Topological invariants for phase transition points of one-dimensional Z2\mathbb{Z}_2 topological systems

We study topological properties of phase transition points of two topologically non-trivial $\mathbb{Z}_2$ classes (D and DIII) in one dimension by assigning a Berry phase defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter. While the topological property of the $\mathbb{Z}_2$ system is generally characterized by a $\mathbb{Z}_2$ topological invariant, we identify that it has a correspondence to the quantized Berry phase protected by the particle-hole symmetry, and then give a proper definition of Berry phase to the phase transition point. By applying our scheme to some specific models of class D and DIII, we demonstrate that the topological phase transition can be well characterized by the Berry phase of the transition point, which reflects the change of Berry phases of topologically different phases across the phase transition point.Comment: 6 pages, 5 figure

Winding numbers of phase transition points for one-dimensional topological systems

We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.Comment: 5 pages, 5 figure

A Theory of Pricing Private Data

Personal data has value to both its owner and to institutions who would like to analyze it. Privacy mechanisms protect the owner's data while releasing to analysts noisy versions of aggregate query results. But such strict protections of individual's data have not yet found wide use in practice. Instead, Internet companies, for example, commonly provide free services in return for valuable sensitive information from users, which they exploit and sometimes sell to third parties. As the awareness of the value of the personal data increases, so has the drive to compensate the end user for her private information. The idea of monetizing private data can improve over the narrower view of hiding private data, since it empowers individuals to control their data through financial means. In this paper we propose a theoretical framework for assigning prices to noisy query answers, as a function of their accuracy, and for dividing the price amongst data owners who deserve compensation for their loss of privacy. Our framework adopts and extends key principles from both differential privacy and query pricing in data markets. We identify essential properties of the price function and micro-payments, and characterize valid solutions.Comment: 25 pages, 2 figures. Best Paper Award, to appear in the 16th International Conference on Database Theory (ICDT), 201

Dys-regulated Gene Expression Networks by Meta-Analysis of Microarray Data on Oral Squamous Cell Carcinoma

Background: Oral squamous cell carcinoma (OSCC) is the sixth most common type of carcinoma worldwide. Development of OSCC is a multi-step process involving genes related to cell cycle, growth control, apoptosis, DNA damage response and other cellular regulators. The pathogenic pathways involved in this tumor are mostly unknown and therefore a better characterization of OSCC gene expression profile would represent a considerable advance. The availability of publicly available gene expression datasets has opened up new challenges especially for the integration of data generated by different research groups and different array platforms with the purpose of obtaining new insights on the biological process investigated.

Results: In this work we performed a meta-analysis on four microarray and four datasets of gene expression data on OSCC in order to evaluate the degree of agreement of the biological results obtained by these different studies and to identify common regulatory pathways that could be responsible of tumor growth. Sixteen dys-regulated pathways implicated in OSCC were mined out from the four published datasets, and most importantly three pathways were first reported. Those regulatory pathways and biological processes which are significantly enriched have been investigated by means of literatures and meanwhile, four genes of the maximally altered pathways, ECM-receptor interaction, were validated and identified by qRT-PCR as a possible candidate of aggressiveness of OSCC.

Conclusion: we have developed a robust method for analyzing pathways altered in OSCC using three expression array data sets. This study sets a stage for the further discovery of the basic mechanisms that may underlie a diseased state and would help in identifying critical nodes in the pathway that can be targeted for diagnosis and therapeutic intervention. In addition, those who are interested in our approach can obtain the software package (MATLAB platform) by email freely