Two New Upper Bounds for the Maximum k-plex Problem

A k-plex in a graph is a vertex set where each vertex is non-adjacent to at most k vertices (including itself) in this set, and the Maximum k-plex Problem (MKP) is to find the largest k-plex in the graph. MKP is a practical NP-hard problem, and the k-plex model has many important real-world applications, such as the analysis of various complex networks. Branch-and-bound (BnB) algorithms are a type of well-studied and effective exact algorithms for MKP. Recent BnB MKP algorithms involve two kinds of upper bounds based on graph coloring and partition, respectively, that work in different perspectives and thus are complementary with each other. In this paper, we first propose a new coloring-based upper bound, termed Relaxed Graph Color Bound (RelaxGCB), that significantly improves the previous coloring-based upper bound. Then we propose another new upper bound, termed SeesawUB, inspired by the seesaw playing game, that incorporates RelaxGCB and a partition-based upper bound in a novel way, making use of their complementarity. We apply RelaxGCB and SeesawUB to state-of-the-art BnB MKP algorithms and produce four new algorithms. Extensive experiments show the excellent performance and robustness of the new algorithms with our proposed upper bounds

KD-Club: An Efficient Exact Algorithm with New Coloring-based Upper Bound for the Maximum k-Defective Clique Problem

The Maximum k-Defective Clique Problem (MDCP) aims to find a maximum k-defective clique in a given graph, where a k-defective clique is a relaxation clique missing at most k edges. MDCP is NP-hard and finds many real-world applications in analyzing dense but not necessarily complete subgraphs. Exact algorithms for MDCP mainly follow the Branch-and-bound (BnB) framework, whose performance heavily depends on the quality of the upper bound on the cardinality of a maximum k-defective clique. The state-of-the-art BnB MDCP algorithms calculate the upper bound quickly but conservatively as they ignore many possible missing edges. In this paper, we propose a novel CoLoring-based Upper Bound (CLUB) that uses graph coloring techniques ingeniously to detect independent sets so as to detect missing edges ignored by the previous methods. We then develop a new BnB algorithm for MDCP, called KD-Club, using CLUB in both the preprocessing stage for graph reduction and the BnB searching process for branch pruning. Extensive experiments show that KD-Club significantly outperforms state-of-the-art BnB MDCP algorithms on the number of solved instances within the cut-off time, having much smaller search tree and shorter solving time on various benchmarks

Non-linear relationship between sleep duration and blood pressure in children with short stature

BackgroundEvidence regarding the relationship between sleep duration and blood pressure is controversial. Therefore, the aim of this study was to investigate the relationship between sleep duration and blood pressure in children with short stature.MethodsA total of 1,085 participants with short stature were enrolled from the Affiliated Hospital of Jining Medical University in China. The variables involved in this study included sleep duration, anthropometric indicators and biochemical parameters. Sleep duration was evaluated in a face-to-face interview.ResultsThe average age of the 1,085 selected participants was 10.2 ± 3.5 years old, and approximately 763 (70.32%) of them were male. The results of adjusted linear regression showed that sleep duration was negatively associated with systolic blood pressure z scores (SBP-Z) and diastolic blood pressure z scores (DBP-Z) after adjusting for confounders (β −0.07, 95% CI −0.13, −0.01 P = 0.038; β −0.05, 95% CI −0.10, −0.01 P = 0.035, respectively). A nonlinear relationship was detected between sleep duration and blood pressure, including SBP-Z, DBP-Z and mean arterial pressure z scores (MAP-Z). The inflection point of the nonlinear relationship between sleep duration and SBP-Z is 10 h, and the inflection point of DBP-Z and MAP-Z is 8 h.ConclusionThis study revealed a nonlinear relationship between sleep duration and blood pressure in children with short stature. The findings suggest that the optimal sleep duration in children with short stature was 8–10 h, and sleep durations either too short or too long were associated with increased blood pressure levels

AvatarCraft: Transforming Text into Neural Human Avatars with Parameterized Shape and Pose Control

Neural implicit fields are powerful for representing 3D scenes and generating high-quality novel views, but it remains challenging to use such implicit representations for creating a 3D human avatar with a specific identity and artistic style that can be easily animated. Our proposed method, AvatarCraft, addresses this challenge by using diffusion models to guide the learning of geometry and texture for a neural avatar based on a single text prompt. We carefully design the optimization framework of neural implicit fields, including a coarse-to-fine multi-bounding box training strategy, shape regularization, and diffusion-based constraints, to produce high-quality geometry and texture. Additionally, we make the human avatar animatable by deforming the neural implicit field with an explicit warping field that maps the target human mesh to a template human mesh, both represented using parametric human models. This simplifies animation and reshaping of the generated avatar by controlling pose and shape parameters. Extensive experiments on various text descriptions show that AvatarCraft is effective and robust in creating human avatars and rendering novel views, poses, and shapes. Our project page is: https://avatar-craft.github.io/.Comment: ICCV 2023 Camera Read