Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension

We consider the one-dimensional model of a spin glass with independent Gaussian-distributed random interactions, that have mean zero and variance $1/|i-j|^{2\sigma}$, between the spins at sites $i$ and $j$ for all $i\neq j$. It is known that, for $\sigma>1$, there is no phase transition at any non-zero temperature in this model. We prove rigorously that, for $\sigma>3/2$, any Newman-Stein metastate for the ground states (i.e.\ the frequencies with which distinct ground states are observed in finite size samples in the limit of infinite size, for given disorder) is trivial and unique. In other words, for given disorder and asymptotically at large sizes, the same ground state, or its global spin flip, is obtained (almost) always. The proof consists of two parts: one is a theorem (based on one by Newman and Stein for short-range two-dimensional models), valid for all $\sigma>1$, that establishes triviality under a convergence hypothesis on something similar to the energies of domain walls, and the other (based on older results for the one-dimensional model) establishes that the hypothesis is true for $\sigma>3/2$. In addition, we derive heuristic scaling arguments and rigorous exponent inequalities which tend to support the validity of the hypothesis under broader conditions. The constructions of various metastates are extended to all values $\sigma>1/2$. Triviality of the metastate in bond-diluted power-law models for $\sigma>1$ is proved directly.Comment: 18 pages. v2: subsection on bond-diluted models added, few extra references. 19 pages. v3: published version; a few changes; 20 page

Effect of treatments on root/shoot ratio in <i>Ficus</i> saplings under two soil nutrient levels.

<p>Significant differences between treatments are marked with different letters (mean ± SE, n = 5 in 2009, n = 12 in 2011, <i>P</i><0.05).</p

Effect of treatments on RGR of <i>Ficus</i> saplings under two soil nutrient levels.

<p>Significant differences between treatments are marked with different letters (mean ± SE, n = 5 in 2009, n = 12 in 2011, <i>P</i><0.05). RGR, relative growth rate (mg·g⁻¹·d⁻¹).</p

RGR as a function of <i>P</i>_sat and <i>P</i>_sat as a function of <i>G</i>_s in <i>Ficus</i> saplings under two soil nutrient levels.

<p>Significant differences between treatments are marked with different letters (mean ± SE, n = 3, <i>P</i><0.05). Black shapes, fertile, white shapes, infertile. RGR relative growth rate (mg·g⁻¹·d⁻¹); <i>P</i>_sat, light saturated photosynthetic rate (μmol m⁻²s⁻¹); <i>G</i>_s, stomatal conductance (mol H₂O m⁻²s⁻¹).</p

Compensatory growth of three <i>Ficus</i> species in response to herbivore treatment.

<p>Plant biomass above the line indicates overcompensatory regrowth, on the line indicates fullcompensatory regrowth, below the line indicates undercompensatory regrowth (Biomass in the damaged state  =  biomass in control state, slope  = 1) (n = 5 in 2009, n = 12 in 2011).</p

Effect of treatments on photosynthetic characteristics of <i>Ficus</i> saplings under two soil nutrient levels.

<p>Significant differences between treatments are marked with different letters (mean ± SE, n = 3, <i>P</i><0.05). <i>P</i>_sat, light saturated photosynthetic rate (μmol m⁻²s⁻¹); <i>G</i>_s, stomatal conductance (mol H₂O m⁻²s⁻¹); WUE, water use efficiency (μmol mol⁻¹).</p

Primer sequences and related information for each candidate reference gene.

<p>Primer sequences and related information for each candidate reference gene.</p

Average expression stability values (M values) calculated by geNorm.

<p>(A) Different fruit ripening stages, (B) Dark treatment, (C) Phytoplasma infection, (D) Different tissue/organs.</p

Expression Stabilities of Candidate Reference Genes for RT-qPCR in Chinese Jujube (<i>Ziziphus jujuba</i> Mill.) under a Variety of Conditions

<div><p>Reverse transcription-quantitative real-time polymerase chain reaction (RT-qPCR) is a powerful method for evaluating patterns of gene expression. Jujube whole-genome sequencing has been completed, and analysis of gene function, an important part of any follow-up study, requires the appropriate selection of reference genes. Indeed, suitable reference gene selection for RT-qPCR is critical for accurate normalization of target gene expression. In this study, the software packages geNorm and NormFinder were employed to examine the expression stabilities of nine candidate reference genes under a variety of conditions. <i>Actin-depolymerizing factor 1</i> (<i>ACT1</i>), <i>Histone-H3</i> (<i>His3</i>), and <i>Polyadenylate-binding protein-interacting protein</i> (<i>PAIP</i>) were determined to be the most stably expressed genes during five stages of fruit development and <i>ACT1</i>, <i>SiR-Fd</i>, <i>BTF3</i>, and <i>Tubulin alpha chain</i> (<i>TUA</i>) across different tissues/organs. Whereas <i>ACT1</i>, <i>Basic Transcription factor 3</i> (<i>BTF3</i>), <i>Glyceraldehyde-3-phosphate dehydrogenase</i> (<i>GADPH</i>), and <i>PAIP</i> were the most stable under dark conditions. <i>ACT1</i>, <i>PAIP</i>, <i>BTF3</i>, and <i>Elongation factor 1- gamma</i> (<i>EF1γ</i>) were the most stably expressed genes under phytoplasma infection. Among these genes, <i>SiR-Fd</i> and <i>PAIP</i> are here first reported as stable reference genes. When normalized using these most stable reference genes, the expression patterns of four target genes were found to be in accordance with physiological data, indicating that the reference genes selected in our study are suitable for use in such analyses. This study provides appropriate reference genes and corresponding primers for further RT-qPCR studies in Chinese jujube and emphasizes the importance of validating reference genes for gene expression analysis under variable experimental conditions.</p></div

Adjustable Tribological Behavior of Glucose-Sensitive Hydrogels

Stimuli-responsive hydrogels have been considered to have various applications in numerous fields. In the present work, a double-network (DN) hydrogel has been synthesized. The copolymers of 2-acrylamide-2-methylpropane sulfonic acid (AMPS) and acrylamide (AM) [P­(AMPS-<i>co</i>-AM)] are prepared as the 1st network and poly­(acrylic acid) as the 2nd network. This DN hydrogel is sensitive to glucose by introducing the glucose-sensitive group phenylboronic acid to the network. The tribological properties of this glucose-sensitive DN hydrogel have been investigated using a universal mechanical tester (UMT-5). The tribological results show that the friction coefficient varied with the glucose solution. The friction coefficient increased to a maximum of 0.06, and finally decreased to 0.025 with the increase in the glucose concentration. An adjustable friction coefficient of the hydrogel, between 0.025 and 0.056, was achieved along with the change of lubricant. According to the tribological experimental results and the analysis of the DN structure, it can be deduced that a hydrated layer exists in the interface of the hydrogel. The hydrated layers consisting of water molecules are bounded with the hydrophilic group of the hydrogel network by hydrogen bonds. The change in the number of water molecules leads to the difference in the water content of the hydrogel, which further resulted in the various tribological properties. In addition, the hydrogel’s mesh size also has an impact on the change in friction coefficient. In general, the adjustable friction of the hydrogel in a glucose environment is achieved