A wide range of dark matter candidates have been proposed and are actively being searched for in a large number of experiments, both at high (TeV) and low (sub meV) energies. One dark matter candidate, a deeply bound
Recently, room temperature superconductivity was measured in a carbonaceous sulfur hydride material whose identity remains unknown. Herein, firstprinciples calculations are performed to provide a chemical basis for structural candidates derived by doping H_{3}S with low levels of carbon. Pressure stabilizes unusual bonding configurations about the carbon atoms, which can be sixfold coordinated as CH_{6}entities within the cubic H_{3}S framework, or fourfold coordinated as methane intercalated into the HS lattice, with or without an additional hydrogen in the framework. The doping breaks degenerate bands, lowering the density of states at the Fermi level (
 Award ID(s):
 2104881
 NSFPAR ID:
 10366509
 Publisher / Repository:
 Nature Publishing Group
 Date Published:
 Journal Name:
 npj Computational Materials
 Volume:
 8
 Issue:
 1
 ISSN:
 20573960
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A<sc>bstract</sc> We report the first measurement of the inclusive
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Abstract In a Merlin–Arthur proof system, the proof verifier (Arthur) accepts valid proofs (from Merlin) with probability 1, and rejects invalid proofs with probability arbitrarily close to 1. The running time of such a system is defined to be the length of Merlin’s proof plus the running time of Arthur. We provide new Merlin–Arthur proof systems for some key problems in finegrained complexity. In several cases our proof systems have optimal running time. Our main results include:
Certifying that a list of
n integers has no 3SUM solution can be done in Merlin–Arthur time . Previously, Carmosino et al. [ITCS 2016] showed that the problem has a nondeterministic algorithm running in$$\tilde{O}(n)$$ $\stackrel{~}{O}\left(n\right)$ time (that is, there is a proof system with proofs of length$$\tilde{O}(n^{1.5})$$ $\stackrel{~}{O}\left({n}^{1.5}\right)$ and a deterministic verifier running in$$\tilde{O}(n^{1.5})$$ $\stackrel{~}{O}\left({n}^{1.5}\right)$ time).$$\tilde{O}(n^{1.5})$$ $\stackrel{~}{O}\left({n}^{1.5}\right)$Counting the number of
k cliques with total edge weight equal to zero in ann node graph can be done in Merlin–Arthur time (where$${\tilde{O}}(n^{\lceil k/2\rceil })$$ $\stackrel{~}{O}\left({n}^{\lceil k/2\rceil}\right)$ ). For odd$$k\ge 3$$ $k\ge 3$k , this bound can be further improved for sparse graphs: for example, counting the number of zeroweight triangles in anm edge graph can be done in Merlin–Arthur time . Previous Merlin–Arthur protocols by Williams [CCC’16] and Björklund and Kaski [PODC’16] could only count$${\tilde{O}}(m)$$ $\stackrel{~}{O}\left(m\right)$k cliques in unweighted graphs, and had worse running times for smallk .Computing the AllPairs Shortest Distances matrix for an
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