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All human societies present unique narratives that shape their customs and beliefs. Despite cultural differences, some symbolic elements (e.g., heroes and tricksters) are common across many cultures. Here, we reconcile these seemingly contradictory aspects by analyzing mythological themes and traditions at various scales. Our analysis revealed that global mythologies exhibit both geographic and thematic nesting across different scales, manifesting in a layered structure. The largest geographic clusters correspond to the New and Old Worlds, which further divide into smaller bioregions. This hierarchical manifestation closely aligns with historical human migration patterns at a large scale, suggesting that narrative themes were carried through deep history. At smaller scales, the correspondence with bioregions indicates that these themes are locally adapted and diffused into variations across cultures over time. Our approach, which treats myths and traditions as random variables without considering factors like geography, history, or story lineage, suggests that the manifestation of mythology has been well-preserved over time and thus opens exciting research avenues to reconstruct historical patterns and provide insight into human cultural narratives.

Nonlinear simulations of neutron star mergers are complicated by the need to represent turbulent dynamics. As we cannot (yet) perform simulations that resolve accurately both the gravitational-wave scale and the smallest scales at which magneto/hydrodynamic turbulence plays a role, we need to rely on approximations. Addressing this problem in the context of large-eddy models, we outline a coherent Lagrangian filtering framework that allows us to explore the many issues that arise, linking conceptual problems to practical implementations and the interpretation of the results. We develop understanding crucial for quantifying unavoidable uncertainties in current and future numerical relativity simulations and consider the implications for neutron-star parameter estimation and constraints on the equation of state of matter under extreme conditions., Comment: 15 pages, comments welcome

Many lung diseases require detailed visualisation for accurate diagnosis and treatment. High-resolution computed tomography (CT) is the gold-standard technique for non-invasive lung disease detection, but it presents a risk to the patient through the relatively high ionising radiation dose required. Utilising the X-ray phase information may allow improvements in image resolution at equal or lower radiation levels than current clinical imaging. Propagation-based phase-contrast imaging requires minimal adaption of existing medical systems, and is well suited to lung imaging due to the strong phase gradients introduced by the lung-air material interfaces. Herein, propagation-based phase contrast CT is demonstrated for large animals, namely lambs, as a model for paediatric patients, using monochromatic radiation and a photon-counting detector at the Imaging and Medical Beamline of the Australian Synchrotron. Image quality, normalised against radiation dose, was optimised as a function of the beam energy and propagation distance, with the optimal conditions used to test the available image quality at very low radiation dose. The resulting CT images demonstrate superior resolution to existing high-resolution CT systems, pushing dose to the quantum limit to comply with current Australian guidelines for infant chest CT exposure of $<2.5\:\text{mSv}$ effective dose. Constituent raw projections are shown to have significant proportions of pixels with zero photon counts that would create severe information loss in conventional CT. Phase retrieval enabled clear visualisation of minor lung airways at doses up to 1,225$\pm$31\% times lower than conventional CT reconstruction, at a voxel size of just 75$\mathrm{\mu}$m.

Code Large Language Models (Code LLMs) have excelled at tasks like code completion but often miss deeper semantics such as execution effects and dynamic states. This paper aims to bridge the gap between Code LLMs' reliance on static text data and the need for thorough semantic understanding for complex tasks like debugging and program repair. We introduce a novel strategy to train Code LLMs with comprehensive semantics, encompassing high-level functional descriptions, local execution effects of individual statements, and overall input/output behavior, thereby linking static code text with dynamic execution states. We begin by collecting PyX, a clean code corpus of fully executable samples with functional descriptions and execution tracing. We propose training Code LLMs to write code and represent and reason about execution behaviors using natural language, mimicking human verbal debugging. This approach led to the development of SemCoder, a Code LLM with only 6.7B parameters, which shows competitive performance with GPT-3.5-turbo on code generation and execution reasoning tasks. SemCoder achieves 81.1% on HumanEval (GPT-3.5-turbo: 76.8%) and 54.5% on CRUXEval-I (GPT-3.5-turbo: 50.3%). We also study the effectiveness of SemCoder's monologue-style execution reasoning compared to concrete scratchpad reasoning, showing that our approach integrates semantics from multiple dimensions more smoothly. Finally, we demonstrate the potential of applying learned semantics to improve Code LLMs' debugging and self-refining capabilities.

We present a formulation of special relativistic, dissipative hydrodynamics (SRDHD) derived from the well-established M\"uller- Israel-Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and timescale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation timescales, it is roughly an order of magnitude faster than standard methods near the ideal limit., Comment: 16 pages, 13 figures. Intention to submit to MNRAS

Pre-trained code language models have achieved promising performance in code generation and improved the programming efficiency of human developers. However, their self-refinement capability is typically overlooked by the existing evaluations of code LMs, which focus only on the accuracy of the one-time prediction. For the cases when code LMs fail to implement the correct program, developers actually find it hard to debug and fix the faulty prediction since it is not written by the developers themselves. Unfortunately, our study reveals that code LMs cannot efficiently self-refine their faulty generations as well. In this paper, we propose CYCLE framework, learning to self-refine the faulty generation according to the available feedback, such as the execution results reported by the test suites. We evaluate CYCLE on three popular code generation benchmarks, HumanEval, MBPP, and APPS. The results reveal that CYCLE successfully maintains, sometimes improves, the quality of one-time code generation, while significantly improving the self-refinement capability of code LMs. We implement four variants of CYCLE with varied numbers of parameters across 350M, 1B, 2B, and 3B, and the experiments show that CYCLE consistently boosts the code generation performance, by up to 63.5%, across benchmarks and varied model sizes. We also notice that CYCLE outperforms code LMs that have 3$\times$ more parameters in self-refinement., Comment: Camera-ready for OOPSLA'24

Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.

Code Large Language Models (Code LLMs) are being increasingly employed in real-life applications, so evaluating them is critical. While the conventional accuracy evaluates the performance of Code LLMs on a set of individual tasks, their self-consistency across different tasks is overlooked. Intuitively, a trustworthy model should be self-consistent when generating natural language specifications for its own code and generating code for its own specifications. Failure to preserve self-consistency reveals a lack of understanding of the shared semantics underlying natural language and programming language, and therefore undermines the trustworthiness of a model. In this paper, we first formally define the self-consistency of Code LLMs and then design a framework, IdentityChain, which effectively and efficiently evaluates the self-consistency and conventional accuracy of a model at the same time. We study eleven Code LLMs and show that they fail to preserve self-consistency, which is indeed a distinct aspect from conventional accuracy. Furthermore, we show that IdentityChain can be used as a model debugging tool to expose weaknesses of Code LLMs by demonstrating three major weaknesses that we identify in current models using IdentityChain. Our code is available at https://github.com/marcusm117/IdentityChain., Comment: ICLR 2024

Dark-field X-ray imaging is a novel modality which visualises scattering from unresolved microstructure. Most dark-field imaging techniques rely on crystals or structured illumination, but recent work has shown that dark-field effects are observable in straightforward propagation-based imaging (PBI). Based on the single-material X-ray Fokker--Planck equation with an a priori dark-field energy dependence, we propose an algorithm to extract phase and dark-field effects from dual-energy PBI images. We successfully apply the dark-field retrieval algorithm to simulated and experimental dual-energy data, and show that by accounting for dark-field effects, projected thickness reconstruction is improved compared to the classic Paganin algorithm. With the emergence of spectral detectors, the method could enable single-exposure dark-field imaging of dynamic and living samples., Comment: 21 pages, 17 figures

A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based representations, the misfit is instead minimized in a small subspace spanned by the first few eigenfunctions of a judicious elliptic operator, which itself depends on the previous iteration. By repeatedly adapting both the dimension and the basis of the search space, regularization is inherently incorporated at each iteration without the need for extra Tikhonov penalization. Convergence is proved under an angle condition, which is included into the resulting \emph{Adaptive Spectral Inversion} (ASI) algorithm. The ASI approach compares favorably to standard grid-based inversion using $L^2$-Tikhonov regularization when applied to an elliptic inverse problem. The improved accuracy resulting from the newly included angle condition is further demonstrated via numerical experiments from time-dependent inverse scattering problems.