use this transmutation operator to establish a completeness of an infinite system of solutions of the stationary Schr\"odinger equation from a certain class. The system of solutions is obtained as an application of the theory of bicomplex pseudoanalytic functions and its completeness was a long sought result. Its use for constructing reproducing kernels and solving boundary and eigenvalue problems has been considered even without the required completeness justification. The obtained result on the completeness opens the way for further development and application of the tools of pseudoanalytic function theory

A Moving Magnetic Trap Decelerator: a New Source for Cold Atoms and Molecules

We present an experimental realization of a moving magnetic trap decelerator, where paramagnetic particles entrained in a cold supersonic beam are decelerated in a co-moving magnetic trap. Our method allows for an efficient slowing of both paramagnetic atoms and molecules to near stopping velocities. We show that under realistic conditions we will be able to trap and decelerate a large fraction of the initial supersonic beam. We present our first results on deceleration in a moving magnetic trap by bringing metastable neon atoms to near rest. Our estimated phase space volume occupied by decelerated particles at final velocity of 50 m/s shows an improvement of two orders of magnitude as compared to currently available deceleration techniques

Transmutations for Darboux transformed operators with applications

We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schr\"odinger operator. Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schr\"odinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2. It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. Given a kernel K_1 of the transmutation operator T_1 we find the kernel K_2 of T_2 in a closed form in terms of K_1. As a corollary interesting commutation relations between T_1 and T_2 are obtained which then are used in order to construct the transmutation operator for the one-dimensional Dirac system with a scalar potential

Super-resolution image reconstruction using non-linear filtering techniques

Super-resolution (SR) reconstruction is a filtering technique that aims to combine a sequence of under-sampled and degraded low-resolution images to produce an image at a higher resolution. The reconstruction attempts to take advantage of the additional spatio-temporal data available in the sequence of images portraying the same scene. The fundamental problem addressed in super-resolution is a typical example of an inverse problem, wherein multiple low-resolution (LR) images are used to solve for the original high-resolution (HR) image. Super-resolution has already proved useful in many practical cases where multiple frames of the same scene can be obtained, including medical applications, satellite imaging and astronomical observatories. The application of super resolution filtering in consumer cameras and mobile devices shall be possible in the future, especially that the computational and memory resources in these devices are increasing all the time. For that goal, several research problems need to be investigated, i.e., precise modeling of the image capture process, fast filtering methods, accurate methods for motion estimation and optimal techniques for combining pixel values from the motion compensated images. In this thesis, we investigate a number of topics related to the performance problems mentioned above. We develop novel solutions to improve the image quality captured by the sensors of a camera phone. Particularly, we present a framework for producing a high-resolution color image directly from a sequence of images captured by a CMOS sensor that is overlaid with a color filter array. In the proposed framework, we introduce a super-resolution algorithm that interpolates the subsampled color components and reduces the optical blurring. The results confirm that it is possible to improve the overall image quality by using few consecutive shots of the same scene. Achieving accurate and fast registration of the input images is a critical step in super-resolution processing. Motivated by this basic requirement, we propose a novel recursive method for pixel-based motion estimation. We use recursive least mean square filtering (LMS) along different scanning directions to track the stationary shifts between a pair of LR images, which results in smooth estimates of the displacements at sub-pixel accuracy. The initial results indicate good performance, especially for tracking smooth global motion. One important advantage of the proposed method is that it can be easily integrated into super-resolution algorithms thanks to its relative low computational complexity. The overall performance of super-resolution is particularly degraded in the presence of motion outliers. Therefore, it is essential to develop methods to enhance the robustness of the fusion process. Towards this goal, we propose an integrated adaptive filtering method to reject the outlier image regions. The proposed approach consists in applying non-linear filtering techniques to improve the performance and robustness against motion outliers. In particular, we applied median filtering for robust fusion of the LR images, and we used generalized order statistic filters (OSF) for the enhancement of binary text images. Compared with conventional super-resolution algorithms, the proposed algorithms preserved well the fine details in the images, additionally, the result images exhibited less artifacts in the presence of registration errors. This confirms the advantage of using order statistic filtering in image super-resolution

Super-resolution image reconstruction using non-linear filtering techniques

Super-resolution (SR) reconstruction is a filtering technique that aims to combine a sequence of under-sampled and degraded low-resolution images to produce an image at a higher resolution. The reconstruction attempts to take advantage of the additional spatio-temporal data available in the sequence of images portraying the same scene. The fundamental problem addressed in super-resolution is a typical example of an inverse problem, wherein multiple low-resolution (LR) images are used to solve for the original high-resolution (HR) image. Super-resolution has already proved useful in many practical cases where multiple frames of the same scene can be obtained, including medical applications, satellite imaging and astronomical observatories. The application of super resolution filtering in consumer cameras and mobile devices shall be possible in the future, especially that the computational and memory resources in these devices are increasing all the time. For that goal, several research problems need to be investigated, i.e., precise modeling of the image capture process, fast filtering methods, accurate methods for motion estimation and optimal techniques for combining pixel values from the motion compensated images. In this thesis, we investigate a number of topics related to the performance problems mentioned above. We develop novel solutions to improve the image quality captured by the sensors of a camera phone. Particularly, we present a framework for producing a high-resolution color image directly from a sequence of images captured by a CMOS sensor that is overlaid with a color filter array. In the proposed framework, we introduce a super-resolution algorithm that interpolates the subsampled color components and reduces the optical blurring. The results confirm that it is possible to improve the overall image quality by using few consecutive shots of the same scene. Achieving accurate and fast registration of the input images is a critical step in super-resolution processing. Motivated by this basic requirement, we propose a novel recursive method for pixel-based motion estimation. We use recursive least mean square filtering (LMS) along different scanning directions to track the stationary shifts between a pair of LR images, which results in smooth estimates of the displacements at sub-pixel accuracy. The initial results indicate good performance, especially for tracking smooth global motion. One important advantage of the proposed method is that it can be easily integrated into super-resolution algorithms thanks to its relative low computational complexity. The overall performance of super-resolution is particularly degraded in the presence of motion outliers. Therefore, it is essential to develop methods to enhance the robustness of the fusion process. Towards this goal, we propose an integrated adaptive filtering method to reject the outlier image regions. The proposed approach consists in applying non-linear filtering techniques to improve the performance and robustness against motion outliers. In particular, we applied median filtering for robust fusion of the LR images, and we used generalized order statistic filters (OSF) for the enhancement of binary text images. Compared with conventional super-resolution algorithms, the proposed algorithms preserved well the fine details in the images, additionally, the result images exhibited less artifacts in the presence of registration errors. This confirms the advantage of using order statistic filtering in image super-resolution