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Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025
GismoPower’s Final Research Report documents the outcomes of a DOE SBIR Phase II project focused on advancing the MEGA® (Mobile Electricity Generating Appliance), a trailerable, plug-in solar canopy appliance designed to deliver appliance-class electricity generation for homes, small businesses and renters. The project’s core objective was to remove the technical and regulatory barriers that have historically prevented plug-in solar systems from being safely certified, permitted, and interconnected in the United States.
Abstract Anomaly Detection is becoming increasingly popular within the experimental physics community. At experiments such as the Large Hadron Collider, anomaly detection is growing in interest for finding new physics beyond the Standard Model. This paper details the implementation of a novel Machine Learning architecture, called Flux+Mutability, which combines cutting-edge conditional generative models with clustering algorithms. In the ‘flux’ stage we learn the distribution of a reference class. The ‘mutability’ stage at inference addresses if data significantly deviates from the reference class. We demonstrate the validity of our approach and its connection to multiple problems spanning from one-class classification to anomaly detection. In particular, we apply our method to the isolation of neutral showers in an electromagnetic calorimeter and show its performance in detecting anomalous dijets events from standard QCD background. This approach limits assumptions on the reference sample and remains agnostic to the complementary class of objects of a given problem. We describe the possibility of dynamically generating a reference population and defining selection criteria via quantile cuts. Remarkably this flexible architecture can be deployed for a wide range of problems, and applications like multi-class classification or data quality control are left for further exploration.
Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices. -- Highlights: •Different PT-symmetries lead to qualitatively different systems. •Construction of non-perturbative Dyson maps and isospectral Hermitian counterparts. •Numerical discussion of the eigenvalue spectra for one of the E(2)-systems. •Established link to systems studied in the context of optical lattices. •Setup for the E(3)-algebra is provided.
Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.
Class I ribonucleotide reductases (RNRs) share a common mechanism of nucleotide reduction in a catalytic α subunit. All RNRs initiate catalysis with a thiyl radical, generated in class I enzymes by a metallocofactor in a separate β subunit. Class Id RNRs use a simple mechanism of cofactor activation involving oxidation of a Mn II 2 cluster by free superoxide to yield a metal-based Mn III Mn IV oxidant. This simple cofactor assembly pathway suggests that class Id RNRs may be representative of the evolutionary precursors to more complex class Ia–c enzymes. X-ray crystal structures of two class Id α proteins from Flavobacterium johnsoniae (Fj) and Actinobacillus ureae (Au) reveal that this subunit is distinctly small. The enzyme completely lacks common N-terminal ATP-cone allosteric motifs that regulate overall activity, a process that normally occurs by dATP-induced formation of inhibitory quaternary structures to prevent productive β subunit association. Class Id RNR activity is insensitive to dATP in the Fj and Au enzymes evaluated here, as expected. However, the class Id α protein from Fj adopts higher-order structures, detected crystallographically and in solution. The Au enzyme does not exhibit these quaternary forms. Our study reveals structural similarity between bacterial class Id and eukaryotic class Ia α subunits in conservation of an internal auxiliary domain. Overall, our findings with the Fj enzyme illustrate that nucleotide-independent higher-order quaternary structures can form in simple RNRs with truncated or missing allosteric motifs.
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Two crucial challenges faced in the design of ocean wave energy converters (WECs) are maintaining high capacity factors and remaining robust in everchanging, harsh ocean environments. This study introduces a novel mechanism for achieving reactive WEC control with a soft hydraulic power take-off, thereby addressing both challenges. The device of interest involves a hydraulic pump, constructed from a fluidic flexible matrix composite (F2MC), which is cyclically stretched by driving waves and pressurizes working fluid through a turbine-generator. This class of fiber-reinforced stretch hoses is established for ocean use as robust moorings and shock absorbers. The dynamic properties of the F2MC pump depend on internal pressure, which can be controlled by a continuously variable transmission between the turbine and generator, allowing the system to be adapted for better performance over a wide range of wave conditions. This work presents a dynamic model for operation and adaptive behavior of this power take-off system, experimentally validates components of the model, and performs dynamic simulations of the system that show increases in power production and capacity factor compared to non-adaptive operation for a variety of driving wave conditions. This work develops the basis for future large-scale experimental testing and controller design of this system.
Here, we report on the synthesis of submicron Li 1+x V 3 O 8 fibers through a facile mixed ethanol/water solution-mediated solvothermal route in the absence of surfactants. All the raw materials used are commercially available, relatively inexpensive, and low-toxic, and these can be handled in an ambient atmosphere, rendering this synthetic route as reasonably facile and efficient. To ensure a desirable and acceptable sample crystallinity and purity, we introduced a postannealing treatment at 500°C. The monoclinic phase formation of the fiber sample was probed in detail using a series of X-ray diffraction, scanning electron microscopy, transmission electron microscopy, infrared spectroscopy, X-ray photoelectron spectroscopy, high resolution transmission electron microscopy, and selected area electron diffraction measurements. Both morphology and chemical composition could be carefully and systematically tuned in terms of generating a class of novel, pure, and well-defined motifs of Li 1+x V 3 O 8 . A plausible mechanism for the formation of submicron-diameter fibers has been discussed in addition to the expected phase transformation within our Li-V-O materials. Our comprehensive study should provide for needed fundamental insights into putting forth a viable synthesis strategy for the generation of well-defined morphological variants of layered oxide materials for battery applications.
We introduce adversarial learning methods for data-driven generative modeling of dynamics of nth-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.
Project Objectives - Of the myriad specialized metabolites that plants deploy to adapt to environmental challenges, terpenes form the largest group. In many major crops, unique terpene blends serve as key stress defenses that directly impact plant fitness and yield. In addition, terpenes, such as bisabolene and pinene, are used for producing renewable biofuels. Essential to advancing a broader use of terpenes for biofuel feedstock engineering is a system-wide knowledge of the diverse biosynthetic machinery and defensive potential of often species-specific terpene blends. The proposed project would merge genome-wide enzyme discovery with comparative –omics, protein structural and plant microbiome studies to define the biosynthesis and stress-defensive functions of the switchgrass (Panicum virgatum) terpene network. These insights would be combined with developing and applying non-transgenic genome editing tools to design plants with desirable terpene blends for higher productivity and biofuel production on marginal lands. As a dedicated lignocellulosic feedstock for U.S. biofuel production with high net energy yield, stress tolerance, and available genome resources, switchgrass is well-suited for devising new avenues for biofuel production. Project Description – The diversity of plant terpene defenses is governed by species-specific families of terpene synthase (TPS) and cytochrome P450 monooxygenase (P450) enzymes. Mining of the switchgrass genome (genotype Alamo) identified ~100 TPS and P450 candidate genes, and combinatorial biochemical analysis of synthesized TPSs and P450s revealed more than a dozen enzymes with common and novel activities. In addition, several identified terpene metabolites and the corresponding transcripts were up-regulated in response to abiotic stressors. These findings demonstrate a unique switchgrass terpene network with probable importance to abiotic stress tolerance, thus providing a large chemical portfolio for optimizing crop resistance, yield, and biofuel composition. Leveraging these preliminary data, we propose to generate a genome-wide map of the switchgrass terpene metabolic network through multi-gene co-expression analyses that allow the efficient cross-validation of TPS and P450 functions. Key enzymes would further be applied to structure-function studies via X-ray protein crystallography, homology modeling and site-directed mutagenesis to gain mechanistic insight into the catalytic specificity of switchgrass terpene metabolism and provide gene and amino acid targets for genome editing. In tandem with terpene pathway discovery, system-wide metabolomics, transcriptomics and proteomics studies in switchgrass accessions of contrasting drought tolerance would define the role of switchgrass terpene metabolism in conferring abiotic stress resilience. Metabolic changes would be assessed in a combined approach of targeted (terpenes) and untargeted metabolite profiling using a high-resolution LC-MS/MS approach, differential gene expression analyses through multiplexed Illumina RNA sequencing, and quantitative analysis of high-priority pathway enzymes using multiple reaction monitoring (MRM). Drawing on these insights, knock-down/out mutants of stress-associated pathway nodes would be generated by optimizing transient virus-induced gene silencing (VIGS) and CRISPR/Cas9 systems under control of the Tobacco Rattle Virus (TRV). The resulting mutant lines would then be analyzed for stress susceptibility and the impact on the root microbiome to define gene functions in planta. Knowledge of terpene pathways, enzyme mechanisms and bioactivities would be applied to enhance switchgrass stress resilience and to tailor-make terpene blends for biofuel production. Here, TRV-enabled CRISPR/Cas9 genome editing, including allele-specific knock-out of redundant genes, engineering of enzyme specificity via structure-guided point mutations, and overexpression of terpene genes relevant to stress-protection or biofuel production, would be used to increase metabolic flux toward desired pathways. Broader Impacts - Integrating the system-wide discovery, mechanistic analysis and non-transgenic genome engineering of the switchgrass terpene network aligns the required steps to unlock the chemical potential of this important metabolite class to generate crops that are more resistant to stress and provide advanced biofuel production in light of rising climate pressures as foreseeable challenges for bioenergy crop cultivation. The proposed project would further offer interdisciplinary student training through active involvement in the project and integration of research concepts and outcomes into newly-developed graduate and undergraduate courses on Plant Biotechnology.
Purpose: To construct a Monte Carlo (MC)-based simulation model for analyzing the dependence of tumor oxygen distribution on different variables related to tumor vasculature [blood velocity, vessel-to-vessel proximity (vessel proximity), and inflowing oxygen partial pressure (pO{sub 2})]. Methods: A voxel-based tissue model containing parallel capillaries with square cross-sections (sides of 10 μm) was constructed. Green's function was used for diffusion calculations and Michaelis-Menten's kinetics to manage oxygen consumption. The model was tuned to approximately reproduce the oxygenational status of a renal carcinoma; the depth oxygenation curves (DOC) were fitted with an analytical expression to facilitate rapid MC simulations of tumor oxygen distribution. DOCs were simulated with three variables at three settings each (blood velocity, vessel proximity, and inflowing pO{sub 2}), which resulted in 27 combinations of conditions. To create a model that simulated variable oxygen distributions, the oxygen tension at a specific point was randomly sampled with trilinear interpolation in the dataset from the first simulation. Six correlations between blood velocity, vessel proximity, and inflowing pO{sub 2} were hypothesized. Variable models with correlated parameters were compared to each other and to a nonvariable, DOC-based model to evaluate the differences in simulated oxygen distributions and tumor radiosensitivities for different tumor sizes. Results: For tumors with radii ranging from 5 to 30 mm, the nonvariable DOC model tended to generate normal or log-normal oxygen distributions, with a cut-off at zero. The pO{sub 2} distributions simulated with the six-variable DOC models were quite different from the distributions generated with the nonvariable DOC model; in the former case the variable models simulated oxygen distributions that were more similar to in vivo results found in the literature. For larger tumors, the oxygen distributions became truncated in the lower end, due to anoxia, but smaller tumors showed undisturbed oxygen distributions. The six different models with correlated parameters generated three classes of oxygen distributions. The first was a hypothetical, negative covariance between vessel proximity and pO{sub 2} (VPO-C scenario); the second was a hypothetical positive covariance between vessel proximity and pO{sub 2} (VPO+C scenario); and the third was the hypothesis of no correlation between vessel proximity and pO{sub 2} (UP scenario). The VPO-C scenario produced a distinctly different oxygen distribution than the two other scenarios. The shape of the VPO-C scenario was similar to that of the nonvariable DOC model, and the larger the tumor, the greater the similarity between the two models. For all simulations, the mean oxygen tension decreased and the hypoxic fraction increased with tumor size. The absorbed dose required for definitive tumor control was highest for the VPO+C scenario, followed by the UP and VPO-C scenarios. Conclusions: A novel MC algorithm was presented which simulated oxygen distributions and radiation response for various biological parameter values. The analysis showed that the VPO-C scenario generated a clearly different oxygen distribution from the VPO+C scenario; the former exhibited a lower hypoxic fraction and higher radiosensitivity. In future studies, this modeling approach might be valuable for qualitative analyses of factors that affect oxygen distribution as well as analyses of specific experimental and clinical situations.
We extend the single-fluid solvability conditions to include plasma systems at arbitrary $\beta$ with arbitrary flows and external forcing terms. This treatment includes both the isotropic and the anisotropic cases. The generalized conditions that result can be used to generate certain classes of single-fluid equilibria.
The details of how soil microorganisms contribute to stable soil organic carbon pools are a pressing knowledge gap with direct implications for soil health and climate mitigation. It is now recognized that microbial necromass contributes substantially to the formation of stable soil carbon. However, the quantification of necromass in soils has largely been limited to model molecules such as aminosugar biomarkers. The abundance and chemical composition of other persistent microbial residues remain unresolved, particularly concerning how these pools may vary with microbial community structure, soil texture, and management practices. We use yearlong soil incubation experiments with an isotopic tracer to quantify the composition of persistent residues derived from microbial communities inhabiting sand or silt dominated soil with annual (corn) or perennial (switchgrass) monocultures. Persistent microbial residues were recovered in diverse soil biomolecular pools including metabolites, proteins, lipids, and mineral-associated organic matter (MAOM). The relative abundances of microbial contributions to necromass pools were consistent across cropping systems and soil textures. The greatest residue accumulation was not recovered in MAOM but in the light density fraction of soil debris that persisted after extraction by chemical fractionation using organic solvents. Necromass abundance was positively correlated with microbial biomass abundance and revealed a possible role of cell wall morphology in enhancing microbial carbon persistence; while gram-negative bacteria accounted for the greatest contribution to microbial-derived carbon by mass at one year, residues from gram-positive Actinobacteria and Firmicutes showed greater durability. Together these results offer a quantitative assessment of the relative importance of diverse molecular classes for generating durable soil carbon.
Earth system models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the robust analysis of risks associated with extreme weather events. While low-cost climate emulators have emerged as an alternative to emulate ESMs and enable rapid analysis of future climate, many of these emulators only provide output on at most a monthly frequency. This temporal resolution is insufficient for analyzing events that require daily characterization, such as heat waves or heavy precipitation. We propose using diffusion models, a class of generative deep learning models, to effectively downscale ESM output from a monthly to a daily frequency. Trained on a handful of ESM realizations, reflecting a wide range of radiative forcings, our DiffESM model takes monthly mean precipitation or temperature as input, and is capable of producing daily values with statistical characteristics close to ESM output. Combined with a low-cost emulator providing monthly means, this approach requires only a small fraction of the computational resources needed to run a large ensemble. We evaluate model behavior using a number of extreme metrics, showing that DiffESM closely matches the spatio-temporal behavior of the ESM output it emulates in terms of the frequency and spatial characteristics of phenomena such as heat waves, dry spells, or rainfall intensity.