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

Can P2P Technology Benefit Eyeball ISPs? A Cooperative Profit Distribution Answer

Peer-to-Peer (P2P) technology has been regarded as a promising way to help Content Providers (CPs) cost-effectively distribute content. However, under the traditional Internet pricing mechanism, the fact that most P2P traffic flows among peers can dramatically decrease the profit of ISPs, who may take actions against P2P and impede the progress of P2P technology. In this paper, we develop a mathematical framework to analyze such economic issues. Inspired by the idea from cooperative game theory, we propose a cooperative profit-distribution model based on Nash Bargaining Solution (NBS), in which eyeball ISPs and Peer-assisted CPs (PCPs) form two coalitions respectively and then compute a fair Pareto point to determine profit distribution. Moreover, we design a fair and feasible mechanism for profit distribution within each coalition. We show that such a cooperative method not only guarantees the fair profit distribution among network participators, but also helps to improve the economic efficiency of the overall network system. To our knowledge, this is the first work that systematically studies solutions for P2P caused unbalanced profit distribution and gives a feasible cooperative method to increase and fairly share profit

Linearization of a warped f(R)f(R) theory in the higher-order frame II: the equation of motion approach

Without using conformal transformation, a simple type of five-dimensional $f(R)-$brane model is linearized directly in its higher-order frame. In this paper, the linearization is conducted in the equation of motion approach. We first derive all the linear perturbation equations without specifying a gauge condition. Then by taking the curvature gauge we derive the master equations of the linear perturbations. We show that these equations are equivalent to those obtained in the quadratical action approach [Phys. Rev. D 95 (2017) 104060], except the vector sector, in which a constraint equation can be obtained in the equation of motion approach but absent in the quadratical action approach. Our work sets an example on how to linearize higher-order theories without using conformal transformation, and might be useful for studying more complicated theories.Comment: 12 page

Deep Learning Based Phase Reconstruction for Speaker Separation: A Trigonometric Perspective

This study investigates phase reconstruction for deep learning based monaural talker-independent speaker separation in the short-time Fourier transform (STFT) domain. The key observation is that, for a mixture of two sources, with their magnitudes accurately estimated and under a geometric constraint, the absolute phase difference between each source and the mixture can be uniquely determined; in addition, the source phases at each time-frequency (T-F) unit can be narrowed down to only two candidates. To pick the right candidate, we propose three algorithms based on iterative phase reconstruction, group delay estimation, and phase-difference sign prediction. State-of-the-art results are obtained on the publicly available wsj0-2mix and 3mix corpus.Comment: 5 pages, in submission to ICASSP-201

Difference Discrete Connection and Curvature on Cubic Lattice

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.Comment: 29 page