Universal Compressed Sensing

In this paper, the problem of developing universal algorithms for compressed sensing of stochastic processes is studied. First, R\'enyi's notion of information dimension (ID) is generalized to analog stationary processes. This provides a measure of complexity for such processes and is connected to the number of measurements required for their accurate recovery. Then a minimum entropy pursuit (MEP) optimization approach is proposed, and it is proven that it can reliably recover any stationary process satisfying some mixing constraints from sufficient number of randomized linear measurements, without having any prior information about the distribution of the process. It is proved that a Lagrangian-type approximation of the MEP optimization problem, referred to as Lagrangian-MEP problem, is identical to a heuristic implementable algorithm proposed by Baron et al. It is shown that for the right choice of parameters the Lagrangian-MEP algorithm, in addition to having the same asymptotic performance as MEP optimization, is also robust to the measurement noise. For memoryless sources with a discrete-continuous mixture distribution, the fundamental limits of the minimum number of required measurements by a non-universal compressed sensing decoder is characterized by Wu et al. For such sources, it is proved that there is no loss in universal coding, and both the MEP and the Lagrangian-MEP asymptotically achieve the optimal performance

The Child is Father of the Man: Foresee the Success at the Early Stage

Understanding the dynamic mechanisms that drive the high-impact scientific work (e.g., research papers, patents) is a long-debated research topic and has many important implications, ranging from personal career development and recruitment search, to the jurisdiction of research resources. Recent advances in characterizing and modeling scientific success have made it possible to forecast the long-term impact of scientific work, where data mining techniques, supervised learning in particular, play an essential role. Despite much progress, several key algorithmic challenges in relation to predicting long-term scientific impact have largely remained open. In this paper, we propose a joint predictive model to forecast the long-term scientific impact at the early stage, which simultaneously addresses a number of these open challenges, including the scholarly feature design, the non-linearity, the domain-heterogeneity and dynamics. In particular, we formulate it as a regularized optimization problem and propose effective and scalable algorithms to solve it. We perform extensive empirical evaluations on large, real scholarly data sets to validate the effectiveness and the efficiency of our method.Comment: Correct some typos in our KDD pape

Compression-Based Compressed Sensing

Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be recovered from their under-determined set of linear projections. Currently, there is a large gap between the complexity of the structures studied in the area of compressed sensing and those employed by the state-of-the-art compression codes. Recent results in the literature on deterministic signals aim at bridging this gap through devising compressed sensing decoders that employ compression codes. This paper focuses on structured stochastic processes and studies the application of rate-distortion codes to compressed sensing of such signals. The performance of the formerly-proposed compressible signal pursuit (CSP) algorithm is studied in this stochastic setting. It is proved that in the very low distortion regime, as the blocklength grows to infinity, the CSP algorithm reliably and robustly recovers $n$ instances of a stationary process from random linear projections as long as their count is slightly more than $n$ times the rate-distortion dimension (RDD) of the source. It is also shown that under some regularity conditions, the RDD of a stationary process is equal to its information dimension (ID). This connection establishes the optimality of the CSP algorithm at least for memoryless stationary sources, for which the fundamental limits are known. Finally, it is shown that the CSP algorithm combined by a family of universal variable-length fixed-distortion compression codes yields a family of universal compressed sensing recovery algorithms

Electronic, dielectric and optical properties of two dimensional and bulk ice: a multi-scale simulation study

The intercalated water into nanopores exhibits anomalous properties such as ultralow dielectric constant.~Multi-scale modeling and simulations are used to investigate the dielectric properties of various crystalline two-dimensional ices and bulk ices. Although, the structural properties of two-dimensional (2D-) ices have been extensively studied, much less is known about their electronic and optical properties. First, by using density functional theory (DFT) and density functional perturbation theory (DFPT), we calculate the key electronic, optical and dielectric properties of 2D-ices. Performing DFPT calculations, both the ionic and electronic contributions of the dielectric constant are computed. The in-plane electronic dielectric constant is found to be larger than the out-of-plane dielectric constant for all the studied 2D-ices. The in-plane dielectric constant of the electronic response is found to be isotropic for all the studied ices. Secondly, we determined the dipolar dielectric constant of 2D-ices using molecular dynamics simulations (MDS) at finite temperature. The total out-of-plane dielectric constant is found to be larger than 2 for all the studied 2D-ices. Within the framework of the random-phase approximation (RPA), the absorption energy ranges for 2D-ices are found to be in the ultraviolet spectra. For the comparison purposes, we also elucidate the electronic, dielectric and optical properties of four crystalline ices (ice VIII, ice XI, ice Ic and ice Ih) and bulk water

Constructive role of dissipation for driven coupled bosonic modes

We describe four cases of childhood B-cell progenitor acute lymphoblastic leukaemia (BCP-ALL) and one of T-cell (T-ALL) with unexpected numbers of interphase signals for ETV6 with an ETV6-RUNX1 fusion probe. Three fusion negative cases each had a telomeric part of 12p terminating within intron 2 of ETV6, attached to sequences from 5q, 7p and 7q, respectively. Two fusion positive cases, with partial insertions of ETV6 into chromosome 21, also had a breakpoint in intron 2. Fluorescence in situ hybridisation ( FISH), array comparative genomic hybridization (aCGH) and Molecular Copy-Number Counting (MCC) results were concordant for the T-cell case. Sequences downstream of TLX3 on chromosome 5 were deleted, leaving the intact gene closely apposed to the first two exons of ETV6 and its upstream promoter. qRT-PCR showed a significant upregulation of TLX3. In this study we provide the first incontrovertible evidence that the upstream promoter of ETV6 attached to the first two exons of the gene was responsible for the ectopic expression of a proto-oncogene that became abnormally close as the result of deletion and translocation. We have also shown breakpoints in intron 2 of ETV6 in two cases of insertion with ETV6-RUNX1 fusion