29,695 research outputs found
Enumeration of labelled 4-regular planar graphs
We present the first combinatorial scheme for counting labelled 4-regular
planar graphs through a complete recursive decomposition. More precisely, we
show that the exponential generating function of labelled 4-regular planar
graphs can be computed effectively as the solution of a system of equations,
from which the coefficients can be extracted. As a byproduct, we also enumerate
labelled 3-connected 4-regular planar graphs, and simple 4-regular rooted maps
Voicing Transformations and a Linear Representation of Uniform Triadic Transformations (Preprint name)
Motivated by analytical methods in mathematical music theory, we determine the structure of the subgroup of generated by the three voicing reflections. We determine the centralizer of in both and the monoid of affine transformations, and recover a Lewinian duality for trichords containing a generator of . We present a variety of musical examples, including Wagner's hexatonic Grail motive and the diatonic falling fifths as cyclic orbits, an elaboration of our earlier work with Satyendra on Schoenberg, String Quartet in minor, op. 7, and an affine musical map of Joseph Schillinger. Finally, we observe, perhaps unexpectedly, that the retrograde inversion enchaining operation RICH (for arbitrary 3-tuples) belongs to the setwise stabilizer in of root position triads. This allows a more economical description of a passage in Webern, Concerto for Nine Instruments, op. 24 in terms of a morphism of group actions. Some of the proofs are located in the Supplementary Material file, so that this main article can focus on the applications
Universal Quantum Hamiltonians
Quantum many-body systems exhibit an extremely diverse range of phases and
physical phenomena. Here, we prove that the entire physics of any other quantum
many-body system is replicated in certain simple, "universal" spin-lattice
models. We first characterise precisely what it means for one quantum many-body
system to replicate the entire physics of another. We then show that certain
very simple spin-lattice models are universal in this very strong sense.
Examples include the Heisenberg and XY models on a 2D square lattice (with
non-uniform coupling strengths). We go on to fully classify all two-qubit
interactions, determining which are universal and which can only simulate more
restricted classes of models. Our results put the practical field of analogue
Hamiltonian simulation on a rigorous footing and take a significant step
towards justifying why error correction may not be required for this
application of quantum information technology.Comment: 78 pages, 9 figures, 44 theorems etc. v2: Trivial fixes. v3: updated
and simplified proof of Thm. 9; 82 pages, 47 theorems etc. v3: Small fix in
proof of time-evolution lemma (this fix not in published version
Reionization and Cosmic Dawn: theory and simulations
We highlight recent progress in the sophistication and diversification of
cosmic dawn and reionization simulations. The application of these modeling
tools to current observations has allowed us narrow down the timing of
reionization, which we now know to within dz ~ 1 for the bulk of reionization.
The strongest constraints come from the optical depth to the CMB measured with
the {\it Planck} satellite and the first detection of ongoing reionization from
the spectra of the z=7.1 QSOs ULASJ1120+0641. However, we still know virtually
nothing about the astrophysical sources during the first billion years. The
revolution in our understanding will be led by upcoming interferometric
observations of the cosmic 21-cm signal. The properties of the sources and
sinks of UV and X-ray photons are encoded in the 3D patterns of the signal. The
development of Bayesian parameter recovery techniques, which tap into the
wealth of the 21-cm signal, will soon usher in an era of precision
astrophysical cosmology.Comment: Invited review for the IAU Symposium 333 "Peering towards Cosmic
Dawn", Dubrovnik, October 2-6, 2017; to appear in the proceedings, eds. Vibor
Jelic and Thijs van der Hulst [8 pages, 3 figures
From SO/Sp instantons to W-algebra blocks
We study instanton partition functions for N=2 superconformal Sp(1) and SO(4)
gauge theories. We find that they agree with the corresponding U(2) instanton
partitions functions only after a non-trivial mapping of the microscopic gauge
couplings, since the instanton counting involves different renormalization
schemes. Geometrically, this mapping relates the Gaiotto curves of the
different realizations as double coverings. We then formulate an AGT-type
correspondence between Sp(1)/SO(4) instanton partition functions and chiral
blocks with an underlying W(2,2)-algebra symmetry. This form of the
correspondence eliminates the need to divide out extra U(1) factors. Finally,
to check this correspondence for linear quivers, we compute expressions for the
Sp(1)-SO(4) half-bifundamental.Comment: 83 pages, 29 figures; minor change
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Imaging striatal dopamine release using a nongenetically encoded near infrared fluorescent catecholamine nanosensor.
Neuromodulation plays a critical role in brain function in both health and disease, and new tools that capture neuromodulation with high spatial and temporal resolution are needed. Here, we introduce a synthetic catecholamine nanosensor with fluorescent emission in the near infrared range (1000-1300 nm), near infrared catecholamine nanosensor (nIRCat). We demonstrate that nIRCats can be used to measure electrically and optogenetically evoked dopamine release in brain tissue, revealing hotspots with a median size of 2 µm. We also demonstrated that nIRCats are compatible with dopamine pharmacology and show D2 autoreceptor modulation of evoked dopamine release, which varied as a function of initial release magnitude at different hotspots. Together, our data demonstrate that nIRCats and other nanosensors of this class can serve as versatile synthetic optical tools to monitor neuromodulatory neurotransmitter release with high spatial resolution
Quiver Theories from D6-branes via Mirror Symmetry
We study N=1 four dimensional quiver theories arising on the worldvolume of
D3-branes at del Pezzo singularities of Calabi-Yau threefolds. We argue that
under local mirror symmetry D3-branes become D6-branes wrapped on a three torus
in the mirror manifold. The type IIB (p,q) 5-brane web description of the local
del Pezzo, being closely related to the geometry of its mirror manifold,
encodes the geometry of 3-cycles and is used to obtain gauge groups, quiver
diagrams and the charges of the fractional branes.Comment: 30 pages, citations adde
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