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Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi-Yau targets at large volume. Focusing on the examples of K3 and the quintic, we show that the spectrum, averaged over a region in complex structure moduli space, possesses the same statistical properties as the Gaussian orthogonal ensemble of random matrix theory.
A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as e$^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of $\mathcal{N} = 2$ and (small) $\mathcal{N} = 4$ JT supergravity, and then explore the new cases of spectra from $\mathcal{N} = 3$ and $\mathcal{N} = 4$ large JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.
Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time evolution is driven by the continuous limit of certain 2-local random unitary circuits. We study both cases where the unitaries are chosen with and without a conserved U(1) charge and focus on two aspects of the dynamics. First, we study analytically and numerically the growth of the entanglement entropy of the system, showing that two different time scales appear: one is intrinsic to the internal dynamics (the scrambling time), while the other depends on the system-environment coupling. In the presence of a U(1) conserved charge, we show that the entanglement follows a Page-like behavior in time: it begins to decrease in the middle stage of the “evaporation”, and decreases monotonically afterwards. Second, we study the time needed to retrieve information initially injected in the system from measurements on the environment qudits. Based on explicit numerical computations, we characterize such time both when the retriever has control over the initial configuration or not, showing that different scales appear in the two cases.
For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S R = 2EW, where S R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.
In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.
Using coarse graining, the upscaled mechanical properties of a solid with small scale heterogeneities are derived. The method maps internal forces at the small scale onto peridynamic bond forces in the coarse grained mesh. These upscaled bond forces are used to calibrate a peridynamic material model with position-dependent parameters. These parameters incorporate mesoscale variations in the statistics of the small scale system. The upscaled peridynamic model can have a much coarser discretization than the original small scale model, allowing larger scale simulations to be performed efficiently. The convergence properties of the method are investigated for representative random microstructures. In conclusion, a bond breakage criterion for the upscaled peridynamic material model is also demonstrated.
The chemical short-range order (CSRO) in crystalline materials influences the properties, and its effect is significant in the context of multicomponent materials. Here, we propose a scheme for the CSRO parameter or Δ-parameter in terms of the number of like and unlike bonds in the multicomponent systems. The OPERA or Order Parameter Engineering for RAndom Systems scheme for semi-canonical and canonical ensembles is proposed. The proposed framework of Δ-parameter with OPERA framework can generate the single-phase supercell with desired CSRO without explicit energy calculations and provides a computationally efficient scheme for exploration of the CSRO. We demonstrate the applicability of the Δ-parameter as a scalar quantity for describing the CSRO in multicomponent alloys and oxides (FCC-CoCrNi, BCC-MoNbTaW, and (CoCuMgNiZn)O).
Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).
Triggered by a controversy surrounding a universal behavior of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) – that the power spectrum is merely determined by the spectral form factor – breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.
This work compared the 3D Random Pore Model (3D-RPM) with experimental and characterization data to systematically study the effect of nuclear graphite microstructure and air oxidation temperature. It is well known that oxidation-induced weight loss at elevated temperatures degrades graphite structure and properties; however, a fundamental understanding of the role of graphite microstructure is still unclear. In this work, three diverse grades of nuclear graphite—IG-110, NBG-18, and PCEA—were examined and tested at air oxidation temperatures of 600, 650, 700, and 750 °C following ASTM D7542. Here, the 3D-RPM reproduced the microstructure and temperature dependence of mass loss curves for these grades. For the first time, measurements and modeling were combined to show how bulk density and the amount and spatial distribution of open and closed porosity affects oxidation. IG-110 was less dense and had an open pore network that is finer and more uniformly spread, and showed fastest oxidation. PCEA porosity was less uniform and showed less oxidation, while NBG-18 was more dense, had the least fine and uniform porosity, and showed the slowest oxidation. In general, oxidation proceeds faster if open porosity is more uniformly distributed and can incrementally access closed pore surface area with more ease.
Magnesium-silicate-hydrate (M-S-H) cement has emerged as an alternative binder with potentially lower energy requirements and emissions. Due to the intrinsically low pH values of its matrix, however, normal steel reinforcement is not appropriate for M-S-H system. To toughen the matrix and to overcome the brittle nature of the material, a new strain hardening magnesium-silicate-hydrate composite (SHMSHC) is developed for the first time by incorporating 2 vol% short and randomly oriented polyvinyl alcohol (PVA) microfibers. The resulting SHMSHC exhibits significant strain hardening with a tensile strain capacity of more than 3%, a compressive strength beyond 50 MPa and a tensile strength of around 3 MPa. Remarkably, saturated multiple cracking with a tight crack width less than 10 μm invisible to the human naked eyes was observed. The newly developed SHMSHC addresses the fundamental challenge of M-S-H binder and is expected to widen possible application areas of M-S-H system.
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.
A uranium hydride (UH 3 ) corrosion kinetics model has been developed, based on dimensionally restricted nucleation kinetics, which combines heretofore separate reaction and nucleation kinetics models into a single predictive construct. This theoretical framework accounts for the superficial and random pitting behaviour of UH 3 corrosion. The model can be used to generate the net corrosion surface area and volume fractions for a uranium specimen, generally accounting for its geometric form factor through the surface-to-volume ratio. Furthermore, the combined corrosion kinetics model enables the generation of quantities which may be directly compared to those obtained by non-destructive, non-contact evaluation methods.
Background: Neonatal hypothermia is a common source of morbidity and mortality in low resource settings. We developed the Dream Warmer, a low cost, re-usable non-electric infant warmer to prevent and treat hypothermia. Methods: We conducted a cluster-randomized stepped-wedge trial. The primary aim was to assess the effect on overall euthermia rates of introducing the warmer compared to standard of care in rural Rwandan hospitals. The secondary aims were to assess effects of warmer introduction on mortality, as well as the safety and feasibility of the warmer. Ten district hospitals participated in the study from November 19th 2019 to July 15th 2020. Patients were eligible to use the warmer if they were 1) hypothermic (temp < 36·5 °C) or 2) or at risk of hypothermia (weight < 2·5 kg or estimated post menstrual age < 35 weeks) when Kangaroo Mother Care was not available. An encounter was defined as the data from an individual infant on a single day. Trial of a Non Electric Infant Warmer for Prevention and Treatment of Hypothermia in Rwanda [NCT03890211]. Findings: Over the study period, 3179 patients were enrolled across the ten neonatal wards, yielding 12,748 encounters; 464 unique infants used the warmer 892 times, 79% eligible due to hypothermia. Because of limited study nurse resources, the warmer was used in only 18% of eligible encounters. Despite this low rate of warmer use, the rate of euthermia rose from 51% (95% CI 50–52%) of encounters pre-intervention to 67% (66–68%) post-intervention; p < 0·0001. Among the encounters in which the warmer was used, only 11% (9–13%) remained hypothermic. While mortality rates pre- and post-intervention did not change, mortality rate among those who used the warmer was significantly lower than among those who did not (0·9% vs 2·8%, p = 0·01). Use of the warmer did not affect hyperthermia rates. There were no safety concerns or instances of incorrect warmer use. Interpretation: Introduction of the warmer increased rates of euthermia with no associated safety concerns.
One of the most downloaded articles in 2017 from the International Journal of Radiation Oncology, Biology, and Physics was a study suggesting that music therapy during radiation therapy (RT) simulation substantially reduces anxiety. To further evaluate the potential of music's clinical efficacy in the context of radiation therapy, we conducted a randomized trial evaluating the influence of genre-based music chosen by the study participant on anxiety during the first RT treatment session with a method that is applicable to routine clinical practice.
We conducted a phase 3 randomized clinical trial to assess whether radical hemithoracic radiation therapy (RHR) compared with palliative radiation therapy (PR) can achieve overall survival (OS) advantages in patients with malignant pleural mesothelioma (MPM).
The phase 2 randomized study SABR-COMET demonstrated that in patients with controlled primary tumors and 1 to 5 oligometastatic lesions, SABR was associated with improved progression-free survival (PFS) compared with standard of care (SoC), but with higher costs and treatment-related toxicities. The aim of this study was to assess the cost-effectiveness of SABR versus SoC in this setting.
In the modern era, improvements in radiation therapy techniques have paved the way for simultaneous integrated boost irradiation in adjuvant breast radiation therapy after breast conservation surgery. Nevertheless, randomized trials supporting the noninferiority of this treatment to historical standards of care approach are lacking.