On the rigidity of admissible pairs of rational homogeneous spaces of Picard number one which are of deletion type

The notion of admissible pairs of rational homogeneous spaces of Picard number one and their rigidity in terms of the geometric substructures was formulated by Mok and Zhang. The rigidity is known for subdiagram type. While when the admissible pair is of deletion type, the rigidity no longer holds and we need additional conditions. Mok gave a general criterion to handle the admissible pairs which are not of subdiagram type. In this short note we give some examples of admissible pairs of irreducible compact Hermitian symmetric spaces of deletion type to be rigid under the assumption of rational saturation, as an application of Mok's theorem.Comment: 12 page

More Efficient On-the-Fly Verification Methods of Colored Petri Nets

Colored Petri Nets (CP-nets or CPNs) are powerful modeling language for concurrent systems. As for CPNs' model checking, the mainstream method is unfolding that transforms a CPN into an equivalent P/T net. However the equivalent P/T net tends to be too enormous to be handled. As for checking CPN models without unfolding, we present three practical on-the-fly verification methods which are all focused on how to make state space generation more efficient. The first one is a basic one, based on a standard state space generation algorithm, but its efficiency is low. The second one is an overall improvement of the first. The third one sacrifices some applicability for higher efficiency. We implemented the three algorithms and validated great efficiency of latter two algorithms through experimental results

Gradient-Semantic Compensation for Incremental Semantic Segmentation

Incremental semantic segmentation aims to continually learn the segmentation of new coming classes without accessing the training data of previously learned classes. However, most current methods fail to address catastrophic forgetting and background shift since they 1) treat all previous classes equally without considering different forgetting paces caused by imbalanced gradient back-propagation; 2) lack strong semantic guidance between classes. To tackle the above challenges, in this paper, we propose a Gradient-Semantic Compensation (GSC) model, which surmounts incremental semantic segmentation from both gradient and semantic perspectives. Specifically, to address catastrophic forgetting from the gradient aspect, we develop a step-aware gradient compensation that can balance forgetting paces of previously seen classes via re-weighting gradient backpropagation. Meanwhile, we propose a soft-sharp semantic relation distillation to distill consistent inter-class semantic relations via soft labels for alleviating catastrophic forgetting from the semantic aspect. In addition, we develop a prototypical pseudo re-labeling that provides strong semantic guidance to mitigate background shift. It produces high-quality pseudo labels for old classes in the background by measuring distances between pixels and class-wise prototypes. Extensive experiments on three public datasets, i.e., Pascal VOC 2012, ADE20K, and Cityscapes, demonstrate the effectiveness of our proposed GSC model

Apparent horizon and gravitational thermodynamics of Universe in the Eddington-Born-Infeld theory

The thermodynamics of Universe in the Eddington-Born-Infeld (EBI) theory was restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon $\Upsilon_{A}$ and the evolution of Universe. We started in rewriting the EBI action of the Palatini approach into the Bigravity-type action with an extra metric $q_{\mu\nu}$. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon $\Upsilon_{A}$ including timelike, spacelike and null characters, which depends on the value of the parameter of state $w_{m}$ in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by $\Upsilon_{A}$ in EBI Universe were obtained. Finally, applying the positive-heat-out sign convention, we derived the generalized second law of gravitational thermodynamics in EBI universe.Comment: 23 pages, 0 figure

EnPAC: Petri Net Model Checking for Linear Temporal Logic

State generation and exploration (counterexample search) are two cores of explicit-state Petri net model checking for linear temporal logic (LTL). Traditional state generation updates a structure to reduce the computation of all transitions and frequently encodes/decodes to read each encoded state. We present the optimized calculation of enabled transitions on demand by dynamic fireset to avoid such a structure. And we propose direct read/write (DRW) operation on encoded markings without decoding and re-encoding to make state generation faster and reduce memory consumption. To search counterexamples more quickly under an on-the-fly framework, we add heuristic information to the Buchi automaton to guide the exploration in the direction of accepted states. The above strategies can optimize existing methods for LTL model checking. We implement these optimization strategies in a Petri net model-checking tool called EnPAC (Enhanced Petri-net Analyser and Checker) for linear temporal logic. Then, we evaluate it on the benchmarks of MCC (Model Checking Contest), which shows a drastic improvement over the existing methods.Comment: 11 pages, 5 figure