Low-Rank Optimal Transport for Robust Domain Adaptation

When encountering the distribution shift between the source(training) and target(test) domains, domain adaptation attempts to adjust the classifiers to be capable of dealing with different domains. Previous domain adaptation research has achieved a lot of success both in theory and practice under the assumption that all the examples in the source domain are welllabeled and of high quality. However, the methods consistently lose robustness in noisy settings where data from the source domain have corrupted labels or features which is common in reality. Therefore, robust domain adaptation has been introduced to deal with such problems. In this paper, we attempt to solve two interrelated problems with robust domain adaptation:distribution shift across domains and sample noises of the source domain. To disentangle these challenges, an optimal transport approach with low-rank constraints is applied to guide the domain adaptation model training process to avoid noisy information influence. For the domain shift problem, the optimal transport mechanism can learn the joint data representations between the source and target domains using a measurement of discrepancy and preserve the discriminative information. The rank constraint on the transport matrix can help recover the corrupted subspace structures and eliminate the noise to some extent when dealing with corrupted source data. The solution to this relaxed and regularized optimal transport framework is a convex optimization problem that can be solved using the Augmented Lagrange Multiplier method, whose convergence can be mathematically proved. The effectiveness of the proposed method is evaluated through extensive experiments on both synthetic and real-world datasets.

WEAK SOLUTIONS OF MONGE-AMPRE TYPE EQUATIONS IN OPTIMAL TRANSPORTATION

This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.

ENTROPICAL OPTIMAL TRANSPORT,SCHRODINGER'S SYSTEM AND ALGORITHMS

In this exposition paper we present the optimal transport problem of Monge-Ampère-Kantorovitch(MAK in short)and its approximative entropical regularization.Contrary to the MAK optimal transport problem,the solution of the entropical optimal transport problem is always unique,and is characterized by the Schrödinger system.The relationship between the Schrödinger system,the associated Bernstein process and the optimal transport was developed by Léonard[32,33](and by Mikami[39]earlier via an h-process).We present Sinkhorn’s algorithm for solving the Schrödinger system and the recent results on its convergence rate.We study the gradient descent algorithm based on the dual optimal question and prove its exponential convergence,whose rate might be independent of the regularization constant.This exposition is motivated by recent applications of optimal transport to different domains such as machine learning,image processing,econometrics,astrophysics etc..

RFPose-OT:RF-based 3D human pose estimation via optimal transport theory

This paper introduces a novel framework,i.e.,RFPose-OT,to enable three-dimensional(3D)human pose estimation from radio frequency(RF)signals.Different from existing methods that predict human poses from RF signals at the signal level directly,we consider the structure difference between the RF signals and the human poses,propose a transformation of the RF signals to the pose domain at the feature level based on the optimal transport(OT)theory,and generate human poses from the transformed features.To evaluate RFPose-OT,we build a radio system and a multi-view camera system to acquire the RF signal data and the ground-truth human poses.The experimental results in a basic indoor environment,an occlusion indoor environment,and an outdoor environment demonstrate that RFPose-OT can predict 3D human poses with higher precision than state-of-the-art methods.

Robust and accurate optimal transportation map by self-adaptive

Optimal transportation plays a fundamental role in many fi elds in engineering and medicine,including surface parameterization in graphics,registration in computer vision,and generative models in deep learning.For quadratic distance cost,optimal transportation map is the gradient of the Brenier potential,which can be obtained by solving the Monge-Ampère equation.Furthermore,it is induced to a geometric convex optimization problem.The Monge-Ampère equation is highly non-linear,and during the solving process,the intermediate solutions have to be strictly convex.Specifi cally,the accuracy of the discrete solution heavily depends on the sampling pattern of the target measure.In this work,we propose a self-adaptive sampling algorithm which greatly reduces the sampling bias and improves the accuracy and robustness of the discrete solutions.Experimental results demonstrate the efficiency and efficacy of our method.

Analysis of minimum specific energy consumption and optimal transport concentration of slurry pipeline transport systems

Slurry pipeline transport is widely used in several industrial processes.Calculating the specific power consumption(SPC)and determining the best working conditions are important for the design and operation of transportation systems.Based on the Shanghai Jiao Tong University high-concentration multi-sized slurry pressure drop(SJTU-HMSPD)pipeline-resistance-calculation model,the SJTU-SPC model for calculating the power required to transport a unit volume of solid materials over a unit pipeline length is established for a slurry transport system.The said system demonstrates a uniformity coefficient in the 1.26–7.98 range,median particle size of 0.075–4 mm,particle volume concentration of 10–60%,and pipeline diameter of 0.203–0.8 m.The results obtained were successfully verified against existing experimental data.The influence of parameters,such as particle-gradation uniformity coefficient,median particle size,pipe diameter,and particle volume concentration,on the SPC were analysed.The results revealed that the greater is the uniformity coefficient,the smaller is the minimum specific energy consumption and the larger the optimal transport concentration for a constant,median particle size slurry.As observed,the optimal transport concentration for broad-graded sand equalled approximately 48%.These results supplement the conclusions of existing research,indicating that the optimal transport concentration is approximately 30%and provides theoretical support for high concentration transportation of broad graded slurry.

Optimal transport maps on infinite dimensional spaces

We will give a survey on results concerning Girsanov transforma- tions, transportation cost inequalities, convexity of entropy, and optimal transport maps on some infinite dimensional spaces. Some open Problems will be arisen.

A Multilevel Method for the Solution of Time Dependent Optimal Transport

In this paper we present a new computationally efficientnumerical scheme for the minimizing flow for the computation of the optimal L 2 mass transport map-ping using the fluid approach.We review the method and discuss its numerical properties.We then derive a new scaleable,efficient discretization and a solution technique for the problem and show that the problem is equivalent to a mixed form formulation of a nonlinear fluid flow in porous media.We demonstrate the effec-tiveness of our approach using a number of numerical experiments.

Study on Rural Solid Waste Collection and Transportation Mode and Route Optimization Strategy in the Cold Regions of Northern China

Rural vitalization is a major strategy for reform and development of agriculture and rural areas in China,the key task of which is improving rural living environment.Imperfect rural solid waste(RSW)collection and transportation system exacerbates the pollution of RSW to rural living environment,while it has not been established and improved in the cold region of Northern China due to climate and economy.Through the analysis of the current situation of RSW source separation,collection,transportation and disposal in China,an RSW collection and transportation system suitable for the northern cold region was developed.Considering the low winter temperature in the northern cold region,different requirements for RSW collection,transportation and terminal disposal,scattered source points and single terminal disposal nodes in rural areas,the study focused on determining the number and location of transfer stations,established a model for transfer stations selection and RSW collection and transportation routes optimization for RSW collection and transportation system,and proposed the elite retention particle swarm optimization–genetic algorithm(ERPSO–GA).The rural area of Baiquan County was taken as a representative case,the collection and transportation scheme of which was given,and the feasibility of the scheme was clarified by simulation experiment.

Self-Organized Optimization of Transport on Complex Networks

We propose a self-organized optimization mechanism to improve the transport capacity of complex gradient networks. We find that, regardless of network topology, the congestion pressure can be strongly reduced by the self-organized optimization mechanism. Furthermore, the random scale-free topology is more efficient to reduce congestion compared with the random Poisson topology under the optimization mechanism. The reason is that the optimization mechanism introduces the correlations between the gradient field and the local topology of the substrate network. Due to the correlations, the cutoff degree of the gradient network is strongly reduced and the number of the nodes exerting their maximal transport capacity consumedly increases. Our work presents evidence supporting the idea that scale-free networks can efficiently improve their transport capacity by self- organized mechanism under gradient-driven transport mode.

The Role of Short Sea Shipping Concept in Black SeaRegion as a Connection between Eurasian TransportSystems

Despite of fluctuations in world trade as a result of economic cycles,the evolution of the political processes remains the trend of sustained growth of trade flows.This ends up in a rise in both the demand for logistics services and the requirements for them.In this sense,the critically important is the strategic development of the transport systems as a support for the improvement of competitive logistics.An important aspect is the promotion of multimodal transport,which in search of the best transport solutions will reduce the use of relatively expensive and environmentally unfriendly road transportation.This will be at the expense of the efficient combination of different modes in which the concept of short sea shipping(SSS)occupies a central place.Although this concept is widely applied in many places in the Black Sea,it still has significant potential.It was prompted by stagnation in economic relations as a result of political and economic crises in the region since the late twentieth and early twenty-first century.To evaluate the potential of the concept in the development of transport is done research on intermodal logistics network in the logistics corridor Central Asia-Central Europe.To optimize intermodal transport links a comparative analysis of the various transport alternatives on the route Tehran-Budapest is done.On this basis it is made optimization assessment on three main criteria cost,delivery time and environmental protection and basic recommendations on strategic planning development of the Bulgarian transport infrastructure are given.An essential aspect is the encouragement of multimodal transportation,which in looking for the best transport solutions can cut back the utilization of comparatively costly and environmentally harmful road transportation.This would be at the expense of the adequate combination of different modes of transportation in which the concept of SSS has a fundamental area.Despite this concept is widely applied in various regions,in the Black Sea it still has an important future due to stagnation in economic relations as a result of political confrontations and economic crises within the region since the late twentieth and early twenty-first century.To assess the capability of the concept in the development of transport is done research on intermodal logistics network in the logistics corridor Central Asia-Central Europe.To improve intermodal transport links a comparative analysis of the various transport options on the routes Astana-Budapest and Tehran-Budapest are made.On this basis it is proposed an optimization assessment on three main criteria cost,delivery time and environmental protection,and fundamental suggestions on strategic development of the Bulgarian transport infrastructure are proposed.

A Geometric Understanding of Deep Learning

This work introduces an optimal transportation(OT)view of generative adversarial networks(GANs).Natural datasets have intrinsic patterns,which can be summarized as the manifold distribution principle:the distribution of a class of data is close to a low-dimensional manifold.GANs mainly accomplish two tasks:manifold learning and probability distribution transformation.The latter can be carried out using the classical OT method.From the OT perspective,the generator computes the OT map,while the discriminator computes the Wasserstein distance between the generated data distribution and the real data distribution;both can be reduced to a convex geometric optimization process.Furthermore,OT theory discovers the intrinsic collaborative-instead of competitive-relation between the generator and the discriminator,and the fundamental reason for mode collapse.We also propose a novel generative model,which uses an autoencoder(AE)for manifold learning and OT map for probability distribution transformation.This AE–OT model improves the theoretical rigor and transparency,as well as the computational stability and efficiency;in particular,it eliminates the mode collapse.The experimental results validate our hypothesis,and demonstrate the advantages of our proposed model.

Deep density estimation via invertible block-triangular mapping

In this work,we develop an invertible transport map,called KRnet,for density estimation by coupling the Knothe–Rosenblatt(KR)rearrangement and the flow-based generative model,which generalizes the real-valued non-volume preserving(real NVP)model(arX-iv:1605.08803v3).The triangular structure of the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange of information between dimensions,which not only accelerates the training process but also improves the accuracy significantly.We have also introduced several new layers into the generative model to improve both robustness and effectiveness,including a reformulated affine coupling layer,a rotation layer and a component-wise nonlinear invertible layer.The KRnet can be used for both density estimation and sample generation especially when the dimensionality is relatively high.Numerical experiments have been presented to demonstrate the performance of KRnet.

Path selection and mechanism innovation of improving railway energy efficiency–from foreign experience and Chinese practice

Purpose–Under the dual pressure of resources and environment,many countries have focused on the role of railways in promoting low-carbon development of integrated transportation and of even the whole society.This paper aims to provide a comprehensive study on methods to improve railway energy efficiency in other national railways and achievements made by China’s railways in the past practice,and then to propose ways in which in the future China’s railways could rationally select the path of improving energy efficiency regarding the needs of the nation’s ever-shifting development and carry out the re-engineering for mechanism innovation in energy conservation and emission reduction process.Design/methodology/approach–This paper first studies other national railways that have tried to promote the improvement of railway energy efficiency by the ways of technology,management and structural reconstruction to reduce energy consumption and carbon emissions.Among them,the effect of structural energy conservation and emission reduction has become more prominent.It has become the main energy conservation and emission reduction measure adopted by foreign railway sectors.The practice of energy conservation and emission reduction of railways in various countries has tended to shift from a technical level to a structural one.Findings–Key aspects in improving energy efficiency include re-optimization of energy structure,reinnovation of energy-saving technologies and optimization of transportation organization.Path selection includes continuing to promote electrified railway construction,increasing the use of new and renewable energy sources,and promoting the reform of railway transportation organizations.Originality/value–This paper provides further challenges and research directions in the proposed area and has referential value for the methodologies,approaches for practice in a Chinese context.To achieve the expected goals,relevant supporting policies and measures need to be formulated,including actively guiding integrated transportation toward railway-oriented development,promoting innovation in energy-saving and emission reduction mechanisms and strengthening policy incentives,focusing on improving the energy efficiency of railways through market behavior.At the same time,it is necessary to pay attention to new phenomena in the railway industry for track and analysis.

Outlier Robust Feature Correspondence by Learning Based Matching Process

Feature correspondence is a crucial aspect of various computer vision and robot vision tasks.Unlike traditional optimization-based matching techniques,researchers have recently adopted a learning-based approach for matching,but these methods face challenges in dealing with outlier features.This paper presents an outlier robust feature correspondence method that employs a pruned attentional graph neural network and a matching layer to address the outlier issue.Additionally,the authors introduce a modified cross-entropy matching loss to handle the outlier problem.As a result,the proposed method significantly enhances the performance of learning-based matching algorithms in the presence of outlier features.Benchmark experiments confirm the effectiveness of the proposed approach.

A Dynamical System-Based Framework for Dimension Reduction

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.

SOLUTION OF OPTIMAL TR A NSPORTATION PROBLEMS USING A MULTIGRID LINEAR PROGR AMMING APPROACH

We compute and visualize solutions to the Optimal Transportation(OT)problem for a wide class of cost functions.The standard linear programming(LP)discretization of the continuous problem becomes intractable for moderate grid sizes.A grid refinement method results in a linear cost algorithm.Weak convergence of solutions is established and barycentric projection of transference plans is used to improve the accuracy of solutions.Optimal maps between nonconvex domains,partial OT free boundaries,and high accuracy barycenters are presented.

On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion

The quadraticWasserstein metric has shown its power in comparing prob-ability densities.It is successfully applied in waveform inversion by generating ob-jective functions robust to cycle skipping and insensitive to data noise.As an alter-native approach that converts seismic signals to probability densities,the squaring scaling method has good convexity and thus is worth exploring.In this work,we apply the quadratic Wasserstein metric with squaring scaling to regional seismic to-mography.However,there may be interference between different seismic phases in a broad time window.The squaring scaling distorts the signal by magnifying the unbalance of the mass of different seismic phases and also breaks the linear super-position property.As a result,illegal mass transportation between different seismic phases will occur when comparing signals using the quadratic Wasserstein metric.Furthermore,it gives inaccurate Fr´echet derivative,which in turn affects the inver-sion results.By combining the prior seismic knowledge of clear seismic phase sep-aration and carefully designing the normalization method,we overcome the above problems.Therefore,we develop a robust and efficient inversion method based on optimal transport theory to reveal subsurface velocity structures.Several numerical experiments are conducted to verify our method.

Geometry-preserving full-waveform tomography and its application in the Longmen Shan area

Classic L2-norm-based waveform tomography is often plagued by insurmountable cycle skipping problems;as a result,the iterative inversion falls into local minima,yielding erroneous images.According to the optimal transportation theory,we adopt a novel geometry-preserving misfit function based on the quadratic Wasserstein metric(W2-norm),which improves the stability and convexity of the inverse problem.Numerical experiments illustrate that W2-norm-based full-waveform tomography has a larger convergence radius and a faster convergence rate than the L2-norm and can effectively mitigate cycle skipping issues.We apply this method to the Longmen Shan area and obtain a reliable lithospheric velocity model.Our tomographic results indicate that the crystalline crust underlying the Sichuan Basin wedges into the crustal interior of the Tibetan Plateau,and the mid-lower crust of the eastern Tibetan Plateau is characterized by low shear-wave velocities,indicating that ductile crustal flow and strong interactions between terranes jointly dominate the uplift behavior of the Longmen Shan.Furthermore,we find that large earthquakes(e.g.,the Wenchuan and Lushan events)occur not only at the junction between high-and low-velocity regions but also in the transition zone from positive to negative radial anisotropy.These findings improve our understanding of the mechanism responsible for large earthquakes in this region.

Timetable optimization for single bus line based on hybrid vehicle size model

This study proposes a flexible timetable optimization method based on hybrid vehicle size model to tackle the bus demand fluctuations in transit operation. Three different models for hybrid vehicle, large vehicle and small vehicle are built in this study, respectively. With the operation data of Shanghai Transit Route 55 at peak and off-peak hours, a heuristic algorithm was proposed to solve the problem. The results indicate that the hybrid vehicle size model excels the other two modes both in the total time and total cost. The study verifies the rationality of the strategy of hybrid vehicle size model and highlights the importance of the adaptive vehicle size in dealing with the bus demand fluctuation. The main innovation of the study is that unlike traditional timetables, the arrangement of the scheduling interval and the corresponding bus type or size are both involved in the timetable of hybrid vehicle size bus mode, which will be more effective to solve the problem of passenger demand fluctuation. Findings from this research would provide a new perspective to improve the level of regular bus service.