The log term of Szego Kernel

In this paper, we study the relations between the log term of the Szeg\"o kernel of the unit circle bundle of the dual line bundle of an ample line bundle over a compact K\"ahlermanifold. We proved a local rigidity theorem. The result is related to the classical Ramadanov Conjecture.Comment: We corrected a typo in the title in this versio

Metric Learning in Codebook Generation of Bag-of-Words for Person Re-identification

Person re-identification is generally divided into two part: first how to represent a pedestrian by discriminative visual descriptors and second how to compare them by suitable distance metrics. Conventional methods isolate these two parts, the first part usually unsupervised and the second part supervised. The Bag-of-Words (BoW) model is a widely used image representing descriptor in part one. Its codebook is simply generated by clustering visual features in Euclidian space. In this paper, we propose to use part two metric learning techniques in the codebook generation phase of BoW. In particular, the proposed codebook is clustered under Mahalanobis distance which is learned supervised. Extensive experiments prove that our proposed method is effective. With several low level features extracted on superpixel and fused together, our method outperforms state-of-the-art on person re-identification benchmarks including VIPeR, PRID450S, and Market1501

Phase-Aligned Spectral Filtering for Decomposing Spatiotemporal Dynamics

Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about such dynamics via data assimilation and modeling. It is assumed that the observed spatiotemporal data represent superimposed lower-rank smooth oscillations and movements from a generative dynamic system, mixed with higher-rank random noises. Separating the signals from noises is essential for us to visualize, model and understand these lower-rank dynamic systems. It is also often the case that such a lower-rank dynamic system have multiple independent components, corresponding to different trends or functionalities of the system under study. In this paper, we present a novel filtering framework for identifying lower-rank dynamics and its components embedded in a high dimensional spatiotemporal system. It is based on an approach of structural decomposition and phase-aligned construction in the frequency domain. In both our simulated examples and real data applications, we illustrate that the proposed method is able to separate and identify meaningful lower-rank movements, while existing methods fail.Comment: 29 pages, 10 figure

Constructing virtual Euler cycles and classes

The constructions of the virtual Euler (or moduli) cycles and their properties are explained and developed systematically in the general abstract settings.Comment: 181 pages, V2; Section 2.1 is rewritten; a new Section 2.2 is added; the original Section 2.2-Section 2.7 become Section 2.3-Section 2.8; Sections 3,4 are rewritten; other places have also some small change

Extending PPTL for Verifying Heap Evolution Properties

In this paper, we integrate separation logic with Propositional Projection Temporal Logic (PPTL) to obtain a two-dimensional logic, namely PPTL^{\tiny\mbox{SL}}. The spatial dimension is realized by a decidable fragment of separation logic which can be used to describe linked lists, and the temporal dimension is expressed by PPTL. We show that PPTL and PPTL^{\tiny\mbox{SL}} are closely related in their syntax structures. That is, for any PPTL^{\tiny\mbox{SL}} formula in a restricted form, there exists an "isomorphic" PPTL formula. The "isomorphic" PPTL formulas can be obtained by first an equisatisfiable translation and then an isomorphic mapping. As a result, existing theory of PPTL, such as decision procedure for satisfiability and model checking algorithm, can be reused for PPTL^{\tiny\mbox{SL}}

Evaluating Surrogate Marker Information using Censored Data

Given the long follow-up periods that are often required for treatment or intervention studies, the potential to use surrogate markers to decrease the required follow-up time is a very attractive goal. However, previous studies have shown that using inadequate markers or making inappropriate assumptions about the relationship between the primary outcome and surrogate marker can lead to inaccurate conclusions regarding the treatment effect. Currently available methods for identifying and validating surrogate markers tend to rely on restrictive model assumptions and/or focus on uncensored outcomes. The ability to use such methods in practice when the primary outcome of interest is a time-to-event outcome is difficult due to censoring and missing surrogate information among those who experience the primary outcome before surrogate marker measurement. In this paper, we propose a novel definition of the proportion of treatment effect explained by surrogate information collected up to a specified time in the setting of a time-to-event primary outcome. Our proposed approach accommodates a setting where individuals may experience the primary outcome before the surrogate marker is measured. We propose a robust nonparametric procedure to estimate the defined quantity using censored data and use a perturbation-resampling procedure for variance estimation. Simulation studies demonstrate that the proposed procedures perform well in finite samples. We illustrate the proposed procedures by investigating two potential surrogate markers for diabetes using data from the Diabetes Prevention Program.Comment: This article has been submitted to Statistics in Medicin

WeText: Scene Text Detection under Weak Supervision

The requiring of large amounts of annotated training data has become a common constraint on various deep learning systems. In this paper, we propose a weakly supervised scene text detection method (WeText) that trains robust and accurate scene text detection models by learning from unannotated or weakly annotated data. With a "light" supervised model trained on a small fully annotated dataset, we explore semi-supervised and weakly supervised learning on a large unannotated dataset and a large weakly annotated dataset, respectively. For the unsupervised learning, the light supervised model is applied to the unannotated dataset to search for more character training samples, which are further combined with the small annotated dataset to retrain a superior character detection model. For the weakly supervised learning, the character searching is guided by high-level annotations of words/text lines that are widely available and also much easier to prepare. In addition, we design an unified scene character detector by adapting regression based deep networks, which greatly relieves the error accumulation issue that widely exists in most traditional approaches. Extensive experiments across different unannotated and weakly annotated datasets show that the scene text detection performance can be clearly boosted under both scenarios, where the weakly supervised learning can achieve the state-of-the-art performance by using only 229 fully annotated scene text images.Comment: accepted by ICCV201

Amplitude Space Sharing among the Macro-Cell and Small-Cell Users

The crushing demand for wireless data services will soon exceed the capability of the current homogeneous cellular architecture. An emerging solution is to overlay small-cell networks with the macro-cell networks. In this paper, we propose an amplitude space sharing (ASS) method among the macro-cell user and small-cell users. By transmit layer design and data-rate optimization, the signals and interferences are promised to be separable at each receiver and the network sum-rate is maximized. The Han-Koboyashi coding is employed and optimal power allocation is derived for the one small-cell scenario, and a simple ASS transmission scheme is developed for the multiple small-cells scenarios. Simulation results show great superiority over other interference management schemes.Comment: 6 pages, 5 figures, submitted to IEEE Int. Conf. on Communications (ICC) 201

A note on uniformization of Riemann surfaces by Ricci flow

In this note we clarify that the Rcci flow can be used to give an independent proof of the uniformization theorem of Riemann surfaces.Comment: 3 pages, no figure, minor change

An interpretable LSTM neural network for autoregressive exogenous model

In this paper, we propose an interpretable LSTM recurrent neural network, i.e., multi-variable LSTM for time series with exogenous variables. Currently, widely used attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, our multi-variable LSTM equipped with tensorized hidden states is developed to learn variable specific representations, which give rise to both temporal and variable level attention. Preliminary experiments demonstrate comparable prediction performance of multi-variable LSTM w.r.t. encoder-decoder based baselines. More interestingly, variable importance in real datasets characterized by the variable attention is highly in line with that determined by statistical Granger causality test, which exhibits the prospect of multi-variable LSTM as a simple and uniform end-to-end framework for both forecasting and knowledge discovery