D-optimal matrices of orders 118, 138, 150, 154 and 174

We construct supplementary difference sets (SDS) with parameters $(59;28,22;21)$, $(69;31,27;24)$, $(75;36,29;28)$, $(77;34,31;27)$ and $(87;38,36;31)$. These SDSs give D-optimal designs (DO-designs) of two-circulant type of orders 118,138,150,154 and 174. Until now, no DO-designs of orders 138,154 and 174 were known. While a DO-design (not of two-circulant type) of order 150 was constructed previously by Holzmann and Kharaghani, no such design of two-circulant type was known. The smallest undecided order for DO-designs is now 198. We use a novel property of the compression map to speed up some computations.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1409.596

Formation of a "Cluster Molecule" (C20)2 and its thermal stability

The possible formation of a "cluster molecule" (C20)2 from two single C20 fullerenes is studied by the tight-binding method. Several (C20)2 isomers in which C20 fullerenes are bound by strong covalent forces and retain their identity are found; actually, these C20 fullerenes play the role of "atoms" in the "cluster molecule". The so-called open-[2+2] isomer has a minimum energy. Its formation path and thermal stability at T = 2000 - 4000 K are analyzed in detail. This isomer loses its molecular structure due to either the decay of one of C20 fullerenes or the coalescence of two C20 fullerenes into a C40 cluster. The energy barriers for the metastable open-[2+2] configuration are calculated to be U = 2 - 5 eV.Comment: 21 pages, 8 figure

Decay and fusion as two different mechanisms of stability loss for the (C_20)_2 cluster dimer

The thermal stability of the (C_20)_2 cluster dimer consisting of two C_20 fullerenes is examined using a tight-binding approach. Molecular dynamics simulations of the (C_20)_2 dimer at temperatures T = 2000 - 3500 K show that the finite lifetime \tau of this metastable system is determined by two fundamentally different processes, the decay of one of the C_20 fullerenes and the fusion of two C_20 fullerenes into the C_40 cluster. The activation energies for these processes Ea = 3.4 and 2.7 eV, respectively, as well as their frequency factors, have been determined by analyzing the dependence of \tau on T.Comment: Slightly modified version of the paper to appear in JETP Let

Stability of C20 fullerene chains

The stability of (C20)N chains with N = 3 - 7 is analyzed by numerical simulation using a tight-binding potential and molecular dynamics. Various channels of losing the cluster-chain structure of the (C20)N complexes are observed, including the decay of C20 clusters, their coalescence, and the separation of one C20 fullerene from the chain.Comment: To appear in JETP Letter

Structure and Stability of Two-Dimensional Complexes of C_20 Fullerenes

Two-dimensional complexes of C_20 fullerenes connected to each other by covalent bonds have been studied. Several isomers with different types of intercluster bonds have been revealed. The lifetimes of the (C_20)_MxM systems with M = 2 and 3 have been directly calculated at T = 1800 - 3300 K making use of molecular dynamics. It has been shown that these complexes lose their periodic cluster structure due to either coalescence of two fullerenes C_20 or decay of C_20 fullerenes. The activation energies of these processes exceed 2 eV.Comment: 17 pages, 5 figure

Improved Bootstrapping for Approximate Homomorphic Encryption

Since Cheon et al. introduced a homomorphic encryption scheme for approximate arithmetic (Asiacrypt ’17), it has been recognized as suitable for important real-life usecases of homomorphic encryption, including training of machine learning models over encrypted data. A follow up work by Cheon et al. (Eurocrypt ’18) described an approximate bootstrapping procedure for the scheme. In this work, we improve upon the previous bootstrapping result. We improve the amortized bootstrapping time per plaintext slot by two orders of magnitude, from ∼ 1 second to ∼ 0.01 second. To achieve this result, we adopt a smart level-collapsing technique for evaluating DFT-like linear transforms on a ciphertext. Also, we replace the Taylor approximation of the sine function with a more accurate and numerically stable Chebyshev approximation, and design a modified version of the Paterson-Stockmeyer algorithm for fast evaluation of Chebyshev polynomials over encrypted data