Four Dimensional Quantum Topology Changes of Spacetimes

We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant negative curvature solutions of the Einstein equation i.e. hyperbolic geometries. Using four dimensional polytopes, we can explicitly construct hyperbolic manifolds with topologically non-trivial boundaries which describe topology changes. These instanton-like solutions are constructed out of 8-cell's, 16-cell's or 24-cell's and have several points at infinity called cusps. The hyperbolic manifolds are non-compact because of the cusps but have finite volumes. Then we evaluate topology change amplitudes in the WKB approximation in terms of the volumes of these manifolds. We find that the more complicated are the topology changes, the more likely are suppressed.Comment: 26 pages, revtex, 13 figures. The calculation of volume and grammatical errors are correcte

Group Sparse Precoding for Cloud-RAN with Multiple User Antennas

Cloud radio access network (C-RAN) has become a promising network architecture to support the massive data traffic in the next generation cellular networks. In a C-RAN, a massive number of low-cost remote antenna ports (RAPs) are connected to a single baseband unit (BBU) pool via high-speed low-latency fronthaul links, which enables efficient resource allocation and interference management. As the RAPs are geographically distributed, the group sparse beamforming schemes attracts extensive studies, where a subset of RAPs is assigned to be active and a high spectral efficiency can be achieved. However, most studies assumes that each user is equipped with a single antenna. How to design the group sparse precoder for the multiple antenna users remains little understood, as it requires the joint optimization of the mutual coupling transmit and receive beamformers. This paper formulates an optimal joint RAP selection and precoding design problem in a C-RAN with multiple antennas at each user. Specifically, we assume a fixed transmit power constraint for each RAP, and investigate the optimal tradeoff between the sum rate and the number of active RAPs. Motivated by the compressive sensing theory, this paper formulates the group sparse precoding problem by inducing the $\ell_0$-norm as a penalty and then uses the reweighted $\ell_1$ heuristic to find a solution. By adopting the idea of block diagonalization precoding, the problem can be formulated as a convex optimization, and an efficient algorithm is proposed based on its Lagrangian dual. Simulation results verify that our proposed algorithm can achieve almost the same sum rate as that obtained from exhaustive search

Evaluation and optimal design of spectral sensitivities for digital color imaging

The quality of an image captured by color imaging system primarily depends on three factors: sensor spectral sensitivity, illumination and scene. While illumination is very important to be known, the sensitivity characteristics is critical to the success of imaging applications, and is necessary to be optimally designed under practical constraints. The ultimate image quality is judged subjectively by human visual system. This dissertation addresses the evaluation and optimal design of spectral sensitivity functions for digital color imaging devices. Color imaging fundamentals and device characterization are discussed in the first place. For the evaluation of spectral sensitivity functions, this dissertation concentrates on the consideration of imaging noise characteristics. Both signal-independent and signal-dependent noises form an imaging noise model and noises will be propagated while signal is processed. A new colorimetric quality metric, unified measure of goodness (UMG), which addresses color accuracy and noise performance simultaneously, is introduced and compared with other available quality metrics. Through comparison, UMG is designated as a primary evaluation metric. On the optimal design of spectral sensitivity functions, three generic approaches, optimization through enumeration evaluation, optimization of parameterized functions, and optimization of additional channel, are analyzed in the case of the filter fabrication process is unknown. Otherwise a hierarchical design approach is introduced, which emphasizes the use of the primary metric but the initial optimization results are refined through the application of multiple secondary metrics. Finally the validity of UMG as a primary metric and the hierarchical approach are experimentally tested and verified

Blind source separation by fully nonnegative constrained iterative volume maximization

Blind source separation (BSS) has been widely discussed in many real applications. Recently, under the assumption that both of the sources and the mixing matrix are nonnegative, Wang develop an amazing BSS method by using volume maximization. However, the algorithm that they have proposed can guarantee the nonnegativities of the sources only, but cannot obtain a nonnegative mixing matrix necessarily. In this letter, by introducing additional constraints, a method for fully nonnegative constrained iterative volume maximization (FNCIVM) is proposed. The result is with more interpretation, while the algorithm is based on solving a single linear programming problem. Numerical experiments with synthetic signals and real-world images are performed, which show the effectiveness of the proposed method

Blind Source Separation by Nonnegative Matrix Factorization with Minimum-Volume Constraint

Recently, nonnegative matrix factorization (NMF) attracts more and more attentions for the promising of wide applications. A problem that still remains is that, however, the factors resulted from it may not necessarily be realistically interpretable. Some constraints are usually added to the standard NMF to generate such interpretive results. In this paper, a minimum-volume constrained NMF is proposed and an efficient multiplicative update algorithm is developed based on the natural gradient optimization. The proposed method can be applied to the blind source separation (BSS) problem, a hot topic with many potential applications, especially if the sources are mutually dependent. Simulation results of BSS for images show the superiority of the proposed method

Experimental investigations of secondary load cycle formation in wave force on a circular cylinder under steep regular waves

When a large wave interacts with a marine structure, it would lead to a high-frequency structure response, and impose great threats to marine structures. In this paper, wave forces on a vertical cylinder in regular waves with moderate to extreme steepness were measured experimentally. The secondary load cycle phenomenon in wave force time history was observed and its generation mechanism was analyzed. It is found that secondary load cycle strongly depends on wave steepness. When the wave steepness exceeds critical values, the secondary load cycle phenomenon appears in the time history of wave force, and a high frequency response accompanied this phenomenon. Further, a new critical wave steepness kA = 0.3tanh(kh) (A is wave crest height, k is wavenumber and h is water depth) is found to distinguish the secondary load cycle occurrence. Here the wave steepness threshold value is no more a constant value that was proposed before, it varies with water depth and becomes smaller with the decrease of water depth. Moreover, the secondary load cycle and the subsequent high-frequency response are divided from the wave force signal based on the empirical mode decomposition (EMD) method. The results show that the high-frequency response locates in the natural frequency region of cylinders, which is much higher than the high-order wave components. Finally, the generation mechanism of this phenomenon is explained. As a steep wave passes a cylinder, a large wave run-up would be generated on the front side of the cylinder. One part of water body of the run-up swashes down and impacts the wave surface heavily. The other part of wave run-up fills into the cavity on the lee side of the cylinder, and generates violent turbulence. Both processes are found to lead to an instant impact on the structure, and then excite structural high-frequency vibration. This instant impact expresses as secondary load cycle in wave force history. These new findings from experimental studies have provided new insights into the generation mechanism and the associated changes in wave properties during the formation of secondary load cycle.</p