A mammalian Wnt5a-Ror2-Vangl2 axis controls the cytoskeleton and confers cellular properties required for alveologenesis.

Alveolar formation increases the surface area for gas-exchange and is key to the physiological function of the lung. Alveolar epithelial cells, myofibroblasts and endothelial cells undergo coordinated morphogenesis to generate epithelial folds (secondary septa) to form alveoli. A mechanistic understanding of alveologenesis remains incomplete. We found that the planar cell polarity (PCP) pathway is required in alveolar epithelial cells and myofibroblasts for alveologenesis in mammals. Our studies uncovered a Wnt5a-Ror2-Vangl2 cascade that endows cellular properties and novel mechanisms of alveologenesis. This includes PDGF secretion from alveolar type I and type II cells, cell shape changes of type I cells and migration of myofibroblasts. All these cellular properties are conferred by changes in the cytoskeleton and represent a new facet of PCP function. These results extend our current model of PCP signaling from polarizing a field of epithelial cells to conferring new properties at subcellular levels to regulate collective cell behavior

Controlling work in process during semiconductor assembly and test operations

In the semiconductor industry, products go through a series of steps over a three- to four-month period that begins with the fabrication of chips and ends with assembly and test (AT) and shipment. This paper introduces a mid-term planning model for scheduling AT operations aimed at minimizing the difference between customer demand and product completions each day. A secondary objective is to maximize daily throughput. Typically, semiconductor companies have 1000s of products or devices in their catalog that can be organized into unique groups of up to 100 devices each. This simplifies the planning process because it is only necessary to consider the groups as a whole rather than the individual devices when constructing schedules. In all, we developed and tested three related models. Each provides daily run rates at each processing step or logpoint for each device group for up to one month at a time. The models are distinguished by how cycle time is treated. The first takes a steady-state approach and uses Little’s Law to formulate a WIP target constraint based on the average cycle time at each processing step. The second and third include integer and fractional cycle times in the variable definitions. To find solutions, raw production data are analyzed in a preprocessing step and then converted to input files in a standard format. FlopC++ from the COIN-OR open source software project is used to write and solve the model. Testing was done using three datasets from the Taiwan AT facility of a global semiconductor firm. By comparing model output with historical data for 6 device groups and 33 logpoints, we were able to realize decreases in shortages of up to 40% per month.Mechanical Engineerin

A fourth-order unfitted characteristic finite element method for solving the advection-diffusion equation on time-varying domains

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for interface tracking, the fourth-order backward differentiation formula for temporal integration, and an unfitted finite element method for spatial discretization. Our convergence analysis includes errors of discretely representing the moving boundary, tracing boundary markers, and the spatial discretization and the temporal integration of the governing equation. Numerical experiments are performed on a rotating domain and a severely deformed domain to verify our theoretical results and to demonstrate the optimal convergence of the proposed method

A Customized Augmented Lagrangian Method for Block-Structured Integer Programming

Integer programming with block structures has received considerable attention recently and is widely used in many practical applications such as train timetabling and vehicle routing problems. It is known to be NP-hard due to the presence of integer variables. We define a novel augmented Lagrangian function by directly penalizing the inequality constraints and establish the strong duality between the primal problem and the augmented Lagrangian dual problem. Then, a customized augmented Lagrangian method is proposed to address the block-structures. In particular, the minimization of the augmented Lagrangian function is decomposed into multiple subproblems by decoupling the linking constraints and these subproblems can be efficiently solved using the block coordinate descent method. We also establish the convergence property of the proposed method. To make the algorithm more practical, we further introduce several refinement techniques to identify high-quality feasible solutions. Numerical experiments on a few interesting scenarios show that our proposed algorithm often achieves a satisfactory solution and is quite effective

A Universal Trust-Region Method for Convex and Nonconvex Optimization

This paper presents a universal trust-region method simultaneously incorporating quadratic regularization and the ball constraint. We introduce a novel mechanism to set the parameters in the proposed method that unifies the analysis for convex and nonconvex optimization. Our method exhibits an iteration complexity of $\tilde O(\epsilon^{-3/2})$ to find an approximate second-order stationary point for nonconvex optimization. Meanwhile, the analysis reveals that the universal method attains an $O(\epsilon^{-1/2})$ complexity bound for convex optimization and can be accelerated. These results are complementary to the existing literature as the trust-region method was historically conceived for nonconvex optimization. Finally, we develop an adaptive universal method to address practical implementations. The numerical results show the effectiveness of our method in both nonconvex and convex problems

Trust Region Methods For Nonconvex Stochastic Optimization Beyond Lipschitz Smoothness

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular significance within the realms of deep neural networks and distributionally robust optimization (DRO). We demonstrate the significant advantage of trust region methods for stochastic nonconvex optimization under such generalized smoothness assumption. We show that first-order trust region methods can recover the normalized and clipped stochastic gradient as special cases and then provide a unified analysis to show their convergence to first-order stationary conditions. Motivated by the important application of DRO, we propose a generalized high-order smoothness condition, under which second-order trust region methods can achieve a complexity of $\mathcal{O}(\epsilon^{-3.5})$ for convergence to second-order stationary points. By incorporating variance reduction, the second-order trust region method obtains an even better complexity of $\mathcal{O}(\epsilon^{-3})$, matching the optimal bound for standard smooth optimization. To our best knowledge, this is the first work to show convergence beyond the first-order stationary condition for generalized smooth optimization. Preliminary experiments show that our proposed algorithms perform favorably compared with existing methods

Homogeneous Second-Order Descent Framework: A Fast Alternative to Newton-Type Methods

This paper proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric eigenvalue procedures and thus grant an advantage in ill-conditioned problems. Moreover, GHM extends the ordinary homogeneous model (OHM) to allow adaptiveness in the construction of the aggregated matrix. Consequently, HSODF is able to recover some well-known second-order methods, such as trust-region methods and gradient regularized methods, while maintaining comparable iteration complexity bounds. We also study two specific realizations of HSODF. One is adaptive HSODM, which has a parameter-free $O(\epsilon^{-3/2})$ global complexity bound for nonconvex second-order Lipschitz continuous objective functions. The other one is homotopy HSODM, which is proven to have a global linear rate of convergence without strong convexity. The efficiency of our approach to ill-conditioned and high-dimensional problems is justified by some preliminary numerical results.Comment: improved writin

A Homogenization Approach for Gradient-Dominated Stochastic Optimization

Gradient dominance property is a condition weaker than strong convexity, yet it sufficiently ensures global convergence for first-order methods even in non-convex optimization. This property finds application in various machine learning domains, including matrix decomposition, linear neural networks, and policy-based reinforcement learning (RL). In this paper, we study the stochastic homogeneous second-order descent method (SHSODM) for gradient-dominated optimization with $\alpha \in [1, 2]$ based on a recently proposed homogenization approach. Theoretically, we show that SHSODM achieves a sample complexity of $O(\epsilon^{-7/(2 \alpha) +1})$ for $\alpha \in [1, 3/2)$ and $\tilde{O}(\epsilon^{-2/\alpha})$ for $\alpha \in [3/2, 2]$. We further provide a SHSODM with a variance reduction technique enjoying an improved sample complexity of $O( \epsilon ^{-( 7-3\alpha ) /( 2\alpha )})$ for $\alpha \in [1,3/2)$. Our results match the state-of-the-art sample complexity bounds for stochastic gradient-dominated optimization without \emph{cubic regularization}. Since the homogenization approach only relies on solving extremal eigenvector problems instead of Newton-type systems, our methods gain the advantage of cheaper iterations and robustness in ill-conditioned problems. Numerical experiments on several RL tasks demonstrate the efficiency of SHSODM compared to other off-the-shelf methods

Next-Generation Simulation Illuminates Scientific Problems of Organised Complexity

As artificial intelligence becomes increasingly prevalent in scientific research, data-driven methodologies appear to overshadow traditional approaches in resolving scientific problems. In this Perspective, we revisit a classic classification of scientific problems and acknowledge that a series of unresolved problems remain. Throughout the history of researching scientific problems, scientists have continuously formed new paradigms facilitated by advances in data, algorithms, and computational power. To better tackle unresolved problems, especially those of organised complexity, a novel paradigm is necessitated. While recognising that the strengths of new paradigms have expanded the scope of resolvable scientific problems, we aware that the continued advancement of data, algorithms, and computational power alone is hardly to bring a new paradigm. We posit that the integration of paradigms, which capitalises on the strengths of each, represents a promising approach. Specifically, we focus on next-generation simulation (NGS), which can serve as a platform to integrate methods from different paradigms. We propose a methodology, sophisticated behavioural simulation (SBS), to realise it. SBS represents a higher level of paradigms integration based on foundational models to simulate complex systems, such as social systems involving sophisticated human strategies and behaviours. NGS extends beyond the capabilities of traditional mathematical modelling simulations and agent-based modelling simulations, and therefore, positions itself as a potential solution to problems of organised complexity in complex systems

A Homogeneous Second-Order Descent Method for Nonconvex Optimization

In this paper, we introduce a Homogeneous Second-Order Descent Method (HSODM) using the homogenized quadratic approximation to the original function. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian integrated matrix is computed at each iteration. Therefore, the algorithm is a single-loop method that does not need to switch to other sophisticated algorithms and is easy to implement. We show that HSODM has a global convergence rate of $O(\epsilon^{-3/2})$ to find an $\epsilon$-approximate second-order stationary point, and has a local quadratic convergence rate under the standard assumptions. The numerical results demonstrate the advantage of the proposed method over other second-order methods.Comment: Add inexactness, significantly improve the pape