arXiv subjects

Oliver Russell

Publications and source records attributed to Oliver Russell.

5 recordsLinked to original sources

arXiv2026

Model structures and electron transfer properties of conductive nickel-organic nanoribbons in cable bacteria

Cable bacteria are multicellular bacteria capable of centimeter-scale conduction through a regular fiber network embedded in their cell envelope. The conductivity of these fibers is extremely high for biological materials, and rivals that of the best synthetic conductive polymers, but the underlying electron transport mechanism remains elusive. Recent microscopic and spectroscopic evidence indicates that each fiber embeds a bundle of intertwined nanoribbons as the conductive conduit. Each nanoribbon consists of a one-dimensional nickel-organic framework, built from stacked nickel bis(1,2-dithiolene) oligomers (NiBiD units) as molecular building blocks. Here we performed DFT calculations of nanoribbon model structures, in order to characterize their electronic properties, examine potential stacking configurations and verify whether these structures can support efficient conductance. Our simulations indicate that nanoribbons are comprised of tightly stacked AA or AB-type packings of NiBiD units. In the most energetically stable structure (AB-type) some Ni centers are predicted to be 5-fold coordinated due to formation of an inter-layer Ni-S coordination bond. In several energetically low-lying structures, the electronic coupling between neighboring molecules exceeds the critical threshold for charge delocalization permitting efficient charge transport beyond small polaron hopping. Our results hence reveal that nanoribbons based on NiBiD units exhibit favorable charge transfer properties that may explain the unusually high conductivities measured in the fibers of cable bacteria.

physics.chem-ph↗

arXiv2022

Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality

We prove the three-dimensional Gaussian product inequality (GPI) $E[X_1^{2}X_2^{2m_2}X_3^{2m_3}]\ge E[X_1^{2}]E[X_2^{2m_2}]E[X_3^{2m_3}]$ for any centered Gaussian random vector $(X_1,X_2,X_3)$ and $m_2,m_3\in\mathbb{N}$. We discover a novel inequality for the moment ratio $\frac{|E[ X_2^{2m_2+1}X_3^{2m_3+1}]|}{E[ X_2^{2m_2}X_3^{2m_3}]}$, which implies the 3D-GPI. The interplay between computing and hard analysis plays a crucial role in the proofs.

math.PR↗

arXiv2022

An Opposite Gaussian Product Inequality

The long-standing Gaussian product inequality (GPI) conjecture states that $E [\prod_{j=1}^{n}|X_j|^{\alpha_j}]\geq\prod_{j=1}^{n}E[|X_j|^{\alpha_j}]$ for any centered Gaussian random vector $(X_1,\dots,X_n)$ and any non-negative real numbers $\alpha_j$, $j=1,\ldots,{n}$. In this note, we prove a novel "opposite GPI" for centered bivariate Gaussian random variables when $-1<\alpha_1<0$ and $\alpha_2>0$: $E[|X_1|^{\alpha_1}|X_2|^{\alpha_2}]\le E[|X_1|^{\alpha_1}]E[|X_2|^{\alpha_2}]$. This completes the picture of bivariate Gaussian product relations.

math.PR↗

arXiv2022

Using Sums-of-Squares to Prove Gaussian Product Inequalities

The long-standing Gaussian product inequality (GPI) conjecture states that $E [\prod_{j=1}^{n}X_j^{2m_j}]\geq\prod_{j=1}^{n}E[X_j^{2m_j}]$ for any centered Gaussian random vector $(X_1,\dots,X_n)$ and $m_1,\dots,m_n\in\mathbb{N}$. In this paper, we describe a computational algorithm involving sums-of-squares representations of multivariate polynomials that can be used to resolve the GPI conjecture. To exhibit the power of this novel method, we apply it to prove two new GPIs: $E[X_1^{2m_1}X_2^{6}X_3^{4}]\ge E[X_1^{2m_1}]E[X_2^{6}]E[X_3^{4}]$ and $E[X_1^{2m_1}X_2^{2}X_3^{2}X_4^{2}]\ge E[X_1^{2m_1}]E[X_2^{2}]E[X_3^{2}]E[X_4^{2}]$.

math.PR↗

arXiv2022

Some New Gaussian Product Inequalities

The Gaussian product inequality is a long-standing conjecture. In this paper, we investigate the three-dimensional inequality $E[X_1^{2}X_2^{2m_2}X_3^{2m_3}]\ge E[X_1^{2}]E[X_2^{2m_2}]E[X_3^{2m_3}]$ for any centered Gaussian random vector $(X_1,X_2,X_3)$ and $m_2,m_3\in\mathbb{N}$. First, we show that this inequality is implied by a combinatorial inequality. The combinatorial inequality can be verified directly for small values of $m_2$ and arbitrary $m_3$. Hence the corresponding cases of the three-dimensional inequality are proved. Second, we show that the three-dimensional inequality is equivalent to an improved Cauchy-Schwarz inequality. This observation leads us to derive some novel moment inequalities for bivariate Gaussian random variables.

math.PR↗