The minimal and next minimal volumes of normal KSBA stable surfaces with pg≥2p_g\ge 2

In this paper we investigate the minimal and the next minimal volumes of normal KSBA stable surfaces with $p_g\ge 2$. We show that in case of $|K_X|$ not composed with a pencil, the minimal and next minimal volumes are $2p_g-4$ and $2p_g-4+\frac{1}{3}$. In case of $|K_X|$ composed with a pencil, the minimal and next minimal volumes are $\frac{p_g-1}{p_g+1}(p_g-1)$ and $\mathrm{min}\{\frac{2p_g-2}{2p_g+1}(p_g-1), \frac{(3p_g-2)p_g-4}{3(p_g+2)}\}$. We also characterize the surfaces achieving the minimal volumes.Comment: 31 pages, 6 figure

On Revenue Maximization with Sharp Multi-Unit Demands

We consider markets consisting of a set of indivisible items, and buyers that have {\em sharp} multi-unit demand. This means that each buyer $i$ wants a specific number $d_i$ of items; a bundle of size less than $d_i$ has no value, while a bundle of size greater than $d_i$ is worth no more than the most valued $d_i$ items (valuations being additive). We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of "correlated values" where each buyer $i$ has a valuation v_i\qual_j for item $j$, where $v_i$ and \qual_j are positive quantities associated with buyer $i$ and item $j$ respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard.Comment: page2

StrokeGAN: Reducing Mode Collapse in Chinese Font Generation via Stroke Encoding

The generation of stylish Chinese fonts is an important problem involved in many applications. Most of existing generation methods are based on the deep generative models, particularly, the generative adversarial networks (GAN) based models. However, these deep generative models may suffer from the mode collapse issue, which significantly degrades the diversity and quality of generated results. In this paper, we introduce a one-bit stroke encoding to capture the key mode information of Chinese characters and then incorporate it into CycleGAN, a popular deep generative model for Chinese font generation. As a result we propose an efficient method called StrokeGAN, mainly motivated by the observation that the stroke encoding contains amount of mode information of Chinese characters. In order to reconstruct the one-bit stroke encoding of the associated generated characters, we introduce a stroke-encoding reconstruction loss imposed on the discriminator. Equipped with such one-bit stroke encoding and stroke-encoding reconstruction loss, the mode collapse issue of CycleGAN can be significantly alleviated, with an improved preservation of strokes and diversity of generated characters. The effectiveness of StrokeGAN is demonstrated by a series of generation tasks over nine datasets with different fonts. The numerical results demonstrate that StrokeGAN generally outperforms the state-of-the-art methods in terms of content and recognition accuracies, as well as certain stroke error, and also generates more realistic characters.Comment: 10 pages, our codes and data are available at: https://github.com/JinshanZeng/StrokeGA

Mass segmentation using a combined method for cancer detection

<p>Abstract</p> <p>Background</p> <p>Breast cancer is one of the leading causes of cancer death for women all over the world and mammography is thought of as one of the main tools for early detection of breast cancer. In order to detect the breast cancer, computer aided technology has been introduced. In computer aided cancer detection, the detection and segmentation of mass are very important. The shape of mass can be used as one of the factors to determine whether the mass is malignant or benign. However, many of the current methods are semi-automatic. In this paper, we investigate fully automatic segmentation method.</p> <p>Results</p> <p>In this paper, a new mass segmentation algorithm is proposed. In the proposed algorithm, a fully automatic marker-controlled watershed transform is proposed to segment the mass region roughly, and then a level set is used to refine the segmentation. For over-segmentation caused by watershed, we also investigated different noise reduction technologies. Images from DDSM were used in the experiments and the results show that the new algorithm can improve the accuracy of mass segmentation.</p> <p>Conclusions</p> <p>The new algorithm combines the advantages of both methods. The combination of the watershed based segmentation and level set method can improve the efficiency of the segmentation. Besides, the introduction of noise reduction technologies can reduce over-segmentation.</p

SLLEN: Semantic-aware Low-light Image Enhancement Network

How to effectively explore semantic feature is vital for low-light image enhancement (LLE). Existing methods usually utilize the semantic feature that is only drawn from the semantic map produced by high-level semantic segmentation network (SSN). However, if the semantic map is not accurately estimated, it would affect the high-level semantic feature (HSF) extraction, which accordingly interferes with LLE. In this paper, we develop a simple yet effective two-branch semantic-aware LLE network (SLLEN) that neatly integrates the random intermediate embedding feature (IEF) (i.e., the information extracted from the intermediate layer of semantic segmentation network) together with the HSF into a unified framework for better LLE. Specifically, for one branch, we utilize an attention mechanism to integrate HSF into low-level feature. For the other branch, we extract IEF to guide the adjustment of low-level feature using nonlinear transformation manner. Finally, semantic-aware features obtained from two branches are fused and decoded for image enhancement. It is worth mentioning that IEF has some randomness compared to HSF despite their similarity on semantic characteristics, thus its introduction can allow network to learn more possibilities by leveraging the latent relationships between the low-level feature and semantic feature, just like the famous saying "God rolls the dice" in Physics Nobel Prize 2022. Comparisons between the proposed SLLEN and other state-of-the-art techniques demonstrate the superiority of SLLEN with respect to LLE quality over all the comparable alternatives