Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka's Theorem

We find the capacity pre-log of a temporally correlated Rayleigh block-fading SIMO channel in the noncoherent setting. It is well known that for block-length L and rank of the channel covariance matrix equal to Q, the capacity pre-log in the SISO case is given by 1-Q/L. Here, Q/L can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to 1/L and can, hence, be made to vanish in the large-L limit, even if Q/L remains constant as L goes to infinity. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna's channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka's Theorem on the Resolution of Singularities

Multi-View Multiple Clusterings using Deep Matrix Factorization

Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and interesting from different perspectives. However, how to find multiple, meaningful, and diverse clustering results from multi-view data is still a rarely studied and challenging topic in multi-view clustering and multiple clusterings. In this paper, we introduce a deep matrix factorization based solution (DMClusts) to discover multiple clusterings. DMClusts gradually factorizes multi-view data matrices into representational subspaces layer-by-layer and generates one clustering in each layer. To enforce the diversity between generated clusterings, it minimizes a new redundancy quantification term derived from the proximity between samples in these subspaces. We further introduce an iterative optimization procedure to simultaneously seek multiple clusterings with quality and diversity. Experimental results on benchmark datasets confirm that DMClusts outperforms state-of-the-art multiple clustering solutions

Recovery of antioxidant gene expression in sacred lotus (Nelumbo nucifera Gaertn.) embryonic axes enhances tolerance to extreme high temperature

Sacred lotus (Nelumbo nucifera Gaertn.) seed is long-living and have various stress-resistance characteristics. We investigated the protecting mechanisms of lotus seeds against extreme high temperature by comparison of expression patterns of antioxidant genes in embryonic axes between exposure and non-exposure to extreme high temperature. It was shown that viability of seeds did not severely decline after exposure to 90°C for 24 h. Germination and growth were inhibited and H2O2 was accumulated at high level in the lotus embryonic axes germinated after heat treatment. Transcriptional levels of superoxide dismutase (SOD), ascorbate peroxidase (APX), peroxidase (POD), glutathione peroxidase (GPX) and thioredoxin-dependent peroxidase (TPX) encoding genes were induced to rise at late germination stage. Transcriptional levels of APX, POD, GPX and alternative oxidase (AOX) encoding genes were also immediately stimulated and up-regulated after heat treatment. These results suggest that the embryonic axes of sacred lotus maintain a protective and recovery mechanism from heat damage during and after exposure to extreme high temperature. Furthermore, the recovery of antioxidant gene expression enhanced tolerance to extreme high-temperature stress in sacred lotus.Keywords: Antioxidant gene, high temperature, seed germination, Nelumbo nucifera Gaert

Alkyl substituted cucurbit[6]uril assisted competitive fluorescence recognition of lysine and methionine in aqueous solution

The use of competitive ratiometric fluorescence indicator displacement chemosensors derived from two alkyl substituted cucurbit[6]uril-based host-guest complexes is reported. In particular, the differing binding abilities of two cucurbit[6]uril derivatives towards the target analytes led to a useful ratiometric detection signal output for the discrimination of lysine and methionine versus the other tested α-amino acids in aqueous solution

Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy, this study provides a tight minimax error bound of $O(\frac{ds}{n\epsilon^2})$, where $d$ represents the dimension of the numerical vector and $s$ denotes the number of non-zero entries. By converting the conditional/unconditional numerical mean estimation problem into a frequency estimation problem, we develop an optimal and efficient mechanism called Collision. In contrast, existing methods exhibit sub-optimal error rates of $O(\frac{d^2}{n\epsilon^2})$ or $O(\frac{ds^2}{n\epsilon^2})$. Specifically, for unconditional mean estimation, we leverage the negative correlation between two frequencies in each dimension and propose the CoCo mechanism, which further reduces estimation errors for mean values compared to Collision. Moreover, to surpass the error barrier in local privacy, we examine privacy amplification in the shuffle model for the proposed mechanisms and derive precisely tight amplification bounds. Our experiments validate and compare our mechanisms with existing approaches, demonstrating significant error reductions for frequency estimation and mean estimation on numerical vectors.Comment: Full version of "Hiding Numerical Vectors in Local Private and Shuffled Messages" (IJCAI 2021

Fine-grained Private Knowledge Distillation

Knowledge distillation has emerged as a scalable and effective way for privacy-preserving machine learning. One remaining drawback is that it consumes privacy in a model-level (i.e., client-level) manner, every distillation query incurs privacy loss of one client's all records. In order to attain fine-grained privacy accountant and improve utility, this work proposes a model-free reverse $k$-NN labeling method towards record-level private knowledge distillation, where each record is employed for labeling at most $k$ queries. Theoretically, we provide bounds of labeling error rate under the centralized/local/shuffle model of differential privacy (w.r.t. the number of records per query, privacy budgets). Experimentally, we demonstrate that it achieves new state-of-the-art accuracy with one order of magnitude lower of privacy loss. Specifically, on the CIFAR-$10$ dataset, it reaches $82.1\%$ test accuracy with centralized privacy budget $1.0$; on the MNIST/SVHN dataset, it reaches $99.1\%$/$95.6\%$ accuracy respectively with budget $0.1$. It is the first time deep learning with differential privacy achieve comparable accuracy with reasonable data privacy protection (i.e., $\exp(\epsilon)\leq 1.5$). Our code is available at https://github.com/liyuntong9/rknn