Inflation and Alternatives with Blue Tensor Spectra

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.Comment: 13 pages, 10 figures. v2: references and minor improvements added. v3: version to appear on JCA

Hierarchical Information and the Rate of Information Diffusion

The rate of information diffusion and consequently price discovery, is conditional upon not only the design of the market microstructure, but also the informational structure. This paper presents a market microstructure model showing that an increasing number of information hierarchies among informed competitive traders leads to a slower information diffusion rate and informational inefficiency. The model illustrates that informed traders may prefer trading with each other rather than with noise traders in the presence of the information hierarchies. Furthermore, we show that momentum can be generated from the predictable patterns of noise traders, which are assumed to be a function of past pricesInformation hierarchies, Information diffusion rate, Momentum

Trading Frequency and Volatility Clustering

Volatility clustering, with autocorrelations of the hyperbolic decay rate, is unquestionably one of the most important stylized facts of financial time series. This paper presents a market microstructure model, that is able to generate volatility clustering with hyperbolic autocorrelations through traders with multiple trading frequencies using Bayesian information updating in an incomplete market. The model illustrates that signal extraction, which is induced by multiple trading frequency, can increase the persistence of the volatility of returns. Furthermore, we show that the local temporal memory of the underlying time series of returns and their volatility varies greatly varies with the number of traders in the marketTrading frequency, Volatility clustering, Signal extraction, Hyperbolic decay

Inflationary NonGaussianity from Thermal Fluctuations

We calculate the contribution of the fluctuations with the thermal origin to the inflationary nonGaussianity. We find that even a small component of radiation can lead to a large nonGaussianity. We show that this thermal nonGaussianity always has positive $f_{\rm NL}$. We illustrate our result in the chain inflation model and the very weakly dissipative warm inflation model. We show that $f_{NL}\sim {\cal O}(1)$ is general in such models. If we allow modified equation of state, or some decoupling effects, the large thermal nonGaussianity of order $f_{\rm NL}>5$ or even $f_{\rm NL}\sim 100$ can be produced. We also show that the power spectrum of chain inflation should have a thermal origin. In the Appendix A, we made a clarification on the different conventions used in the literature related to the calculation of $f_{\rm NL}$.Comment: 20 pages, 1 figure. v2, v3: references and acknowledgments update

Generalized Space-time Noncommutative Inflation

We study the noncommutative inflation with a time-dependent noncommutativity between space and time. From the numerical analysis of power law inflation, there are clues that the CMB spectrum indicates a nonconstant noncommutative inflation. Then we extend our treatment to the inflation models with more general noncommutativity and find that the scalar perturbation power spectrum depends sensitively on the time varying of the spacetime noncommutativity. This stringy effect may be probed in the future cosmological observations.Comment: 15 pages, 2 figure

A two-stage video coding framework with both self-adaptive redundant dictionary and adaptively orthonormalized DCT basis

In this work, we propose a two-stage video coding framework, as an extension of our previous one-stage framework in [1]. The two-stage frameworks consists two different dictionaries. Specifically, the first stage directly finds the sparse representation of a block with a self-adaptive dictionary consisting of all possible inter-prediction candidates by solving an L0-norm minimization problem using an improved orthogonal matching pursuit with embedded orthonormalization (eOMP) algorithm, and the second stage codes the residual using DCT dictionary adaptively orthonormalized to the subspace spanned by the first stage atoms. The transition of the first stage and the second stage is determined based on both stages' quantization stepsizes and a threshold. We further propose a complete context adaptive entropy coder to efficiently code the locations and the coefficients of chosen first stage atoms. Simulation results show that the proposed coder significantly improves the RD performance over our previous one-stage coder. More importantly, the two-stage coder, using a fixed block size and inter-prediction only, outperforms the H.264 coder (x264) and is competitive with the HEVC reference coder (HM) over a large rate range