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Pattern recognition methods and hidden Markov models can be effective tools for online health monitoring of communications systems. Previous work has assumed that the states in the system model are exhaustive. This can be a significant drawback in real-world fault monitoring applications where it is difficult if not impossible to model all the possible fault states of the system in advance.
Markov random fields have been used for image segmentation since their introduction in the1980s. This work applies a method from Principal Component Thermography to enhance thecontrast in damage regions in 3D images derived from X-ray computed tomography (CT)inspections. The developed method is applied to sizing of small cracks in thin Inconel tubes designed as probability of detection (POD) samples for radiographic inspection.Misclassification errors arising from artifacts due to beam-hardening are reduced by fitting the boundary of the segmented damage region with the arc of an ellipse. Results are comparedagainst those obtained through manual inspection.
Heterogeneity across a broad range of scales in geologic porous media often manifests in observations of non-Fickian or anomalous transport. While traditional anomalous transport models can successfully make predictions in certain geological systems, increasing evidence suggests that assumptions relating to independent and identically distributed increments constrain where and when they can be reliably applied. A relatively novel model, the Spatial Markov model (SMM), relaxes the assumption of independence. The SMM belongs to the family of correlated continuous time random walks and has shown promise across a wide range of transport problems relevant to natural porous media. It has been successfully used to model conservative as well as more recently reactive transport in highly complex flows ranging from pore scales to much larger scales of interest in geology and subsurface hydrology. In this review paper we summarize its original development and provide a comprehensive review of its advances and applications as well as lay out a vision for its future development.
The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this study, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.
Here, in this work, we develop a novel Bayesian approach to study the adsorption and desorption of CO onto a Pd(111) surface, a process of great importance in natural sciences. The motivation for this work comes from the recent availability of time-resolved infrared spectroscopy data and the need for model interpretability and uncertainty quantification in chemical processes. The objective is to learn the relevant parameters that characterize the process: coverage with time, rate constants, activation energies, and pre-exponential factors. Our approach consists of three main schemes: (i) a problem design and probabilistic model for the whole system, (ii) a particle Markov chain Monte Carlo sampler to learn the hidden coverages and rate constant parameters, and (iii) two Bayesian formulations to infer the activation energies and pre-exponential factors. The flexibility of the Bayesian framework allows for uncertainty quantification where possible and integration of mathematical constraints in the model to reflect the system physically. We found that our results for the activation energies and pre-exponential factor are in agreement with those reported in the experimental literature, independently, and we provide discussions on the advantages and disadvantages as well as applicability to other systems.
Here, we develop off-lattice simulations of semiflexible polymer chains subjected to applied mechanical forces by using Markov Chain Monte Carlo. Our approach models the polymer as a chain of fixed length bonds, with configurations updated through adaptive nonlocal Monte Carlo moves. This proposed method enables precise calculation of a polymer’s response to a wide range of mechanical forces, which traditional on-lattice models cannot achieve. Our approach has shown excellent agreement with theoretical predictions of persistence length and end-to-end distance in quiescent states as well as stretching distances under tension. Moreover, our model eliminates the orientational bias present in on-lattice models, which significantly impacts calculations such as the scattering function, a crucial technique for revealing the polymer conformation.
Abstract The density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard correction to treat strongly correlated electronic states. Unfortunately, the values of the Hubbard U and J parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the U and J parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest U correction. PBE has the smallest standard deviation and its U and J parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.
Reinforcement learning has witnessed recent applications to a variety of tasks in quantum programming. The underlying assumption is that those tasks could be modeled as Markov decision processes (MDPs). Here, we investigate the feasibility of this assumption by exploring its consequences for single-qubit quantum state preparation and gate compilation. By forming discrete MDPs, we solve for the optimal policy exactly through policy iteration. We find optimal paths that correspond to the shortest possible sequence of gates to prepare a state or compile a gate, up to some target accuracy. Our method works in both the absence and presence of noise and compares favorably to other quantum compilation methods, such as the Ross–Selinger algorithm. This work provides theoretical insight into why reinforcement learning may be successfully used to find optimally short gate sequences in quantum programming.
Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging due to the high dimension in which simulations are carried out and, consequently, due to the very large amount of data that are typically generated. Coarse graining is a popular technique for addressing this problem by providing compact and expressive representations. Coarse graining, however, potentially comes at the cost of accuracy, as dynamical information is, in general, lost when projecting the problem in a lower-dimensional space. This article shows how to eliminate coarse-graining error using two key ideas. First, we represent coarse-grained dynamics as a Markov renewal process. Second, we outline a data-driven, non-parametric Mori–Zwanzig approach for computing jump times of the renewal process. Numerical tests on a small protein illustrate the method.
Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed must be able to efficiently correct for minimal mis-synchronisation between channels and achieve the best detector performance. We present an iterative time calibration method based on Markov Chains, suitable for detector systems with multiple readout channels. Starting from correlated hit pairs alone, and without requiring an external reference time measurement, the method solves for fixed per-channel offsets, with precision limited only by the intrinsic single-channel resolution. A mathematical proof that the method is able to find the correct time offsets to be assigned to each detector channel in order to achieve inter-channel synchronisation is given, and it is shown that the number of iterations to reach convergence within the desired precision is controllable with a single parameter. Numerical studies are used to confirm unbiased recovery of true offsets. Finally, the application of the calibration method to the Super Fine-Grained Detector (SuperFGD) and the Time of Flight (TOF) detector at the upgraded T2K near detector (ND280) shows good improvement in overall timing resolution, demonstrating the effectiveness in a real-world scenario and scalability.
Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To illustrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.
Abstract Summary Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a practical MCMC method in the open-source software package PyBioNetFit (PyBNF), which is designed to support parameterization of mathematical models for biological systems. The new MCMC method, am, incorporates an adaptive move proposal distribution. For warm starts, sampling can be initiated at a specified location in parameter space and with a multivariate Gaussian proposal distribution defined initially by a specified covariance matrix. Multiple chains can be generated in parallel using a computer cluster. We demonstrate that am can be used to successfully solve real-world Bayesian inference problems, including forecasting of new Coronavirus Disease 2019 case detection with Bayesian quantification of forecast uncertainty. Availability and implementation PyBNF version 1.1.9, the first stable release with am, is available at PyPI and can be installed using the pip package-management system on platforms that have a working installation of Python 3. PyBNF relies on libRoadRunner and BioNetGen for simulations (e.g. numerical integration of ordinary differential equations defined in SBML or BNGL files) and Dask.Distributed for task scheduling on Linux computer clusters. The Python source code can be freely downloaded/cloned from GitHub and used and modified under terms of the BSD-3 license (https://github.com/lanl/pybnf). Online documentation covering installation/usage is available (https://pybnf.readthedocs.io/en/latest/). A tutorial video is available on YouTube (https://www.youtube.com/watch?v=2aRqpqFOiS4&t=63s). Supplementary information Supplementary data are available at Bioinformatics online.
We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.
Global QCD analyses of nuclear parton distribution functions (nPDFs) have traditionally relied on the Hessian method for uncertainty estimation. However, the inherent Gaussian approximation and reliance on local curvature often prove insufficient for nPDF fits, which are frequently characterized by limited data constraints and non-Gaussian likelihoods. In this paper, we present the first nPDF determination based on Markov Chain Monte Carlo (MCMC) techniques, implemented within the nCTEQ framework using an adaptive Metropolis-Hastings algorithm. The MCMC approach enables a direct mapping of the posterior distribution and reveals a highly nontrivial parameter-space structure, including multiple modes and pronounced non-Gaussian behavior, particularly for the valence PDFs. We perform the first single-nucleus global analysis of lead PDFs using exclusively lead data and compare it to a multi-nuclei fit employing a standard analytic A dependence. The inclusion of lighter nuclei reduces quark uncertainties and modifies the shape of the lead PDFs, while leaving the gluon distribution largely unaffected. A complementary Hessian analysis exposes systematic limitations of the Gaussian approximation. Our results demonstrate that MCMC methods provide a more reliable framework for uncertainty quantification in nPDF determinations.
We demonstrate the application of pattern recognition algorithms via hidden Markov models (HMM) for qubit readout. This scheme provides a state-path trajectory approach capable of detecting qubit-state transitions and makes for a robust classification scheme with higher starting-state assignment fidelity than when compared to a multivariate Gaussian or a support vector machine scheme. Therefore, the method also eliminates the qubit-dependent readout time optimization requirement in current schemes. Using a HMM state discriminator we estimate fidelities reaching the ideal limit. Unsupervised learning gives access to transition matrix, priors, and IQ distributions, providing a toolbox for studying qubit-state dynamics during strong projective readout.
HipMCL is a high-performance distributed memory implementation of the popular Markov Cluster Algorithm (MCL) and can cluster large-scale networks within hours using a few thousand CPU-equipped nodes. It relies on sparse matrix computations and heavily makes use of the sparse matrix-sparse matrix multiplication kernel (SpGEMM). The existing parallel algorithms in HipMCL are not scalable to Exascale architectures, both due to their communication costs dominating the runtime at large concurrencies and also due to their inability to take advantage of accelerators that are increasingly popular. In this work, we systematically remove scalability and performance bottlenecks of HipMCL. We enable GPUs by performing the expensive expansion phase of the MCL algorithm on GPU. Additionally, we propose a CPU-GPU joint distributed SpGEMM algorithm called pipelined Sparse SUMMA and integrate a probabilistic memory requirement estimator that is fast and accurate. Furthermore, we develop a new merging algorithm for the incremental processing of partial results produced by the GPUs, which improves the overlap efficiency and the peak memory usage. We also integrate a recent and faster algorithm for performing SpGEMM on CPUs. We validate our new algorithms and optimizations with extensive evaluations. With the enabling of the GPUs and integration of new algorithms, HipMCL is up to 12.4x faster, being able to cluster a network with 70 million proteins and 68 billion connections just under 15 minutes using 1024 nodes of ORNL's Summit supercomputer.
Markov chain Monte Carlo sampler useful for a variety of problems for optimization, numerical integration, and generating draws from a probability distribution. They are often used in physical and mathematical problems, especially when it is difficult or impossible to use other approaches. This disclosure is for new bug fixes and enhancements to an existing open source library that is already in the public domain under the MIT license. https://github.com/jellis18/PTMCMCSampler
SAND2024-13027O The CHMMPP: A c++ Library for Constrained Hidden Markov Models (HMM) software supports the analysis of multivariate time series data to detect patterns using HMM. Many applications involve the detection and characterization of hidden or latent states in a complex system using observable states and variables. This software supports inference of latent states integrating both an HMM and application-specific constraints that reflect known relationships in hidden states. The CHMMPP software supports application-specific and generic methods for constrained inference. This includes a framework for customized Viterbi methods, constrained inference of hidden states with A* and integer programming methods, and various constraint-informed methods for learning HMM model parameters. CHMMPP focuses on supporting generic methods that enable the agile expression of complex sets of constraints that naturally arise in many real-world applications.