Local Model Checking Algorithm Based on Mu-calculus with Partial Orders

The propositionalμ-calculus can be divided into two categories, global model checking algorithm and local model checking algorithm. Both of them aim at reducing time complexity and space complexity effectively. This paper analyzes the computing process of alternating fixpoint nested in detail and designs an efficient local model checking algorithm based on the propositional μ-calculus by a group of partial ordered relation, and its time complexity is O(d2(dn)d/2+2) (d is the depth of fixpoint nesting,  is the maximum of number of nodes), space complexity is O(d(dn)d/2). As far as we know, up till now, the best local model checking algorithm whose index of time complexity is d. In this paper, the index for time complexity of this algorithm is reduced from d to d/2. It is more efficient than algorithms of previous research

Network analysis of circular permutations in multidomain proteins reveals functional linkages for uncharacterized proteins.

Various studies have implicated different multidomain proteins in cancer. However, there has been little or no detailed study on the role of circular multidomain proteins in the general problem of cancer or on specific cancer types. This work represents an initial attempt at investigating the potential for predicting linkages between known cancer-associated proteins with uncharacterized or hypothetical multidomain proteins, based primarily on circular permutation (CP) relationships. First, we propose an efficient algorithm for rapid identification of both exact and approximate CPs in multidomain proteins. Using the circular relations identified, we construct networks between multidomain proteins, based on which we perform functional annotation of multidomain proteins. We then extend the method to construct subnetworks for selected cancer subtypes, and performed prediction of potential link-ages between uncharacterized multidomain proteins and the selected cancer types. We include practical results showing the performance of the proposed methods

Topological Wannier cycles for the bulk and edges

Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral topological characteristics are extended from edge states to corner states. However, the chiral symmetry protecting the corner states is often broken in genuine materials, leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant. Here, we show that a local artificial gauge flux can serve as a robust probe of the Wannier type higher-order topological insulators which is effective even when the chiral symmetry is broken. The resultant observable signature is the emergence of the cyclic spectral flows traversing one or multiple band gaps. These spectral flows are associated with the local modes bound to the artificial gauge flux. This phenomenon is essentially due to the cyclic transformation of the Wannier orbitals when the local gauge flux acts on them. We extend topological Wannier cycles to systems with C2 and C3 symmetries and show that they can probe both the bulk and the edge Wannier centers, yielding rich topological phenomena