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)

Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones

Z3-connectivity of 4-edge-connected 2-triangular graphs

AbstractA graph G is k-triangular if each edge of G is in at least k triangles. It is conjectured that every 4-edge-connected 1-triangular graph admits a nowhere-zero Z3-flow. However, it has been proved that not all such graphs are Z3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z3-connected. The result is best possible. This result provides evidence to support the Z3-connectivity conjecture by Jaeger et al that every 5-edge-connected graph is Z3-connected

Reconstruction of Daily 30 m Data from HJ CCD, GF-1 WFV, Landsat, and MODIS Data for Crop Monitoring

With the recent launch of new satellites and the developments of spatiotemporal data fusion methods, we are entering an era of high spatiotemporal resolution remote-sensing analysis. This study proposed a method to reconstruct daily 30 m remote-sensing data for monitoring crop types and phenology in two study areas located in Xinjiang Province, China. First, the Spatial and Temporal Data Fusion Approach (STDFA) was used to reconstruct the time series high spatiotemporal resolution data from the Huanjing satellite charge coupled device (HJ CCD), Gaofen satellite no. 1 wide field-of-view camera (GF-1 WFV), Landsat, and Moderate Resolution Imaging Spectroradiometer (MODIS) data. Then, the reconstructed time series were applied to extract crop phenology using a Hybrid Piecewise Logistic Model (HPLM). In addition, the onset date of greenness increase (OGI) and greenness decrease (OGD) were also calculated using the simulated phenology. Finally, crop types were mapped using the phenology information. The results show that the reconstructed high spatiotemporal data had a high quality with a proportion of good observations (PGQ) higher than 0.95 and the HPLM approach can simulate time series Normalized Different Vegetation Index (NDVI) very well with R2 ranging from 0.635 to 0.952 in Luntai and 0.719 to 0.991 in Bole, respectively. The reconstructed high spatiotemporal data were able to extract crop phenology in single crop fields, which provided a very detailed pattern relative to that from time series MODIS data. Moreover, the crop types can be classified using the reconstructed time series high spatiotemporal data with overall accuracy equal to 0.91 in Luntai and 0.95 in Bole, which is 0.028 and 0.046 higher than those obtained by using multi-temporal Landsat NDVI data

Annealing tunable charge density wave order in a magnetic kagome material FeGe

In the magnetic kagome metal FeGe, a charge density wave (CDW) order emerges inside the antiferromagnetic phase, providing a fertile playground to investigate the interplay between charge and magnetic orders. Here, we demonstrate that the CDW order, as well as magnetic properties, can be reversibly tuned on a large scale through post-growth annealing treatments. The antiferromagnetic and CDW transitions vary systematically as functions of both the temperature and the time period of annealing. Long-range CDW order with a maximum $T_{\mathrm{CDW}}$ and a minimum $T_{\mathrm{N}}$ can be realized in crystals annealed at \SI{320}{\degreeCelsius} for over 48 h. Using magnetization and magnetostrictive coefficient measurements, it is found that the CDW transition is rather stable against an external magnetic field and spin-flop transition. On the other hand, the critical field for spin-flop transition is significantly reduced in the long-range ordered CDW phase. Our results indicate that the CDW in FeGe is immune to variations in magnetic orders, while the magnetocrystalline anisotropy energy and the corresponding magnetic ground state can be altered significantly by the charge order. These findings provide crucial clues for further investigation and a better understanding of the nature of the CDW order in FeGe.Comment: 8 pages, 4 figure