Private Multiplicative Weights Beyond Linear Queries

A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these analyses can leak that sensitive information, it is important to be able to solve convex minimization in a privacy-preserving way. A series of recent results show how to accurately solve a single convex minimization problem in a differentially private manner. However, the same data is often analyzed repeatedly, and little is known about solving multiple convex minimization problems with differential privacy. For simpler data analyses, such as linear queries, there are remarkable differentially private algorithms such as the private multiplicative weights mechanism (Hardt and Rothblum, FOCS 2010) that accurately answer exponentially many distinct queries. In this work, we extend these results to the case of convex minimization and show how to give accurate and differentially private solutions to *exponentially many* convex minimization problems on a sensitive dataset

Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

A physical layer network coding based modify-and-forward with opportunistic secure cooperative transmission protocol

This paper investigates a new secure relaying scheme, namely physical layer network coding based modify-and-forward (PMF), in which a relay node linearly combines the decoded data sent by a source node with an encrypted key before conveying the mixed data to a destination node. We first derive the general expression for the generalized secrecy outage probability (GSOP) of the PMF scheme and then use it to analyse the GSOP performance of various relaying and direct transmission strategies. The GSOP performance comparison indicates that these transmission strategies offer different advantages depending on the channel conditions and target secrecy rates, and relaying is not always desirable in terms of secrecy. Subsequently, we develop an opportunistic secure transmission protocol for cooperative wireless relay networks and formulate an optimisation problem to determine secrecy rate thresholds (SRTs) to dynamically select the optimal transmission strategy for achieving the lowest GSOP. The conditions for the existence of the SRTs are derived for various channel scenarios

Gene expression profiling of noninvasive primary urothelial tumours using microarrays

At present, the mechanism leading to bladder cancer is still poorly understood, and our knowledge about early events in tumorigenesis is limited. This study describes the changes in gene expression occurring during the neoplastic transition from normal bladder urothelium to primary Ta tumours. Using DNA microarrays, we identified novel differentially expressed genes in Ta tumours compared to normal bladder, and genes that were altered in high-grade tumours. Among the mostly changed genes between normal bladder and Ta tumours, we found genes related to the cytoskeleton (keratin 7 and syndecan 1), and transcription (high mobility group AT-hook 1). Altered genes in high-grade tumours were related to cell cycle (cyclin-dependent kinase 4) and transcription (jun d proto-oncogene). Furthermore, we showed the presence of high keratin 7 transcript expression in bladder cancer, and Western blotting analysis revealed three major molecular isoforms of keratin 7 in the tissues. These could be detected in urine sediments from bladder tumour patients