Metal-organic networks (MONs) is a family of chemical compounds consisting of clusters or metal ions and organic ligands. These are studied as one, two or three dimensional structures of porous materials and subclasses of coordination polymers. MONs are mostly used in catalysis for the separation & purification of gases and as conducting solids or super-capacitors. In some situations, these networks are found to be stable in the process of removal or solvent of the guest molecules and could be restored with some other chemical compounds. The physical stability and mechanical properties of these networks have become a topic of great interest due to the aforesaid characteristics. Topological indices (TIs) are numeric quantities that are used to forecast the natural relationships among the physico-chemical characteristics of the chemical compounds in their fundamental network. During the studies of the MONs, TIs show an essential role in the theoretical & environmental chemistry and pharmacology. In this paper, we compute various latest developed degree-based TIs for two different metal-organic networks with increasing number of layers consisting on both metal and organic ligands vertices as well. A comparison among the computed different versions of the TIs with the help of the numerical values and their graphs is also included. INDEX TERMS Topological indices, chemical compounds, metals-organic networks.

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Proxy Re-Encryption (PRE) is a cryptographic primitive that allows a proxy to turn an Alice’s ciphertext into a Bob’s ciphertext on the same plaintext. All of the PRE schemes are public key encryption and semantic security. Deterministic Public Key Encryption (D-PKE) provides an alternative to randomized public key encryption in various scenarios where the latter exhibits inherent drawbacks. In this paper, we construct the first multi-use unidirectional D-PRE scheme from Lattices in the auxiliary-input setting. We also prove that it is PRIV1-INDr secure in the standard model based on the LWR. Finally, an identity-based D-PRE is obtained from the basic construction.

Genome-wide association studies can provide researchers some reference on gene mapping of complex trait, a key point of which is how to improve the power of association test. Recently, two-stage approaches are widely used to genome-wide association analysis. In the first stage, a screening test is used to select markers, and in the second stage, a family-based association test is performed based on a smaller set of the selected markers. Here, we modify an existing two-stage approach and propose a new test statistic for the association analysis. Simulation studies are conducted to compare the type I error rates and powers of the proposed approach with those of the existing two-stage approaches. Simulation results show that the new two-stage approach has greater power than the other two-stage approaches to some extent.