Geometry of Numbers

We develop a global cohomology theory for number fields by offering topological cohomology groups, an arithmetical duality, a Riemann-Roch type theorem, and two types of vanishing theorem. As applications, we study moduli spaces of semi-stable lattices, and introduce non-abelian zeta functions for number fields.Comment: A paper by Tsukasa Hayashi is adde

Unsupervised Spoken Term Detection with Spoken Queries by Multi-level Acoustic Patterns with Varying Model Granularity

This paper presents a new approach for unsupervised Spoken Term Detection with spoken queries using multiple sets of acoustic patterns automatically discovered from the target corpus. The different pattern HMM configurations(number of states per model, number of distinct models, number of Gaussians per state)form a three-dimensional model granularity space. Different sets of acoustic patterns automatically discovered on different points properly distributed over this three-dimensional space are complementary to one another, thus can jointly capture the characteristics of the spoken terms. By representing the spoken content and spoken query as sequences of acoustic patterns, a series of approaches for matching the pattern index sequences while considering the signal variations are developed. In this way, not only the on-line computation load can be reduced, but the signal distributions caused by different speakers and acoustic conditions can be reasonably taken care of. The results indicate that this approach significantly outperformed the unsupervised feature-based DTW baseline by 16.16\% in mean average precision on the TIMIT corpus.Comment: Accepted by ICASSP 201

A new model to predict weak-lensing peak counts II. Parameter constraint strategies

Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analyses. In this work, we explore and compare various strategies for constraining parameter using our model, focusing on the matter density $\Omega_\mathrm{m}$ and the density fluctuation amplitude $\sigma_8$. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique which makes a weaker assumption compared to the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. We find that neglecting the CDC effect enlarges parameter contours by 22%, and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in an excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.Comment: 15 pages, 11 figures. Accepted versio