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

A flop formula for Donaldson-Thomas invariants

Let $X$ and $X'$ be nonsingular projective $3$-folds related by a flop of a disjoint union of $(-2)$-curves. We prove a flop formula relating the Donaldson-Thomas invariants of $X$ to those of $X'$, which implies some simple relations among BPS state counts. As an application, we show that if $X$ satisfies the GW/DT correspondence for primary insertions and descendants of the point class, then so does $X'$. We also propose a conjectural flop formula for general flops.Comment: Corrected typo

On Conjecture O\mathcal O for projective complete intersections

We prove that Fano complete intersections in projective spaces satisfy Conjecture $\mathcal O$ proposed by Galkin-Golyshev-Iritani.Comment: 8 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 P1\mathbb P^1-orbifolds

For a $\mathbb P^1$-orbifold $\mathscr C$, 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 $\mathscr C$ is generically semisimple iff $\mathscr C$ is Fano, i.e. it has positive orbifold Euler characteristic.Comment: 16 pages. Comments are welcome

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 $[\mathbb C^3 /\mathbb Z_5 (1, 1, 3)]$.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