Accelerating Random Kaczmarz Algorithm Based on Clustering Information

Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes. Using the property of randomly sampled data in high-dimensional space, we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma. Additionally, we theoretically demonstrate convergence improvement on block Kaczmarz algorithm

On Black Hole Stability in Critical Gravities

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition.Comment: 16 pages, minor corrections, further comments and references adde

f(R) Gravities, Killing Spinor Equations, "BPS" Domain Walls and Cosmology

We derive the condition on f(R) gravities that admit Killing spinor equations and construct explicit such examples. The Killing spinor equations can be used to reduce the fourth-order differential equations of motion to the first order for both the domain wall and FLRW cosmological solutions. We obtain exact "BPS" domain walls that describe the smooth Randall-Sundrum II, AdS wormholes and the RG flow from IR to UV. We also obtain exact smooth cosmological solutions that describe the evolution from an inflationary starting point with a larger cosmological constant to an ever-expanding universe with a smaller cosmological constant. In addition, We find exact smooth solutions of pre-big bang models, bouncing or crunching universes. An important feature is that the scalar curvature R of all these metrics is varying rather than a constant. Another intriguing feature is that there are two different f(R) gravities that give rise to the same "BPS" solution. We also study linearized f(R) gravities in (A)dS vacua.Comment: 37 pages, discussion on gravity trapping in RSII modified, typos corrected, further comments and references added; version to appear in JHE

Variations in decay resistance of cryptomeria fortunei

Cryptomeria fortunei has been widely planted in many cities in southern China. Eventually some of this material may be utilized for timber, but there are relatively few studies of durability of this resource.   There is also some question as to whether Cryptomeria fortunei is a synonym for Cryptomeria japonica or Japanese cedar (Sugi). Evaluating the durability of the Chinese resource will help ensure that the decay resistance of this urban plantation resource is properly categorized. The decay resistance of Cryptomeria fortunei wood was assessed in soil block and agar block tests against Trametes versicolor, Gloeophyllum trabeum and Rhodonia placenta. Hot water and ethanol extractive contents of the heartwood were determined on sections from various distances above ground and then FTIR spectroscopy was used to characterize the wood before and after fungal exposure. Weight losses in sapwood were consistent with the minimal decay resistance of this portion of the wood. Inner and outer heartwood weight losses were more variable suggesting that the heartwood of this species would be considered to be only moderately durable.  Extractives were weakly correlated with decay resistance. FTIR results were more variable, although they suggested heavier attack of lignin components by the brown rot fungi. The results suggest that Cryptomeria fortunei would need to be protected from the weather unless supplemental preservative treatments were applied

Active headrest combined with a depth camera-based ear-positioning system

Active headrests can reduce low-frequency noise around ears based on active noise control (ANC) system. Both the control system using fixed control filters and the remote microphone-based adaptive control system provide good noise reduction performance when the head is in the original position. However, their performance degrades significantly when the head is in motion. In this paper, a human ear-positioning system based on the depth camera is introduced to address this problem. The system uses RTMpose model to estimate the two-dimensional (2D) positions of the ears in the color frame, and then derives the corresponding three-dimensional (3D) coordinates in the depth frame with a depth camera. Experimental results show that the ear-positioning system can effectively track the movement of ears, and the broadband noise reduction performance of the active headrest combined with the system is significantly improved when the human head is translating or rotating

f(R) Theories of Supergravities and Pseudo-supergravities

We present f(R) theories of ten-dimensional supergravities, including the fermionic sector up to the quadratic order in fermion fields. They are obtained by performing the conformal scaling on the usual supergravities to the f(R) frame in which the dilaton becomes an auxiliary field and can be integrated out. The f(R) frame coincides with that of M-theory, D2-branes or NS-NS 5-branes. We study various BPS p-brane solutions and their near-horizon AdS \times sphere geometries in the context of the f(R) theories. We find that new solutions emerge with global structures that do not exist in the corresponding solutions of the original supergravity description. In lower dimensions, We construct the f(R) theory of N=2, D=5 gauged supergravity with a vector multiplet, and that for the four-dimensional U(1)^4 gauged theory with three vector fields set equal. We find that some previously-known BPS singular "superstars" become wormholes in the f(R) theories. We also construct a large class of f(R) (gauged) pseudo-supergravities. In addition we show that the breathing mode in the Kaluza-Klein reduction of Gauss-Bonnet gravity on S^1 is an auxiliary field and can be integrated out.Comment: Latex, 46 page

Learning-based real-time imaging through dynamic scattering media

Imaging through dynamic scattering media is one of the most challenging yet fascinating problems in optics, with applications spanning from biological detection to remote sensing. In this study, we propose a comprehensive learning-based technique that facilitates real-time, non-invasive, incoherent imaging of real-world objects through dense and dynamic scattering media. We conduct extensive experiments, demonstrating the capability of our technique to see through turbid water and natural fog. The experimental results indicate that the proposed technique surpasses existing approaches in numerous aspects and holds significant potential for imaging applications across a broad spectrum of disciplines