Displacement Estimation Error in Laser Scanning Monitoring of Retaining Structures Considering Roughness

Point clouds were obtained after laser scanning of the concrete panel, SMW, and sheet pile which is most widely used in retaining structures. The surface condition of the point cloud affects the displacement calculation, and hence both local roughness and global curvature of each point cloud were analyzed using the different sizes of the kernel. The curvature of the three retaining structures was also analyzed by the azimuth angle. In this paper, artificial displacements are generated for the point clouds of 100%, 80%, 60%, 40%, and 20% of the retaining structures, and displacement and analysis errors were calculated using the C2C, C2M, and M3C2 methods. C2C method is affected by the resolution of the point cloud, and the C2M method underestimates the displacement by the location of the points in the curvature of the retaining structures. M3C2 method had the lowest error, and the optimized M3C2 parameters for analyzing the displacement were presented.

The globalization theorem for the Curvature-Dimension condition

The Lott–Sturm–Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition locally: an essentially non-branching metric-measure space $$(X,\mathsf {d},{\mathfrak {m}})$$ ( X , d , m ) (so that $$(\text {supp}({\mathfrak {m}}),\mathsf {d})$$ ( supp ( m ) , d ) is a length-space and $${\mathfrak {m}}(X) < \infty $$ m ( X ) < ∞ ) verifying the local Curvature-Dimension condition $${\mathsf {CD}}_{loc}(K,N)$$ CD loc ( K , N ) with parameters $$K \in {\mathbb {R}}$$ K ∈ R and $$N \in (1,\infty )$$ N ∈ ( 1 , ∞ ) , also verifies the global Curvature-Dimension condition $${\mathsf {CD}}(K,N)$$ CD ( K , N ) . In other words, the Curvature-Dimension condition enjoys the globalization (or local-to-global) property, answering a question which had remained open since the beginning of the theory. For the proof, we establish an equivalence between $$L^1$$ L 1 - and $$L^2$$ L 2 -optimal-transport–based interpolation. The challenge is not merely a technical one, and several new conceptual ingredients which are of independent interest are developed: an explicit change-of-variables formula for densities of Wasserstein geodesics depending on a second-order temporal derivative of associated Kantorovich potentials; a surprising third-order theory for the latter Kantorovich potentials, which holds in complete generality on any proper geodesic space; and a certain rigidity property of the change-of-variables formula, allowing us to bootstrap the a-priori available regularity. As a consequence, numerous variants of the Curvature-Dimension condition proposed by various authors throughout the years are shown to, in fact, all be equivalent in the above setting, thereby unifying the theory.

Boosting Variational Inference With Locally Adaptive Step-Sizes

Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.

A Framework for Automatic Morphological Feature Extraction and Analysis of Abdominal Organs in MRI Volumes

The accurate 3D reconstruction of organs from radiological scans is an essential tool in computer-aided diagnosis (CADx) and plays a critical role in clinical, biomedical and forensic science research. The structure and shape of the organ, combined with morphological measurements such as volume and curvature, can provide significant guidance towards establishing progression or severity of a condition, and thus support improved diagnosis and therapy planning. Furthermore, the classification and stratification of organ abnormalities aim to explore and investigate organ deformations following injury, trauma and illness. This paper presents a framework for automatic morphological feature extraction in computer-aided 3D organ reconstructions following organ segmentation in 3D radiological scans. Two different magnetic resonance imaging (MRI) datasets are evaluated. Using the MRI scans of 85 adult volunteers, the overall mean volume for the pancreas organ is 69.30 ± 32.50cm3, and the 3D global curvature is (35.23 ± 6.83) × 10−3. Another experiment evaluates the MRI scans of 30 volunteers, and achieves mean liver volume of 1547.48 ± 204.19cm3 and 3D global curvature (19.87 ± 3.62) × 10− 3. Both experiments highlight a negative correlation between 3D curvature and volume with a statistical difference (p < 0.0001). Such a tool can support the investigation into organ related conditions such as obesity, type 2 diabetes mellitus and liver disease.

The effects of the global surface curvature on Makyoh-topogaphy imaging

The effects of the global curvature of the reflecting surface on Makyoh (magic-mirror) topography imaging is analysed based on a geometrical optical model. It is shown that the effects can be taken into account by introducing an equivalent screen-to-sample distance which is a function of the real screen-to-sample distance and the global curvature. The special limiting cases are discussed and analysed for practical applications. Full Text: PDF ReferencesK. Kugimiya, "“Makyoh”: The 2000 year old technology still alive", J. Cryst. Growth 103, 420 (1990). CrossRef P. Blaustein, S. Hahn, "Realtime inspection of wafer surfaces", Solid State Technol. 32, 27 (1989). CrossRef Z.J. Pei, G.R. Fisher, M. Bhagavat, S. Kassir, "A grinding-based manufacturing method for silicon wafers: an experimental investigation", Int. J. Machine Tools Manufacture 45, 1140 (2005). CrossRef F. Riesz, "Makyoh topography: a simple yet powerful optical method for flatness and defect characterization of mirror-like surfaces", Proc. SPIE 5458, 86 (2004). CrossRef T. Hirogaki, E. Aoyama, R. Machinaka, H. Sueda, K. Ogawa, J. Japan Soc. Precision Eng. 73, 96 (2007). CrossRef G. Saines, M.G. Tomilin, "Magic mirrors of the Orient", J. Opt. Technol. 66, 758 (1999). CrossRef W.E. Ayrton, J. Perry, "The Magic Mirror of Japan. Part I", Proc. Roy. Soc. London 28, 127 (1878). CrossRef M.V. Berry, "Oriental magic mirrors and the Laplacian image", Eur. J. Phys. 27, 109 (2006). CrossRef F. Riesz, "Sensitivity and detectability in Makyoh imaging", Optik 122, 2115 (2011). CrossRef Z.J. Laczik, "Quantitative Makyoh topography", Opt. Eng. 39, 2562 (2000). CrossRef F. Riesz, "Geometrical optical model of the image formation in Makyoh (magic-mirror) topography", J. Phys. D: Appl. Phys. 33, 3033 (2000). CrossRef F. Riesz, "Camera length and field of view in Makyoh-topography instruments", Rev. Sci. Instr. 72, 1591 (2001). CrossRef J. Szabó, F. Riesz, B. Szentpáli, "Makyoh Topography: Curvature Measurements and Implications for the Image Formation", Japan. J. Appl. Phys. 35, L258 (1996). CrossRef F. Riesz, "Non-linearity and related features of Makyoh (magic-mirror) imaging", J. Opt. 15, 075709 (2013). CrossRef A.V. Gitin, "System approach to image formation in a magic mirror", Appl. Opt. 48, 1268 (2009). CrossRef

Time travel

The prospect of a machine in which one could be transported through time is no longer mere fantasy, having become in this century the subject of serious scientific and philosophical debate. From Einstein’s special theory of relativity we have learned that a form of time travel into the future may be accomplished by moving quickly, and therefore ageing slowly (exploiting the time dilation effect). And in 1949 Kurt Gödel announced his discovery of (general relativistic) spacetimes whose global curvature allows voyages into the past as well. Since then the study of time travel has had three main strands. First, there has been research by theoretical physicists into the character and plausibility of structures, beyond those found by Gödel, that could engender closed timelike lines and closed causal chains. These phenomena include rotating universes, black holes, traversable wormholes and infinite cosmic strings (Earman 1995). Second, there has been concern with the semantic issue of whether the terms ‘cause’, ‘time’ and ‘travel’ are applicable, strictly speaking, to such bizarre models, given how different they are from the contexts in which those terms are normally employed (Yourgrau 1993). However, one may be sceptical about the significance of this issue, since the questions of primary interest – focused on the nature and reality of the Gödel-style models – seem independent of whether their description requires a shift in the meanings of those words. And, third, there has been considerable discussion within both physics and philosophy of various alleged paradoxes of time travel, and of their power to preclude the spacetime models in which time travel could occur.

Solving Separable Nonsmooth Problems Using Frank-Wolfe with Uniform Affine Approximations

Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to their ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximation. This typically restricts FW to smooth functions for which the approximation quality, indicated by a global curvature measure, is reasonably good. In this paper, we propose a modified FW algorithm amenable to nonsmooth functions, subject to a separability assumption, by optimizing for approximation quality over all affine functions, given a neighborhood of interest. We analyze theoretical properties of the proposed algorithm and demonstrate that it overcomes many issues associated with existing methods in the context of nonsmooth low-rank matrix estimation.

The role of global curvature on the structure and propagation of weakly unstable cylindrical detonations

The role of the global curvature on the structure and propagation of cylindrical detonations is studied allowing and without allowing the development of cellular structures through two-dimensional (2-D) and 1-D simulations, respectively. It is shown that as the detonation transitions from being overdriven to the Chapman–Jouguet (CJ) state, its structure evolves from no cell, to growing cells and then to diverging cells. Furthermore, the increased dimension of the average structure of the cellular cylindrical detonation, coupled with the curved transverse wave, leads to bulk un-reacted pockets as the cells grow, and consequently lower average propagation velocities as compared to those associated with smooth fronts. As the global detonation front expands and its curvature decreases, the extent of the un-reacted pockets diminishes and the average velocity of the cellular cylindrical detonation eventually degenerates to that of the smooth fronts. Consequently, the presence of cellular instability renders detonation more difficult to initiate for weakly unstable detonations.