The criticality problem in nuclear engineering asks for the principal eigen-pair of a Boltzmann operator describing neutron transport in a reactor core. Being able to reliably design, and control such reactors requires assessing these quantities within quantifiable accuracy tolerances. In this paper we propose a paradigm that deviates from the common practice of approximately solving the corresponding spectral problem with a fixed, presumably sufficiently fine discretization. Instead, the present approach is based on first contriving iterative schemes, formulated in function space, that are shown to converge at a quantitative rate without assuming any a priori excess regularity properties, and that exploit only properties of the optical parameters in the underlying radiative transfer model. We develop the analytical and numerical tools for approximately realizing each iteration step withing judiciously chosen accuracy tolerances, verified by a posteriori estimates, so as to still warrant quantifiable convergence to the exact eigen-pair. This is carried out in full first for a Newton scheme. Since this is only locally convergent we analyze in addition the convergence of a power iteration in function space to produce sufficiently accurate initial guesses. Here we have to deal with intrinsic difficulties posed by compact but unsymmetric operators preventing standard arguments used in the finite dimensional case. Our main point is that we can avoid any condition on an initial guess to be already in a small neighborhood of the exact solution. We close with a discussion of remaining intrinsic obstructions to a certifiable numerical implementation, mainly related to not knowing the gap between the principal eigenvalue and the next smaller one in modulus.
相關內容
Solidity compiler plays a key role in enabling the development of smart contract applications on Ethereum by governing the syntax of a domain-specific language called Solidity and performing compilation and optimization of Solidity code. The correctness of Solidity compiler is critical in fostering transparency, efficiency, and trust in industries reliant on smart contracts. However, like other software systems, Solidity compiler is prone to bugs, which may produce incorrect bytecodes on blockchain platforms, resulting in severe security concerns. As a domain-specific compiler for smart contracts, Solidity compiler differs from other compilers in many perspectives, posing unique challenges to detect its bugs. To understand the bugs in Solidity compiler and benefit future research, in this paper, we present the first systematic study on 533 Solidity compiler bugs. We carefully examined their characteristics (including symptoms, root causes, and distribution), and their triggering test cases. Our study leads to seven bug-revealing takeaways for Solidity compiler. Moreover, to study the limitations of Solidity compiler fuzzers and bring our findings into practical scenarios, we evaluate three Solidity compiler fuzzers on our constructed benchmark. The results show that these fuzzers are inefficient in detecting Solidity compiler bugs. The inefficiency arises from their failure to consider the interesting bug-inducing features, bug-related compilation flags, and test oracles
Serotonergic neurons in the raphe nuclei exhibit diverse electrophysiological properties and functional roles, yet conventional identification methods rely on restrictive criteria that likely overlook atypical serotonergic cells. The use of convolutional neural network (CNN) for comprehensive classification of both typical and atypical serotonergic neurons is an interesting one, but the key challenge is often given by the limited experimental data available for training. This study presents a procedure for synthetic data generation that combines smoothed spike waveforms with heterogeneous noise masks from real recordings. This approach expanded the training set while mitigating overfitting of background noise signatures. CNN models trained on the augmented dataset achieved high accuracy (96.2% true positive rate, 88.8% true negative rate) on non-homogeneous test data collected under different experimental conditions than the training, validation and testing data.
We demonstrate the effectiveness of simple observer-based linear feedback policies for "pixels-to-torques" control of robotic systems using only a robot-facing camera. Specifically, we show that the matrices of an image-based Luenberger observer (linear state estimator) for a "student" output-feedback policy can be learned from demonstration data provided by a "teacher" state-feedback policy via simple linear-least-squares regression. The resulting linear output-feedback controller maps directly from high-dimensional raw images to torques while being amenable to the rich set of analytical tools from linear systems theory, allowing us to enforce closed-loop stability constraints in the learning problem. We also investigate a nonlinear extension of the method via the Koopman embedding. Finally, we demonstrate the surprising effectiveness of linear pixels-to-torques policies on a cartpole system, both in simulation and on real-world hardware. The policy successfully executes both stabilizing and swing-up trajectory tracking tasks using only camera feedback while subject to model mismatch, process and sensor noise, perturbations, and occlusions.
We consider a family of boundary integral operators supported on a collection of parametrically defined bounded Lipschitz boundaries. Consequently, the boundary integral operators themselves also depend on the parametric variables, thus leading to a parameter-to-operator map. The main result of this article is to establish the analytic or holomorphic dependence of said boundary integral operators upon the parametric variables, i.e., of the parameter-to-operator map. As a direct consequence we also establish holomorphic dependence of solutions to boundary integral equations, i.e.,~holomorphy of the parameter-to-solution map. To this end, we construct a holomorphic extension to complex-valued boundary deformations and investigate the \emph{complex} Fr\'echet differentiability of boundary integral operators with respect to each parametric variable. The established parametric holomorphy results have been identified as a key property to overcome the so-called curse of dimensionality in the approximation of parametric maps with distributed, high-dimensional inputs. To demonstrate the applicability of the derived results, we consider as a concrete example the sound-soft Helmholtz acoustic scattering problem and its frequency-robust boundary integral formulations. For this particular application, we explore the consequences of our results in reduced order modelling, Bayesian shape inversion, and the construction of efficient surrogates using artificial neural networks.
Justifying the correct implementation of the non-functional requirements (e.g., safety, security) of mission-critical systems is crucial to prevent system failure. The later could have severe consequences such as the death of people and financial losses. Assurance cases can be used to prevent system failure, They are structured arguments that allow arguing and relaying various safety-critical systems' requirements extensively as well as checking the compliance of such systems with industrial standards to support their certification. Still, the creation of assurance cases is usually manual, error-prone, and time-consuming. Besides, it may involve numerous alterations as the system evolves. To overcome the bottlenecks in creating assurance cases, existing approaches usually promote the reuse of common structured evidence-based arguments (i.e. patterns) to aid the creation of assurance cases. To gain insights into the advancements of the research on assurance case patterns, we relied on SEGRESS to conduct a bibliometric analysis of 92 primary studies published within the past two decades. This allows capturing the evolutionary trends and patterns characterizing the research in that field. Our findings notably indicate the emergence of new assurance case patterns to support the assurance of ML-enabled systems that are characterized by their evolving requirements (e.g., cybersecurity and ethics).
The pervasive role played by software in virtually all industries has fostered ever-increasing development of applied research in software engineering. In this chapter, we contribute our experience in using the V-Model as a framework for teaching how to conduct applied research in empirical software engineering. The foundational idea of using the V-Model is presented, and guidance for using it to frame the research is provided. Furthermore, we show how the framework has been instantiated throughout nearly two decades of PhD theses done at the University of Kaiserslautern (RPTU Kaiserslautern) in partnership with Fraunhofer IESE, including the most frequent usage patterns, how the different empirical methods fit into the framework, and the lessons we have learned from this experience.
Solving the Traveling Salesperson Problem (TSP) remains a persistent challenge, despite its fundamental role in numerous generalized applications in modern contexts. Heuristic solvers address the demand for finding high-quality solutions efficiently. Among these solvers, the Lin-Kernighan-Helsgaun (LKH) heuristic stands out, as it complements the performance of genetic algorithms across a diverse range of problem instances. However, frequent timeouts on challenging instances hinder the practical applicability of the solver. Within this work, we investigate a previously overlooked factor contributing to many timeouts: The use of a fixed candidate set based on a tree structure. Our investigations reveal that candidate sets based on Hamiltonian circuits contain more optimal edges. We thus propose to integrate this promising initialization strategy, in the form of POPMUSIC, within an efficient restart version of LKH. As confirmed by our experimental studies, this refined TSP heuristic is much more efficient - causing fewer timeouts and improving the performance (in terms of penalized average runtime) by an order of magnitude - and thereby challenges the state of the art in TSP solving.
Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191