Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets

Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear programming relaxation attack using local marginal polytope for randomly generated Goldreich's generators. We assume that $u(n)\in \omega(1)\cap o(n)$ input variables are known. In that case, we show that when $r\ge 3$, there is an exact threshold $\mu_\mathrm{c}(k,r):=\binom{k}{r}^{-1}\frac{(r-2)^{r-2}}{r(r-1)^{r-1}}$ such that for $m=\mu\frac{n^{r-1}}{u(n)^{r-2}}$, the LP relaxation can determine linearly many input variables of Goldreich's generator if $\mu>\mu_\mathrm{c}(k,r)$, and that the LP relaxation cannot determine $\frac1{r-2} u(n)$ input variables of Goldreich's generator if $\mu<\mu_\mathrm{c}(k,r)$. This paper uses characterization of LP solutions by combinatorial structures called stopping sets on a bipartite graph, which is related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur

Novel Charge Order and Superconductivity in Two-Dimensional Frustrated Lattice at Quarter Filling

Motivated by the various physical properties observed in $\theta$-(BEDT-TTF)$_2$X, we study the ground state of extended Hubbard model on two-dimensional anisotropic triangular lattice at 1/4-filling with variational Monte Carlo method. It is shown that the nearest-neighbor Coulomb interaction enhances the charge fluctuation and it induces the anomalous state such as charge-ordered metallic state and the triplet next-nearest-neighbor $f$-wave superconductivity. We discuss the relation to the real materials and propose the unified view of the family of $\theta$-(BEDT-TTF)$_2$X.Comment: 4 pages, 5 figure

Phase Diagram of Spinless Fermions on an Anisotropic Triangular Lattice at Half-filling

The strong coupling phase diagram of the spinless fermions on the anisotropic triangular lattice at half-filling is presented. The geometry of inter-site Coulomb interactions rules the phase diagram. Unconventional charge ordered phases are detected which are the recently reported pinball liquid and the striped chains. Both are induced by the quantum dynamics out of classical disordered states and afford extremely correlated metallic states and the particular domain wall-type of excitations, respectively. The disorder once killed by the quantum effect revives at the finite temperature, which is discussed in the terms of the organic $\theta$-ET$_2X$.Comment: 4pages 6figure

Nonlinear Conduction by Melting of Stripe-Type Charge Order in Organic Conductors with Triangular Lattices

We theoretically discuss the mechanism for the peculiar nonlinear conduction in quasi-two-dimensional organic conductors \theta-(BEDT-TTF)2X [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] through the melting of stripe-type charge order. An extended Peierls-Hubbard model attached to metallic electrodes is investigated by a nonequilibrium Green's function technique. A novel current-voltage characteristic appears in a coexistent state of stripe-type and nonstripe 3-fold charge orders, where the applied bias melts mainly the stripe-type charge order through the reduction of lattice distortion, whereas the 3-fold charge order survives. These contrastive responses of the two different charge orders are consistent with the experimental observations.Comment: 5 pages, 4 figures, to appear in J. Phys. Soc. Jp

Skeletal open bite with amelogenesis imperfecta treated with compression osteogenesis : a case report

Background: We successfully treated a 37-year-old male who had skeletal open bite with severe amelogenesis imperfecta (AI) with orthodontics, compression osteogenesis, and prosthodontics. Case presentation: The patient was diagnosed with severe anterior open bite caused by severe AI. Corticotomy was performed on both buccal and palatal sides of the molar regions, and anchor plates were placed onto the bilateral zygomatic buttress and the center of the hard palate. After corticotomy, posterior maxillary segments were moved 3.5 mm superiorly to correct skeletal open bite with elastic chains. After 8-month, overbite had decreased by 2.0 mm. After further 5 months of prosthodontic preparation, orthodontic appliances were removed, and provisional crowns were set on all teeth. The anterior open bite was corrected, and ideal occlusion with a Class I molar relationship was achieved. The upper first molars were intruded 3.5 mm, resulting in 3.0o counter-clockwise rotation of the mandible. The total active treatment period was 16 months. Acceptable occlusion with a good facial profile was well maintained throughout the 8-year retention period. Conclusions: Our results indicate long-term stability after interdisciplinary treatment combining orthodontics, oral surgery, and prosthodontics in a patient with severe anterior open bite and AI

Purification and immunochemical characterization of alpha-fetoprotein from rat fetal serum and liver

Two alpha1-globulin bands of fetal serum with relative mobilities against bromophenol blue of 0.55 and 0.58 on 7% polyacrylamide gel electrophoresis reacted with a monospecific rabbit antiserum to alpha-fetoprotein (AFP). The former globulin band was clearly detected in the fetal liver supernatant. AFP was immunochemically purified from both the fetal serum and liver, and their electrophoretic and immunochemical properties were compared. Liver AFP purified by immunoadsorbent column yielded electrophoretic mobilities and relative amounts of the two electrophoretically distinct components identical with the purified serum AFP. The immunological reactivity of the two components of the purified preparations from serum and liver against the monospecific anti-AFP serum was also indistinguishable. After the removal of the sialic acid residues from purified serum and liver AFP by treatment with neuraminidase for 6 to 12 hr, disc electrophoretic patterns on 5% polyacrylamide gel and immunoelectrophoretic patterns of the treated AFP were found to be closely similar in both preparations. It may be possible to conclude that serum and liver AFP are structurally indistinguishable and probably identical.</p

The Origin of the Charge Ordering and Its Relevance to Superconductivity in θ\theta-(BEDT-TTF)2_2X: The Effect of the Fermi Surface Nesting and the Distant Electron-Electron Interactions

The origin of the charge ordering in organic compounds $\theta$-(BEDT-TTF)$_2 X$ ($X=MM'$(SCN)$_4$, $M=$Tl,Rb,Co, $M'=$Cs,Zn) is studied using an extended Hubbard model. Calculating the charge susceptibility within random phase approximation (RPA), we find that the $(3\times 3)\sim (3\times 4)$ charge ordering observed at relatively high temperatures can be considered as a consequence of a cooperation between the Fermi surface nesting, controlled by the hopping integral in the $c$ direction, and the electron-electron interactions, where the distant (next nearest neighbor) interactions that have not been taken into account in most of the previous studies play an important role.Mean field analysis at T=0 also supports the RPA results, and further shows that in the $3\times 3$ charge ordered state, some portions of the Fermi surface remain ungapped and are nested with a nesting vector close to the modulation wave vector of the horizontal stripe ordering observed at low temperatures in $X=MM'$(SCN)$_4$. We further study the possibility of superconductivity by taking into account the distant off-site repulsions and the band structure corresponding to $X=$I$_3$, in which superconductivity is experimentally observed. We find that there is a close competition between $d_{xy}$-wave-like singlet pairing and $p_{x+2y}$-wave-like triplet pairing due to a cooperation between the charge and the spin fluctuations. The present analysis provides a possible unified understanding of the experimental phase diagram of the $\theta$-(BEDT-TTF)$_2 X$ family, ranging from a charge ordered insulator to a superconductor.Comment: 13 pages, 18 figures (Figs.5,6,7,14,15,18 compressed using jpeg2ps