Low-Congestion Shortcut and Graph Parameters

Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Omega~(sqrt{n} + D) rounds for many global problems, where n is the number of nodes and D is the diameter of the input graph. Since such a lower bound is derived from special "hard-core" instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts is initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. Specifically, given a specific graph class X, an f-round algorithm of constructing shortcuts of quality q for any instance in X results in O~(q + f)-round algorithms of solving several fundamental graph problems such as minimum spanning tree and minimum cut, for X. The main interest on this line is to identify the graph classes allowing the shortcuts which are efficient in the sense of breaking O~(sqrt{n}+D)-round general lower bounds. In this paper, we consider the relationship between the quality of low-congestion shortcuts and three major graph parameters, chordality, diameter, and clique-width. The main contribution of the paper is threefold: (1) We show an O(1)-round algorithm which constructs a low-congestion shortcut with quality O(kD) for any k-chordal graph, and prove that the quality and running time of this construction is nearly optimal up to polylogarithmic factors. (2) We present two algorithms, each of which constructs a low-congestion shortcut with quality O~(n^{1/4}) in O~(n^{1/4}) rounds for graphs of D=3, and that with quality O~(n^{1/3}) in O~(n^{1/3}) rounds for graphs of D=4 respectively. These results obviously deduce two MST algorithms running in O~(n^{1/4}) and O~(n^{1/3}) rounds for D=3 and 4 respectively, which almost close the long-standing complexity gap of the MST construction in small-diameter graphs originally posed by Lotker et al. [Distributed Computing 2006]. (3) We show that bounding clique-width does not help the construction of good shortcuts by presenting a network topology of clique-width six where the construction of MST is as expensive as the general case

Cutting edge of high-entropy alloy superconductors from the perspective of materials research

High-entropy alloys (HEAs) are a new class of materials which are being energetically studied around the world. HEAs are characterized by a multi-component alloy in which five or more elements randomly occupy a crystallographic site. The conventional HEA concept has developed into simple crystal structures such as face-centered-cubic (fcc), body-centered-cubic (bcc) and hexagonal-closed packing (hcp) structures. The highly atomic-disordered state produces many superior mechanical or thermal properties. Superconductivity has been one of the topics of focus in the field of HEAs since the discovery of the bcc HEA superconductor in 2014. A characteristic of superconductivity is robustness against atomic disorder or extremely high pressure. The materials research on HEA superconductors has just begun, and there are open possibilities for unexpectedly finding new phenomena. The present review updates the research status of HEA superconductors. We survey bcc and hcp HEA superconductors and discuss the simple material design. The concept of HEA is extended to materials possessing multiple crystallographic sites; thus, we also introduce multi-site HEA superconductors with the CsCl-type, {\alpha}-Mn-type, A15, NaCl-type, {\sigma}-phase and layered structures and discuss the materials research on multi-site HEA superconductors. Finally, we present the new perspectives of eutectic HEA superconductors and gum metal HEA superconductors.Comment: to be published in Metal

Materials Research on High-Entropy Alloy Superconductors

The first purpose of this chapter is materials research on face-centered-cubic (fcc) high-entropy alloy (HEA) superconductors, which have not yet been reported. We have investigated several Nb-containing multicomponent alloys. Although we succeeded in obtaining Nb-containing samples with the dominant fcc phases, no superconducting signals appeared in these samples down to 3 K. The microstructure analyses revealed that all samples were multi-phase, but the existence of several new Nb-containing HEA phases was confirmed in them. The second purpose is the report of materials research on the Mn5Si3-type HEA superconductors. This hexagonal structure offers various intermetallic compounds, which often undergo a superconducting state. The Mn5Si3-type HEA is classified into the multisite HEA, which possesses the high degree of freedom in the materials design and is good platform for studying exotic HEA superconductors. We have successfully found a single-phase Mn5Si3-type HEA, which, however, does not show a superconducting property down to 3 K. The attempt of controlling the valence electron count was not successful

Probing dynamics of carbon dioxide in a metal-organic framework under high pressure by high-resolution solid-state NMR

The application of high-resolution NMR analysis for CO2 adsorbed in an MOF under high pressure is reported for the first time. The results showed that CO2 adsorbed in MOF-74 had a unusual slow mobility (τ ~ 10-8 s). CO2–CO2 interactions suppressed the mobility of CO2 under high pressure, which, in turn, would have contributed to the stability of CO2 at adsorption sites