NP/CLPNP/CLP Equivalence: A Phenomenon Hidden Among Sparsity Models for Information Processing

It is proved in this paper that to every underdetermined linear system $Ax=b$ there corresponds a constant $p(A,b)>0$ such that every solution to the $l_p$-norm minimization problem also solves the $l_0$-norm minimization problem whenever $0<p<p(A,b)$. This phenomenon is named $NP/CLP$ equivalence.Comment: submitted to IEEE Transactions on Information Theory in June 201

Non-convex Fraction Function Penalty: Sparse Signals Recovered from Quasi-linear Systems

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is no longer suitable. Compared with the compressed sensing under the linear circumstance, this nonlinear compressed sensing is much more difficult, in fact also NP-hard, combinatorial problem, because of the discrete and discontinuous nature of the $\ell_{0}$-norm and the nonlinearity. In order to get a convenience for sparse signal recovery, we set most of the nonlinear models have a smooth quasi-linear nature in this paper, and study a non-convex fraction function $\rho_{a}$ in this quasi-linear compressed sensing. We propose an iterative fraction thresholding algorithm to solve the regularization problem $(QP_{a}^{\lambda})$ for all $a>0$. With the change of parameter $a>0$, our algorithm could get a promising result, which is one of the advantages for our algorithm compared with other algorithms. Numerical experiments show that our method performs much better compared with some state-of-art methods

Nanoscale Lasers Based on Carbon Peapods

A scheme of nanoscale lasers based on the so-called carbon peapods is examined in details. Since there is considerable cylindrical empty space in the middle of a single-wall carbon nanotube (SWCNT), it can serve as a laser resonant cavity that consists of two highly reflecting, alignment &#8220;mirrors&#8221; separated by some distance. These mirrors refer to the ordered arrays of C60 inside SWCNTs, which have photonic bandgap structures. Meanwhile, ideally single-mode lasers are supposed to be produced in the nanoscale resonant cavity.Comment: 6 pages, 2 figure

Carbon deposition on Ni/YSZ anode SOFC for direct methane steam reforming

Solid Oxide Fuel Cells (SOFCs) are electrochemical devices that produce electricity directly from oxidizing fuels. Compared to direct combustion of hydrogen to generate power, it has a big advantage in aspects from efficiency and safety when using hydrogen as the fuel of SOFCs. Hydrocarbon reforming is one of the conventional methods to convert natural gas into hydrogen. While considering the difficulty in storage and transportation of hydrogen, we can utilize the supporting materials on the anode side of SOFCs as catalyst to generate hydrogen via hydrocarbon reforming process and pour the hydrogen as fuel into the SOFC system. Ni/YSZ is the most commonly used as anode material for SOFCs because of its cost-effective and well suitable for anode-supported fuel cell design requirements. While there are also some drawbacks, the biggest one is the performance degradation of fuel cell caused by solid carbon formation, which may block gas diffusion tunnel. Moreover, the accumulation of carbon on catalysts can crack the cell. In the report, methane steam reforming and carbon deposition on Ni catalyst from the thermodynamic and kinetic views are discussed. The process of carbon deposition on Ni catalyst is also described. In order to face the challenge, some measures have been taken to suppress the effect including optimizing system parameters, addition of other metal elements and synthesizing smaller Ni particle catalyst. In the future, a lot of work should be done on adjusting catalyst compositions, feed compositions, and reaction conditions, especially on developing new materials that fit the system perfectly

Minimization of fraction function penalty in compressed sensing

In the paper, we study the minimization problem of a non-convex sparsity promoting penalty function $$P_{a}(x)=\sum_{i=1}^{n}p_{a}(x_{i})=\sum_{i=1}^{n}\frac{a|x_{i}|}{1+a|x_{i}|}$$ in compressed sensing, which is called fraction function. Firstly, we discuss the equivalence of $\ell_{0}$ minimization and fraction function minimization. It is proved that there corresponds a constant $a^{**}>0$ such that, whenever $a>a^{**}$, every solution to $(FP_{a})$ also solves $(P_{0})$, that the uniqueness of global minimizer of $(FP_{a})$ and its equivalence to $(P_{0})$ if the sensing matrix $A$ satisfies a restricted isometry property (RIP) and, last but the most important, that the optimal solution to the regularization problem $(FP_{a}^\lambda)$ also solves $(FP_{a})$ if the certain condition is satisfied, which is similar to the regularization problem in convex optimal theory. Secondly, we study the properties of the optimal solution to the regularization problem $(FP^{\lambda}_{a})$ including the first-order and the second optimality condition and the lower and upper bound of the absolute value for its nonzero entries. Finally, we derive the closed form representation of the optimal solution to the regularization problem ($FP_{a}^{\lambda}$) for all positive values of parameter $a$, and propose an iterative $FP$ thresholding algorithm to solve the regularization problem $(FP_{a}^{\lambda})$. We also provide a series of experiments to assess performance of the $FP$ algorithm, and the experiment results show that, compared with soft thresholding algorithm and half thresholding algorithms, the $FP$ algorithm performs the best in sparse signal recovery with and without measurement noise.Comment: 12 page

Deep Networks as Approximators of Optimal Transfers Solutions in Multitarget Missions

In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate solutions to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, fuel consumption of fuel-optimal low-thrust transfers, and the total dv of minimum-dv J2-perturbed multi-impulse transfers. To generate the training data, low-thrust trajectories are optimized using the indirect method and J2-perturbed multi-impulse trajectories are optimized using J2 homotopy and particle swarm optimization. The hyper-parameters of our deep networks are searched by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with extremely high accuracy; resulting into a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and investigated with respect to their capability of predicting cases well outside of the training data

Generalized singular value thresholding operator to affine matrix rank minimization problem

It is well known that the affine matrix rank minimization problem is NP-hard and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to the combinational nature of the rank function. In this paper, a generalized singular value thresholding operator is generated to solve the affine matrix rank minimization problem. Numerical experiments show that our algorithm performs effectively in finding a low-rank matrix compared with some state-of-art methods

Nonconvex fraction function recovery sparse signal by convex optimization algorithm

In this paper, we will generate a convex iterative FP thresholding algorithm to solve the problem $(FP^{\lambda}_{a})$. Two schemes of convex iterative FP thresholding algorithms are generated. One is convex iterative FP thresholding algorithm-Scheme 1 and the other is convex iterative FP thresholding algorithm-Scheme 2. A global convergence theorem is proved for the convex iterative FP thresholding algorithm-Scheme 1. Under an adaptive rule, the convex iterative FP thresholding algorithm-Scheme 2 will be adaptive both for the choice of the regularized parameter $\lambda$ and parameter $a$. These are the advantages for our two schemes of convex iterative FP thresholding algorithm compared with our previous proposed two schemes of iterative FP thresholding algorithm. At last, we provide a series of numerical simulations to test the performance of the convex iterative FP thresholding algorithm-Scheme 2, and the simulation results show that our convex iterative FP thresholding algorithm-Scheme 2 performs very well in recovering a sparse signal

Energy-Aware Aggregation of Dynamic Temporal Workload in Data Centers

Data center providers seek to minimize their total cost of ownership (TCO), while power consumption has become a social concern. We present formulations to minimize server energy consumption and server cost under three different data center server setups (homogeneous, heterogeneous, and hybrid hetero-homogeneous clusters) with dynamic temporal workload. Our studies show that the homogeneous model significantly differs from the heterogeneous model in computational time (by an order of magnitude). To be able to compute optimal configurations in near real-time for large scale data centers, we propose two modes, aggregation by maximum and aggregation by mean. In addition, we propose two aggregation methods, static (periodic) aggregation and dynamic (aperiodic) aggregation. We found that in the aggregation by maximum mode, the dynamic aggregation resulted in cost savings of up to approximately 18% over the static aggregation. In the aggregation by mean mode, the dynamic aggregation by mean could save up to approximately 50% workload rearrangement compared to the static aggregation by mean mode. Overall, our methodology helps to understand the trade-off in energy-aware aggregation

Capacity of the Gaussian Two-Pair Two-Way Relay Channel to Within 1/2 Bit

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within 1/2 bit for arbitrary channel conditions. In the proof, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. Further, we present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. Finally, judicious power allocation at the relay is necessary to approach the channel capacity under various channel conditions.Comment: 77 pages, 9 figures, journa