On variational solutions for whole brain serial-section histology using a Sobolev prior in the computational anatomy random orbit model

The application of maximum a posteriori (MAP) detection to DS-CDMA systems in time-selective fading channels is investigated. By sampling the outputs of a matched filter and combining antenna array elements, strong multiple-access interference (MAI) is estimated and suppressed. By incorporating channel approximations, Kalman filtering, and the probability density of the prediction error, a joint channel estimation and MAP detection algorithm is developed. Unknown channel parameters are identified by using an algorithm similar to the extended Kalman filter (EKF). Also, differential modulation is applied to eliminate the need for pilot insertion. Through computer simulations, a near-optimum bit-error-rate (BER) performance is found.

Galaxy formation models within cosmological hydrodynamical simulations contain numerous parameters with nontrivial influences over the resulting properties of simulated cosmic structures and galaxy populations. It is computationally challenging to sample these high dimensional parameter spaces with simulations, in particular for halos in the high-mass end of the mass function. In this work, we develop a novel sampling and reduced variance regression method, CARPoolGP, which leverages built-in correlations between samples in different locations of high dimensional parameter spaces to provide an efficient way to explore parameter space and generate low-variance emulations of summary statistics. We use this method to extend the Cosmology and Astrophysics with machinE Learning Simulations to include a set of 768 zoom-in simulations of halos in the mass range of 1013–1014.5 M ⊙ h −1 that span a 28-dimensional parameter space in the IllustrisTNG model. With these simulations and the CARPoolGP emulation method, we explore parameter trends in the Compton Y–M, black hole mass–halo mass, and metallicity–mass relations, as well as thermodynamic profiles and quenched fractions of satellite galaxies. We use these emulations to provide a physical picture of the complex interplay between supernova and active galactic nuclei feedback. We then use emulations of the Y–M relation of massive halos to perform Fisher forecasts on astrophysical parameters for future Sunyaev–Zeldovich observations and find a significant improvement in forecasted constraints. We publicly release both the simulation suite and CARPoolGP software package.

In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians [Moulines97] and the mixing matrix elements distributions by a Gaussian [Djafari99a]. We model the mixture of Gaussians hierarchically by mean of hidden variables representing the labels of the mixture. Then, we consider the joint a posteriori distribution of sources, mixing matrix elements, labels of the mixture and other parameters of the mixture with appropriate prior probability laws to eliminate degeneracy of the likelihood function of variance parameters and we propose two iterative algorithms to estimate jointly sources, mixing matrix and hyperparameters: Joint MAP (Maximum a posteriori) algorithm and penalized EM algorithm. The illustrative example is taken in [Macchi99] to compare with other algorithms proposed in literature. Keywords: Source separation, Gaussian mixture, classification, JMAP algorithm, Penalized EM algorithm.

Glycan structures account for up to 35% of the mass of cardiac sodium ( Nav ) channels. To question whether and how reduced sialylation affects Nav activity and cardiac electrical signaling, we conducted a series of in vitro experiments on ventricular apex myocytes under two different glycosylation conditions, reduced protein sialylation (ST3Gal4(-/-)) and full glycosylation (control). Although aberrant electrical signaling is observed in reduced sialylation, realizing a better understanding of mechanistic details of pathological variations in INa and AP is difficult without performing in silico studies. However, computer model of Nav channels and cardiac myocytes involves greater levels of complexity, e.g., high-dimensional parameter space, nonlinear and nonconvex equations. Traditional linear and nonlinear optimization methods have encountered many difficulties for model calibration. This paper presents a new statistical metamodeling approach for efficient computer experiments and optimization of Nav models. First, we utilize a fractional factorial design to identify control variables from the large set of model parameters, thereby reducing the dimensionality of parametric space. Further, we develop the Gaussian process model as a surrogate of expensive and time-consuming computer models and then identify the next best design point that yields the maximal probability of improvement. This process iterates until convergence, and the performance is evaluated and validated with real-world experimental data. Experimental results show the proposed algorithm achieves superior performance in modeling the kinetics of Nav channels under a variety of glycosylation conditions. As a result, in silico models provide a better understanding of glyco-altered mechanistic details in state transitions and distributions of Nav channels. Notably, ST3Gal4(-/-) myocytes are shown to have higher probabilities accumulated in intermediate inactivation during the repolarization and yield a shorter refractory period than WTs. The proposed statistical design of computer experiments is generally extensible to many other disciplines that involve large-scale and computationally expensive models.

We propose a method for optimizing control policies for assistive lower-limb devices. The method frames parameter selection as a dueling bandits problem in which a user indicates his or her qualitative preferences between pairs of parameter sets chosen from a library. We generate the library through an offline optimization procedure that seeks to reproduce the varied gaits of healthy human subjects. By separating the parameter selection process into online and offline portions, the method can handle high-dimensional parameter spaces and produces policies that can generalize to different gait scenarios such as speed variation. We evaluate the method on five subjects walking on a powered knee and ankle prosthesis governed by a neuromuscular control policy that has 43 parameters. We find the five subjects preferred four different parameter sets from the library and that the resulting optima resemble intact subject gait data. This result suggests the offline portion of the optimization method indeed produces control parameters that can adapt to different gaits. Moreover, we find that for three out of the four parameter sets we tested, the procedure also generates parameters that improve the ability of the prosthesis to adapt to increasing gait speed by increasing ankle net work production. The results encourage further research and exploration in clinical settings toward advanced prosthesis controls that employ online learning.

<p style='text-indent:20px;'>In this paper, we investigate the use of the Euler characteristic for the topological data analysis, particularly over higher dimensional parameter spaces. The Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, primarily in the context of random fields. The goal of this paper, is to present the extension of using the Euler characteristic in higher dimensional parameter spaces. The topological data analysis of higher dimensional parameter spaces using stronger invariants such as homology, has and continues to be the subject of intense research. However, as important theoretical and computational obstacles remain, the use of the Euler characteristic represents an important intermediary step toward multi-parameter topological data analysis. We show the usefulness of the techniques using generated examples as well as a real world dataset of detecting diabetic retinopathy in retinal images.</p>

Obtaining the set of cosmological parameters consistent with observational data is an important exercise in current cosmological research. It involves finding the global maximum of the likelihood function in the multi-dimensional parameter space. Currently sampling based methods, which are in general stochastic in nature, like Markov-Chain Monte Carlo(MCMC), are being commonly used for parameter estimation. The beauty of stochastic methods is that the computational cost grows, at the most, linearly in place of exponentially (as in grid based approaches) with the dimensionality of the search space. MCMC methods sample the full joint probability distribution (posterior) from which one and two dimensional probability distributions, best fit (average) values of parameters and then error bars can be computed. In the present work we demonstrate the application of another stochastic method, named Particle Swarm Optimization (PSO), that is widely used in the field of engineering and artificial intelligence, for cosmological parameter estimation from WMAP seven years data. We find that there is a good agreement between the values of the best fit parameters obtained from PSO and publicly available code COSMOMC. However, there is a slight disagreement between error bars mainly due to the fact that errors are computed differently in PSO. Apart from presenting the results of our exercise, we also discuss the merits of PSO and explain its usefulness in more extensive search in higher dimensional parameter space.

The logarithmic law of the wall loses part of its predictive power in flows with system rotation. Previous work on the topic of mean flow scaling has mostly focused on flows with streamwise, spanwise, or wall-normal system rotation. The main objective of this work is to establish the mean flow scaling for wall-bounded flows with small but arbitrarily directional system rotation. Our approach is as follows. First, we apply dimensional analysis to the Reynolds-averaged momentum equation. We show that when a boundary-layer flow is subjected to small system rotation, the constant stress layer survives, and the mean flow U+ is a universal function of y+, Ωx+, Ωy+, and Ωz+, where U is the mean flow, y is the distance from the wall, Ωi is the system rotation speed in the ith direction (in the locally defined coordinate), and the superscript + denotes normalization by the local wall units. Second, we survey the three-dimensional parameter space of Ωx,y,z+ and determine U+(y+,Ωx+,Ωy+,Ωz+) for small Ω+. Here, we conduct direct numerical simulation (DNS) of a Reτ = 180 channel at various rotation conditions. This approach is conventionally considered as “brutal force.” However, as we will show in this work, the Bayesian approach allows us to very efficiently sample the parameter space. Four independent surveys are conducted with 146 DNSs, and the resulting Bayesian surrogate agrees well with our DNSs. Finally, we upscale to high Reynolds numbers via wall-modeled large-eddy simulation. In general, the present framework provides a path for surrogate modeling in a high-dimensional parameter space at high Reynolds numbers when sampling in a designated parameter space is possible at only a few conditions and at a low Reynolds number.

The use of effective distance functions has been explored for many data mining problems including clustering, nearest neighbor search, and indexing. Recent research results show that if the Pearson variation of the distance distribution converges to zero with increasing dimensionality, the distance function will become unstable (or meaningless) in high dimensional space even with the commonly used Lp metric on the Euclidean space. This result has spawned many subsequent studies. We first comment that although the prior work provided the sufficient condition for the unstability of a distance function, the corresponding proof has some defects. Also, the necessary condition for unstability (i.e., the negation of the sufficient condition for the stability) of a distance function, which is required for function design, remains unknown. Consequently, we first provide in this paper a general proof for the sufficient condition of unstability. More importantly, we go further to prove that the rapid degradation of Pearson variation for a distance distribution is in fact a necessary condition of the resulting unstability. With the result, we will then have the necessary and the sufficient conditions for unstability, which in turn imply the sufficient and necessary conditions for stability. This theoretical result derived leads to a powerful means to design a meaningful distance function. Explicitly, in light of our results, we design in this paper a meaningful distance function, called Shrinkage-Divergence Proximity (abbreviated as SDP), based on a given distance function. It is empirically shown that the SDP significantly outperforms prior measures for its being stable in high dimensional data space and robust to noise, and is thus deemed more suitable for distance-based clustering applications than the priorly

Chapter 3 - Efficient Medical Image Parsing

The petrogenesis of rocks can be investigated by integrating multiple datasets and numerical methods. Petrology benefits from the abundance of field, petrographic, geochronological and geochemical data. Moreover, the growing number of numerical methods opens new opportunities for inversion. Inversion allows the quantification of useful parameters, offering deeper insights into natural processes. However, an increasing number of parameters to invert for is accompanied by significant computational costs. Therefore, relevant algorithms are needed to perform inversion and uncertainty quantification in high-dimensional spaces. Here, we demonstrate the use of Hamiltonian Monte Carlo for inverse diffusion modeling in a petrological framework. Hamiltonian Monte Carlo is a gradient-based method that efficiently explores high-dimensional parameter spaces. We implemented it using the Turing.jl package in Julia which makes use of Automatic Differentiation to efficiently explore the parameter space. Our analysis focused on the calculation of the initial cooling rate, equilibration temperature and effective mineral grain size. We fit compositional garnet data and Ar-muscovite geochronological data from the Pindos metamorphic sole (Greece) by using two different forward diffusion models. Our joint inversion shows an initial equilibration temperature of 632.3 ± 9.3 °C and a cooling rate of 202.6 ± 72.0 °C/Myr. These values reproduce not only thermobarometric and geochronological observations but also fit the garnet composition profiles and the 40Ar/39Ar age of muscovite. We finally aim to highlight the potential of Hamiltonian Monte Carlo as a robust method to perform high-dimensional inversion and constrain complex petrological processes.

Simulation-based design optimization utilizes computational models that rely on assumptions and approximations. There is a need therefore, to ensure that the obtained designs will exhibit the desired behavior as anticipated given the model predictions. The common approach to accomplish that is to validate the utilized computational models prior to the design optimization process. However, this is practically an impossible task especially for design problems with high-dimensional design and parameter spaces. We have recently proposed a different approach for maximizing confidence in the designs generated during a sequential simulation-based optimization process based on calibrating the computational models when necessary and within local subdomains of the design space. In that work, the size of the local domains was held fixed and not linked to uncertainty, and the confidence in designs was quantified using Bayesian hypothesis testing. In this article, we present an improved methodology. Specifically, we use a statistical methodology to account for uncertainty and to determine the size of the local domains at each stage of the sequential design optimization process using parametric bootstrapping that involves maximum likelihood estimators of model parameters. The sequential process continues until the local domain does not change from stage to stage during the design optimization process, ensuring convergence to an optimal design. The proposed methodology is illustrated with the design of a thermal insulator using one-dimensional, linear heat conduction in a solid slab with heat flux boundary conditions.

Quantifying Rigid and Nonrigid Motion of Liver Tumors During Stereotactic Body Radiation Therapy

A majority of experimental disciplines face the challenge of exploring large and high-dimensional parameter spaces in search of new scientific discoveries. Materials science is no exception; the wide variety of synthesis, processing, and environmental conditions that influence material properties gives rise to particularly vast parameter spaces. Recent advances have led to an increase in the efficiency of materials discovery by increasingly automating the exploration processes. Methods for autonomous experimentation have become more sophisticated recently, allowing for multi-dimensional parameter spaces to be explored efficiently and with minimal human intervention, thereby liberating the scientists to focus on interpretations and big-picture decisions. Gaussian process regression (GPR) techniques have emerged as the method of choice for steering many classes of experiments. We have recently demonstrated the positive impact of GPR-driven decision-making algorithms on autonomously-steered experiments at a synchrotron beamline. However, due to the complexity of the experiments, GPR often cannot be used in its most basic form, but rather has to be tuned to account for the special requirements of the experiments. Two requirements seem to be of particular importance, namely inhomogeneous measurement noise (input-dependent or non-i.i.d.) and anisotropic kernel functions, which are the two concepts that we tackle in this paper. Our synthetic and experimental tests demonstrate the importance of both concepts for experiments in materials science and the benefits that result from including them in the autonomous decision-making process.

Informative path planning is an important and challenging problem in robotics that remains to be solved in a manner that allows for wide-spread implementation and real-world practical adoption. Among various reasons for this, one is the lack of approaches that allow for informative path planning in high-dimensional spaces and non-trivial sensor constraints. In this work we present a sampling-based approach that allows us to tackle the challenges of large and high-dimensional search spaces. This is done by performing informed sampling in the high-dimensional continuous space and incorporating potential information gain along edges in the reward estimation. This method rapidly generates a global path that maximizes information gain for the given path budget constraints. We discuss the details of our implementation for an example use case of searching for multiple objects of interest in a large search space using a fixed-wing UAV with a forward-facing camera. We compare our approach to a sampling-based planner baseline and demonstrate how our contributions allow our approach to consistently out-perform the baseline by 18.0%. With this we thus present a practical and generalizable informative path planning framework that can be used for very large environments, limited budgets, and high dimensional search spaces, such as robots with motion constraints or high-dimensional configuration spaces. [Code] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> Codebase: https://github.com/castacks/tigris [Video] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> Video: https://youtu.be/bMw5nUGL5GQ