97,434 research outputs found
Move ordering and communities in complex networks describing the game of go
We analyze the game of go from the point of view of complex networks. We
construct three different directed networks of increasing complexity, defining
nodes as local patterns on plaquettes of increasing sizes, and links as actual
successions of these patterns in databases of real games. We discuss the
peculiarities of these networks compared to other types of networks. We explore
the ranking vectors and community structure of the networks and show that this
approach enables to extract groups of moves with common strategic properties.
We also investigate different networks built from games with players of
different levels or from different phases of the game. We discuss how the study
of the community structure of these networks may help to improve the computer
simulations of the game. More generally, we believe such studies may help to
improve the understanding of human decision process.Comment: 14 pages, 21 figure
Microscopic mechanism for the 1/8 magnetization plateau in SrCu_2(BO_3)_2
The frustrated quantum magnet SrCu_2(BO_3)_2 shows a remarkably rich phase
diagram in an external magnetic field including a sequence of magnetization
plateaux. The by far experimentally most studied and most prominent
magnetization plateau is the 1/8 plateau. Theoretically, one expects that this
material is well described by the Shastry-Sutherland model. But recent
microscopic calculations indicate that the 1/8 plateau is energetically not
favored. Here we report on a very simple microscopic mechanism which naturally
leads to a 1/8 plateau for realistic values of the magnetic exchange constants.
We show that the 1/8 plateau with a diamond unit cell benefits most compared to
other plateau structures from quantum fluctuations which to a large part are
induced by Dzyaloshinskii-Moriya interactions. Physically, such couplings
result in kinetic terms in an effective hardcore boson description leading to a
renormalization of the energy of the different plateaux structures which we
treat in this work on the mean-field level. The stability of the resulting
plateaux are discussed. Furthermore, our results indicate a series of stripe
structures above 1/8 and a stable magnetization plateau at 1/6. Most
qualitative aspects of our microscopic theory agree well with a recently
formulated phenomenological theory for the experimental data of SrCu_2(BO_3)_2.
Interestingly, our calculations point to a rather large ratio of the magnetic
couplings in the Shastry-Sutherland model such that non-perturbative effects
become essential for the understanding of the frustrated quantum magnet
SrCu_2(BO_3)_2.Comment: 24 pages, 24 figure
Learning physical descriptors for materials science by compressed sensing
The availability of big data in materials science offers new routes for
analyzing materials properties and functions and achieving scientific
understanding. Finding structure in these data that is not directly visible by
standard tools and exploitation of the scientific information requires new and
dedicated methodology based on approaches from statistical learning, compressed
sensing, and other recent methods from applied mathematics, computer science,
statistics, signal processing, and information science. In this paper, we
explain and demonstrate a compressed-sensing based methodology for feature
selection, specifically for discovering physical descriptors, i.e., physical
parameters that describe the material and its properties of interest, and
associated equations that explicitly and quantitatively describe those relevant
properties. As showcase application and proof of concept, we describe how to
build a physical model for the quantitative prediction of the crystal structure
of binary compound semiconductors
Scalable Focused Ion Beam Creation of Nearly Lifetime-Limited Single Quantum Emitters in Diamond Nanostructures
The controlled creation of defect center---nanocavity systems is one of the
outstanding challenges for efficiently interfacing spin quantum memories with
photons for photon-based entanglement operations in a quantum network. Here, we
demonstrate direct, maskless creation of atom-like single silicon-vacancy (SiV)
centers in diamond nanostructures via focused ion beam implantation with nm lateral precision and nm positioning accuracy relative to a
nanocavity. Moreover, we determine the Si+ ion to SiV center conversion yield
to and observe a 10-fold conversion yield increase by additional
electron irradiation. We extract inhomogeneously broadened ensemble emission
linewidths of GHz, and close to lifetime-limited single-emitter
transition linewidths down to MHz corresponding to -times
the natural linewidth. This demonstration of deterministic creation of
optically coherent solid-state single quantum systems is an important step
towards development of scalable quantum optical devices
Applications of Graphical Condensation for Enumerating Matchings and Tilings
A technique called graphical condensation is used to prove various
combinatorial identities among numbers of (perfect) matchings of planar
bipartite graphs and tilings of regions. Graphical condensation involves
superimposing matchings of a graph onto matchings of a smaller subgraph, and
then re-partitioning the united matching (actually a multigraph) into matchings
of two other subgraphs, in one of two possible ways. This technique can be used
to enumerate perfect matchings of a wide variety of bipartite planar graphs.
Applications include domino tilings of Aztec diamonds and rectangles, diabolo
tilings of fortresses, plane partitions, and transpose complement plane
partitions.Comment: 25 pages; 21 figures Corrected typos; Updated references; Some text
revised, but content essentially the sam
Mesoscopic Wigner crystallization in two dimensional lattice models
The quantum-classical crossover from the Fermi liquid towards the Wigner
solid is numerically revisited, considering small square lattice models where
electrons interact via a Coulomb potential. The studies of models without
disorder and spin and including disorder and spin show that the electron solid
is formed in two stages, giving rise to an intriguing solid-liquid regime at
intermediate couplingsComment: To appear in the proceedings of the XXXVIth Rencontres de Moriond
edited by T. Martin and G. Montambau
Universal properties of highly frustrated quantum magnets in strong magnetic fields
The purpose of the present paper is two-fold. On the one hand, we review some
recent studies on the low-temperature strong-field thermodynamic properties of
frustrated quantum spin antiferromagnets which admit the so-called
localized-magnon eigenstates. One the other hand, we provide some complementary
new results. We focus on the linear independence of the localized-magnon
states, the estimation of their degeneracy with the help of auxiliary classical
lattice-gas models and the analysis of the contribution of these states to
thermodynamics.Comment: Paper based on the invited talk given by J. Richter at the
International Conference "Statistical Physics 2006. Condensed Matter: Theory
and Applications" dedicated to the 90th anniversary of Ilya Lifshitz
(Kharkiv, 11-15 September, 2006
Structural trends in clusters of quadrupolar spheres
The influence of quadrupolar interactions on the structure of small clusters
is investigated by adding a point quadrupole of variable strength to the
Lennard-Jones potential. Competition arises between sheet-like arrangements of
the particles, favoured by the quadrupoles, and compact structures, favoured by
the isotropic Lennard-Jones attraction. Putative global potential energy minima
are obtained for clusters of up to 25 particles using the basin-hopping
algorithm. A number of structural motifs and growth sequences emerge, including
star-like structures, tubes, shells and sheets. The results are discussed in
the context of colloidal self-assembly.Comment: 8 pages, 6 figure
Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible
We analyze the computational complexity of the many types of
pencil-and-paper-style puzzles featured in the 2016 puzzle video game The
Witness. In all puzzles, the goal is to draw a simple path in a rectangular
grid graph from a start vertex to a destination vertex. The different puzzle
types place different constraints on the path: preventing some edges from being
visited (broken edges); forcing some edges or vertices to be visited
(hexagons); forcing some cells to have certain numbers of incident path edges
(triangles); or forcing the regions formed by the path to be partially
monochromatic (squares), have exactly two special cells (stars), or be singly
covered by given shapes (polyominoes) and/or negatively counting shapes
(antipolyominoes). We show that any one of these clue types (except the first)
is enough to make path finding NP-complete ("witnesses exist but are hard to
find"), even for rectangular boards. Furthermore, we show that a final clue
type (antibody), which necessarily "cancels" the effect of another clue in the
same region, makes path finding -complete ("witnesses do not exist"),
even with a single antibody (combined with many anti/polyominoes), and the
problem gets no harder with many antibodies. On the positive side, we give a
polynomial-time algorithm for monomino clues, by reducing to hexagon clues on
the boundary of the puzzle, even in the presence of broken edges, and solving
"subset Hamiltonian path" for terminals on the boundary of an embedded planar
graph in polynomial time.Comment: 72 pages, 59 figures. Revised proof of Lemma 3.5. A short version of
this paper appeared at the 9th International Conference on Fun with
Algorithms (FUN 2018
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