The Wigner solution of quark gap equation at nonzero current quark mass and partial restoration of chiral symmetry at finite chemical potential

According to the generally accepted phase diagram of QCD, at low temperature and high baryon number density the chiral phase transition of QCD is of first order and the co-existence of the Nambu-Goldstone phase and the Wigner phase should appear. This is in conflict with the usual claim that the quark gap equation has no Wigner solution in the case of nonzero current quark mass. In this paper we analyze the reason why the Wigner solution does not exist in the usual treatment and try to propose a new approach to discuss this question. As a first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study the Wigner solution at finite current quark mass. We then generalize this approach to the case of finite chemical potential and discuss partial restoration of chiral symmetry at finite chemical potential and compare our results with those in the normal NJL model.Comment: 7 pages, 5 figures, and 1 table, discussion at finite chemical potential adde

Generalized Simple Regenerating Codes: Trading Sub-packetization and Fault Tolerance

Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes

BLT: Bidirectional Layout Transformer for Controllable Layout Generation

Creating visual layouts is a critical step in graphic design. Automatic generation of such layouts is essential for scalable and diverse visual designs. To advance conditional layout generation, we introduce BLT, a bidirectional layout transformer. BLT differs from previous work on transformers in adopting non-autoregressive transformers. In training, BLT learns to predict the masked attributes by attending to surrounding attributes in two directions. During inference, BLT first generates a draft layout from the input and then iteratively refines it into a high-quality layout by masking out low-confident attributes. The masks generated in both training and inference are controlled by a new hierarchical sampling policy. We verify the proposed model on six benchmarks of diverse design tasks. Experimental results demonstrate two benefits compared to the state-of-the-art layout transformer models. First, our model empowers layout transformers to fulfill controllable layout generation. Second, it achieves up to 10x speedup in generating a layout at inference time than the layout transformer baseline. Code is released at https://shawnkx.github.io/blt.Comment: ECCV 202