We construct an example of a group
Charge transport in biomolecules is crucial for many biological and technological applications, including biomolecular electronics devices and biosensors. RNA has become the focus of research because of its importance in biomedicine, but its charge transport properties are not well understood. Here, we use the Scanning Tunneling Microscopy-assisted molecular break junction method to measure the electrical conductance of particular 5-base and 10-base single-stranded (ss) RNA sequences capable of base stacking. These ssRNA sequences show single-molecule conductance values around
- PAR ID:
- 10473958
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 13
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
Abstract for a finite abelian group$$G = \mathbb {Z}^2 \times G_0$$ , a subset$$G_0$$ E of , and two finite subsets$$G_0$$ of$$F_1,F_2$$ G , such that it is undecidable in ZFC whether can be tiled by translations of$$\mathbb {Z}^2\times E$$ . In particular, this implies that this tiling problem is$$F_1,F_2$$ aperiodic , in the sense that (in the standard universe of ZFC) there exist translational tilings ofE by the tiles , but no periodic tilings. Previously, such aperiodic or undecidable translational tilings were only constructed for sets of eleven or more tiles (mostly in$$F_1,F_2$$ ). A similar construction also applies for$$\mathbb {Z}^2$$ for sufficiently large$$G=\mathbb {Z}^d$$ d . If one allows the group to be non-abelian, a variant of the construction produces an undecidable translational tiling with only one tile$$G_0$$ F . The argument proceeds by first observing that a single tiling equation is able to encode an arbitrary system of tiling equations, which in turn can encode an arbitrary system of certain functional equations once one has two or more tiles. In particular, one can use two tiles to encode tiling problems for an arbitrary number of tiles. -
Abstract The elliptic flow
of$$(v_2)$$ mesons from beauty-hadron decays (non-prompt$${\textrm{D}}^{0}$$ was measured in midcentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair$${\textrm{D}}^{0})$$ TeV with the ALICE detector at the LHC. The$$\sqrt{s_{\textrm{NN}}} = 5.02$$ mesons were reconstructed at midrapidity$${\textrm{D}}^{0}$$ from their hadronic decay$$(|y|<0.8)$$ , in the transverse momentum interval$$\mathrm {D^0 \rightarrow K^-\uppi ^+}$$ GeV/$$2< p_{\textrm{T}} < 12$$ c . The result indicates a positive for non-prompt$$v_2$$ mesons with a significance of 2.7$${{\textrm{D}}^{0}}$$ . The non-prompt$$\sigma $$ -meson$${{\textrm{D}}^{0}}$$ is lower than that of prompt non-strange D mesons with 3.2$$v_2$$ significance in$$\sigma $$ , and compatible with the$$2< p_\textrm{T} < 8~\textrm{GeV}/c$$ of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.$$v_2$$ -
Abstract Let
X be ann -element point set in thek -dimensional unit cube where$$[0,1]^k$$ . According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour)$$k \ge 2$$ through the$$x_1, x_2, \ldots , x_n$$ n points, such that , where$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} \le c_k$$ is the Euclidean distance between$$|x-y|$$ x andy , and is an absolute constant that depends only on$$c_k$$ k , where . From the other direction, for every$$x_{n+1} \equiv x_1$$ and$$k \ge 2$$ , there exist$$n \ge 2$$ n points in , such that their shortest tour satisfies$$[0,1]^k$$ . For the plane, the best constant is$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} = 2^{1/k} \cdot \sqrt{k}$$ and this is the only exact value known. Bollobás and Meir showed that one can take$$c_2=2$$ for every$$c_k = 9 \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ and conjectured that the best constant is$$k \ge 3$$ , for every$$c_k = 2^{1/k} \cdot \sqrt{k}$$ . Here we significantly improve the upper bound and show that one can take$$k \ge 2$$ or$$c_k = 3 \sqrt{5} \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ . Our bounds are constructive. We also show that$$c_k = 2.91 \sqrt{k} \ (1+o_k(1))$$ , which disproves the conjecture for$$c_3 \ge 2^{7/6}$$ . Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed.$$k=3$$ -
Abstract A well-known open problem of Meir and Moser asks if the squares of sidelength 1/
n for can be packed perfectly into a rectangle of area$$n\ge 2$$ . In this paper we show that for any$$\sum _{n=2}^\infty n^{-2}=\pi ^2/6-1$$ , and any$$1/2 that is sufficiently large depending on$$n_0$$ t , the squares of sidelength for$$n^{-t}$$ can be packed perfectly into a square of area$$n\ge n_0$$ . This was previously known (if one packs a rectangle instead of a square) for$$\sum _{n=n_0}^\infty n^{-2t}$$ (in which case one can take$$1/2 ).$$n_0=1$$ -
Abstract The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,
/$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$ , as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$ /$$\mathrm {[Fe{(CN)}_6]^{4-}}$$ . We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from$$\mathrm {[Fe{(CN)}_6]^{3-}}$$ to$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$ there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$ to$$\mathrm {[Fe{(CN)}_6]^{4-}}$$ we observed an increase in covalency without altering the bond nature. Distinct$$\mathrm {[Fe{(CN)}_6]^{3-}}$$ back-donation disparity could be confirmed by comparison with the isolated CN$$\pi $$ system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.$$^-$$ Graphical abstract The adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies