Hypercubes are famous interconnection networks. The shuffle cubes are proposed as its variation with lower diameter. In this paper, we concentrate on the fault tolerant hamiltonicity and hamiltonian connectivity of the shuffle cube. We say that a graph G is f-hamiltonian if there is a hamiltonian cycle in G − F and is f-hamiltonian connected if there is a hamiltonian path between any two vertic...

We introduce a pre-computation technique that drastically reduces the online computational complexity of mix-nets based on homomorphic cryptosystems. More precisely, we show that there is a permutation commitment scheme that allows a mix-server to: (1) commit to a permutation and efficiently prove knowledge of doing so correctly in the offline phase, and (2) shuffle its input and give an extrem...

Combining transmission electron microscopes and density functional theory calculations, we report the nucleation and growth mechanisms of room temperature rolling induced face-centered cubic titanium (fcc-Ti) in polycrystalline hexagonal close packed titanium (hcp-Ti). Fcc-Ti and hcp-Ti take the orientation relation: 〈0001〉hcp||〈001〉fcc and , different from the conventional one. The nucleation ...

In this work an efficient model for parallel computing, called Shuffled Mesh (SM), is introduced. This bounded degree model has the mesh as subgraph and it is based on the union of mesh and shuffle-exchange topologies. It is shown that an N-processor SM combines the features of mesh, shuffle-exchange, hypercubic networks, mesh of trees and hypercube, and is able to support all the algorithms de...

The dislocation widths, Peierls barriers and Peierls stresses for shuffle screw dislocations in diamond structure crystals, Si and Ge, have been calculated by the improved P-N theory. The widths are about 0.6b, where b is the Burgers vector. The Peierls barrier for shuffle screw dislocation in Si and Ge, is about 3.61~4.61meV/Å and 5.31~13.32meV/Å, respectively. The Peierls stress is about 0.28...

In this paper, we propose a novel and efficient protocol for proving the correctness of a shuffle, without leaking how the shuffle was performed. Using this protocol, we can prove the correctness of a shuffle of n data with roughly 18n exponentiations, where as the protocol of Sako-Kilian[SK95] required 642n and that of Abe[Ab99] required 22n logn. The length of proof will be only 2n bits in ou...

Four T7 products, DNA polymerase, gene 4 protein, RNA polymerase, and DNA binding protein, have been purified from phage-infected cells. It has been previously shown (Hinkle, D. C., and Richardson, C. C. (1975) J. Biol. Chem 250, 5523-5529; Kolodner, R., and Richardson, C, C. (1978) J. Biol. Chem 253, 574-584) that two T7 products, DNA polymerase and gene 4 protein, catalyze extensive synthesis...

The positive part $U_q^+$ of $U_q(\widehat{\mathfrak{sl}}_2)$ admits an embedding into a $q$-shuffle algebra. This was introduced by M. Rosso in 1995. In 2019, Terwilliger the alternating elements $\{W_{-n}\}_{n \in \mathbb{N}}$, $\{W_{n+1}\}_{n $\{G_{n+1}\}_{n $\{\tilde{G}_{n+1}\}_{n \mathbb{N}}$ using embedding. He showed that form PBW basis for $U_q^+$, and he expressed this basis. his calcu...

We consider Kelly networks with shuffling of customers within each queue. Specifically, each arrival, departure or movement of customer from one queue to another triggers a shuffle of the other customers at each queue. The shuffle distribution may depend on the network state and on the customer that triggers the shuffle. We prove that the stationary distribution of the network state remains the...

We revisit shuffling in public [AW07a], a scheme which allows a shuffle to be precomputed. We show how to obfuscate a Paillier shuffle with O(N log N) exponentiations, leading to a very robust and efficient mixnet: when distributed over O(N) nodes the mixnet achieves mixing in polylogarithmic time, independent of the level of privacy or verifiability required. Our construction involves the use ...