Mean field stochastic control under sublinear expectation

Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a stochastic differential equation driven by a $G$-Brownian motion, whose coefficients depend not only on the control, the controlled state process but also on its law under the $G$-expectation. Also the associated cost functional is of mean-field type. Under the assumption of a convex control state space we study the stochastic maximum principle, which gives a necessary optimality condition for control processes. Under additional convexity assumptions on the Hamiltonian it is shown that this necessary condition is also a sufficient one. The main difficulty which we have to overcome in our work consists in the differentiation of the $G$-expectation of parameterized random variables. As particularly delicate it turns out to handle with the $G$-expectation of a function of the controlled state process inside the running cost of the cost function. For this we have to study a measurable selection theorem for set-valued functions whose values are subsets of the representing set of probability measures for the $G$-expectation.Comment: 34 page

Ideal isotropic auxetic networks from random networks

Auxetic materials are characterized by a negative Poisson's ratio, $\mathrm{\nu}$. As the Poisson's ratio becomes negative and approaches the lower isotropic mechanical limit of $\mathrm{\nu = -1}$, materials show enhanced resistance to impact and shear, making them suitable for applications ranging from robotics to impact mitigation. Past experimental efforts aimed at reaching the $\mathrm{\nu = -1}$ limit have resulted in highly anisotropic materials, which show a negative Poisson's ratio only when subjected to deformations along specific directions. Isotropic designs have only attained moderately auxetic behavior, or have led to structures that cannot be manufactured in 3D. Here, we present a design strategy to create isotropic structures from disordered networks that leads to Poisson's ratios as low as $\mathrm{\nu = -0.98}$. The materials conceived through this approach are successfully fabricated in the laboratory and behave as predicted. The Poisson's ratio $\mathrm{\nu}$ is found to depend on network structure and bond strengths; this sheds light on the structural motifs that lead to auxetic behavior. The ideas introduced here can be generalized to 3D, a wide range of materials, and a spectrum of length scales, thereby providing a general platform that could impact technology.Comment: 16 pages, 6 figure

Designing Case Study Research for Pedagogical Application and Scholarly Outcomes

The purpose of this paper is to present the pedagogical/andragogical model of case study research in capstone courses in collegiate aviation programs. As higher education continues to advance in examining new or different ways to engage students, case study research in a capstone course affords seniors the opportunity to engage in learning how to plan, investigate, write a case study research report and present their findings on a topic of interest

El Quimbo, la represión del Huila

Este trabajo se realiza con el fin de luchar, defender y proteger el territorio, la biodiversidad, la soberanía y las comunidades que, por diferentes medios han puesto su grito de auxilio solicitando apoyo y ayuda y mostrando siempre su oposición a la imposición de megaproyectos energéticos, mineros, y agro combustibles debido a sus fuertes impactos negativos ambientales, ecológicos, económicos, sociales y culturales, específicamente en el caso del Megaproyecto Hidroeléctrico el Quimbo, pero aun así, las autoridades pertinentes, el gobierno, la sociedad y las empresas responsables hacen caso omiso a la oposición de los afectados y pasan por encima de ellos violando los derechos primordiales de la vida e ignorando el gran atropello que se comete con estas acciones.Pregrad

Relationship Between Government and Enterprises in the Face of Risk Pension Insurance Fund Under the Background of Aging

At present, China’s population aging is accelerating. The aging population problem is a stern challenge to pension insurance. This paper explore the risk of problems pension fund faces from two aspects of the government and enterprises, and to analyze the relationship between government and enterprises in the face of risk of the old-age insurance fund, namely the game relationships and partnerships. Finally, put forward the countermeasures and suggestions for the risk of pension funds. Key words: Pension insurance fund; Government; Enterprise

The marfan syndrome: Abnormal aortic elastic properties

Aortic distensibility and aortic stiffness index were measured at the ascending aorta (3 cm above the aortic valve) and the mid-portion of the abdominal aorta from the changes in echocardiographic diameters and pulse pressure in 14 patients with the Marfan syndrome and 15 age- and gender-matched normal control subjects. The following formulas were used: 1) Aortic distensibility = 2(Changes in aortic diameter)/(Diastolic aortic diameter) (Pulse pressure); and 2) Aortic stiffness index = ln(Systolic blood pressure)/(Diastolic blood pressure)(Changes in aortic diameter)/Diastolic aortic diameter. Pulse wave velocity was also measured.Compared with normal subjects, patients with the Marfan syndrome had decreased aortic distensibility in the ascending and the abdominal aorta (2.9 ± 1.3 vs. 5.6 ± 1.4 cm2 dynes-1, p < 0.001 and 4.5 ± 2.1, vs. 7.7 ± 2.5, cm2 dynes-1, p < 0.001, respectively) and had an increased aortic stiffness index in the ascending and the abdominal aorta (10.9 ± 5.6 vs. 5.9 ± 2.2, p < 0.005 and 7.1 ± 3.1 vs. 3.9 ± 1.2, p < 0.005, respectively). Aortic diameters in the ascending aorta were larger in these patients than in normal subjects, but those in the abdominal aorta were similar in the two groups. Linear correlations for both aortic distensibility and stiffness index were found between the ascending and the abdominal aorta (r = 0.85 and 0.71, respectively). Pulse wave velocity was more rapid in the patients than in the normal subjects (11.6 ± 2.5 vs. 9.5 ± 1.4 m/s, respectively, p < 0.01).Thus, aortic elastic properties are abnormal in patients with the Marfan syndrome irrespective of the aortic diameter, which suggests an intrinsic abnormality of the aortic arterial wall

Transcripción y análisis del solo de batería Stompin’ at the Savoy de Max Roach

This final assignment presents 32 bars of a drum solo by Max Roach. The solo is over a music composition called Stompin’ at the Savoy, included in de cd Brown and Roach. Besides the drum transcription, a theoretical analysis is also presented...Este trabajo presenta una transcripción de 32 compases del solo de batería de Max Roach en la composición Stompin’ at the Savoy, incluida en el disco Brown and Roach. Además de la transcripción también se ha elaborado un análisis teórico de dicha composición..

A Critical Review of Large Language Model on Software Engineering: An Example from ChatGPT and Automated Program Repair

Large Language Models (LLMs) have been gaining increasing attention and demonstrated promising performance across a variety of Software Engineering (SE) tasks, such as Automated Program Repair (APR), code summarization, and code completion. For example, ChatGPT, the latest black-box LLM, has been investigated by numerous recent research studies and has shown impressive performance in various tasks. However, there exists a potential risk of data leakage since these LLMs are usually close-sourced with unknown specific training details, e.g., pre-training datasets. In this paper, we seek to review the bug-fixing capabilities of ChatGPT on a clean APR benchmark with different research objectives. We first introduce {\benchmark}, a new benchmark with buggy and the corresponding fixed programs from competitive programming problems starting from 2023, after the training cutoff point of ChatGPT. The results on {\benchmark} show that ChatGPT is able to fix 109 out of 151 buggy programs using the basic prompt within 35 independent rounds, outperforming state-of-the-art LLMs CodeT5 and PLBART by 27.5\% and 62.4\% prediction accuracy. We also investigate the impact of three types of prompts, i.e., problem description, error feedback, and bug localization, leading to additional 34 fixed bugs. Besides, we provide additional discussion from the interactive nature of ChatGPT to illustrate the capacity of a dialog-based repair workflow with 9 additional fixed bugs. Inspired by the findings, we further pinpoint various challenges and opportunities for advanced SE study equipped with such LLMs (e.g.,~ChatGPT) in the near future. More importantly, our work calls for more research on the reevaluation of the achievements obtained by existing black-box LLMs across various SE tasks, not limited to ChatGPT on APR

Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes

We discuss expansions for the Cotton-York tensor near infinity for arbitrary slices of stationary spacetimes. From these expansions it follows directly that a necessary condition for the existence of conformally flat slices in stationary solutions is the vanishing of a certain quantity of quadrupolar nature (obstruction). The obstruction is nonzero for the Kerr solution. Thus, the Kerr metric admits no conformally flat slices. An analysis of higher orders in the expansions of the Cotton-York tensor for solutions such that the obstruction vanishes suggests that the only stationary solution admitting conformally flat slices are the Schwarzschild family of solutions.Comment: Revised version to appear in Class. Quantum Grav. with 13 pages. Section 2 regarding multipolar expansions of stationary spacetimes largely expanded. A Maple script demonstrating the calculations in the axially symmetric case is available upon request from the autho

Mechanistic Insights on the Semihydrogenation of Alkynes over Different Nanostructured Photocatalysts

A single molecule microscopy study of the interaction of dye-modified alkanes, alkenes and alkynes with nanostructured catalysts based on TiO 2 reveals significant differences in the desorption kinetics of the probe molecules depending on the chemical nature of the catalyst. A comparison of TiO 2 with materials decorated with palladium (Pd@TiO 2) or molybdenum/cobalt (MoCo@TiO 2) reveals kinetic differences that justify in part the better performance of MoCo@TiO 2 in semi-hydrogenation reactions. Whereas single-molecule desorption rate is ~50% higher for MoCo@TiO 2 than Pd@TiO 2 , analysis at the bench scale indicate alkene-to-alkane conversion is about 10 times faster for Pd (k 2 Pd = 0.02 s-1) than for MoCo (k 2 MoCo = 0.002 s-1) catalysts. This suggests selectivity is not solely determined by the desorption processes and that the hydrogenation rate constant (k 21) for the on-surface hydrogenation of alkenes to alkanes is much faster for Pd@TiO 2 than for MoCo@TiO 2. Thus, the latter shows greater selectivity towards 2 partial hydrogenation reactions compared with Pd@TiO 2 , whose excellent hydrogenation performance becomes a disadvantage for the selectivity needed for semi-hydrogenation processes