Zero-Regret Performative Prediction Under Inequality Constraints

Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance, public policy, and recommendation systems. To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many real-world learning problems are subject to constraints. This paper bridges this gap by studying performative prediction under inequality constraints. Unlike most existing work that provides only performative stable points, we aim to find the optimal solutions. Anticipating performative gradients is a challenging task, due to the agnostic performative effect on data distributions. To address this issue, we first develop a robust primal-dual framework that requires only approximate gradients up to a certain accuracy, yet delivers the same order of performance as the stochastic primal-dual algorithm without performativity. Based on this framework, we then propose an adaptive primal-dual algorithm for location families. Our analysis demonstrates that the proposed adaptive primal-dual algorithm attains \ca{O}(\sqrt{T}) regret and constraint violations, using only $\sqrt{T} + 2T$ samples, where $T$ is the time horizon. To our best knowledge, this is the first study and analysis on the optimality of the performative prediction problem under inequality constraints. Finally, we validate the effectiveness of our algorithm and theoretical results through numerical simulations

The Wound Healing Responses and Corneal Biomechanics after Keratorefractive Surgery

Corneal biomechanics have been concerned recently since it is not only found to play an important role in the wound healing process after corneal refractive surgeries, but also essential to improve the predictability and safety of refractive procedures. Corneal biomechanics and wound healing responses are linked in time and space and may also cause complications of keratectasia, haze formation, and regression. This review focuses on wound healing and biomechanics of the corneal refractive procedures. Identifying corneal wound healing from the biomechanical point of view is mandatory to improve the outcomes and reduce the complications

The Application of Shape Gradient for the Incompressible Fluid in Shape Optimization

This paper is concerned with the numerical simulation for shape optimization of the Stokes flow around a solid body. The shape gradient for the shape optimization problem in a viscous incompressible flow is evaluated by the velocity method. The flow is governed by the steady-state Stokes equations coupled with a thermal model. The structure of continuous shape gradient of the cost functional is derived by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. A gradient-type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose, and the proposed algorithm is feasible and effective

A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants

A hybrid method is developed to simulate two-phase flows with soluble surfactants. In this method, the interface and bulk surfactant concentration equations of diffuse-interface form, which include source terms to consider surfactant adsorption and desorption dynamics, are solved in the entire fluid domain by the finite difference method, while two-phase flows are solved by a lattice Boltzmann color-gradient model, which can accurately simulate binary fluids with unequal densities. The flow and interface surfactant concentration fields are coupled by a modified Langmuir equation of state, which allows for surfactant concentration beyond critical micelle concentration. The capability and accuracy of the hybrid method are first validated by simulating three numerical examples, including the adsorption of bulk surfactants onto the interface of a stationary droplet, the droplet migration in a constant surfactant gradient, and the deformation of a surfactant-laden droplet in a simple shear flow, in which the numerical results are compared with theoretical solutions and available literature data. Then, the hybrid method is applied to simulate the buoyancy-driven bubble rise in a surfactant solution, in which the influence of surfactants is identified for varying wall confinement, Eotvos number and Biot number. It is found that surfactants exhibit a retardation effect on the bubble rise due to the Marangoni stress that resists interface motion, and the retardation effect weakens as the Eotvos or Biot number increases. We further show that the weakened retardation effect at higher Biot numbers is attributed to a decreased non-uniform effect of surfactants at the interface

Minocycline inhibits nerve cell apoptosis caused by intracerebral hemorrhage in young mice via TRAIL signaling pathway

Purpose: To investigate the influence of minocycline on nerve cell apoptosis caused by intracerebral hemorrhage (ICH) in young mouse model, and the mechanism of action involved. Methods:C57BL/6 mice were divided into control group, ICH group and minocycline treatment group (MC group, 25 mg/kg). Terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling (TUNEL) assay was conducted to determine nerve cell apoptosis in the brain tissues. The expression levels of genes and proteins related to apoptosis and TRAIL signaling pathway were measured by reverse transcription-polymerase chain reaction (RT-PCR) and Western blotting.Results: The levels of Glu, Cr, Na+, IL-6, IL-1β and TNF-β were significantly increased in ICH group, and the content of K+ was significantly raised in MC group (p < 0.05). TUNEL staining showed that there were more apoptotic cells, dominated by glial cells in ICH group, and fewer apoptotic cells in MC group. Gene assay results indicate that ICH group exhibited markedly raised mRNA levels of caspase-3, TNF-β and TRAIL1, as well as lowered levels of B-cell lymphoma-2 (Bcl-2) (p < 0.05). The results of protein assay showed that the protein levels of caspase-3 and TRAIL1 rose while that of Bcl-2 declined significantly in ICH group. However, the expression trends of the genes and proteins in MC group were the opposite of those in the ICH group.Conclusion: Minocycline inhibits nerve cell apoptosis caused by ICH in the young mouse model by repressing the expression of the TRAIL signaling pathway. The findings may provide new insight intothe treatment of ICH

Low Expression of DYRK2 (Dual Specificity Tyrosine Phosphorylation Regulated Kinase 2) Correlates with Poor Prognosis in Colorectal Cancer.

Dual-specificity tyrosine-phosphorylation-regulated kinase 2 (DYRK2) is a member of dual-specificity kinase family, which could phosphorylate both Ser/Thr and Tyr substrates. The role of DYRK2 in human cancer remains controversial. For example, overexpression of DYRK2 predicts a better survival in human non-small cell lung cancer. In contrast, amplification of DYRK2 gene occurs in esophageal/lung adenocarcinoma, implying the role of DYRK2 as a potential oncogene. However, its clinical role in colorectal cancer (CRC) has not been explored. In this study, we analyzed the expression of DYRK2 from Oncomine database and found that DYRK2 level is lower in primary or metastatic CRC compared to adjacent normal colon tissue or non-metastatic CRC, respectively, in 6 colorectal carcinoma data sets. The correlation between DYRK2 expression and clinical outcome in 181 CRC patients was also investigated by real-time PCR and IHC. DYRK2 expression was significantly down-regulated in colorectal cancer tissues compared with adjacent non-tumorous tissues. Functional studies confirmed that DYRK2 inhibited cell invasion and migration in both HCT116 and SW480 cells and functioned as a tumor suppressor in CRC cells. Furthermore, the lower DYRK2 levels were correlated with tumor sites (P = 0.023), advanced clinical stages (P = 0.006) and shorter survival in the advanced clinical stages. Univariate and multivariate analyses indicated that DYRK2 expression was an independent prognostic factor (P < 0.001). Taking all, we concluded that DYRK2 a novel prognostic biomarker of human colorectal cancer

Hydro-mechanical behaviours of highly compacted sand-bentonite mixture

AbstractThis paper presents the results of laboratory testing on a heavily compacted sand-bentonite mixture. To measure the soil-water retention curve (SWRC) of the mixture over a large range of suction, a pressure plate apparatus and filter papers were used. The obtained SWRC shows that the measurements via the two methods consistently agree with each other. By using a suction-controlled oedometer for unsaturated soils, a series of one-dimensional compression tests were performed on the unsaturated compacted sand-bentonite mixture at different constant suctions. The testing results indicate that the yield stress increases and compression index decreases with the increase of imposed suction. The results also demonstrate that the mixture wetted to saturation and subsequently dried to a certain suction level has a lower yield stress than that wetted directly to the same suction