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Let $k$ be an algebraically closed field of characteristic zero. Let $C/k$ be a projective smooth curve with function field $K=k(C)$ and $G/k$ be a connected reductive group. Let $F$ be a principal $G$-bundle on $C$. Let $P \subseteq G$ be a parabolic subgroup and $\lambda: P \longrightarrow G$ be a strictly anti-dominant character. Then $F/P \longrightarrow C$ is a flag bundle and $\mathcal{L}_\lambda=F \times_P k_\lambda$ on $F/P$ is a relatively ample line bundle. Let $h_{\mathcal{L}_\lambda}$ be the height function on $X=(F/P)_K$ induced by $\mathcal{L}_\lambda$. We compute its height filtration and successive minima: the height filtration is given by a Bruhat decomposition and successive minima are given by slopes. An interesting application is that, in this case, Zhang's inequality on successive minima can be enhanced into an equality. This is proved from the convex geometry point of view. Let $f \in N^1(F/P)$ be the numerical class of a vertical fiber. We also compute the augmented base loci $\mathrm{B}_+(\mathcal{L}_\lambda-tf)$ for any $t \in \mathbb{R}$ and it turns out that they are almost the same as the height filtration, which accords with the philosophy in Arakelov geometry that the positivity of the line bundle $\mathcal{L}_\lambda$ is equivalent to the positivity of its induced height function $h_{\mathcal{L}_\lambda}$. As a corollary, we compute the $k$-th movable cones of flag bundles over curves for all $k$., Comment: 20 pages, comments welcome

In this article, we generalize the arithmetic degree and its related theory to dynamical systems defined over an arbitrary field $\mathbf{k}$ of characteristic $0$. We first consider a dynamical system $(X,f)$ over a finitely generated field $K$ over $\mathbb{Q}$, we introduce the arithmetic degrees $\alpha(f,\cdot)$ for $\overline{K}$-points by using Moriwaki heights. We study the arithmetic dynamical degree of $(X,f)$ and establish the relative degree formula. The relative degree formula gives a proof of the fundamental inequality, that is, the upper arithmetic degree $\overline{\alpha}(f,x)$ is less than or equal to the first dynamical degree $\lambda_1(f)$ in this setting. By taking spread-outs, we extend the definition of arithmetic degrees to dynamical systems over the field $\mathbf k$. We demonstrate that our definition is independent of the choice of the spread-out. Moreover, in this setting, we prove certain special cases of the Kawaguchi-Silverman conjecture. A main novelty of this paper is that, we give a characterization of arithmetic degrees of "transcendental points" in the case $\mathbf{k}=\mathbb{C}$, from which we deduce that $\alpha(f,x)=\lambda_1(f)$ for very general $x\in X(\mathbb{C})$ when $f$ is an endomorphism.

By giving an estimate on the minimal slopes, we prove a Hilbert-Samuel formula for semiample and semipositive adelic line bundles. We also show the birational invariance of the arithmetic {\chi}-volume and its continuous extension on the semiample cone., Comment: arXiv admin note: text overlap with arXiv:2009.08663

As an essential technique for data privacy protection, reversible data hiding in encrypted images (RDHEI) methods have drawn intensive research interest in recent years. In response to the increasing demand for protecting data privacy, novel methods that perform RDHEI are continually being developed. We propose two effective multi-MSB (most significant bit) replacement-based approaches that yield comparably high data embedding capacity, improve overall processing speed, and enhance reconstructed images' quality. Our first method, Efficient Multi-MSB Replacement-RDHEI (EMR-RDHEI), obtains higher data embedding rates (DERs, also known as payloads) and better visual quality in reconstructed images when compared with many other state-of-the-art methods. Our second method, Lossless Multi-MSB Replacement-RDHEI (LMR-RDHEI), can losslessly recover original images after an information embedding process is performed. To verify the accuracy of our methods, we compared them with other recent RDHEI techniques and performed extensive experiments using the widely accepted BOWS-2 dataset. Our experimental results showed that the DER of our EMR-RDHEI method ranged from 1.2087 bit per pixel (bpp) to 6.2682 bpp with an average of 3.2457 bpp. For the LMR-RDHEI method, the average DER was 2.5325 bpp, with a range between 0.2129 bpp and 6.0168 bpp. Our results demonstrate that these methods outperform many other state-of-the-art RDHEI algorithms. Additionally, the multi-MSB replacement-based approach provides a clean design and efficient vectorized implementation., Comment: 14 pages; journal

In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic 0. This can be applied to prove the equidistribution of generic and small points with respect to a big and semipositive adelic line bundle. Our methods can be applied to the finite places of number fields as well. We also show the continuity of $\chi$-volumes over function fields.

For any line bundle written as a subtraction of two ample line bundles, Siu's inequality gives a criterion on its bigness. We generalize this inequality to a relative case. The arithmetic meaning behind the inequality leads to its application on algebraic dynamic systems, which is the equidistribution theorem of generic and small net of subvarieties over a function field.

By some result on the study of arithemtic over trivially valued field, we find its applications to Arakelov geometry over adelic curves. We prove a partial result of the continuity of arithmetic $\chi$-volume along semiample divisors. Moreover, we give a upper bound estimate of arithmetic Hilbert-Samuel function.

Small intestinal capsule endoscopy is the mainstream method for inspecting small intestinal lesions,but a single small intestinal capsule endoscopy will produce 60,000 - 120,000 images, the majority of which are similar and have no diagnostic value. It takes 2 - 3 hours for doctors to identify lesions from these images. This is time-consuming and increase the probability of misdiagnosis and missed diagnosis since doctors are likely to experience visual fatigue while focusing on a large number of similar images for an extended period of time.In order to solve these problems, we proposed a similar wireless capsule endoscope (WCE) image screening method based on structural similarity analysis and the hierarchical clustering of visually salient sub-image blocks. The similarity clustering of images was automatically identified by hierarchical clustering based on the hue,saturation,value (HSV) spatial color characteristics of the images,and the keyframe images were extracted based on the structural similarity of the visually salient sub-image blocks, in order to accurately identify and screen out similar small intestinal capsule endoscopic images. Subsequently, the proposed method was applied to the capsule endoscope imaging workstation. After screening out similar images in the complete data gathered by the Type I OMOM Small Intestinal Capsule Endoscope from 52 cases covering 17 common types of small intestinal lesions, we obtained a lesion recall of 100% and an average similar image reduction ratio of 76%. With similar images screened out, the average play time of the OMOM image workstation was 18 minutes, which greatly reduced the time spent by doctors viewing the images.

In the setting of Arakelov geometry over adelic curves, we introduce the $\chi$-volume function and show some general properties. This article is dedicated to talk about the continuity of $\chi$-volume function. By discussing its relationship with volume function, we prove its continuity around adelic $\mathbb{Q}$-ample $\mathbb{Q}$-Cartier divisors and its continuity in the trivially valued case. The study of the variation of arithmetic Okounkov bodies leads us to its continuous extension on arithmetic surfaces., Comment: 38 pages, 0 figures