Real-world bipartite communities tend to exhibit relaxed internal connectivity as their size increases, making traditional biclique models too restrictive for cohesive subgraph discovery. In this paper, we propose the Biflexi, a novel bipartite subgraph model that employs flexible, size-adaptive degree thresholds based on sublinear constraints. Our approach dynamically adjusts connectivity requirements according to subgraph size, enabling the discovery of larger and more realistic cohesive structures. We prove that the Maximum Biflexi problem is NP-hard and develop an efficient heuristic algorithm. Experimental results on real-world datasets demonstrate the effectiveness and scalability of our algorithm and the applicability of our model.

Identifying cohesive subgraphs within networks is a fundamental problem in graph theory, relevant to various domains. The traditional clique problem, which finds fully connected subgraphs, often faces limitations due to its strict connectivity requirements. This paper introduces a novel degree-based relaxation model called Flexi-clique, where the degree constraint is adjusted sub-linearly based on the subgraph size. We establish that the maximum Flexi-clique problem is NP-hard and propose an efficient and effective peeling algorithm to address it. Our extensive experimental evaluation of real-world datasets demonstrates the effectiveness and efficiency of our approach in discovering large, cohesive subgraphs in networks.

We present Symphony, an $E(3)$ equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for molecules utilize rotationally invariant features to respect the 3D symmetries of molecules. In contrast, Symphony uses message-passing with higher-degree $E(3)$-equivariant features. This allows a novel representation of probability distributions via spherical harmonic signals to efficiently model the 3D geometry of molecules. We show that Symphony is able to accurately generate small molecules from the QM9 dataset, outperforming existing autoregressive models and approaching the performance of diffusion models. Our code is available at https://github.com/atomicarchitects/symphony.

A synthetic aperture radar (SAR) is electromagnetic equipment which is composed of digital parts. It transmits and receives microwaves for observing long distance. In digital system, system clock is an important factor that determines waveform resolution. The SAR system is consist of FPGA, DAC, and other digital parts. In the SAR system, clock of FPGA and DAC are an upper limit for generation of chirp signal. However, digital parts are mostly expensive due to its specification. In this paper, we develop two types of digital waveform generator and propose a method for chirp waveform generation using relatively low cost parts. We test the chirp waveform generators. One used Virtex-5 and one DDS, and the other used Kintex-7 and four DDSs. In addition, we compare the waveform quality using impulse response function. As a results, peak to side-lobe ratio is -14.68 dB and -11.54 dB, and integrated side-lobe ratio is -21.78 dB and -15.48 dB, relatively.