On Geometric Alignment in Low Doubling Dimension

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the alignment of geometric patterns in high dimension finds several novel applications, and has attracted more and more attentions. However, the research is still rather limited in terms of algorithms. To the best of our knowledge, most existing approaches for high dimensional alignment are just simple extensions of their counterparts for 2D and 3D cases, and often suffer from the issues such as high complexities. In this paper, we propose an effective framework to compress the high dimensional geometric patterns and approximately preserve the alignment quality. As a consequence, existing alignment approach can be applied to the compressed geometric patterns and thus the time complexity is significantly reduced. Our idea is inspired by the observation that high dimensional data often has a low intrinsic dimension. We adopt the widely used notion "doubling dimension" to measure the extents of our compression and the resulting approximation. Finally, we test our method on both random and real datasets, the experimental results reveal that running the alignment algorithm on compressed patterns can achieve similar qualities, comparing with the results on the original patterns, but the running times (including the times cost for compression) are substantially lower

Streaming Semidefinite Programs: O(n)O(\sqrt{n}) Passes, Small Space and Fast Runtime

We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\times n$ together with a vector $b\in \mathbb{R}^m$ are streamed to us one-by-one. The goal is to find a matrix $X\in \mathbb{R}^{n\times n}$ such that $\langle C, X\rangle$ is maximized, subject to $\langle A_i, X\rangle=b_i$ for all $i\in [m]$ and $X\succeq 0$. Previous algorithmic studies of SDP primarily focus on \emph{time-efficiency}, and all of them require a prohibitively large $\Omega(mn^2)$ space in order to store \emph{all the constraints}. Such space consumption is necessary for fast algorithms as it is the size of the input. In this work, we design an interior point method (IPM) that uses $\widetilde O(m^2+n^2)$ space, which is strictly sublinear in the regime $n\gg m$. Our algorithm takes $O(\sqrt n\log(1/\epsilon))$ passes, which is standard for IPM. Moreover, when $m$ is much smaller than $n$, our algorithm also matches the time complexity of the state-of-the-art SDP solvers. To achieve such a sublinear space bound, we design a novel sketching method that enables one to compute a spectral approximation to the Hessian matrix in $O(m^2)$ space. To the best of our knowledge, this is the first method that successfully applies sketching technique to improve SDP algorithm in terms of space (also time)

CD4+ T cell–independent vaccination against Pneumocystis carinii in mice

Host defenses are profoundly compromised in HIV-infected hosts due to progressive depletion of CD4(+) T lymphocytes. Moreover, deficient CD4(+) T lymphocytes impair vaccination approaches to prevent opportunistic infection. Therefore, we investigated a CD4(+) T cell–independent vaccine approach to a prototypic AIDS-defining infection, Pneumocystis carinii (PC) pneumonia. Here, we demonstrate that bone marrow–derived dendritic cells (DCs) expressing the murine CD40 ligand, when pulsed ex vivo by PC antigen, elicited significant titers of anti-PC IgG in CD4-deficient mice. Vaccinated animals demonstrated significant protection from PC infection, and this protection was the result of an effective humoral response, since adoptive transfer of CD4-depleted splenocytes or serum conferred this protection to CD4-deficient mice. Western blot analysis of PC antigen revealed that DC-vaccinated, CD4-deficient mice predominantly reacted to a 55-kDa PC antigen. These studies show promise for advances in CD4-independent vaccination against HIV-related pathogens

Study on characteristic of epileptic multi-electroencephalograph base on Hilbert-Huang transform and brain network dynamics

Lots of studies have been carried out on characteristic of epileptic Electroencephalograph (EEG). However, traditional EEG characteristic research methods lack exploration of spatial information. To study the characteristics of epileptic EEG signals from the perspective of the whole brain，this paper proposed combination methods of multi-channel characteristics from time-frequency and spatial domains. This paper was from two aspects: Firstly, signals were converted into 2D Hilbert Spectrum (HS) images which reflected the time-frequency characteristics by Hilbert-Huang Transform (HHT). These images were identified by Convolutional Neural Network (CNN) model whose sensitivity was 99.8%, accuracy was 98.7%, specificity was 97.4%, F1-score was 98.7%, and AUC-ROC was 99.9%. Secondly, the multi-channel signals were converted into brain networks which reflected the spatial characteristics by Symbolic Transfer Entropy (STE) among different channels EEG. And the results show that there are different network properties between ictal and interictal phase and the signals during the ictal enter the synchronization state more quickly, which was verified by Kuramoto model. To summarize, our results show that there was different characteristics among channels for the ictal and interictal phase, which can provide effective physical non-invasive indicators for the identification and prediction of epileptic seizures

Facile One-Pot Synthesis of Self-Assembled Folate-Biotin-Pullulan Nanoparticles for Targeted Intracellular Anticancer Drug Delivery

The self-assembled folate-biotin-pullulan (FBP) nanoparticles (NPs) were prepared by facile one-pot synthesis and their physicochemical properties were characterized. The self-assembled FBP NPs were used as an anticancer drug nanocarrier entrapping doxorubicin (DOX) for targeting folate-receptors-overexpressing cancer cells. The identification of prepared NPs to folate-receptor-expressing cancer cells (KB cells) was affirmed by cell viability measurement, folate competition test, and flow cytometric analysis. Compared with the naked DOX and DOX/BP NPs, the DOX/FBP NPs had lower IC50 value compared to KB cells as a result of the folate-receptor-mediated endocytosis process. The cytotoxicity of DOX/FBP NPs to KB cells could be inhibited competitively by free folate. The cellular intake pattern of naked DOX and drug-loaded NPs was identified by confocal laser scanning microscopy (CLSM) observation and the higher cellular uptake of drug for DOX/FBP NPs over naked DOX was observed. The prepared FBP NPs had the potential to be used as a powerful carrier to target anticancer drugs to folate-receptor-expressing tumor cells and reduce cytotoxicity to normal tissues

Efficient Asynchronize Stochastic Gradient Algorithm with Structured Data

Deep learning has achieved impressive success in a variety of fields because of its good generalization. However, it has been a challenging problem to quickly train a neural network with a large number of layers. The existing works utilize the locality-sensitive hashing technique or some data structures on space partitioning to alleviate the training cost in each iteration. In this work, we try accelerating the computations in each iteration from the perspective of input data points. Specifically, for a two-layer fully connected neural network, when the training data have some special properties, e.g., Kronecker structure, each iteration can be completed in sublinear time in the data dimension