4,061 research outputs found
Stable pair invariants under blow-ups
We use degeneration formula to study the change of stable pair invariants of
3-folds under blow-ups and obtain some closed blow-up formulae. Related results
on Donaldson-Thomas invariants are also discussed. Our results give positive
evidence for GW/DT/P correspondence, and also give partial correspondence for
varieties not necessarily toric or complete intersections.Comment: 19 pages. Comments are welcome
On a conjectural solution to open KdV and Virasoro
In this note, we present a recursive formula for the full partition function
Z of descendent integrals over moduli spaces of open and closed Riemann
surfaces, assuming the conjecture recently proposed by Pandharipande, Solomon
and Tessler that Z satisfies the open KdV and Virasoro equations.Comment: 6 pages. Comments are welcome
On semisimplicity of quantum cohomology of -orbifolds
For a -orbifold , we prove that its big quantum
cohomology is generically semisimple. As a corollary, we verify a conjecture of
Dubrovin for orbi-curves. We also show that the small quantum cohomology of
is generically semisimple iff is Fano, i.e. it has
positive orbifold Euler characteristic.Comment: 16 pages. Comments are welcome
On Conjecture for projective complete intersections
We prove that Fano complete intersections in projective spaces satisfy
Conjecture proposed by Galkin-Golyshev-Iritani.Comment: 8 pages. Comments are welcome
A flop formula for Donaldson-Thomas invariants
Let and be nonsingular projective -folds related by a flop of a
disjoint union of -curves. We prove a flop formula relating the
Donaldson-Thomas invariants of to those of , which implies some simple
relations among BPS state counts. As an application, we show that if
satisfies the GW/DT correspondence for primary insertions and descendants of
the point class, then so does . We also propose a conjectural flop formula
for general flops.Comment: Corrected typo
Quantum McKay correspondence for disc invariants of toric Calabi-Yau 3-orbifolds
We announce a result on quantum McKay correspondence for disc invariants of
outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a
special example .Comment: 5 pages, 2 figures. Accepted by Acta Mathematica Sinica, English
Serie
Emergence and percolation of rigid domains during colloidal glass transition
Using video microscopy, we measure local spatial constraints in disordered
binary colloidal samples, ranging from dilute fluids to jammed glasses, and
probe their spatial and temporal correlations to local dynamics during the
glass transition. We observe the emergence of significant correlations between
constraints and local dynamics within the Lindemann criterion, which coincides
with the onset of glassy dynamics in supercooled liquids. Rigid domains in
fluids are identified based on local constraints, and demonstrate a percolation
transition near glass transition, accompanied by the emergence of dynamical
heterogeneities. Our results show that the spatial constraints instead of the
geometry of amorphous structures is the key that connects the complex
spatial-temporal correlations in disordered materials.Comment: 7 pages, 3 figure
Contrasting magnetism in isovalent layered LaSr3NiRuO4H4 and LaSrNiRuO4 due to distinct spin-orbital states
The recently synthesized first 4d transition-metal oxide-hydride
LaSr3NiRuO4H4 with the unusual high H:O ratio surprisingly displays no magnetic
order down to 1.8 K. This is in sharp contrast to the similar unusual
low-valent Ni+ - Ru2+ layered oxide LaSrNiRuO4 which has a rather high
ferromagnetic (FM) ordering Curie temperature TC about 250 K. In this work,
using density functional calculations with aid of crystal field level diagrams
and superexchange pictures, we find that the contrasting magnetism is due to
the distinct spin-orbital states of the Ru2+ ions (in addition to the common
Ni+ S=1/2 state but with a different orbital state): the Ru2+ S=0 state in
LaSr3NiRuO4H4, but the Ru2+ S=1 state in LaSrNiRuO4. The Ru2+ S=0 state has the
(xy)2(xz; yz)4 occupation due to the RuH4O2 octahedral coordination, and then
the nonmagnetic Ru2+ ions dilute the S=1/2 Ni+ sublattice which consequently
has a very weak antiferromagnetic (AF) superexchange and thus accounts for no
presence of magnetic order down to 1.8 K in LaSr3NiRuO4H4. In strong contrast,
the Ru2+ S=1 state in LaSrNiRuO4 has the (3z2-r2)2(xz; yz)3(xy)1 occupation due
to the planar square RuO4 coordination, and then the multi-orbital FM
superexchange between the S=1/2 Ni+ and S=1 Ru2+ ions gives rise to the high TC
in LaSrNiRuO4. This work highlights the importance of spin-orbital states in
determining the distinct magnetism.Comment: 6 pages, 4 figures, 1 tabl
Scroll wave drift along steps, troughs and corners
Three-dimensional excitable systems can create nonlinear scroll waves that
rotate around one-dimensional phase singularities. Recent theoretical work
predicts that these filaments drift along step-like height variations. Here we
test this prediction using experiments with thin layers of the
Belousov-Zhabotinsky reaction. We observe that over short distances scroll
waves are attracted towards the step and then rapidly commence a steady drift
along the step line. The translating filaments always reside in the shallow
subsystem and terminate on the step plateau near the edge. Accordingly
filaments in the deep subsystem initially collide with and shorten at the step
wall. The drift speeds obey the predicted proportional dependence on the
logarithm of the height ratio and the direction depends on the vortex
chirality. We also observe drift along the perimeter of rectangular plateaus
and find that the filaments perform sharp turns at the corners. In addition, we
investigate rectangular troughs for which vortices of equal chirality can drift
in different directions. The latter two effects are reproduced in numerical
simulations with the Barkley model. The simulations show that narrow troughs
instigate scroll wave encounters that induce repulsive interaction and symmetry
breaking. Similar phenomena could exist in the geometrical complicated
ventricles of the human heart where reentrant vortex waves cause tachycardia
and fibrillation
Controllable Unsupervised Text Attribute Transfer via Editing Entangled Latent Representation
Unsupervised text attribute transfer automatically transforms a text to alter
a specific attribute (e.g. sentiment) without using any parallel data, while
simultaneously preserving its attribute-independent content. The dominant
approaches are trying to model the content-independent attribute separately,
e.g., learning different attributes' representations or using multiple
attribute-specific decoders. However, it may lead to inflexibility from the
perspective of controlling the degree of transfer or transferring over multiple
aspects at the same time. To address the above problems, we propose a more
flexible unsupervised text attribute transfer framework which replaces the
process of modeling attribute with minimal editing of latent representations
based on an attribute classifier. Specifically, we first propose a
Transformer-based autoencoder to learn an entangled latent representation for a
discrete text, then we transform the attribute transfer task to an optimization
problem and propose the Fast-Gradient-Iterative-Modification algorithm to edit
the latent representation until conforming to the target attribute. Extensive
experimental results demonstrate that our model achieves very competitive
performance on three public data sets. Furthermore, we also show that our model
can not only control the degree of transfer freely but also allow to transfer
over multiple aspects at the same time.Comment: Neurips 2019 camera read
- β¦