The theory of N-Mixed-Spin-P fields

This is the first part of the project toward proving the BCOV's Feymann graph sum formula of all genera Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of N-Mixed-Spin-P fields, construct their moduli spaces, their virtual cycles, their virtual localization formulas, and a vanishing result associated with irregular graphs

An Empirical Method to Measure Stochasticity and Multifractality in Nonlinear Time Series

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.Comment: 10 pages, 11 figure

Inflation in de Sitter spacetime and CMB large scales anomaly

The influence of cosmological constant type dark energy in the early universe is investigated. This is accommodated by a new dispersion relation in de Sitter spacetime. We perform a global fitting to explore the cosmological parameters space by using the CosmoMC package with the recently released Planck TT and WMAP Polarization datasets. Using the results from global fitting, we compute a new CMB temperature-temperature spectrum. The obtained TT spectrum has lower power compared with the one based on $\Lambda$CDM model at large scales.Comment: 4 pages, 1 table, 3 figure

CosmoMC Installation and Running Guidelines

CosmoMC is a Fortran 95 Markov-Chain Monte-Carlo (MCMC) engine to explore the cosmological parameter space, plus a Python suite for plotting and presenting results (see http://cosmologist.info/cosmomc/). This document describes the installation of the CosmoMC on a Linux system (Ubuntu 14.04.1 LTS 64-bit version). It is written for those who want to use it in their scientific research but without much training on Linux and the program. Besides a step-by-step installation guide, we also give a brief introduction of how to run the program on both a desktop and a cluster. We share our way to generate the plots that are commonly used in the references of cosmology. For more information, one can refer to the CosmoCoffee forum (http://cosmocoffee.info/viewforum.php?f=11) or contact the authors of this document. Questions and comments would be much appreciated.Comment: 10 pages, 0 figures. Publicly distributed and availabl

Mixed-Spin-P fields of Fermat quintic polynomials

This is the first part of the project toward an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of Mixed-Spin-P fields, construct their moduli spaces, and construct the virtual cycles of these moduli spaces.Comment: Introduction and references updated. 34 page

An effective theory of GW and FJRW invariants of quintics Calabi-Yau manifolds

This is the second part of the project toward an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, the localization formula is derived, and algorithms toward evaluating these Gromov-Witten invariants are derived.Comment: 50 pages; We add to the original version some remarks on the latest progress made by packaging MSP (NMSP) field

A survey on mixed spin P-fields

This is a survey on the mixed spin P-fields (MSP fields for short) theory which provides a platform to understand the phase transition between Gromov-Witten theory of quintic CY 3-folds and Landau-Ginzburg theory of the corresponding quintic polynomials. It discusses key ideas that lead to the definition of MSP fields and how moduli of stable maps to the quintic and that of 5-spin curves appear in the moduli of MSP fields. It also explains some properties of the moduli of MSP fields such as the cosection localisation, the properness of the degeneracy locus, and a torus action on the moduli.. Some vanishings arising from the torus action provide polynomial relations among GW-invarants and FJRW-invaraints which give an effective algorithm for the computation of those invariants. Some examples of computations of genus 1 low degree of GW invariants are provided.Comment: 15 pages, 2 figure

Genus one GW invariants of quintic threefolds via MSP localization

The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. This paper is to apply the algorithm in genus one case. We use the localization formula, the proposed algorithm in [CLLL1, CLLL2], and Zinger's packaging technique to compute the genus one Gromov-Witten invariants of quintic Calabi-Yau threefolds. New hypergeometric series identities are also discovered in the process

Robust Room-Temperature Quantum Spin Hall Effect in Methyl-functionalized InBi honeycomb film

Two-dimensional (2D) group-III-V honeycomb films have attracted significant interest for their potential application in fields of quantum computing and nanoeletronics. Searching for 2D III-V films with high structural stability and large-gap are crucial for the realizations of dissipationless transport edge states using quantum spin Hall (QSH) effect. Based on first-principles calculations, we predict that the methyl-functionalized InBi monolayer (InBiCH3) has no dynamic instability, and host a QSH state with a band gap as large as 0.29 eV, exhibiting an interesting electronic behavior viable for room-temperature applications. The topological characteristic is confirmed by s-pxy bands inversion, topological invariant Z2 number, and the time-reversal symmetry protected helical edge states. Noticeably, the QSH states are tunable and robust against the mechanical strain, electric field and different levels of methyl coverages. We also find that InBiCH3 supported on h-BN substrate maintains a nontrivial QSH state, which harbors the edge states lying within the band gap of substrate. These findings demonstrate that the methyl-functionalized III-V films may be a good QSH platform for device design and fabrication in spintronics.Comment: 24 pages, 6 figure

Constraining the Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In quantum gravity, a foamy structure of space-time leads to Lorentz invariance violation (LIV). As the most energetic astrophysical processes in the Universe, gamma-ray bursts (GRBs) provide an effective way to probe quantum gravity effects. We use continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale $M_\textrm{QG}$. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to the low energy ones. Based on the fact that the LIV-induced time delay can't be longer than the duration of a GRB, we present the most conservative estimation of the quantum gravity energy scales from 20 short GRBs. The most strict constraint, $M_\textrm{QG}>5.05\times10^{14}$ GeV, is from GRB 140622A.Comment: 10 pages, 1 figure, 1 table; Submitted to Chinese Physics