Slopes of smooth curves on Fano manifolds

Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension $n\geq 3$ with respect to smooth curves. The question turns out to be easy for curves of genus $\geq 1$ and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold $(X, -K_X)$ is not slope stable with respect to a smooth curve. Our result also states that a Fano threefold $X$ with Picard number 1 is slope stable with respect to every smooth curve unless $X$ is the projective space.Comment: 13 pages, Theorems in the original version were modified. This paper will be published in the Bulletin of the London Mathematical Societ

Lagrangian fibration structure on the cotangent bundle of a del Pezzo surface of degree 4

In this paper, we show that there is a natural Lagrangian fibration structure on the map $\Phi$ from the cotangent bundle of a del Pezzo surface $X$ of degree 4 to $\mathbb C^2$. Moreover, we describe explicitly all level surfaces of the above natural map $\Phi$.Comment: 23 page

Estimation of Detection Performance for Vehicle FMCW Radars Using EM Simulations

This paper proposes a systematic method for estimating detection performances of a frequency-modulated continuous wave radar using electromagnetic simulations. The proposed systematic method includes a radar system simulator that can obtain range-Doppler images using the electromagnetic (EM) simulations in conjunction with a test setup employed for performance evaluation of multiple targets at different velocities in a traffic environment. This method is then applied for optimizing the half-power beamwidths of the antenna array using an evaluation metric defined to improve the detection strengths for the multiple targets. The optimized antenna has vertical and horizontal half-power beam widths of 10??? and 60???, respectively. The results confirm that that the proposed systematic method is suitable to improve the radar detection performance with the enhanced radar-Doppler images

A Suboptimal Approach to Antenna Design Problem With Kernel Regression

This paper proposes a novel iterative algorithm based on a Kernel regression as a suboptimal approach to reliable and efficient antenna optimization. In our approach, the complex and non-linear cost surface calculated from antenna characteristics is fitted into a simple linear model using Kernels, and an argument that minimizes this Kernel regression model is used as a new input to calculate its cost using numerical simulations. This process is repeated by updating coefficients of the Kernel regression model with new entries until meeting the stopping criteria. At every iteration, existing inputs are partitioned into a limited number of clusters to reduce the computational time and resources and to prevent unexpected over-weighted situations. The proposed approach is validated for the Rastrigins function as well as a real engineering problem using an antipodal Vivaldi antenna in comparison with a genetic algorithm. Furthermore, we explore the most appropriate Kernel that minimizes the least-square error when fitting the antenna cost surface. The results demonstrate that the proposed process is suitable to be used in antenna design problems as a reliable approach with a fast convergence time

Automatic Segmentation of Brachial Artery based on Fuzzy C-Means Pixel Clustering from Ultrasound Images

Automatic extraction of brachial artery and measuring associated indices such as flow-mediated dilatation and Intima-media thickness are important for early detection of cardiovascular disease and other vascular endothelial malfunctions. In this paper, we propose the basic but important component of such decision-assisting medical software development – noise tolerant fully automatic segmentation of brachial artery from ultrasound images. Pixel clustering with Fuzzy C-Means algorithm in the quantization process is the key component of that segmentation with various image processing algorithms involved. This algorithm could be an alternative choice of segmentation process that can replace speckle noise-suffering edge detection procedures in this application domain