Multiple nodal solutions of nonlinear Choquard equations

In this paper, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation \begin{equation*} \ \ \ \ (P)\ \ \ \ \begin{cases} -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \ \ \ \text{in}\ \mathbb{R}^3, \ \ \ \ \\ u\in H^1(\mathbb{R}^3),\\ \end{cases} \end{equation*} where $p\in (\frac{5}{2},5)$. We show that for any positive integer $k$, problem $(P)$ has at least a radially symmetrical solution changing sign exactly $k$-times

The Way to Spray: Modeling Nasal Spray Deposition

Intranasal drug delivery is an alternative method in addition to traditional oral and intravenous doses. Nasal drug delivery has proven to be a very effective technique for nicotine cessation (Hjalmarson et al., 1994), the influenza vaccine (Jackson et al. 1999), and drugs that need to be take continuously, such as insulin (Dondeti et al., 1995). Studies have found that for effective fast-acting body response, the drug needs to be deposited in the highly vascularized mucosal tissue lining the bony turbinates in the nasal cavity. Commercial nasal sprays are continuously optimizing parameters to develop the most effective deposition patterns. In this project, drug deposition is modeled using a simplified 2D depiction of the nasal passageway with uniformly-shaped, spherical spray particles. This problem is implemented in COMSOL by using 2D Navier Stokes fluid flow equations to model the airflow through the nose, and the Particle Tracing module to model the spray trajectory and deposition. The model output was validated by determining the percentages of particles in each region of the nasal passage - anterior, turbinate, posterior, and outlet - and comparing with published experimental data by Cheng et al (2001). A sensitivity analysis was done on the following parameters: particle density, particle size, nozzle spray angle, and nozzle penetration depth. It was found that this model was sensitive to only penetration depth. As penetration depth through the nostril increased, there was a decrease in the particle deposition in the anterior region of the nasal cavity and an increase in the percentage of particles that exited through the outlet. Deposition in the middle and posterior regions was not affected by variation in penetration depth. Our sensitivity analysis demonstrated that variations in spray angle, particle size, and density of the nasal spray fluid do not significantly affect deposition pattern. Therefore, when designing nasal sprays, as long as these parameters remain within the specified ranges, consistent deposition patterns will be achieved. This result also allows for further research on creating sprays that are more concentrated and have encapsulated drugs

Generalization bound for estimating causal effects from observational network data

Estimating causal effects from observational network data is a significant but challenging problem. Existing works in causal inference for observational network data lack an analysis of the generalization bound, which can theoretically provide support for alleviating the complex confounding bias and practically guide the design of learning objectives in a principled manner. To fill this gap, we derive a generalization bound for causal effect estimation in network scenarios by exploiting 1) the reweighting schema based on joint propensity score and 2) the representation learning schema based on Integral Probability Metric (IPM). We provide two perspectives on the generalization bound in terms of reweighting and representation learning, respectively. Motivated by the analysis of the bound, we propose a weighting regression method based on the joint propensity score augmented with representation learning. Extensive experimental studies on two real-world networks with semi-synthetic data demonstrate the effectiveness of our algorithm

Explainability of Traditional and Deep Learning Models on Longitudinal Healthcare Records

Recent advances in deep learning have led to interest in training deep learning models on longitudinal healthcare records to predict a range of medical events, with models demonstrating high predictive performance. Predictive performance is necessary but insufficient, however, with explanations and reasoning from models required to convince clinicians for sustained use. Rigorous evaluation of explainability is often missing, as comparisons between models (traditional versus deep) and various explainability methods have not been well-studied. Furthermore, ground truths needed to evaluate explainability can be highly subjective depending on the clinician's perspective. Our work is one of the first to evaluate explainability performance between and within traditional (XGBoost) and deep learning (LSTM with Attention) models on both a global and individual per-prediction level on longitudinal healthcare data. We compared explainability using three popular methods: 1) SHapley Additive exPlanations (SHAP), 2) Layer-Wise Relevance Propagation (LRP), and 3) Attention. These implementations were applied on synthetically generated datasets with designed ground-truths and a real-world medicare claims dataset. We showed that overall, LSTMs with SHAP or LRP provides superior explainability compared to XGBoost on both the global and local level, while LSTM with dot-product attention failed to produce reasonable ones. With the explosion of the volume of healthcare data and deep learning progress, the need to evaluate explainability will be pivotal towards successful adoption of deep learning models in healthcare settings.Comment: 21 pages, 10 figure

AdaTT: Adaptive Task-to-Task Fusion Network for Multitask Learning in Recommendations

Multi-task learning (MTL) aims at enhancing the performance and efficiency of machine learning models by training them on multiple tasks simultaneously. However, MTL research faces two challenges: 1) modeling the relationships between tasks to effectively share knowledge between them, and 2) jointly learning task-specific and shared knowledge. In this paper, we present a novel model Adaptive Task-to-Task Fusion Network (AdaTT) to address both challenges. AdaTT is a deep fusion network built with task specific and optional shared fusion units at multiple levels. By leveraging a residual mechanism and gating mechanism for task-to-task fusion, these units adaptively learn shared knowledge and task specific knowledge. To evaluate the performance of AdaTT, we conduct experiments on a public benchmark and an industrial recommendation dataset using various task groups. Results demonstrate AdaTT can significantly outperform existing state-of-the-art baselines

Effects of the combination of loxoprofen sodium and sodium hyaluronate on osteoarthritis and knee function

Purpose: To determine the treatment efficacy of the combination of loxoprofen sodium and sodium hyaluronate in osteoarthritis (OA), and its role in knee joint function. Methods: 98 patients with OA admitted to Guang'an People's Hospital, Sichuan, China were allocated into control group (CNG, given loxoprofen sodium n, = 51) and study group (SG, given loxoprofen sodium and sodium hyaluronate, n = 47). Both groups were compared in terms of the levels of inflammatory factor, Lysholm, VAS, WOMAC scores, treatment effects, serum MDA, NO, SOD levels, adverse effects, and blood rheology indices. Results: The study group had higher SOD levels, and higher BALP and BGP than CNG (p < 0.05). SG had lower TRACP-5b and blood rheological indices than CNG (p < 0.05). The difference in the incidence of adverse reactions was not statistically significant between the two groups (p > 0.05). Conclusion: The combination of loxoprofen sodium and sodium hyaluronate effectively improves the function and blood rheological indices of knee joints. It reduces the occurrence of adverse reactions and the level of pain in patients with OA, and improves OA prognosis. However further clinical trials are required prior to application in clinical practice

Hierarchical global fast terminal sliding-mode control for a bridge travelling crane system

The bridge crane system is a typical under-actuated system that is widely used in production and life. Although various scholars have conducted extensive research on the bridge crane system in recent years, there are still many problems, such as the trajectory planning of the cart and the anti-sway control of the cargo. In order to tackle the problem of the anti-sway control of the cargo, a hierarchical global fast terminal sliding-mode control (H-GFTSMC) is developed in this work. First, the Lagrange equations are used to model the system dynamics. Then, an appropriate hierarchical global fast terminal sliding-mode controller is designed to achieve anti-sway control of the cargo, and it is proved that each sliding-mode surface is progressively stable. A series of simulations were implemented to verify the effectiveness of the control method. The simulation results show that the H-GFTSMC has better control performance compared with the proportional–integral–derivative control method. When changing the cable length or adding non-negligible noise to the system, the H-GFTSMC still has good robustness