Incorporating Physics-Based Patterns into Geophysical and Geostatistical Estimation Algorithms

Geophysical imaging systems are inherently non-linear and plagued with the challenge of limited data. These drawbacks make the solution non-unique and sensitive to small data perturbations; hence, regularization is performed to stabilize the solution. Regularization involves the application of a priori specification of the target to modify the solution space in order to make it tractable. However, the traditionally applied regularization model constraints are independent of the physical mechanisms driving the spatiotemporal evolution of the target parameters. To address this limitation, we introduce an innovative inversion scheme, basis-constrained inversion, which seeks to leverage advances in mechanistic modeling of physical phenomena to mimic the physics of the target process, to be incorporated into the regularization of hydrogeophysical and geostatistical estimation algorithms, for improved subsurface characterization. The fundamental protocol of the approach involves the construction of basis vectors from training images, which are then utilized to constrain the optimization problem. The training dataset is generated via Monte Carlo simulations to mimic the perceived physics of the processes prevailing within the system of interest. Two statistical techniques for constructing optimal basis functions, Proper Orthogonal Decomposition (POD) and Maximum Covariance Analysis (MCA), are employed leading to two inversion schemes. While POD is a static imaging technique, MCA is a dynamic inversion strategy. The efficacies of the proposed methodologies are demonstrated based on hypothetical and lab-scale flow and transport experiments

Bone structural similarity score: a multiparametric tool to match properties of biomimetic bone substitutes with their target tissues

Background: One of the hardest tasks in developing or selecting grafts for bone substitution surgery or tissue engineering is to match the structural and mechanical properties of tissue at the recipient site, because of the large variability of tissue properties with anatomical site, sex, age and health conditions of the patient undergoing implantation. We investigated the feasibility of defining a quantitative bone structural similarity score based on differences in the structural properties of synthetic grafts and bone tissue. Methods: Two biocompatible hydroxyapatite porous scaffolds with different nominal pore sizes were compared with trabecular bone tissues from equine humerus and femur. Images of samples’ structures were acquired by high-resolution micro-computed tomography and analyzed to estimate porosity, pore size distribution and interconnectivity, specific surface area, connectivity density and degree of anisotropy. Young’s modulus and stress at break were measured by compression tests. Structural similarity distances between sample pairs were defined based on scaled and weighted differences of the measured properties. Their feasibility was investigated for scoring structural similarity between considered scaffolds or bone tissues. Results: Manhattan distances and Quadrance generally showed sound and consistent similarities between sample pairs, more clearly than simple statistical comparison and with discriminating capacity similar to image-based scores to assess progression of pathologies affecting bone structure. Conclusions: The results suggest that a quantitative and objective bone structural similarity score may be defined to help biomaterials scientists fabricate, and surgeons select, the graft or scaffold best mimicking the structure of a given bone tissue

Joint inversion of receiver functions and surface waves with enhanced preconditioning on densely distributed CNDSN stations: Crustal and upper mantle structure beneath China

We present shear wave velocity structure beneath China by joint modeling of teleseismic receiver function and Rayleigh wave group velocity dispersion data observed at +1000 permanent broadband seismic stations in the Chinese National Digital Seismic Network (CNDSN). A ray-parameter-based stacking method is employed to minimize artifacts in stacking receiver functions from different sources. The Rayleigh wave dispersion curve is extracted from group velocity tomographic models at all applicable periods. Enhanced preconditions are applied on the linearized iterative inversion to regularize and balance multiple types of data. The velocity profile inversion at each station starts from an initial model derived from sediments, crustal thickness, Vp/Vs ratio and Pn/Sn models. This multistep approach not only reduces uncertainty and nonuniqueness of the velocity inversion but also efficiently fills information gap in each data set. We then generate a 3-D S velocity model by combining and smoothing all the 1-D models. The obtained 3-D model reveals crustal and upper mantle velocity structures that are well correlated with tectonic features of China, for example, our model shows a clear east-west bimodal distribution at 35 km deep, low velocity in the crust beneath central and eastern Tibetan plateau, and sedimentary structure in major cratons and basins. Our model is consistent with existing tomographic models in large scale but provides more structural details in regional and local scales

Estimating the bias of a noisy coin

Optimal estimation of a coin's bias using noisy data is surprisingly different from the same problem with noiseless data. We study this problem using entropy risk to quantify estimators' accuracy. We generalize the "add Beta" estimators that work well for noiseless coins, and we find that these hedged maximum-likelihood (HML) estimators achieve a worst-case risk of O(N^{-1/2}) on noisy coins, in contrast to O(1/N) in the noiseless case. We demonstrate that this increased risk is unavoidable and intrinsic to noisy coins, by constructing minimax estimators (numerically). However, minimax estimators introduce extreme bias in return for slight improvements in the worst-case risk. So we introduce a pointwise lower bound on the minimum achievable risk as an alternative to the minimax criterion, and use this bound to show that HML estimators are pretty good. We conclude with a survey of scientific applications of the noisy coin model in social science, physical science, and quantum information science.Comment: 10 page

Mark correlations: relating physical properties to spatial distributions

Mark correlations provide a systematic approach to look at objects both distributed in space and bearing intrinsic information, for instance on physical properties. The interplay of the objects' properties (marks) with the spatial clustering is of vivid interest for many applications; are, e.g., galaxies with high luminosities more strongly clustered than dim ones? Do neighbored pores in a sandstone have similar sizes? How does the shape of impact craters on a planet depend on the geological surface properties? In this article, we give an introduction into the appropriate mathematical framework to deal with such questions, i.e. the theory of marked point processes. After having clarified the notion of segregation effects, we define universal test quantities applicable to realizations of a marked point processes. We show their power using concrete data sets in analyzing the luminosity-dependence of the galaxy clustering, the alignment of dark matter halos in gravitational $N$-body simulations, the morphology- and diameter-dependence of the Martian crater distribution and the size correlations of pores in sandstone. In order to understand our data in more detail, we discuss the Boolean depletion model, the random field model and the Cox random field model. The first model describes depletion effects in the distribution of Martian craters and pores in sandstone, whereas the last one accounts at least qualitatively for the observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics, second Wuppertal conference "Spatial statistics and statistical physics

Multimodal Sensory Integration for Perception and Action in High Functioning Children with Autism Spectrum Disorder

Movement disorders are the earliest observed features of autism spectrum disorder (ASD) present in infancy. Yet we do not understand the neural basis for impaired goal-directed movements in this population. To reach for an object, it is necessary to perceive the state of the arm and the object using multiple sensory modalities (e.g. vision, proprioception), to integrate those sensations into a motor plan, to execute the plan, and to update the plan based on the sensory consequences of action. In this dissertation, I present three studies in which I recorded hand paths of children with ASD and typically developing (TD) controls as they grasped the handle of a robotic device to control a cursor displayed on a video screen. First, participants performed discrete and continuous movements to capture targets. Cursor feedback was perturbed from the hand\u27s actual position to introduce visuo-spatial conflict between sensory and proprioceptive feedback. Relative to controls, children with ASD made greater errors, consistent with deficits of sensorimotor adaptive and strategic compensations. Second, participants performed a two-interval forced-choice discrimination task in which they perceived two movements of the visual cursor and/or the robot handle and then indicated which of the two movements was more curved. Children with ASD were impaired in their ability to discriminate movement kinematics when provided visual and proprioceptive information simultaneously, suggesting deficits of visuo-proprioceptive integration. Finally, participants made goal-directed reaching movements against a load while undergoing simultaneous functional magnetic resonance imaging (MRI). The load remained constant (predictable) within an initial block of trials and then varied randomly within four additional blocks. Children with ASD exhibited greater movement variability compared to controls during both constant and randomly-varying loads. MRI analysis identified marked differences in the extent and intensity of the neural activities supporting goal-directed reaching in children with ASD compared to TD children in both environmental conditions. Taken together, the three studies revealed deficits of multimodal sensory integration in children with ASD during perception and execution of goal-directed movements and ASD-related motor performance deficits have a telltale neural signature, as revealed by functional MR imaging