Optimal Transport Methods in Economics

<p class="MsoNormal" style="mso-pagination:none;mso-layout-grid-align:none; text-autospace:none">This thesis investigates the behaviour of the often used point-wise skill score, the MSESSini a.k.a. BSS, and develops new error metrics that, as opposed to point-wise metrics, take the spatial structure of morphological patterns into account. The MSESSini measures the relative accuracy of a morphological prediction over a prediction of zero morphological change, using the mean-squared error (MSE) as the accuracy measure. The main findings about the MSESSini are: 1) a generic ranking, based on values for MSESSini, has limited validity, since the zero change reference model fails to make model performance comparable across different prediction situations; 2) the combination of larger, persistent and smaller, intermittent scales of cumulative change may lead to an increase of skill with time, without the prediction on either of these scales becoming more skilful with time; 3) in the presence of inevitable location errors, the MSESSini favours predictions that underestimate the variance of cumulative bed changes and 4) existing methods to correct for measurement error are inconsistent in either their skill formulation or their suggested classification scheme. In order to overcome the inherent limitations of point-wise metrics, three novel diagnostic tools for the spatial validation of 2D morphological predictions are developed. First, a field deformation or warping method deforms the predictions towards the observations, minimizing the squared point-wise error. Error measures are formulated based on both the smooth displacement field between predictions and observations and the residual point-wise error field after the deformation. In contrast with the RMSE, the method captures the visual closeness of morphological patterns. Second, an optimal transport method defines the distance between predicted and observed morphological fields in terms of an optimal sediment transport field. The optimal corrective transport field moves the misplaced sediment from the predicted to the observed morphology at the lowest quadratic transportation cost. The root-mean-squared value of the optimal transport field, the RMSTE, is proposed as a new error metric. As opposed to the field deformation method, the optimal transport method is mass-conserving, parameter-free and symmetric. The RMSTE, unlike the RMSE, is able to discriminate between predictions that differ in the misplacement distance of predicted morphological features. It also avoids the consistent reward of the underestimation of morphological variability that the RMSE is prone to. Third, a scale-selective validation approach allows any metric to selectively address multiple spatial scales. It employs a smoothing filter in such a way that, in addition to the domain-averaged statistics, localized validation statistics and maps of prediction quality are obtained per scale (geographic extent or areal size of focus). The employed skill score weights how well the morphological structure and variability are simulated, while avoiding to reward the underestimation of variability. To fully describe prediction quality multiple metrics are required with a weighting determined by the goal of the simulation. Point-wise metrics should be supplemented with an error decomposition, as to avoid undesired underestimation of variability. Further, a set of performance metrics must include a metric, e.g. the RMSTE, that accounts for the spatial structure of the observed and predicted morphological fields.</p>

For assessing and calculating biomass value chains the costs for transportation are the most important factor the economic performance as they form the largest share of the overall production cost. The objective of this work is to develop a methodology that includes not only the distance in the calculation of transportation costs. The main purpose is to also optimize the choice of transport mode depending on the given circumstances. These are especially the distance from the harvesting site to the subsequent processing or storage unit, the transported biomass with its distinctive properties (moisture content, bulk density etc.) and the required harvesting method. To achieve this, a model is elaborated that calculates the minimal overall transportation costs of a biomass-based supply chain comprising fixed and variable costs of the chosen transportation method. This could extend existing supply chain models for the elaboration and assessment of biomass-based value chains by a more comprehensive transportation modelling.

Optimal transport methods have recently established state-of-the-art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe O(N2) memory and O(N2) time requirements for large-scale input or output images with N total pixels. Here we leverage the dual formulation of the optimal transport problem and the separable structure of the cost to implement algorithms with greatly reduced O(N) memory and O(Nlog⁡N) to O(N3/2) time complexity. These algorithms are parallelizable and can solve megapixel-scale beam shaping problems in tens of seconds on a CPU or seconds on a GPU.

A new proof of uniqueness of solutions to kinetic Cucker–Smale model based on optimal transport methods

Motivated by the assessment of racial discrimination in mortgage pricing, we introduce a new methodology for comparing the menus of options borrowers face based on their choices. First, we show how standard regression-based approaches for assessing discrimination in the menus context can lead to misleading and contradictory results. Second, we propose a new methodology that is robust these problems based on relatively weak economic assumptions. More specifically, we use pairwise dominance relationships in choices supplemented by restrictions on the range of plausible menus to define (1) a test statistic for equality in menus and (2) a difference in menus (DIM) metric for assessing whether one group of borrowers would prefer to switch to another group's menus. Our statistics are robust to arbitrary heterogeneity in borrower preferences across racial groups, are sharp in terms of identification, and can be efficiently computed using Optimal Transport methods. Third, we devise a new approach for inference on the value of Optimal Transport problems based on directional differentiation. Fourth, we use our methodology to estimate mortgage pricing differentials by race on a novel data set linking 2018--2019 Home Mortgage Disclosure Act (HMDA) data to Optimal Blue rate locks. We find robust evidence for mortgage pricing differentials by race, particularly among Conforming mortgage borrowers who are relatively creditworthy.

The complexity of entire T cell receptor (TCR) repertoires makes their comparison a difficult but important task. Current methods of TCR repertoire comparison can incur a high loss of distributional information by considering overly simplistic sequence- or repertoire-level characteristics. Optimal transport methods form a suitable approach for such comparison given some distance or metric between values in the sample space, with appealing theoretical and computational properties. In this paper we introduce a nonparametric approach to comparing empirical TCR repertoires that applies the Sinkhorn distance, a fast, contemporary optimal transport method, and a recently-created distance between TCRs called TCRdist. We show that our methods identify meaningful differences between samples from distinct TCR distributions for several case studies, and compete with more complicated methods despite minimal modeling assumptions and a simpler pipeline.

Powder bed fusion is one of the most common types of additive manufacturing processes using granular materials. In this field, improvements in the processing of materials and process repeatability with desired part quality are needed to allow the implementation of powder bed fusion process at full scale across various industrial sectors. The microstructure and the thermo-mechanical properties of the components vary according to the process parameters adopted in the manufacturing process. Physically accurate modeling of the powder bed fusion process can play a vital role in the qualification of components and materials and also can help in predicting the experimental observations. This paper aims to provide a comprehensive review on the state of the art referred to numerical simulation of powder bed fusion, by covering both mesh based approaches such as finite element modeling, finite volume modeling and mesh free methods such as the discrete element modeling, the lattice Boltzmann method, the optimal transportation method and the smoothed particle hydrodynamics approach. Combined approaches of different methods are discussed as well. A case study comparing two different types of models for a similar type of problem has been provided. Moreover, means of experimental techniques used to validate the numerical models are briefly discussed. • Review on various types of mesh based and mesh free models used in powder bed fusion process of additive manufacturing. • Advantages, disadvantages and uses of various models to study different phenomena are discussed. • A comparative case study of mesh based and mesh-free models is provided. • The influence of various process parameters on the mechanical characteristics of the specimen is given.

Incentive problems make securities’ payoffs imperfectly pledgeable, limiting agents’ ability to issue liabilities. We analyze the equilibrium consequences of such endogenous incompleteness in a dynamic exchange economy. Because markets are endogenously incomplete, agents have different intertemporal marginal rates of substitution, so that they value assets differently. Consequently, agents hold different portfolios. This leads to endogenous markets segmentation, which we characterize with optimal transport methods. Moreover, there is a basis going always in the same direction: the price of a security is lower than that of replicating portfolios of long positions. Finally, equilibrium expected returns are concave in factor loadings. (JEL D51, D52, G11, G12)

BackgroundActive and passive surveillance for avian influenza virus (AIV) and Newcastle disease virus (NDV) is widespread in commercial poultry worldwide, therefore optimization of sample collection and transport would be valuable to achieve the best sensitivity and specificity possible, and to develop the most accurate and efficient testing programs. A H7N2 low pathogenicity (LP) AIV strain was selected and used as an indicator virus because it is present in lower concentrations in swabbings and thus requires greater sensitivity for detection compared to highly pathogenic (HP) AIV. For similar reasons a mesogenic strain of NDV was selected. Using oro-pharyngeal and cloacal swabs collected from chickens experimentally exposed to the viruses we evaluated the effects of numerous aspects of sample collection and transport: 1) swab construction material (flocked nylon, non-flocked Dacron, or urethane foam), 2) transport media (brain heart infusion broth [BHI] or phosphate buffered saline [PBS]), 3) media volume (2 ml or 3.5 ml), 4) transporting the swab wet in the vial or removing the swab prior to transport, or transporting the swab dry with no media, and 5) single swabs versus pooling 5 or 11 swabs per vial.ResultsUsing real-time RT-PCR (rRT-PCR), virus isolation (VI) and commercial antigen detection immunoassays for AIV we observed statistically significant differences and consistent trends with some elements of sample collection and transport; media, dry transport and swab construction. Conversely, the number of swabs pooled (1, 5 or 11) and whether the swab was removed prior to transport did not impact virus detection. Similarly, with NDV detection by both VI and rRT-PCR was not affected by the numbers of swabs collected in a single vial (1, 5 or 11).ConclusionsWe observed that flocked and foam swabs were superior to non-flocked swabs, BHI media was better than PBS, and transporting swabs wet was better for virus recovery and detection than transporting them dry. There was no observable difference in detection whether the swab was removed prior to transport or left in the vial. Also, with both AIV and NDV, there was no observed difference in virus detection between pools of 1, 5 or 11 swabs.

We propose and analyze an optimal mass transport method for a random genetic drift problem driven by a Moran process under weak-selection. The continuum limit, formulated as a reaction-advection-diffusion equation known as the Kimura equation, inherits degenerate diffusion from the discrete stochastic process that conveys to the blow-up into Dirac-delta singularities hence brings great challenges to both the analytical and numerical studies. The proposed numerical method can quantitatively capture to the fullest possible extent the development of Dirac-delta singularities for genetic segregation on one hand, and preserves several sets of biologically relevant and computationally favored properties of the random genetic drift on the other. Moreover, the numerical scheme exponentially converges to the unique numerical stationary state in time at a rate independent of the mesh size up to a mesh error. Numerical evidence is given to illustrate and support these properties, and to demonstrate the spatio-temporal dynamics of random generic drift.

Interpretable data integration for single-cell and spatial multi-omics.

Understanding intention behind event processes in texts is important to many applications. One challenging task in this line is event process typing, which aims to tag the process with one action label and one object label describing the overall action of the process and object the process likely affects respectively. To tackle this task, existing methods mainly rely on the matching of the event process level and label level representation, which ignores two important characteristics: Process Hierarchy and Label Hierarchy. In this paper, we propose a Hierarchical Optimal Transport (HOT) method to address the above problem. Specifically, we first explicitly extract the process hierarchy and label hierarchy. Then the HOT optimally matches the two types of hierarchy. Experimental results show that our model outperforms the baseline models, illustrating the effectiveness of our model.

Summary form only given. With the extensive use of renewable energy, the microgrid as an access and management structure of renewable energy has also been widely used. Many microgrids in the using process need to be accessed in external grid. As a part of the union power system, how to dispatching the devices in the microgrid and the external grid scheduling so as to make the entire system running more economically, saving operating costs and fuel costs, is an area worthy of study. The issue of dispatching the union power system of microgrids and external grid involved load forecasting, the basic principles of economical dispatching, the correction of transmission loss, security constraints and so on. Based on these analysis, the economical dispatching and optimal power flow calculation method based on equal incremental rate non-renewable fuels consumption theory was introduced. Optimal power flow(OPF) is often about the issue of the optimal distribution of grid power at a certain moment, which cannot show the randomness of new energy, a continuous time-varying optimal power distribution method was advised for the power system containing microgrids. It was used in a simulation calculating example to show the advance of this method.

Microgrid containing Wind Power(PV) and Photovoltaic(PV) has been an access and management structure of renewable energy. Part of microgrids are not isolate and can be integrated into external grid. How to make the entire system running more economically, saving operating costs and fuel costs? It's an really issue to optimal dispatching the devices power in the microgrid and the external grid. On a series analysis, the economical dispatching and optimal power flow calculation method based on equal incremental rate non-renewable fuels consumption theory was introduced.

Quantifying the structure and dynamics of species interactions in ecological communities is fundamental to studying ecology and evolution. While there are numerous approaches to analysing ecological networks, there is not yet an approach that can (1) quantify dissimilarity in the global structure of ecological networks that range from identical species and interaction composition to zero shared species or interactions and (2) map species between such networks while incorporating additional ecological information, such as species traits or abundances. To address these challenges, we introduce the use of optimal transport distances to quantify ecological network dissimilarity and functionally equivalent species between networks. Specifically, we describe the Gromov–Wasserstein (GW) and Fused Gromov–Wasserstein (FGW) distances. We apply these optimal transport methods to synthetic and empirical data, using mammal food webs throughout sub‐Saharan Africa for illustration. We showcase the application of GW and FGW distances to identify the most functionally similar species between food webs, incorporate additional trait information into network comparisons and quantify food web dissimilarity among geographic regions. Our results demonstrate that GW and FGW distances can effectively differentiate ecological networks based on their topological structure while identifying functionally equivalent species, even when networks have different species. The FGW distance further improves node mapping for basal species by incorporating node‐level traits. We show that these methods allow for a more nuanced understanding of the topological similarities in food web networks among geographic regions compared to an alternative measure of network dissimilarity based on species identities. Optimal transport distances offer a new approach for quantifying functional equivalence between networks and a measure of network dissimilarity suitable for a broader range of uses than existing approaches. OT methods can be harnessed to analyse ecological networks at large spatial scales and compare networks among ecosystems, realms or taxa. Optimal transport‐based distances, therefore, provide a powerful tool for analysing ecological networks with great potential to advance our understanding of ecological community structure and dynamics in a changing world.