Developmental stages and important periods of probability cognition in 6 to 14 year-old students

This study chose 906 students of 6 to 14 years of age and focused on the developmental stages and important periods of probability cognition. The study shows that probability cognition of students aged 6-14 experiences the following 5 stages: slow development stage I (6-7 years old), quick development stage I (8-9 years old), slow development stage II (10 years old), quick development stage II (11-12 years old) and stagnant stage (13-14 years old). Additionally, there are two important periods in students’ cognitive development: 8-9 years old is the first period and 11-12 is the second. Even at the highest development stage, students can just understand the number representation, probability distribution and fraction representation while ca not reach the mastery level, which suggests the limitation of students’ probability cognition. Accordingly, curriculum should take students’ cognitive development level into account and set reasonable cognitive objectives

Efficient Algorithms for Minimizing Compositions of Convex Functions and Random Functions and Its Applications in Network Revenue Management

In this paper, we study a class of nonconvex stochastic optimization in the form of $\min_{x\in\mathcal{X}} F(x):=\mathbb{E}_\xi [f(\phi(x,\xi))]$, where the objective function $F$ is a composition of a convex function $f$ and a random function $\phi$. Leveraging an (implicit) convex reformulation via a variable transformation $u=\mathbb{E}[\phi(x,\xi)]$, we develop stochastic gradient-based algorithms and establish their sample and gradient complexities for achieving an $\epsilon$-global optimal solution. Interestingly, our proposed Mirror Stochastic Gradient (MSG) method operates only in the original $x$-space using gradient estimators of the original nonconvex objective $F$ and achieves $\tilde{\mathcal{O}}(\epsilon^{-2})$ sample and gradient complexities, which matches the lower bounds for solving stochastic convex optimization problems. Under booking limits control, we formulate the air-cargo network revenue management (NRM) problem with random two-dimensional capacity, random consumption, and routing flexibility as a special case of the stochastic nonconvex optimization, where the random function $\phi(x,\xi)=x\wedge\xi$, i.e., the random demand $\xi$ truncates the booking limit decision $x$. Extensive numerical experiments demonstrate the superior performance of our proposed MSG algorithm for booking limit control with higher revenue and lower computation cost than state-of-the-art bid-price-based control policies, especially when the variance of random capacity is large. KEYWORDS: stochastic nonconvex optimization, hidden convexity, air-cargo network revenue management, gradient-based algorithm

Improving Run Time in Three-Dimensional Reservoir Hydrodynamics and Water Quality Modeling

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Avances de investigación en educación matemática

Resumen basado en el de la publicaciónResumen en español, portugués y francésSe presenta un estudio en el que se seleccionaron 906 estudiantes de 6 a 14 años de edad y se estudiaron las etapas de desarrollo y los períodos de cognición de la probabilidad. Se muestra que la cognición probabilística de los estudiantes de 6 a 14 años experimenta las siguientes 5 etapas: desarrollo lento I (6-7 años), desarrollo rápido I (8-9 años), desarrollo lento II (10 años), desarrollo rápido II (11-12 años) y fase consolidada (13-14 años). Además hay dos períodos importantes en el desarrollo cognitivo de los estudiantes: el primero a los 8-9 años de edad y el segundo a los 11-12. Incluso en la etapa de desarrollo más alta, los estudiantes pueden entender la representación numérica, la distribución de probabilidad y la representación fraccional, mientras que no pueden alcanzar el nivel de maestría, lo que sugiere la limitación de la cognición de los estudiantes. En consecuencia, el plan de estudios debe tener en cuenta el nivel de desarrollo cognitivo de los estudiantes y establecer objetivos cognitivos razonablesES

Self-Supervised Tracking via Target-Aware Data Synthesis

While deep-learning based tracking methods have achieved substantial progress, they entail large-scale and high-quality annotated data for sufficient training. To eliminate expensive and exhaustive annotation, we study self-supervised learning for visual tracking. In this work, we develop the Crop-Transform-Paste operation, which is able to synthesize sufficient training data by simulating various appearance variations during tracking, including appearance variations of objects and background interference. Since the target state is known in all synthesized data, existing deep trackers can be trained in routine ways using the synthesized data without human annotation. The proposed target-aware data-synthesis method adapts existing tracking approaches within a self-supervised learning framework without algorithmic changes. Thus, the proposed self-supervised learning mechanism can be seamlessly integrated into existing tracking frameworks to perform training. Extensive experiments show that our method 1) achieves favorable performance against supervised learning schemes under the cases with limited annotations; 2) helps deal with various tracking challenges such as object deformation, occlusion, or background clutter due to its manipulability; 3) performs favorably against state-of-the-art unsupervised tracking methods; 4) boosts the performance of various state-of-the-art supervised learning frameworks, including SiamRPN++, DiMP, and TransT (based on Transformer).Comment: 11 pages, 7 figure

Unifying Knowledge Graph Learning and Recommendation: Towards a Better Understanding of User Preference

10.1145/3308558.3313705WWW 2019151-16

Improving run time in three-dimensional reservoir hydrodynamics and water quality modeling

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Optimal sensor placement and measurement of wind for water quality studies in urban reservoirs

We study the water quality in an urban district, where the surface wind distribution is an essential input but undergoes high spatial and temporal variations due to the impact of surrounding buildings. In this work, we develop an optimal sensor placement scheme to measure the wind distribution over a large urban reservoir using a limited number of wind sensors. Unlike existing solutions that assume Gaussian process of target phenomena, this study measures the wind that inherently exhibits strong non-Gaussian yearly distribution. By leveraging the local monsoon characteristics of wind, we segment a year into different monsoon seasons that follow a unique distribution respectively. We also use computational fluid dynamics to learn the spatial correlation of wind. The output of sensor placement is a set of the most informative locations to deploy the wind sensors, based on the readings of which we can accurately predict the wind over the entire reservoir in real time. Ten wind sensors are deployed. The in-field measurement results of more than 3 months suggest that the proposed sensor placement and spatial prediction scheme provides accurate wind measuremen