A Tutorial on the Spectral Theory of Markov Chains

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically. This tutorial provides an in-depth introduction to Markov chains and explores their connection to graphs and random walks. We use tools from linear algebra and graph theory to describe the transition matrices of different types of Markov chains, with a particular focus on exploring properties of the eigenvalues and eigenvectors corresponding to these matrices. The results presented are relevant to a number of methods in machine learning and data mining, which we describe at various stages. Rather than being a novel academic study in its own right, this text presents a collection of known results, together with some new concepts. Moreover, the tutorial focuses on offering intuition to readers rather than formal understanding and only assumes basic exposure to concepts from linear algebra and probability theory. It is therefore accessible to students and researchers from a wide variety of disciplines.

Photo-responsive hydrogel-based re-programmable metamaterials

This paper explores a novel programmable metamaterial using stimuli-responsive hydrogels with a demonstration of bandgap formation and tuning. Specifically, a photo-responsive hydrogel beam that can achieve re-programmable periodicity in geometric and material properties through patterned light irradiation is designed. Hydrogels consist of polymeric networks and water molecules. Many unique properties of hydrogels, including bio-compatibility, stimuli-responsiveness, and low dissipation make them ideal for enabling re-programmable metamaterials for manipulating structural dynamic response and wave propagation characteristics. Bandgap generation and tunability in photo-responsive hydrogel-based metamaterial (in the form of a diatomic phononic chain) as well as the effects of system parameters such as light exposure pattern and photo-sensitive group concentration on the bandgap width and center frequency are systematically studied. In agreement with finite-element model simulations, it is observed that an increase in light exposure region size reduces both the bandgap width and center frequency, while an increase in the concentration of photo-sensitive group increases bandgap width, attenuation and reduces its center frequency. This work unveils the potential of stimuli-response hydrogels as a new class of low-loss soft metamaterials, unlike most other soft materials that are too lossy to sustain and exploit wave phenomena.

Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements

While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of 2log23 random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl–Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.

A Review of Finite Element Analysis and Artificial Neural Networks as Failure Pressure Prediction Tools for Corroded Pipelines

This paper discusses the capabilities of artificial neural networks (ANNs) when integrated with the finite element method (FEM) and utilized as prediction tools to predict the failure pressure of corroded pipelines. The use of conventional residual strength assessment methods has proven to produce predictions that are conservative, and this, in turn, costs companies by leading to premature maintenance and replacement. ANNs and FEM have proven to be strong failure pressure prediction tools, and they are being utilized to replace the time-consuming methods and conventional codes. FEM is widely used to evaluate the structural integrity of corroded pipelines, and the integration of ANNs into this process greatly reduces the time taken to obtain accurate results.

3D Bioprinting of Model Tissues That Mimic the Tumor Microenvironment

The tumor microenvironment (TME) influences cancer progression. Therefore, engineered TME models are being developed for fundamental research and anti-cancer drug screening. This paper reports the biofabrication of 3D-printed avascular structures that recapitulate several features of the TME. The tumor is represented by a hydrogel droplet uniformly loaded with breast cancer cells (106 cells/mL); it is embedded in the same type of hydrogel containing primary cells-tumor-associated fibroblasts isolated from the peritumoral environment and peripheral blood mononuclear cells. Hoechst staining of cryosectioned tissue constructs demonstrated that cells remodeled the hydrogel and remained viable for weeks. Histological sections revealed heterotypic aggregates of malignant and peritumoral cells; moreover, the constituent cells proliferated in vitro. To investigate the interactions responsible for the experimentally observed cellular rearrangements, we built lattice models of the bioprinted constructs and simulated their evolution using Metropolis Monte Carlo methods. Although unable to replicate the complexity of the TME, the approach presented here enables the self-assembly and co-culture of several cell types of the TME. Further studies will evaluate whether the bioprinted constructs can evolve in vivo in animal models. If they become connected to the host vasculature, they may turn into a fully organized TME.

Atomistic Simulations of Plasma-Enhanced Atomic Layer Deposition

Plasma-enhanced atomic layer deposition (PEALD) is a widely used, powerful layer-by-layer coating technology. Here, we present an atomistic simulation scheme for PEALD processes, combining the Monte Carlo deposition algorithm and structure relaxation using molecular dynamics. In contrast to previous implementations, our approach employs a real, atomistic model of the precursor. This allows us to account for steric hindrance and overlap restrictions at the surface corresponding to the real precursor deposition step. In addition, our scheme takes various process parameters into account, employing predefined probabilities for precursor products at each Monte Carlo deposition step. The new simulation protocol was applied to investigate PEALD synthesis of SiO₂ thin films using the bis-diethylaminosilane precursor. It revealed that increasing the probability for precursor binding to one surface oxygen atom favors amorphous layer growth, a large number of –OH impurities, and the formation of voids. In contrast, a higher probability for precursor binding to two surface oxygen atoms leads to dense SiO₂ film growth and a reduction of –OH impurities. Increasing the probability for the formation of doubly bonded precursor sites is therefore the key factor for the formation of dense SiO₂ PEALD thin films with reduced amounts of voids and –OH impurities.

Using Sacrificial Cell Spheroids for the Bioprinting of Perfusable 3D Tissue and Organ Constructs: A Computational Study

A long-standing problem in tissue engineering is the biofabrication of perfusable tissue constructs that can be readily connected to the patient's vasculature. It was partially solved by three-dimensional (3D) printing of sacrificial material (e.g., hydrogel) strands: upon incorporation in another cell-laden hydrogel, the strands were removed, leaving behind perfusable channels. Their complexity, however, did not match that of the native vasculature. Here, we propose to use multicellular spheroids as a sacrificial material and investigate their potential benefits in the context of 3D bioprinting of cell aggregates and/or cell-laden hydrogels. Our study is based on computer simulations of postprinting cellular rearrangements. The computational model of the biological system is built on a cubic lattice, whereas its evolution is simulated using the Metropolis Monte Carlo algorithm. The simulations describe structural changes in three types of tissue constructs: a tube made of a single cell type, a tube made of two cell types, and a cell-laden hydrogel slab that incorporates a branching tube. In all three constructs, the lumen is obtained after the elimination of the sacrificial cell population. Our study suggests that sacrificial cell spheroids (sacrospheres) enable one to print tissue constructs outfitted with a finer and more complex network of channels than the ones obtained so far. Moreover, cellular interactions might give rise to a tissue microarchitecture that lies beyond the bioprinter's resolution. Although more expensive than inert materials, sacrificial cells have the potential to bring further progress towards the biofabrication of fully vascularized tissue substitutes.

Self-learning kinetic Monte Carlo simulations of diffusion in ferromagnetic α-Fe-Si alloys

Diffusion of Si atom and vacancy in the A2-phase of α-Fe-Si alloys in the ferromagnetic state, with and without magnetic order and in various temperature ranges, are studied using AKSOME, an on-lattice self-learning KMC code. Diffusion of the Si atom and the vacancy are studied in the dilute limit and up to 12 at.% Si, respectively, in the temperature range 350-700 K. Local Si neighborhood dependent activation energies for vacancy hops were calculated on-the-fly using a broken-bond model based on pairwise interaction. The migration barrier and prefactor for the Si diffusion in the dilute limit were obtained and found to agree with published data within the limits of uncertainty. Simulations results show that the prefactor and the migration barrier for the Si diffusion are approximately an order of magnitude higher, and a tenth of an electron-volt higher, respectively, in the magnetic disordered state than in the fully ordered state. However, the net result is that magnetic disorder does not have a significant effect on Si diffusivity within the range of parameters studied in this work. Nevertheless, with increasing temperature, the magnetic disorder increases and its effect on the Si diffusivity also increases. In the case of vacancy diffusion, with increasing Si concentration, its diffusion prefactor decreases while the migration barrier more or less remained constant and the effect of magnetic disorder increases with Si concentration. Important vacancy-Si/Fe atom exchange processes and their activation barriers were identified, and the effect of energetics on ordered phase formation in Fe-Si alloys are discussed.

Improving uncertainty in Widmark equation calculations: Alcohol volume, strength and density

The Widmark equation is probably the most commonly used calculation for medicolegal purposes. Recently the National Research Council (USA) and the Forensic Science Regulator (UK) have called for the uncertainty of all results to be given with all forensic measurements and calculations. To improve the uncertainty of measurement of results from Widmark calculations we have concentrated on the uncertainties of measurement involved in the calculation of amount of alcohol, that of the volume of alcohol, the concentration of alcohol and the density of alcohol as previous studies have investigated some of the other factors involved. Using experimental studies, the scientific literature and legal statutes, we have determined revised and improved uncertainties of the concentration of ethanol for Widmark calculations for both the USA and UK. Based on the calculations that we have performed we recommend the use of Monte Carlo Simulation for the determination of uncertainty of measurement for Widmark Calculations.

Self-learning kinetic Monte Carlo simulations of Al diffusion in Mg

Vacancy-mediated diffusion of an Al atom in the pure Mg matrix is studied using the atomistic, on-lattice self-learning kinetic Monte Carlo (SLKMC) method. Activation barriers for vacancy-Mg and vacancy-Al atom exchange processes are calculated on the fly using the climbing image nudged-elastic-band method and binary Mg-Al modified embedded-atom method interatomic potential. Diffusivities of an Al atom obtained from SLKMC simulations show the same behavior as observed in experimental and theoretical studies available in the literature; that is, an Al atom diffuses faster within the basal plane than along the c-axis. Although the effective activation barriers for an Al atom diffusion from SLKMC simulations are close to experimental and theoretical values, the effective prefactors are lower than those obtained from experiments. We present all the possible vacancy-Mg and vacancy-Al atom exchange processes and their activation barriers identified in SLKMC simulations. A simple mapping scheme to map an HCP lattice onto a simple cubic lattice is described, which enables simulation of the HCP lattice using the on-lattice framework. We also present the pattern recognition scheme which is used in SLKMC simulations to identify the local Al atom configuration around a vacancy.

Risk Assessment for Foodborne Viruses

Risk is an inherent component of human existence, as is our creation of ways to avoid or minimize such risks. The formal process of assessing the likelihood and magnitude of risk, using that information to manage risk, and then communicating the process to others, forms the basis for risk analysis. This chapter provides an overview of the steps of risk analysis with a focus on risk assessment for foodborne viruses, particularly quantitative efforts that model and estimate the risks these viruses pose to human health. Most risk assessments in food and environmental virology performed in the last decade have focused on water, fresh produce, molluscan shellfish, and prepared foods. Recent examples of enteric virus risk modeling efforts are discussed in detail, as are several of the difficulties and intricacies of performing risk assessments for foodborne viruses compared to bacteria and other agents. This is a relatively new area of study, but one that will continue to grow as national and international agencies continue to adopt and require the methodology for food safety and the protection of human health.

Modeling of human artery tissue with probabilistic approach

Accurate modeling of biological soft tissue properties is vital for realistic medical simulation. Mechanical response of biological soft tissue always exhibits a strong variability due to the complex microstructure and different loading conditions. The inhomogeneity in human artery tissue is modeled with a computational probabilistic approach by assuming that the instantaneous stress at a specific strain varies according to normal distribution. Material parameters of the artery tissue which are modeled with a combined logarithmic and polynomial energy equation are represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters are determined using genetic algorithm (GA) and inverse mean-value first-order second-moment (IMVFOSM) method, respectively. This nondeterministic approach was verified using computer simulation based on the Monte-Carlo (MC) method. Cumulative distribution function (CDF) of the MC simulation corresponds well with that of the experimental stress-strain data and the probabilistic approach is further validated using data from other studies. By taking into account the inhomogeneous mechanical properties of human biological tissue, the proposed method is suitable for realistic virtual simulation as well as an accurate computational approach for medical device validation.

Aberration analyses for improving the frontal projection three-dimensional display

The crosstalk severely affects the viewing experience for the auto-stereoscopic 3D displays based on frontal projection lenticular sheet. To suppress unclear stereo vision and ghosts are observed in marginal viewing zones(MVZs), aberration of the lenticular sheet combining with the frontal projector is analyzed and designed. Theoretical and experimental results show that increasing radius of curvature (ROC) or decreasing aperture of the lenticular sheet can suppress the aberration and reduce the crosstalk. A projector array with 20 micro-projectors is used to frontally project 20 parallax images one lenticular sheet with the ROC of 10 mm and the size of 1.9 m × 1.2 m. The 3D image with the high quality is experimentally demonstrated in both the mid-viewing zone and MVZs in the optimal viewing plane. The 3D clear depth of 1.2m can be perceived. To provide an excellent 3D image and enlarge the field of view at the same time, a novel structure of lenticular sheet is presented to reduce aberration, and the crosstalk is well suppressed.

Atomistic kinetic Monte Carlo study of atomic layer deposition derived from density functional theory

To describe the atomic layer deposition (ALD) reactions of HfO2 from Hf(N(CH3)2)4 and H2O, a three-dimensional on-lattice kinetic Monte-Carlo model is developed. In this model, all atomistic reaction pathways in density functional theory (DFT) are implemented as reaction events on the lattice. This contains all steps, from the early stage of adsorption of each ALD precursor, kinetics of the surface protons, interaction between the remaining precursors (steric effect), influence of remaining fragments on adsorption sites (blocking), densification of each ALD precursor, migration of each ALD precursors, and cooperation between the remaining precursors to adsorb H2O (cooperative effect). The essential chemistry of the ALD reactions depends on the local environment at the surface. The coordination number and a neighbor list are used to implement the dependencies. The validity and necessity of the proposed reaction pathways are statistically established at the mesoscale. The formation of one monolayer of precursor fragments is shown at the end of the metal pulse. Adsorption and dissociation of the H2O precursor onto that layer is described, leading to the delivery of oxygen and protons to the surface during the H2O pulse. Through these processes, the remaining precursor fragments desorb from the surface, leaving the surface with bulk-like and OH-terminated HfO2, ready for the next cycle. The migration of the low coordinated remaining precursor fragments is also proposed. This process introduces a slow reordering motion (crawling) at the mesoscale, leading to the smooth and conformal thin film that is characteristic of ALD.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: analytical formulas and kinetic Monte Carlo simulations

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. By including Gaussian white noise to the equations of motion for terrace widths, we formulate large systems of SDEs under different choices of diffusion coefficients for the noise. We simplify this description via (i) perturbation theory and linearization of the step interactions and, alternatively, (ii) a mean-field (MF) approximation whereby widths of adjacent terraces are replaced by a self-consistent field but nonlinearities in step interactions are retained. We derive simplified formulas for the time-dependent terrace-width distribution (TWD) and its steady-state limit. Our MF analytical predictions for the TWD compare favorably with kinetic Monte Carlo simulations under the addition of a suitably conservative white noise in the BCF equations.

A Monte Carlo method for locally multivariate brain mapping

Locally multivariate approaches to functional brain mapping offer a highly appealing complement to conventional statistics, but require restrictive region-of-interest hypotheses, or, in exhaustive search forms (such as the "searchlight" algorithm; Kriegeskorte et al., 2006), are excessively computer intensive. We therefore propose a non-restrictive, comparatively fast yet highly sensitive method based on Monte Carlo approximation principles where locally multivariate maps are computed by averaging across voxelwise condition-discriminative information obtained from repeated stochastic sampling of fixed-size search volumes. On simulated data containing discriminative regions of varying size and contrast-to-noise ratio (CNR), the Monte Carlo method reduced the required computer resources by as much as 75% compared to the searchlight with no reduction in mapping performance. Notably, the Monte Carlo mapping approach not only outperformed the general linear method (GLM), but also produced higher discriminative voxel detection scores than the searchlight irrespective of classifier (linear or nonlinear support vector machine), discriminative region size or CNR. The improved performance was explained by the information-average procedure, and the Monte Carlo approach yielded mapping sensitivities of a few percent lower than an information-average exhaustive search. Finally, we demonstrate the utility of the algorithm on whole-brain, multi-subject functional magnetic resonance imaging (fMRI) data from a tactile study, revealing that the central representation of gentle touch is spatially distributed in somatosensory, insular and visual regions.

Computational modeling of epithelial-mesenchymal transformations

An epithelial-mesenchymal transformation (EMT) involves alterations in cell-cell and cell-matrix adhesion, the detachment of epithelial cells from their neighbors, the degradation of the basal lamina and acquisition of mesenchymal phenotype. Here we present Monte Carlo simulations for a specific EMT in early heart development: the formation of cardiac cushions. Cell rearrangements are described in accordance with Steinberg's differential adhesion hypothesis, which states that cells possess a type-dependent adhesion apparatus and are sufficiently motile to give rise to the tissue conformation with the largest number of strong bonds. We also implement epithelial and mesenchymal cell proliferation, cell type change and extracellular matrix production by mesenchymal cells. Our results show that an EMT is promoted more efficiently by an increase in cell-substrate adhesion than by a decrease in cell-cell adhesion. In addition to cushion tissue formation, the model also accounts for the phenomena of matrix invasion and mesenchymal condensation. We conclude that in order to maintain epithelial integrity during EMT the number of epithelial cells must increase at a controlled rate. Our model predictions are in qualitative agreement with available experimental data.

Effects of impurities on surface morphology: some examples

Small amounts of impurities are known to have remarkably great influence on surface morphology. We discuss three examples that arise in our research. First, we consider impurities codeposited during epitaxial growth, paying particular attention to Cu(100). After many layers of growth, the impurities can dramatically alter the surface morphology, changing the wavelength of the meandering instability and producing small square-base pyramids. Second, we consider the decoration of both island and vacancy island edges on Ag(111) with C(60). We use this system as a prototype to model how edge decoration with impurities can have a striking effect on the shape of the island as well as the dynamics of edge fluctuations. Finally, we show that about one per cent of pentacene quinone impurities alters the size of the critical nucleus in submonolayer pentacene deposition. This provides a platform on which to discuss our recent work characterizing the capture-zone distribution associated with the islands in terms of the generalized Wigner distribution, a simple one-parameter expression in which the characteristic exponent is the size of the smallest stable island.

Relating biophysical properties across scales

A distinguishing feature of a multicellular living system is that it operates at various scales, from the intracellular to organismal. Genes and molecules set up the conditions for the physical processes to act, in particular to shape the embryo. As development continues the changes brought about by the physical processes lead to changes in gene expression. It is this coordinated interplay between genetic and generic (i.e., physical and chemical) processes that constitutes the modern understanding of early morphogenesis. It is natural to assume that in this multiscale process the smaller defines the larger. In case of biophysical properties, in particular, those at the subcellular level are expected to give rise to those at the tissue level and beyond. Indeed, the physical properties of tissues vary greatly from the liquid to solid. Very little is known at present on how tissue level properties are related to cell and subcellular properties. Modern measurement techniques provide quantitative results at both the intracellular and tissue level, but not on the connection between these. In the present work we outline a framework to address this connection. We specifically concentrate on the morphogenetic process of tissue fusion, by following the coalescence of two contiguous multicellular aggregates. The time evolution of this process can accurately be described by the theory of viscous liquids. We also study fusion by Monte Carlo simulations and a novel Cellular Particle Dynamics (CPD) model, which is similar to the earlier introduced Subcellular Element Model (SEM; Newman, 2005). Using the combination of experiments, theory and modeling we are able to relate the measured tissue level biophysical quantities to subcellular parameters. Our approach has validity beyond the particular morphogenetic process considered here and provides a general way to relate biophysical properties across scales.