Approaching the ground states of the random maximum two-satisfiability problem by a greedy single-spin flipping process

In this brief report we explore the energy landscapes of two spin glass models using a greedy single-spin flipping process, {\tt Gmax}. The ground-state energy density of the random maximum two-satisfiability problem is efficiently approached by {\tt Gmax}. The achieved energy density $e(t)$ decreases with the evolution time $t$ as $e(t)-e(\infty)=h (\log_{10} t)^{-z}$ with a small prefactor $h$ and a scaling coefficient $z > 1$, indicating an energy landscape with deep and rugged funnel-shape regions. For the $\pm J$ Viana-Bray spin glass model, however, the greedy single-spin dynamics quickly gets trapped to a local minimal region of the energy landscape.Comment: 5 pages with 4 figures included. Accepted for publication in Physical Review E as a brief repor

Molecular characterization and function analysis of the vitellogenin receptor from the cotton bollworm, Helicoverpa armigera (Hubner) (Lepidoptera, Noctuidae)

Developing oocytes accumulate plentiful yolk protein during oogenesis through receptor-mediated endocytosis. The vitellogenin receptor (VgR), belonging to the low-density lipoprotein receptor (LDLR) family, regulates the absorption of yolk protein. In this work, the full-length vitellogenin receptor (HaVgR) in the cotton bollworm Helicoverpa armigera was identified, encoding a 1817 residue protein. Sequence alignment revealed that the sequence of HaVgR contained all of the conservative structural motifs of LDLR family members, and phylogenetic analysis indicated that HaVgR had a high identity among Lepidoptera and was distinct from that of other insects. Consistent with other insects, HaVgR was specifically expressed in ovarian tissue. The developmental expression pattern showed that HaVgR was first transcribed in the newly metamorphosed female adults, reached a peak in 2-day-old adults and then declined. Western blot analysis also revealed an ovarian-specific and developing expression pattern, which was consistent with the HaVgR mRNA transcription. Moreover, RNAi-mediated HaVgR knockdown strongly reduced the VgR expression in both the mRNA and protein levels, which inhibited the yolk protein deposition in the ovaries, led to the dramatic accumulation of vitellogenin and the up-regulation of HaVg expression in hemolymph, and eventually resulted in a declined fecundity. Together, all of these findings demonstrate that HaVgR is a specific receptor in uptake and transportation of yolk protein for the maturation of oocytes and that it plays a critical role in female reproduction

From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy

A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same spin values by one of two different mechanisms: frozen-core formation and long-range frustrations. While frozen cores are identified by a local whitening algorithm, long-range frustrations are very difficult to trace, and they make an entropic belief-propagation (BP) algorithm fail to converge. For BP to reach a fixed point the spin values of a tiny fraction of variables (chosen according to the whitening algorithm) are externally fixed during the iteration. From the calculated entropy values, we infer that, for a large random 3-SAT formula with constraint density close to the satisfiability threshold, the solutions obtained by the survey-propagation or the walksat algorithm belong neither to the most dominating clusters of the formula nor to the most abundant clusters. This work indicates that a single solution cluster of a random 3-SAT formula may have further community structures.Comment: 13 pages, 6 figures. Final version as published in PR

Core-sheath structured electrospun nanofibrous membranes for oil-water separation

In recent years, both the increasing frequency of oil spill accidents and the urgency to deal seriously with industrial oil-polluted water, encouraged material scientists to design highly efficient, cost effective oil-water separation technologies. We report on electrospun nanofibrous membranes which are composed of core-sheath structured cellulose-acetate (CA)-polyimide (PI) nanofibers. On the surface of the CA-PI fibers a fluorinated polybenzoxazine (F-PBZ) functional layer, in which silica nanoparticles (SNPs) were incorporated, has been applied. Compared with F-PBZ/SNP modified CA fibers reported before for the separation of oil from water, the PI-core of the core-shell F-PBZ/SNP/CA-PI fibers makes the membranes much stronger, being a significant asset in their use. Nanofibrous membranes with a tensile strength higher than 200 MPa, a high water contact angle of 160 degrees and an extremely low oil contact angle of 0 degrees were obtained. F-PBZ/SNP/CA-PI membranes seemed very suitable for gravity-driven oil-water separation as fast and efficient separation (>99%) of oil from water was achieved for various oil-water mixtures. The designed core-sheath structured electrospun nanofibrous membranes may become interesting materials for the treatment of industrial oil-polluted water

Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses

In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range frustrations in the 1RSB solution of a given spin-glass system. We study two well-studied model systems, the minimal vertex-cover problem and the maximal 2-satisfiability problem. This work points to a possible way of improving the zero-temperature 1RSB mean-field theory of spin-glasses.Comment: 5 pages, two figures. To be published in JSTA