Stable Identification of Sources Located on Interface of Nonhomogeneous Media

This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.

Application of the method of integral equations based on the Lorentz lemma for calculation of matching transitions between rectangular waveguides with offset axes

This work presents a brief description of the method of integral equations. Integral equations are obtained on the basis of the integral form of Lorentz's lemma using a non-standard physical approach. This method allows one to calculate the characteristics of various three-dimensional irregularities of the waveguide path. As an example of such irregularity, the considered transition between straight shielded waveguides with offset axes and with different transverse sizes. The main attention is paid to the description of the developed numerical-analytical algorithm for calculating the transmission characteristics of the matching transition. A procedure for obtaining an approximate record of the field components on the surface of an irregular region is presented, which makes it possible to take into account the curvature of the wave surface of an electromagnetic wave propagating in the guiding structure. In this case, the profile of the longitudinal section of the guiding structure can be described by any analytical functions. The concept of a 4W-fold comparison waveguide is introduced. In addition, this paper presents the results of calculating the frequency dependences of the transmission characteristics of the fundamental wave of waveguide transition at displacements of the axis of the second waveguide relative to the axis of the first waveguide by different values. The indicated transmission characteristics are found for single-mode and multimode modes of operation of the waveguide transition. In order to verify the results obtained, they have been compared with the results obtained using a modern licensed computer-aided design tool CST Microwave Studio. To demonstrate the possibility of solving the problem of “functional” optimization using the developed algorithm, the results of calculating the transmission characteristics of a waveguide transition between rectangular waveguides with cosine functions describing the profile of the longitudinal section of an irregular region have been presented. In order to indirectly substantiate the equivalence of the initial integral equations underlying the constructed algorithm and the problem of diffraction of an electromagnetic wave in a waveguide transition, a test problem of calculating the transmission characteristics of a stepped transition of two rectangular regular waveguides with different sizes has been solved. The calculation results have been compared with the results obtained on the basis of the electrodynamic substantiated method of half-inversion of the operator of the original boundary value problem. In addition to all the above, in order to assess the validity of the proposed method and the numerical-analytical algorithm built on its basis, a study of the convergence of the calculated results against the approximation number has been made.

Structural studies of reelin N-terminal region provides insights into a unique structural arrangement and functional multimerization

The large, secreted glycoprotein reelin regulates embryonic brain development as well as adult brain functions. Although reelin binds to its receptors via its central part, the N-terminal region directs multimer formation and is critical for efficient signal transduction. In fact, the inhibitory antibody CR-50 interacts with the N-terminal region and prevents higher-order multimerization and signaling. Reelin is a multidomain protein in which the central part is composed of eight characteristic repeats, named reelin repeats, each of which is further divided by insertion of an EGF module into two subrepeats. In contrast, the N-terminal region shows unique “irregular” domain architecture since it comprises three consecutive subrepeats without the intervening EGF module. Here we determined the crystal structure of the murine reelin fragment named RX-R1 including the irregular region and the first reelin repeat at 2.0 Å resolution. The overall structure of RX-R1 has a branched Y-shaped form. Interestingly, two incomplete subrepeats cooperatively form one entire subrepeat structure, though an additional subrepeat is inserted between them. We further reveal that Arg335 of RX-R1 is crucial for binding CR-50. A possible self-association mechanism via the N-terminal region is proposed based on our results.

An Effective Image Matching Algorithm Based on Rotation Independence

Traditional image matching algorithms has poor accuracy in image comparing, such as histogram intersection method. A new image matching algorithm based on the similarity comparison of irregular shape is presented in this paper, which divides the image into a number of irregular regions according to different colors, and extracts the boundary points of the irregular region to compose an irregular shape. The direction and distance is used to comparing the two irregular shapes if the rotation of the image is not considered, otherwise circular list is used to ignore the image rotation. It can be used widely. If two irregular shapes are similar, the two images are considered similar. Experiment proves that this method can effectively improve the image matching accuracy.