Holographic geometry for non-relativistic systems emerging from generalized flow equations

An intriguing result presented by two of the present authors is that an anti de Sitter space can be derived from a conformal field theory by considering a flow equation. A natural expectation is that given a certain data on the boundary system, the associated geometry would be able to emerge from a flow, even beyond the conformal case. As a step along this line, we examine this scenario for non-relativistic systems with anisotropic scaling symmetries, such as Lifshitz field theories and Schr\"odinger invariant theories. In consequence we obtain a new hybrid geometry of Lifshitz and Schr\"odinger spacetimes as a general holographic geometry in this framework. We confirm that this geometry reduces to each of them by considering special non-relativistic models.Comment: 32 pages, no figure, v2: the definition of the metric operator changed, typos fixed, comments and references added, published versio

Polarization Jumps across Topological Phase Transitions in Two-dimensional Systems

In topological phase transitions involving a change in topological invariants such as the Chern number and the $\mathbb{Z}_2$ topological invariant, the gap closes, and the electric polarization becomes undefined at the transition. In this paper, we show that the jump of polarization across such topological phase transitions in two dimensions is described in terms of positions and monopole charges of Weyl points in the intermediate Weyl semimetal phase. We find that the jump of polarization is described by the Weyl dipole at $\mathbb{Z}_2$ topological phase transitions and at phase transitions without any change in the value of the Chern number. Meanwhile, when the Chern number changes at the phase transition, the jump is expressed in terms of the relative positions of Weyl points measured from a reference point in the reciprocal space.Comment: 12pages, 10 figure

One-Tape Turing Machine and Branching Program Lower Bounds for MCSP

For a size parameter s: ? ? ?, the Minimum Circuit Size Problem (denoted by MCSP[s(n)]) is the problem of deciding whether the minimum circuit size of a given function f : {0,1}? ? {0,1} (represented by a string of length N : = 2?) is at most a threshold s(n). A recent line of work exhibited "hardness magnification" phenomena for MCSP: A very weak lower bound for MCSP implies a breakthrough result in complexity theory. For example, McKay, Murray, and Williams (STOC 2019) implicitly showed that, for some constant ?? > 0, if MCSP[2^{??? n}] cannot be computed by a one-tape Turing machine (with an additional one-way read-only input tape) running in time N^{1.01}, then P?NP. In this paper, we present the following new lower bounds against one-tape Turing machines and branching programs: 1) A randomized two-sided error one-tape Turing machine (with an additional one-way read-only input tape) cannot compute MCSP[2^{???n}] in time N^{1.99}, for some constant ?? > ??. 2) A non-deterministic (or parity) branching program of size o(N^{1.5}/log N) cannot compute MKTP, which is a time-bounded Kolmogorov complexity analogue of MCSP. This is shown by directly applying the Ne?iporuk method to MKTP, which previously appeared to be difficult. 3) The size of any non-deterministic, co-non-deterministic, or parity branching program computing MCSP is at least N^{1.5-o(1)}. These results are the first non-trivial lower bounds for MCSP and MKTP against one-tape Turing machines and non-deterministic branching programs, and essentially match the best-known lower bounds for any explicit functions against these computational models. The first result is based on recent constructions of pseudorandom generators for read-once oblivious branching programs (ROBPs) and combinatorial rectangles (Forbes and Kelley, FOCS 2018; Viola 2019). En route, we obtain several related results: 1) There exists a (local) hitting set generator with seed length O?(?N) secure against read-once polynomial-size non-deterministic branching programs on N-bit inputs. 2) Any read-once co-non-deterministic branching program computing MCSP must have size at least 2^??(N)

Maternal multivitamin intake and orofacial clefts in offspring: Japan Environment and Children's Study (JECS) cohort study

Objectives: Orofacial clefts are common birth defects with a lack of strong evidence regarding their association with maternal nutrition. We aimed to determine whether a relationship exists between maternal nutrient or multivitamin intake and orofacial clefts. Design: This is a prospective, population-based nationwide cohort study. Setting: The study was conducted in 15 regional centres, consisting of local administrative units and study areas. Participants: A total of 98 787 eligible mother–child pairs of the Japan Environment and Children’s Study were included. Intervention: Exposures were maternal nutrition and the use of supplemental multivitamins in mothers. Primary and secondary outcome measures: Outcomes were the occurrence of any orofacial cleft at birth. Multinomial logistic regression analyses were used to evaluate the association between maternal multivitamin intake and the incidence of orofacial clefts. Results: Of the 98 787 children, 69 (0.07%) were diagnosed with cleft lip alone, 113 (0.11%) were diagnosed with cleft lip and palate, and 52 (0.05%) were diagnosed with cleft palate within 1 month after birth. Regarding the total orofacial cleft outcome, statistically significant point estimates of relative risk ratios (RR) were determined for multivitamin intake before pregnancy (RR=1.71; 95% CI 1.06 to 2.77) and during the first trimester (RR=2.00; 95% CI 1.18 to 3.37), but the association was not significant for multivitamin intake after the first trimester (RR=1.34; 95% CI 0.59 to 3.01). Maternal micronutrient intake via food was not associated with the incidence of orofacial clefts in offspring. Conclusions: Intake of multivitamin supplements shortly before conception or during the first trimester of pregnancy was found to be associated with an increased incidence of orofacial clefts at birth. Pregnant women and those intending to become pregnant should be advised of the potential risks of multivitamin supplementation

Magneto-Fluid Coupling - Eruptive Events in the Solar Corona

By modelling the coronal structures by "slowly" evolving Double-Beltrami two-fluid equilibria (created by the interaction of the magnetic and velocity fields), the conditions for catastrophic transformations of the original state are derived. It is shown that, at the transition, much of the magnetic energy of the original state is converted to the the flow kinetic energy.Comment: 4 pages of two-column text (Latex) plus 3 pages of figures, submitted to The Astrophysical Journal Letter

Cloning and functional characterization of a fructan 1-exohydrolase (1-FEH) in edible burdock (Arctium lappa L.)

<p>Abstract</p> <p>Background</p> <p>We have previously reported on the variation of total fructooligosaccharides (FOS), total inulooligosaccharides (IOS) and inulin in the roots of burdock stored at different temperatures. During storage at 0°C, an increase of FOS as a result of the hydrolysis of inulin was observed. Moreover, we suggested that an increase of IOS would likely be due to the synthesis of the IOS by fructosyltransfer from 1-kestose to accumulated fructose and elongated fructose oligomers which can act as acceptors for fructan:fructan 1-fructosyltransferase (1-FFT). However, enzymes such as inulinase or fructan 1-exohydorolase (1-FEH) involved in inulin degradation in burdock roots are still not known. Here, we report the isolation and functional analysis of a gene encoding burdock 1-FEH.</p> <p>Results</p> <p>A cDNA, named <it>aleh1</it>, was obtained by the RACE method following PCR with degenerate primers designed based on amino-acid sequences of FEHs from other plants. The <it>aleh1 </it>encoded a polypeptide of 581 amino acids. The relative molecular mass and isoelectric point (<it>pI</it>) of the deduced polypeptide were calculated to be 65,666 and 4.86. A recombinant protein of <it>aleh1 </it>was produced in <it>Pichia pastoris</it>, and was purified by ion exchange chromatography with DEAE-Sepharose CL-6B, hydrophobic chromatography with Toyopearl HW55S and gel filtration chromatography with Toyopearl HW55S. Purified recombinant protein showed hydrolyzing activity against β-2, 1 type fructans such as 1-kestose, nystose, fructosylnystose and inulin. On the other hand, sucrose, neokestose, 6-kestose and high DP levan were poor substrates.</p> <p>The purified recombinant protein released fructose from sugars extracted from burdock roots. These results indicated that <it>aleh1 </it>encoded 1-FEH.</p

Solution-processed n-type organic thin-film transistors with high field-effect mobility

We report the performance of solution-processed n-type organic thin-film transistors (OTFTs) based on C60 derivatives. Long-chain alkyl-substituted C60, C60-fused N-methylpyrrolidine-meta-C12 phenyl (C60MC12), was used as a semiconducting layer. The C60MC12-thin-film transistor shows high electron mobility of 0.067 cm2/V s in saturation regime. From the result of x-ray diffraction analysis, the C60MC12 active layer forms highly ordered crystalline film. We found that self-assemble ability of long alkyl chains plays an important role for fabrication of highly ordered crystalline film, leading to achievement of high electron mobility in solution-processed n-type OTFTs

Polymer field-effect transistors by a drawing method

We demonstrated the polymer field-effect transistors (FETs) utilizing regioregular poly(3-alkylthiophene)s (P3AT) films prepared by a drawing method. The P3AT film exhibited large optical dichroic ratio, which originated in the polymer backbones aligned to the drawing direction. In-plane anisotropy and enhancement of FET characteristics have been observed that are caused by molecular alignment. In the case of poly(3-dodecylthiophene), the hole mobility along the drawing direction was enhanced by a factor of 25 compared with that of spin-coated film