Optimal Transport Research Articles

High-speed railways, audit partner changes across audit offices and audit quality: Evidence from China

The development of high-speed railways (HSRs) has significant regional economic and social implications. We study a micro externality of such development, namely the impact of HSRs on audit firms' human resource allocation and audit quality. Specifically, we investigate the relationship between the availability of HSRs and audit partner changes across audit offices in China which involves a simultaneous change in audit partner and audit office to reallocate human resources. We find that the advent of HSRs between clients and audit offices increases the likelihood of audit partner changes across audit offices especially for predecessor audit offices with severe human resource constraints due partly to the mandatory auditor rotation requirement. Such audit partner changes across audit offices most likely are reciprocal over time, occur within the optimal HSR transportation interval and can significantly improve audit quality in terms of reducing excessive financing reporting discretions, misstatements and regulatory sanctions, but exert no effect on audit fees. Our study has implications for audit firms’ human resource management in light of infrastructure improvements and for audit policy makers to evaluate the standards for audit partner rotations.

Dynamic Rescheduling for Optimal Transportation Incident Management in Inland Waterways

Dynamic Rescheduling for Optimal Transportation Incident Management in Inland Waterways

Three dimensional branching pipe flows for optimal scalar transport between walls

Abstract We are interested in the design of forcing in the Navier–Stokes equation such that the resultant flow maximises the transport of a passive temperature between two differentially heated walls for a given power supply budget. This problem in the community is also known as ‘wall-to-wall optimal transport’ and can be reduced to optimizing the choice of the divergence-free velocity field in the advection-diffusion equation subject to an enstrophy constraint (which can be understood as a constraint on the power required to generate the flow). Previous work established that the transport cannot scale faster than 1/3-power of the power supply. Recently, Tobasco and Doering (2017 Phys. Rev. Lett. 118 264502) and Doering and Tobasco (2019 Commun. Pure Appl. Math. 72 2385–448) constructed self-similar two-dimensional steady branching flows saturating this bound up to a logarithmic correction. This correction appears to arise due to a topological obstruction inherent to two-dimensional steady flows. In this paper, we present a novel design of three-dimensional ‘branching pipe flows’ that bypasses this obstruction and, consequently, eliminates this logarithmic correction and therefore identifies the optimal scaling as a clean 1/3-power law. Our flows resemble the ones obtained in previous numerical studies of the three-dimensional wall-to-wall problem by Motoki, Kawahara and Shimizu (2018 J. Fluid Mech. 851 R4). We also discuss the implications of this result to the heat transfer problem in Rayleigh–Bénard convection and the problem of anomalous dissipation in a passive scalar.

A Sparse Smoothing Newton Method for Solving Discrete Optimal Transport Problems

The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications. This paper proposes to solve the discrete OT problem by applying a squared smoothing Newton method via the Huber smoothing function for solving the corresponding KKT system directly. The proposed algorithm admits appealing convergence properties and is able to take advantage of the solution sparsity to greatly reduce computational costs. Moreover, the algorithm can be extended to solve problems with similar structures, including the Wasserstein barycenter (WB) problem with fixed supports. To verify the practical performance of the proposed method, we conduct extensive numerical experiments to solve a large set of discrete OT and WB benchmark problems. Our numerical results show that the proposed method is efficient compared to state-of-the-art linear programming (LP) solvers. Moreover, the proposed method consumes less memory than existing LP solvers, which demonstrates the potential usage of our algorithm for solving large-scale OT and WB problems.

Applications of Optimal Transportation

The mathematical theory of optimal transportation is constantly expanding its range of application, while applications give impulses for new research directions in the field. This workshop was specifically devoted to applications of optimal transportation in the natural sciences, and to the recent developments of the theory that have been motivated by these. The bouquet of current applications includes mathematical models for large-scale air motion, dynamics of plasmas, material design, pattern formation in fluids, collective behaviour in biology, and many more. Related theoretical developments are in the analysis of the Hellinger-Kantorovich metric for modeling reaction–diffusion processes, and in efficient numerical methods for multi-marginal optimal transport, to name two of many examples encountered in this workshop.

Multi-objective intermodal transportation planning with real-life application

ABSTRACT This paper explores the optimal route selection problem within an intermodal transportation network that comprises road, rail, sea, and inland waterways. Initially, we propose a multi-objective integer linear programming model that aims to minimize total cost, transport time, and carbon emissions. Subsequently, we apply two multi-objective programming approaches: Fuzzy Goal Programming and Compromise Programming. These approaches are implemented in a real-life case study, aiming to determine the optimal intermodal transportation route from Türkiye (Denizli) to Germany (Duisburg). Four out of the six methods suggest the same road and maritime pathway. Furthermore, this model has the potential to aid decision-makers in selecting routes based on customer requirements and serve as a valuable tool for policymakers in establishing an efficient intermodal transport network.

Investigation of the transportation characteristics of marine dredged-sediment in pipelines based on experimental pipeline models

Marine dredged-sediment(DS) is often transported through pipelines, where factors such as the solid volume concentration and transport rate can significantly influence the efficiency of the process. Inadequate selection of transport rates for a given solid volume concentration can lead to substantial energy losses. The pressure loss Δ P L or pressure loss gradient Δ P L / L are critical parameters for assessing energy loss during pipeline transport. In this study, large-scale indoor experiments on DS pipeline transport were conducted to investigate the effects of the cross-sectional mean flow velocity Vavg and solid concentration ϕ on the transport characteristics of DS. The results show that at higher solid volume concentrations, Δ P L / L increases rapidly with the square of Vavg and then plateaus, followed by a linear growth phase. In addition, a linear relationship is observed between lgf and lgVavg when the flow velocity is below critical velocity (Vavg ) critical ; above (Vavg ) critical , the friction factor f stabilizes at f 0 . Formulas for calculating (Vavg ) critical , f 0 and ϕ were developed. Additionally, a method for determining the optimal transport velocity of DS at varying volume concentrations was established, enabling the identification of the most efficient flow velocity for DS pipeline transportation across different concentrations. HIGHLIGHTS Pipeline model tests were conducted on marine dredged sediments. A formula for predicting pressure loss on the basis of solid concentration was derived. The impact of the solid concentration on the Darcy friction factor was determined. A method for determining the optimal transport velocity was established.

Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach

Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

Monge-Ampère gravity: From the large deviation principle to cosmological simulations through optimal transport

Monge-Ampère gravity: From the large deviation principle to cosmological simulations through optimal transport

Multi-Functional Silole Hole Transport Layer for Efficient and Stable Lead-Tin Perovskite and Tandem Solar Cells.

Despite high theoretical efficiencies and rapid improvements in performance, high-efficiency ≈1.2eV mixed Sn-Pb perovskite solar cells (PSCs) generally rely on poly(3,4-ethylenedioxythiophene) polystyrenesulfonate (PEDOT: PSS) as the hole transport layer (HTL); a material that is considered to be a bottleneck for long-term stability due to its acidity and hygroscopic nature. Seeking to replace PEDOT: PSS with an alternative HTL with improved atmospheric and thermal stability, herein, a silole derivative (Silole-COOH) tuned with optimal electronic properties and efficient carrier transport by incorporating a carboxyl functional group is designed, which results in an optimal band alignment for hole extraction from Sn-Pb perovskites and robust air and thermal stability. Thin films composed of the Silole-COOH exhibit superior conductivity and carrier mobility compared to PEDOT: PSS, in addition to reduced nonradiative quasi-Fermi-level splitting losses at the HTL/perovskite interface and improved quality of Sn-Pb perovskite. Replacement of PEDOT: PSS with Silole-COOH leads to 23.2%-efficient single-junction Sn-Pb PSCs, 25.8%-efficient all-perovskite tandems, and long operating stability in ambient air.

Watertight surface reconstruction method for CAD models based on optimal transport

Watertight surface reconstruction method for CAD models based on optimal transport

A new perspective on denoising based on optimal transport

Abstract In the standard formulation of the classical denoising problem, one is given a probabilistic model relating a latent variable $\varTheta \in \varOmega \subset{\mathbb{R}}^{m} \; (m\ge 1)$ and an observation $Z \in{\mathbb{R}}^{d}$ according to $Z \mid \varTheta \sim p(\cdot \mid \varTheta )$ and $\varTheta \sim G^{*}$, and the goal is to construct a map to recover the latent variable from the observation. The posterior mean, a natural candidate for estimating $\varTheta $ from $Z$, attains the minimum Bayes risk (under the squared error loss) but at the expense of over-shrinking the $Z$, and in general may fail to capture the geometric features of the prior distribution $G^{*}$ (e.g. low dimensionality, discreteness, sparsity). To rectify these drawbacks, in this paper we take a new perspective on this denoising problem that is inspired by optimal transport (OT) theory and use it to study a different, OT-based, denoiser at the population level setting. We rigorously prove that, under general assumptions on the model, this OT-based denoiser is mathematically well-defined and unique, and is closely connected to the solution to a Monge OT problem. We then prove that, under appropriate identifiability assumptions on the model, the OT-based denoiser can be recovered solely from information of the marginal distribution of $Z$ and the posterior mean of the model, after solving a linear relaxation problem over a suitable space of couplings that is reminiscent of standard multimarginal OT problems. In particular, due to Tweedie’s formula, when the likelihood model $\{ p(\cdot \mid \theta ) \}_{\theta \in \varOmega }$ is an exponential family of distributions, the OT-based denoiser can be recovered solely from the marginal distribution of $Z$. In general, our family of OT-like relaxations is of interest in its own right and for the denoising problem suggests alternative numerical methods inspired by the rich literature on computational OT.

ImSpiRE: image feature-aided spatial resolution enhancement method.

The resolution of most spatially resolved transcriptomic technologies usually cannot attain the single-cell level, limiting their applications in biological discoveries. Here, we introduce ImSpiRE, an image feature-aided spatial resolution enhancement method for in situ capturing spatial transcriptome. Taking the information stored in histological images, ImSpiRE solves an optimal transport problem to redistribute the expression profiles of spots to construct new transcriptional profiles with enhanced resolution, together with extending the gene expression profiles into unmeasured regions. Applications to multiple datasets confirm that ImSpiRE can enhance spatial resolution to the subspot level while contributing to the discovery of tissue domains, signaling communication patterns, and spatiotemporal characterization.

Optimal transport through a toll station

Abstract We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions, we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.

Optimal transport reveals dynamic gene regulatory networks via gene velocity estimation.

Inferring gene regulatory networks from gene expression data is an important and challenging problem in the biology community. We propose OTVelo, a methodology that takes time-stamped single-cell gene expression data as input and predicts gene regulation across two time points. It is known that the rate of change of gene expression, which we will refer to as gene velocity, provides crucial information that enhances such inference; however, this information is not always available due to the limitations in sequencing depth. Our algorithm overcomes this limitation by estimating gene velocities using optimal transport. We then infer gene regulation using time-lagged correlation and Granger causality via regularized linear regression. Instead of providing an aggregated network across all time points, our method uncovers the underlying dynamical mechanism across time points. We validate our algorithm on 13 simulated datasets with both synthetic and curated networks and demonstrate its efficacy on 4 experimental data sets.

Visual Inputs Reconstructing through Enhanced 3T fMRI Data from Optimal Transport Guided Generative Adversarial Network

Visual Inputs Reconstructing through Enhanced 3T fMRI Data from Optimal Transport Guided Generative Adversarial Network

Extending quantum detailed balance through optimal transport

We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans and Wasserstein distances between systems on possibly different observable algebras.

MultiMatch: geometry-informed colocalization in multi-color super-resolution microscopy

With recent advances in multi-color super-resolution light microscopy, it is possible to simultaneously visualize multiple subunits within biological structures at nanometer resolution. To optimally evaluate and interpret spatial proximity of stainings on such an image, colocalization analysis tools have to be able to integrate prior knowledge on the local geometry of the recorded biological complex. We present MultiMatch to analyze the abundance and location of chain-like particle arrangements in multi-color microscopy based on multi-marginal optimal unbalanced transport methodology. Our object-based colocalization model statistically addresses the effect of incomplete labeling efficiencies enabling inference on existent, but not fully observable particle chains. We showcase that MultiMatch is able to consistently recover existing chain structures in three-color STED images of DNA origami nanorulers and outperforms geometry-uninformed triplet colocalization methods in this task. MultiMatch generalizes to an arbitrary number of color channels and is provided as a user-friendly Python package comprising colocalization visualizations.

Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures

Designing and optimizing the structure of urban transportation networks is a challenging task. In this study, we propose a method inspired by optimal transport theory and the principle of economy of scale that uses little information in input to generate structures that are similar to those of public transportation networks. Contrarily to standard approaches, it does not assume any initial backbone network infrastructure but rather extracts this directly from a continuous space using only a few origin and destination points, generating networks from scratch. Analyzing a set of urban train, tram and subway networks, we find a noteworthy degree of similarity in several of the studied cases between simulated and real infrastructures. By tuning one parameter, our method can simulate a range of different subway, tram and train networks that can be further used to suggest possible improvements in terms of relevant transportation properties. Outputs of our algorithm provide naturally a principled quantitative measure of similarity between two networks that can be used to automatize the selection of similar simulated networks.

FACE: Feature-preserving CAD model surface reconstruction

Feature lines play a pivotal role in the reconstruction of CAD models. Currently, there is a lack of a robust explicit reconstruction algorithm capable of achieving sharp feature reconstruction in point clouds with noise and non-uniformity. In this paper, we propose a feature-preserving CAD model surface reconstruction algorithm, named FACE. The algorithm initiates with preprocessing the point cloud through denoising and resampling steps, resulting in a high-quality point cloud that is devoid of noise and uniformly distributed. Then, it employs discrete optimal transport to detect feature regions and subsequently generates dense points along potential feature lines to enhance features. Finally, the advancing-front surface reconstruction method, based on normal vector directions, is applied to reconstruct the enhanced point cloud. Extensive experiments demonstrate that, for contaminated point clouds, this algorithm excels not only in reconstructing straight edges and corner points but also in handling curved edges and surfaces, surpassing existing methods.