Sampling algorithms for validation of supervised learning models for Ising-like systems

In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model realizations, the question arises as to how to choose a reasonable number of samples that will form physically meaningful and non-intersecting training and testing datasets. Here, we propose a sampling technique called ID-MH that uses the Metropolis-Hastings algorithm creating Markov process across energy levels within the predefined configuration subspace. We show that application of this method retains phase transitions in both training and testing datasets and serves the purpose of validation of a machine learning algorithm. For larger lattice dimensions, ID-MH is not feasible as it requires knowledge of the complete configuration space. As such, we develop a new "block-ID" sampling strategy: it decomposes the given structure into square blocks with lattice dimension no greater than 5 and uses ID-MH sampling of candidate blocks. Further comparison of the performance of commonly used machine learning methods such as random forests, decision trees, k nearest neighbors and artificial neural networks shows that the PCA-based Decision Tree regressor is the most accurate predictor of magnetizations of the Ising model. For energies, however, the accuracy of prediction is not satisfactory, highlighting the need to consider more algorithmically complex methods (e.g., deep learning).Comment: 43 pages and 16 figure

The Modelling of Biological Growth: a Pattern Theoretic Approach

Mathematical and statistical modeling and analysis of biological growth using images collected over time are important for understanding of normal and abnormal development. In computational anatomy, changes in the shape of a growing anatomical structure have been modeled by means of diffeomorphic transformations in the background coordinate space. Various image and landmark matching algorithms have been developed for inference of large transformations that perform image registration consistent with the material properties of brain anatomy under study. However, from a biological perspective, it is not material constants that regulate growth, it is the genetic control system. A pattern theoretic model called the Growth as Random Iterated Diffeomorphisims (GRID) introduced by Ulf Grenander (Brown University) constructs growth-induced transformations according to fundamental biological principles of growth. They are governed by an underlying genetic control that is expressed in terms of probability laws governing the spatial-temporal patterns of elementary cell decisions (e.g., cell division/death). This thesis addresses computational and stochastic aspects of the GRID model and develops its application to image analysis of growth. The first part of the thesis introduces the original GRID view of growth-induced deformation on a fine time scale as a composition of several, elementary, local deformations each resulting from a random cell decision, a highly localized event in space-time called a seed. A formalization of the proposed model using theory of stochastic processes is presented, namely, an approximation of the GRID model by the diffusion process and the Fokker-Planck equation describing the evolution of the probability density of seed trajectories in space-time. Its time-dependent and stationary numerical solutions reveal bimodal distribution of a random seed trajectory in space-time. The second part of the thesis considers the growth pattern on a coarse time scale which underlies visible shape changes seen in images. It is shown that such a "macroscopic" growth pattern is a solution to a deterministic integro-differential equation in the form of a diffeomorphic flow dependent on the GRID growth variables such as the probability density of cell decisions and the rate of contraction/expansion. Since the GRID variables are unobserved, they have to be estimated from image data. Using the GRID macroscopic growth equation such an estimation problem is formulated as an optimal control problem. The estimated GRID variables are optimal controls that force the image of an initial organism to be continuously transformed into the image of a grown organism. The GRID-based inference method is implemented for inference of growth properties of the Drosophila wing disc directly from confocal micrographs of Wingless gene expression patterns

Shear stress associated with cardiopulmonary bypass induces expression of inflammatory cytokines and necroptosis in monocytes

Cardiopulmonary bypass (CPB) is required during most cardiac surgeries. CBP drives systemic inflammation and multiorgan dysfunction that is especially severe in neonatal patients. Limited understanding of molecular mechanisms underlying CPB-associated inflammation presents a significant barrier to improve clinical outcomes. To better understand these clinical issues, we performed mRNA sequencing on total circulating leukocytes from neonatal patients undergoing CPB. Our data identify myeloid cells, particularly monocytes, as the major cell type driving transcriptional responses to CPB. Furthermore, IL-8 and TNF-α were inflammatory cytokines robustly upregulated in leukocytes from both patients and piglets exposed to CPB. To delineate the molecular mechanism, we exposed THP-1 human monocytic cells to CPB-like conditions, including artificial surfaces, high shear stress, and cooling/rewarming. Shear stress was found to drive cytokine upregulation via calcium-dependent signaling pathways. We also observed that a subpopulation of THP-1 cells died via TNF-α–mediated necroptosis, which we hypothesize contributes to post-CPB inflammation. Our study identifies a shear stress–modulated molecular mechanism that drives systemic inflammation in pediatric CPB patients. These are also the first data to our knowledge to demonstrate that shear stress causes necroptosis. Finally, we observe that calcium and TNF-α signaling are potentially novel targets to ameliorate post-CPB inflammation