Minimal Entropy Conditions for Scalar Conservation Laws with General Convex Fluxes

We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair $(\eta(u),q(u))$ with $\eta(u)$ of strict convexity is sufficient to single out an entropy solution from a broad class of weak solutions in $L^\infty_{\rm loc}$ that satisfy the inequality: $\eta(u)_t+q(u)_x\leq \mu$ in the distributional sense for some non-negative Radon measure $\mu$. Furthermore, we extend this result to the class of weak solutions in $L^p_{\rm loc}$, based on the asymptotic behavior of the flux function $f(u)$ and the entropy function $\eta(u)$ at infinity. The proofs are based on the equivalence between the entropy solutions of one-dimensional scalar conservation laws and the viscosity solutions of the corresponding Hamilton-Jacobi equations, as well as the bilinear form and commutator estimates as employed similarly in the theory of compensated compactness.Comment: 31 pages, to appear in Quarterly of Applied Mathematics, AMS, 202

Minimal entropy conditions for scalar conservation laws with general convex fluxes

We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair (n(u), q(u)) with n(u) of strict convexity is sufficient to single out an entropy solution from a broad class of weak solu-tions in (Formula presented) that satisfy the inequality: n(u) t + q(u) x < µ in the distributional sense for some non-negative Radon measure µ· Furthermore, we extend this result to the class of weak solutions in Llpoc, based on the asymptotic behavior of the flux function f (u) and the entropy function n(u) at infinity. The proofs are based on the equivalence between the entropy solutions of one-dimensional scalar conservation laws and the viscosity solu-tions of the corresponding Hamilton-Jacobi equations, as well as the bilinear form and commutator estimates as employed similarly in the theory of compensated compactness

Maybe We Should Talk:Bringing Together Diverse Perspectives on Supporting Teachers’ Reflective Dialogue

The importance of teachers’ reflection for teachers’ professional development is often emphasized, and reflection holds much potential for learning especially when it takes place in dialogue with (knowledgeable) others and is focused on representations of practice. However, there is variation in theorization, design of learning arrangements, and contexts where teachers’ reflection takes place, and research is taking place in various subfields. Consequently, this workshop aims (1) to build a community of learning scientists who are investigating ways to support teachers’ reflective dialogue, and (2) to explore synergies, divergence, and convergence across the various fields where this learning mechanism is studied. The workshop follows a long-tailed format with a prolonged series of discussion activities before, during, and after the conference takes place. This workshop will contribute to community building, understanding of the convergence and divergence in the field, identification of areas that warrant further discussion, as well as a proposal for future work

Command Filter Backstepping Sliding Model Control for Lower-Limb Exoskeleton

A command filter adaptive fuzzy backstepping control strategy is proposed for lower-limb assisting exoskeleton. Firstly, the human-robot model is established by taking the human body as a passive part, and a coupling torque is introduced to describe the interaction between the exoskeleton and human leg. Then, Vicon motion capture system is employed to obtain the reference trajectory. For the purpose of obviating the “explosion of complexity” in conventional backstepping, a second-order command filter is introduced into the sliding mode control strategy. The fuzzy logic systems (FLSs) are also applied to handle with the chattering problem by estimating the uncertainties and disturbances. Furthermore, the stability of the closed-loop system is proved based on the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the control strategy

Scaling Law of Large Sequential Recommendation Models

Scaling of neural networks has recently shown great potential to improve the model capacity in various fields. Specifically, model performance has a power-law relationship with model size or data size, which provides important guidance for the development of large-scale models. However, there is still limited understanding on the scaling effect of user behavior models in recommender systems, where the unique data characteristics (e.g. data scarcity and sparsity) pose new challenges to explore the scaling effect in recommendation tasks. In this work, we focus on investigating the scaling laws in large sequential recommendation models. Specially, we consider a pure ID-based task formulation, where the interaction history of a user is formatted as a chronological sequence of item IDs. We don't incorporate any side information (e.g. item text), because we would like to explore how scaling law holds from the perspective of user behavior. With specially improved strategies, we scale up the model size to 0.8B parameters, making it feasible to explore the scaling effect in a diverse range of model sizes. As the major findings, we empirically show that scaling law still holds for these trained models, even in data-constrained scenarios. We then fit the curve for scaling law, and successfully predict the test loss of the two largest tested model scales. Furthermore, we examine the performance advantage of scaling effect on five challenging recommendation tasks, considering the unique issues (e.g. cold start, robustness, long-term preference) in recommender systems. We find that scaling up the model size can greatly boost the performance on these challenging tasks, which again verifies the benefits of large recommendation models

Facile fabrication of multi-hydrogen bond self-assembly poly(Maac-co-maam) hydrogel modified pvdf ultrafiltration membrane to enhance anti-fouling property

In this work, a facile preparation method was proposed to reduce natural organics fouling of hydrophobic membrane via UV grafting polymerization with methacrylic acid (MAAc) and methyl acrylamide (MAAm) as hydrophilic monomers, followed by multihydrogen bond self-assembly. The resulting poly(vinylidene fluoride)-membranes were characterized with respect to monomer ratio, chemical structure and morphology, surface potential, and water contact angle, as well as water flux and organic foulants ultrafiltration property. The results indicated that the optimal membrane modified with a poly(MAAc-co-MAAm) polymer gel layer derived from a 1:1 monomer ratio exhibited superior hydrophilicity and excellent gel layer stability, even after ultrasonic treatment or soaking in acid or alkaline aqueous solution. The initial water contact angle of modified membranes was only 36.6° ± 2.9, and dropped to 0° within 13 s. Moreover, flux recovery rates (FRR) of modified membranes tested by bovine serum albumin (BSA), humic acid (HA), and sodium alginate (SA) solution, respectively, were all above 90% after one-cycle filtration (2 h), significantly higher than that of the pure membrane (70–76%). The total fouling rates (R$_{t}$) of the pure membrane for three foulants were as high as 47.8–56.2%, while the Rt values for modified membranes were less than 30.8%. Where R$_{t}$ of BSA dynamic filtration was merely 10.7%. The membrane designed through grafting a thin-layer hydrophilic hydrogel possessed a robust antifouling property and stability, which offers new insights for applications in pure water treatment or protein purificatio

Promoting college students’ systems thinking in asynchronous discussions: Encouraging students initiating questions

IntroductionSystems thinking is one of the most important thinking skills for medical students. Most of the studies focused on designing technological-rich learning environments which usually take several weeks or months to implement. However, the occurring of COVID-19 health crisis does not allow extensive period of time to implement classroom interventions. How to support students’ systems thinking in fully online environments remains an issue. This study examines if encouraging students initiating questions on asynchronous discussion forum supports their systems thinking development.MethodsTwenty-two junior students participated in this study. We compared if and how students developed systems thinking when they were encouraged asking questions in asynchronous discussion forums in one unit with another unit in which traditional method was used. Multiple analytical methods were applied in this study, including, social network analysis, epistemic network analysis, inferential statistical analysis and qualitative analysis.ResultsQuantitative results showed that all students improved systems thinking compared with traditional teaching unit among which leader students improved most. Further analysis on students’ discussion posts suggested leader students asked high systems thinking level questions and provided high level responses. Epistemic network analysis unpacked how leader, regular and peripheral students engaged in initiating questions and providing responses differently.DiscussionThis study provides methodological and practical contributions. Methodologically, this study extends prior methods of applying network analysis beyond its original preservice teacher training contexts; practically, this study provides strategies to practitioners to support students’ asynchronous forum discussions

Recent Advances in RecBole: Extensions with more Practical Considerations

RecBole has recently attracted increasing attention from the research community. As the increase of the number of users, we have received a number of suggestions and update requests. This motivates us to make some significant improvements on our library, so as to meet the user requirements and contribute to the research community. In order to show the recent update in RecBole, we write this technical report to introduce our latest improvements on RecBole. In general, we focus on the flexibility and efficiency of RecBole in the past few months. More specifically, we have four development targets: (1) more flexible data processing, (2) more efficient model training, (3) more reproducible configurations, and (4) more comprehensive user documentation. Readers can download the above updates at: https://github.com/RUCAIBox/RecBole.Comment: 5 pages, 3 figures, 3 table

Mapping Interventions of Teacher Reflective Dialogue

This structured poster session brings together a community of scholars who conduct research on support for teachers' reflective dialogue and its outcomes in diverse contexts. Conjecture mapping is positioned as an approach to develop a shared language around research where teachers' reflective dialogue plays a central role with the aim to advance this diverse field

An optimized sliding rail-assisted micrometer system for sensing volume measurement of open-ended coaxial probes in breast cancer dielectric property analysis

ObjectiveThe open-ended coaxial probe (OECP) method has demonstrated promising potential in biological tissue measurements. However, it still faces challenges such as significant measurement errors and poor repeatability. Research indicates that a substantial portion of these errors originates from tissue heterogeneity. To mitigate errors associated with tissue heterogeneity and accurately interpret the relationship between the dielectric properties and histology of heterogeneous tissue samples, detailed knowledge of the probe’s effective sensing volume is essential.MethodsIn this study, the effective sensing volumes of two commonly used small-aperture probes (with diameters of 2.20 mm and 3.58 mm) were measured. The vertical sensing volume is represented by the sensing depth, while the horizontal sensing volume is characterized by the sensing radius. A measurement model for the sensing volume of the OECP method was established using a heterogeneous dielectric property layered model combined with an optimized sliding rail-assisted micrometer system. Dielectric property bilayer models were constructed using materials with distinct dielectric parameters (Teflon, ethanol, methanol, deionized water) and biological tissue simulants (dimethyl sulfoxide, salt-sugar mixed solution). To validate the sensing volume derived from the aforementioned bilayer model, we conducted experimental measurements on porcine tissue and human breast tissue, both of which exhibit well-defined layered structures. In this experiment, the geometric center of a Teflon cube was designated as the origin for probe movement.ResultsThe measured sensing depth ranges were 0.44 to 0.62 mm for a 2.20 mm diameter probe and 0.75 to 0.98 mm for a 3.58 mm diameter probe. While the corresponding sensing radius ranges of 0.36 to 0.63 mm for the 2.20 mm diameter probe and 0.71 to 0.99 mm for the 3.58 mm diameter probe.ConclusionThe results indicate that both the sensing depth and radius of the probe increase significantly with larger coaxial probe aperture sizes. Furthermore, a smaller aperture reduces the influence of tissue heterogeneity on measurements, while the effective sensing volume remains consistent across frequencies