Variational equalities of entropy in nonuniformly hyperbolic systems

In this paper we prove that for an ergodic hyperbolic measure $\omega$ of a $C^{1+\alpha}$ diffeomorphism $f$ on a Riemannian manifold $M$, there is an $\omega$-full measured set $\widetilde{\Lambda}$ such that for every invariant probability $\mu\in \mathcal{M}_{inv}(\widetilde{\Lambda},f)$, the metric entropy of $\mu$ is equal to the topological entropy of saturated set $G_{\mu}$ consisting of generic points of $\mu$: $$h_\mu(f)=h_{\top}(f,G_{\mu}).$$ Moreover, for every nonempty, compact and connected subset $K$ of $\mathcal{M}_{inv}(\widetilde{\Lambda},f)$ with the same hyperbolic rate, we compute the topological entropy of saturated set $G_K$ of $K$ by the following equality: $$\inf\{h_\mu(f)\mid \mu\in K\}=h_{\top}(f,G_K).$$ In particular these results can be applied (i) to the nonuniformy hyperbolic diffeomorphisms described by Katok, (ii) to the robustly transitive partially hyperbolic diffeomorphisms described by ~Ma{\~{n}}{\'{e}}, (iii) to the robustly transitive non-partially hyperbolic diffeomorphisms described by Bonatti-Viana. In all these cases $\mathcal{M}_{inv}(\widetilde{\Lambda},f)$ contains an open subset of $\mathcal{M}_{erg}(M,f)$.Comment: Transactions of the American Mathematical Society, to appear,see http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2016-06780-X

FINANCIAL STATEMENT FRAUD DETECTION USING TEXT MINING: A SYSTEMIC FUNCTIONAL LINGUISTICS THEORY PERSPECTIVE

Fraudulent financial information made by public companies not only cause significant financial loss to broad shareholders but also result in a great loss of confidence to capital market. Conventional auditing practices, which primarily focus on statistical analysis of structured financial ratios in auditing process, work not so well with the presence of misleading financial reports. This research tries to tap the power of huge amount of largely ignored textual contents in financial statements. With the theoretical guidance of Systemic Functional Linguistics theory (SFL), we develop a systematic text analytic framework for financial statement fraud detection. Seven information types, i.e., topics, opinions, emotions, modality, personal pronouns, writing style, and genres are identified based on ideational, interpersonal, and textual metafunctions in SFL. Under the analytic framework, Latent Dirichlet Allocation algorithm, computational linguistics, term frequency-inverse document frequency method, are integrated to create a synergy for extracting both word-level and document-level features. All these features serve as the input of Liblinear Support Vector Machine classifier. Finally, with application to detect fraud in 1610 firm-year samples from U.S. listed companies, the analytic framework makes a classification with average accuracy at 82.36% under ten-fold cross validation, much better than baseline method using financial ratios

A multi-task learning CNN for image steganalysis

Convolutional neural network (CNN) based image steganalysis are increasingly popular because of their superiority in accuracy. The most straightforward way to employ CNN for image steganalysis is to learn a CNN-based classifier to distinguish whether secret messages have been embedded into an image. However, it is difficult to learn such a classifier because of the weak stego signals and the limited useful information. To address this issue, in this paper, a multi-task learning CNN is proposed. In addition to the typical use of CNN, learning a CNN-based classifier for the whole image, our multi-task CNN is learned with an auxiliary task of the pixel binary classification, estimating whether each pixel in an image has been modified due to steganography. To the best of our knowledge, we are the first to employ CNN to perform the pixel-level classification of such type. Experimental results have justified the effectiveness and efficiency of the proposed multi-task learning CNN