Moments of vicious walkers and M\"obius graph expansions

A system of Brownian motions in one-dimension all started from the origin and conditioned never to collide with each other in a given finite time-interval $(0, T]$ is studied. The spatial distribution of such vicious walkers can be described by using the repulsive eigenvalue-statistics of random Hermitian matrices and it was shown that the present vicious walker model exhibits a transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian orthogonal ensemble (GOE) statistics as the time $t$ is going on from 0 to $T$. In the present paper, we characterize this GUE-to-GOE transition by presenting the graphical expansion formula for the moments of positions of vicious walkers. In the GUE limit $t \to 0$, only the ribbon graphs contribute and the problem is reduced to the classification of orientable surfaces by genus. Following the time evolution of the vicious walkers, however, the graphs with twisted ribbons, called M\"obius graphs, increase their contribution to our expansion formula, and we have to deal with the topology of non-orientable surfaces. Application of the recent exact result of dynamical correlation functions yields closed expressions for the coefficients in the M\"obius expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function and references added. v.3: minor additions and corrections made for publication in Phys.Rev.

PAExM: label-free hyper-resolution photoacoustic expansion microscopy

Reflection-mode ultraviolet photoacoustic microscopy (UV-PAM) is capable of imaging cell nuclei in thick tissue without complex preparation procedures, but it is challenging to distinguish adjacent nuclei due to the limited spatial resolution. Tissue expansion technology has recently been developed to exceed the diffraction-limited fluorescence microscopies, but it is accompanied by limitations including additional staining. Herein, photoacoustic expansion microscopy (PAExM) is presented, which is an advanced histologic imaging strategy combining advantages of fast label-free reflection-mode UV-PAM and the tissue expansion technology. Clustered cell nuclei in an enlarged volume of a mouse brain section can be visually resolved without staining, demonstrating a great potential of the system to be widely used for histologic applications throughout biomedical fields. (C) 2020 Optical Society of America11Nsciescopu

Anisotropy of Several Properties in a Polycrystalline Fe-Mn-Si Based Shape Memory Alloy

The tensile properties, γ ←→ ε transformation and shape recovery have been related to the orientation of tensile axes i.e., along rolling direction(specimen 'A') and toward 45° to the rolling direction(specimen 'B') in a cold-rolled and then annealed Fe-15Mn-10Co-5Cr-3Si alloy. It is revealed that the deformation modes of the specimens 'A' and 'B' with respect to tensile axes are not the same ; tensile deformation of the specimen 'A' is mainly achieved by slip, while that of the specimen 'B' is mainly governed by γ → ε transformation. The yield strengths of the specimens 'A' and 'B' are 569MPa and 745MPa, respectively. The reverse transformation temperature of the specimen 'A' is much higher than that of the specimen 'B', and the shape recovery of the specimen 'B' is much larger than that of the specimen 'A'. The differences between those properties with tensile axes are discussed in association with texture developed in a cold-rolled and then annealed Fe-15Mn-10Co-5Cr-3Si alloy

Pi*-pi* bonding interactions generated by halogen oxidation of zirconium(IV) redox-active ligand complexes.

The new complex, [Zr(pda)2]n (1, pda2- = N,N'-bis(neo-pentyl)-ortho-phenylenediamide, n = 1 or 2), prepared by the reaction of 2 equiv of pdaLi2 with ZrCl4, reacts rapidly with halogen oxidants to afford the new product ZrX2(disq)2 (3, X = Cl, Br, I; disq- = N,N'-bis(neo-pentyl)-ortho-diiminosemiquinonate) in which each redox-active ligand has been oxidized by one electron. The oxidation products 3a-c have been structurally characterized and display an unusual parallel stacked arrangement of the disq- ligands in the solid state, with a separation of approximately 3 A. Density functional calculations show a bonding-type interaction between the SOMOs of the disq- ligands to form a unique HOMO while the antibonding linear combination forms a unique LUMO. This orbital configuration leads to a closed-shell-singlet ground-state electron configuration (S = 0). Temperature-dependent magnetism measurements indicate a low-lying triplet excited state at approximately 750 cm-1. In solution, 3a-c show strong disq--based absorption bands that are invariant across the halide series. Taken together these spectroscopic measurements provide experimental values for the one- and two-electron energies that characterize the pi-stacked bonding interaction between the two disq- ligands

Multifunctional nanoparticles as a tissue adhesive and an injectable marker for image-guided procedures

Tissue adhesives have emerged as an alternative to sutures and staples for wound closure and reconnection of injured tissues after surgery or trauma. Owing to their convenience and effectiveness, these adhesives have received growing attention particularly in minimally invasive procedures. For safe and accurate applications, tissue adhesives should be detectable via clinical imaging modalities and be highly biocompatible for intracorporeal procedures. However, few adhesives meet all these requirements. Herein, we show that biocompatible tantalum oxide/silica core/shell nanoparticles (TSNs) exhibit not only high contrast effects for real-time imaging but also strong adhesive properties. Furthermore, the biocompatible TSNs cause much less cellular toxicity and less inflammation than a clinically used, imageable tissue adhesive (that is, a mixture of cyanoacrylate and Lipiodol). Because of their multifunctional imaging and adhesive property, the TSNs are successfully applied as a hemostatic adhesive for minimally invasive procedures and as an immobilized marker for image-guided procedures. © The Author(s) 20174