HpGAN: Sequence Search with Generative Adversarial Networks

Sequences play an important role in many engineering applications and systems. Searching sequences with desired properties has long been an interesting but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GAN). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for intractable problems with complex objectives which prevent mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary code sets (MOCCS) and optimal odd-length Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications. 2) HpGAN found new sequences which achieve four-times increase of signal-to-interference ratio--benchmarked against the well-known Legendre sequence--of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.

LCuts: Linear Clustering of Bacteria using Recursive Graph Cuts

Bacterial biofilm segmentation poses significant challenges due to lack of apparent structure, poor imaging resolution, limited contrast between conterminous cells and high density of cells that overlap. Although there exist bacterial segmentation algorithms in the existing art, they fail to delineate cells in dense biofilms, especially in 3D imaging scenarios in which the cells are growing and subdividing in a complex manner. A graph-based data clustering method, LCuts, is presented with the application on bacterial cell segmentation. By constructing a weighted graph with node features in locations and principal orientations, the proposed method can automatically classify and detect differently oriented aggregations of linear structures (represent by bacteria in the application). The method assists in the assessment of several facets, such as bacterium tracking, cluster growth, and mapping of migration patterns of bacterial biofilms. Quantitative and qualitative measures for 2D data demonstrate the superiority of proposed method over the state of the art. Preliminary 3D results exhibit reliable classification of the cells with 97% accuracy.

$partial$-reducible handle additions

Let $M$ be a simple 3-manifold, and $F$ be a component of $partial M$ of genus at least 2. Let $alpha$ and $beta$ be separating slopes on $F$. Let $M(alpha)$ (resp. $M(beta)$) be the manifold obtained by adding a 2-handle along $alpha$ (resp. $beta$). If $M(alpha)$ and $M(beta)$ are $partial$-reducible, then the minimal geometric intersection number of $alpha$ and $beta$ is at most 8.