Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation laws

In this paper, we investigate the accuracy-enhancement for the discontinuous Galerkin (DG) method for solving one-dimensional nonlinear symmetric systems of hyperbolic conservation laws. For nonlinear equations, the divided difference estimate is an important tool that allows for superconvergence of the post-processed solutions in the local L2-norm. Therefore, we first prove that the L2-norm of the α-th order (1≤ α≤ k+1) divided difference of the DG error with upwind fluxes is of order k+(3-α)/2, provided that the flux Jacobian matrix, f'(u), is symmetric positive definite. Furthermore, using the duality argument, we are able to derive superconvergence estimates of order 2k+(3-α)/2 for the negative-order norm, indicating that some particular compact kernels can be used to extract at least (3k/2+1)-th order superconvergence for nonlinear systems of conservation laws. Numerical experiments are shown to demonstrate the theoretical results

Transforming Graph Representations for Statistical Relational Learning

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type, (iii) estimating their weight or importance, and (iv) systematically constructing their relevant features. We motivate our taxonomy through detailed examples and use it to survey and compare competing approaches for each of these tasks. We also discuss general conditions for transforming links, nodes, and features. Finally, we highlight challenges that remain to be addressed

Resource Planning in Engineering Services Firms

We develop a model to enable engineering professional services firms to improve the management of their competitive resources, i.e., skilled engineers, to be better able to respond to customer demand. The model was informed by semistructured interviews with senior executives from engineering, information technology (IT) services and technical consulting firms. As a result, we capture many of the complexities associated with the resource planning process in the professional engineering services sector. In the resulting model, the key attributes of supply, demand, and operations constraints are identified. Based on information obtained from the interviews, a number of test firms are created.We then use these test firms to study the impact of various resource planning policies on firm performance. These policies include the skill mix and profile of skilled employees, limits on the number of concurrent projects to which an employee can be assigned, and policies governing employee cross-training and hiring. The impact of these policies is evaluated in terms of business metrics, such as the project completion rate and net revenue. Finally, our model is extended to capture a multiphase rolling planning horizon, where projects may span multiple phases with the goal of ensuring consistency in employee assignment to projects

Can Contracts Replace Qualification in a Sourcing Process With Competitive Suppliers and Imperfect Information?

This paper considers a manufacturer who outsources the production of a product to multiple competing suppliers, who differ in their cost structures and in their capabilities for producing high-quality products. The manufacturer must design the sourcing process to ensure that the selected supplier has sufficient quality capability, while encouraging competition among the suppliers. We develop and analyze a mathematical model of performance-based contracting, a sourcing method that is appropriate when the manufacturer has imperfect information regarding the suppliers’ costs and capabilities. We compare the performance of performance-based contracting with that of a two-stage sourcing process, an alternative sourcing method that is more commonly used in practice. The theoretical results and managerial insights derived from this research can enable manufacturing firms to improve the management of their sourcing processes. In particular, we demonstrate that performance-based contracting with a symmetric linear penalty/reward function will always outperform the two-stage sourcing process from the perspective of the buyer and that the optimal penalty/reward rate is less than or equal to the unit warranty cost. In addition, performance-based contracting generally leads to a higher quality level provided by the winning supplier. However, the winning supplier is generally better off under the two-stage sourcing process

Two Stage Procurement Processes With Competitive Suppliers and Uncertain Supplier Quality

This paper considers a sourcing problem faced by a manufacturer who outsources the manufacturing of a product to one of several competing suppliers, whose cost and quality capabilities are unknown. We consider a two-stage sourcing process in which the first stage is the qualification stage, while the second stage is the supplier selection stage. In the first stage, the manufacturer exerts effort to learn about the quality level of each of the suppliers and then must determine the set of qualified suppliers, subject to some tolerance for error. In the second stage, the manufacturer runs a price-only procurement auction, in which the qualified suppliers compete for the manufacturer’s business.We model this two-stage sourcing process with the goal of obtaining insights into manufacturer’s optimal decisions. We seek to determine the optimal qualification standard, the optimal amount of effort to be exerted in the qualification process and the appropriate tolerance for error in the qualification process, and to understand the interactions between these decision variables. We are particularly interested in understanding how the manufacturer can design the process to 1) ensure the firm only sources from qualified suppliers and 2) encourage competition among the suppliers during supplier selection

Coordinating a Supply Chain With a Manufacturer-Owned Online Channel: A Dual Channel Model Under Price Competition

We consider a dual channel supply chain in which a manufacturer sells a single product to end-users through both a traditional retail channel and a manufacturer-owned direct online channel. We adopt a commonly used linear demand substitution model in which the mean demand in each channel is a function of the prices in each channel.We model each channel as a news vendor problem, with price and order quantity as decision variables. In addition, the manufacturer must choose the wholesale price to charge to the independent retailer. We analyze the optimal decisions for each channel and prove the existence of a unique equilibrium for the system. We compare this equilibrium solution to the solution for an integrated system, in which the manufacturer owns both the online store and the retailer. To enable supply chain coordination, we propose two contract schemes: a modified revenue-sharing contract and gain/loss sharing contract. We show that, in cases where the retail channel has a larger market than the online channel, such contracts enable the manufacturer to maintain price discrimination, selling the products in different channels at different prices. Finally, we perform a comprehensive numerical study to consider the impact of the model parameters on the equilibrium and to demonstrate the performance of the proposed coordination contracts. We conclude that coordination is most critical for products which are highly price sensitive and for systems in which the online and traditional retail channels are not viewed as close substitutes

Contracting Mechanisms for Stable Sourcing Networks

Problem definition: We study profit allocation for a sourcing network, in which a buyer sources froma set of differentiated suppliers with limited capacity under uncertain demand for the final product. Whereas the buyer takes the lead in forming the sourcing network and designing the contract mechanism, due to their substantial bargaining power, the suppliers take the lead in determining the terms of the contract. Academic/practical relevance: We identify contracting mechanisms that will ensure the stability of the sourcing network in the long term, where a stable sourcing network requires an effective profitallocation scheme that motivates all members to join and stay in the network. Methodology: We apply methods from game theory to model the network and analyze the Nash equilibrium of a noncooperative game under a proposed contracting mechanism. We then use a cooperative game model to study the stability of the resulting equilibrium. Results: We show that the optimal network profit, as a set function of the set of suppliers, is submodular, which allows us to demonstrate that the core of the cooperative game is not empty.We also establish a set of conditions that are equivalent to, but much simpler than, the original conditions for the core.We use these results to demonstrate that the proposed fixed-fee contracting mechanism can implement a stable network in the competitive setting by achieving a profit allocation that is in the core of the cooperative game. We also demonstrate that the grand coalition is stable in a farsighted sense under the Shapley value allocation. Managerial implications: Under the fixed-fee mechanism, the buyer’s decisions maximize the network profit, and each supplier earns a profit equal to its marginal contribution.When the aggregate capacity of the supplier network is high relative to demand, or demand is more likely to be small, the fixed-fee mechanism is likely to outperform the Shapley value allocation from the perspective of the buyer

Multi-dimensional filtering: Reducing the dimension through rotation

Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate of the DG solution through this post-processor. These advantages can be exploited during flow visualization, for example by applying the SIAC filter to the DG data before streamline computations [Steffan et al., IEEE-TVCG 14(3): 680-692]. However, introducing these filters in engineering applications can be challenging since a tensor product filter grows in support size as the field dimension increases, becoming computationally expensive. As an alternative, [Walfisch et al., JOMP 38(2);164-184] proposed a univariate filter implemented along the streamline curves. Until now, this technique remained a numerical experiment. In this paper we introduce the line SIAC filter and explore how the orientation, structure and filter size affect the order of accuracy and global errors. We present theoretical error estimates showing how line filtering preserves the properties of traditional tensor product filtering, including smoothness and improvement in the convergence rate. Furthermore, numerical experiments are included, exhibiting how these filters achieve the same accuracy at significantly lower computational costs, becoming an attractive tool for the scientific visualization community

Hydrodynamics in a shallow seasonally low-inflow estuary following eelgrass collapse

Hydrodynamics play a critical role in mediating biological and ecological processes and can have major impacts on the distribution of habitat-forming species. Low-inflow estuaries are widespread in arid regions and during the dry season in Mediterranean climates. There is a growing need to evaluate dynamics and exchange processes in these systems and the resultant ecological linkages. We investigate the role that hydrodynamics play in shaping environmental gradients in a short and seasonally low-inflow estuary located along the central California coast. Since 2007, eelgrass meadows in Morro Bay have declined by more than 90%, representing the collapse of the major biogenic habitat. Despite the large-scale decline, eelgrass beds near the mouth of the bay remain resilient, suggesting that conditions in certain areas of the bay might allow or impede eelgrass retention and recovery. Oceanographic moorings were deployed throughout the bay during the summer dry season to assess spatial differences in environmental conditions and hydrodynamics across gradients in eelgrass survival. Relative to the mouth of the bay, the back bay water mass was significantly warmer (hyperthermal), more saline (hypersaline), less oxygenated, and more turbid, with longer flushing times, all of which have been identified as significant stressors on seagrasses. Moreover, there is weak exchange between the mouth and the back bay that effectively decouples the two water masses during most periods. Though the causes of the decline are not clear, gradients in environmental conditions driven by bay hydrodynamics appear to be preventing eelgrass recovery and restoration attempts in the back bay and keeping this region in an alternative state dominated by unvegetated intertidal mudflats. Ecosystems in low-inflow estuaries may be especially prone to ecological regime shifts or collapse and may require precautionary monitoring and management. This system and the dramatic ecological change that it has experienced, demonstrate the critical role that hydrodynamics play in ecosystem health and habitat suitability