An Improved Algorithm for Fixed-Hub Single Allocation Problem

This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and fully connected; each terminal node is connected to a single hub which routes all its traffic. The goal is to minimize the cost of routing the traffic in the network. In this paper, we propose a linear programming (LP)-based rounding algorithm. The algorithm is based on two ideas. First, we modify the LP relaxation formulation introduced in Ernst and Krishnamoorthy (1996, 1999) by incorporating a set of validity constraints. Then, after obtaining a fractional solution to the LP relaxation, we make use of a geometric rounding algorithm to obtain an integral solution. We show that by incorporating the validity constraints, the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort, and the solution obtained often has a much smaller gap with the optimal solution. We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little cost

UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts. Numerous methods are available for constructing prediction intervals, such as quantile regression and conformal predictions, among others. Nevertheless, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this paper, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions. Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics

Study on the Pricing and Path Scheme Comparison of Transit Freight

This paper aims to optimize the transportation network and transportation organization strategy of Transport through China, enabling operators to obtain greater profits, improving the efficiency of transit freight transport, and solving the problem of transportation pricing and route selection of transit goods. In this paper, the growth trend of transit transport demand is firstly determined. On this basis, the ultimate goal is to maximize the transport profit of the operator. In-depth analysis is made from the perspectives of transport income and transport cost. In addition, through combing existing international transportation routes, the overall transit network map of transit China to central Asian and European countries is drawn. In order to achieve the goal of minimizing transportation expenditure, the model of comparing freight routes is established. The customer is also classified by matrix model. Finally, with the transit transportation from Japan, Korea and other countries as examples, the model in this paper is verified, and the optimal transportation path is obtained through software solution. Compared with the current scheme, it has saved operating costs

Aridity-driven decoupling of δ¹³C between pedogenic carbonate and soil organic matter

Pedogenic carbonate is an invaluable archive for reconstructing continental paleoclimate and paleoecology. The δ¹³C of pedogenic carbonate (δ¹³C_c) has been widely used to document the rise and expansion of C₄ plants over the Cenozoic. This application requires a fundamental presumption that in soil pores, soil-respired CO₂ dominates over atmospheric CO₂ during the formation of pedogenic carbonates. However, the decoupling between δ¹³C_c and δ¹³C of soil organic matter (δ¹³C_(SOM)) have been observed, particularly in arid regions, suggesting that this presumption is not always valid. To evaluate the influence of atmospheric CO₂ on soil δ¹³C_c, here we performed systematic δ¹³C analyses of paleosols across the Chinese Loess Plateau, with the sample ages spanning three intervals: the Holocene, the Late Pleistocene, and the mid-Pliocene warm period. Our paired δ¹³C_c and δ¹³C_(SOM) data reveal broadly divergent trending patterns. Using a two-component CO₂-mixing model, we show substantial incorporations of atmospheric CO₂ (up to 60%) into soil pore space during carbonate precipitation. This result readily explains the enrichment of δ¹³C_c and its divergence from δ¹³C_(SOM). As a consequence, δ¹³C of pedogenic carbonates formed under semiarid and/or arid conditions are largely driven by regional aridity through its control on soil CO₂ composition, and thus cannot be used to evaluate the relative abundance of C₃ versus C₄ plants. Nonetheless, these carbonates can be applied for atmospheric CO₂ reconstructions, even for periods with low CO₂ levels

Aridity-driven decoupling of δ¹³C between pedogenic carbonate and soil organic matter

Pedogenic carbonate is an invaluable archive for reconstructing continental paleoclimate and paleoecology. The δ¹³C of pedogenic carbonate (δ¹³C_c) has been widely used to document the rise and expansion of C₄ plants over the Cenozoic. This application requires a fundamental presumption that in soil pores, soil-respired CO₂ dominates over atmospheric CO₂ during the formation of pedogenic carbonates. However, the decoupling between δ¹³C_c and δ¹³C of soil organic matter (δ¹³C_(SOM)) have been observed, particularly in arid regions, suggesting that this presumption is not always valid. To evaluate the influence of atmospheric CO₂ on soil δ¹³C_c, here we performed systematic δ¹³C analyses of paleosols across the Chinese Loess Plateau, with the sample ages spanning three intervals: the Holocene, the Late Pleistocene, and the mid-Pliocene warm period. Our paired δ¹³C_c and δ¹³C_(SOM) data reveal broadly divergent trending patterns. Using a two-component CO₂-mixing model, we show substantial incorporations of atmospheric CO₂ (up to 60%) into soil pore space during carbonate precipitation. This result readily explains the enrichment of δ¹³C_c and its divergence from δ¹³C_(SOM). As a consequence, δ¹³C of pedogenic carbonates formed under semiarid and/or arid conditions are largely driven by regional aridity through its control on soil CO₂ composition, and thus cannot be used to evaluate the relative abundance of C₃ versus C₄ plants. Nonetheless, these carbonates can be applied for atmospheric CO₂ reconstructions, even for periods with low CO₂ levels

Decentralized Non-Convex Learning with Linearly Coupled Constraints

Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns some local information and a local variable for jointly minimizing a cost function, but local variables are coupled by linear constraints. Most of the existing methods for such problems are only applicable for convex problems or problems with specific linear constraints. There still lacks a distributed algorithm for such problems with general linear constraints and under nonconvex setting. In this paper, to tackle this problem, we propose a new algorithm, called "proximal dual consensus" (PDC) algorithm, which combines a proximal technique and a dual consensus method. We build the theoretical convergence conditions and show that the proposed PDC algorithm can converge to an $\epsilon$-Karush-Kuhn-Tucker solution within $\mathcal{O}(1/\epsilon)$ iterations. For computation reduction, the PDC algorithm can choose to perform cheap gradient descent per iteration while preserving the same order of $\mathcal{O}(1/\epsilon)$ iteration complexity. Numerical results are presented to demonstrate the good performance of the proposed algorithms for solving a regression problem and a classification problem over a network where agents have only partial observations of data features

Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios

Ultrafast Relaxation Dynamics of Photoexcited Dirac Fermion in The Three Dimensional Dirac Semimetal Cadmium Arsenide

Three dimensional (3D) Dirac semimetals which can be seen as 3D analogues of graphene have attracted enormous interests in research recently. In order to apply these ultrahigh-mobility materials in future electronic/optoelectronic devices, it is crucial to understand the relaxation dynamics of photoexcited carriers and their coupling with lattice. In this work, we report ultrafast transient reflection measurements of the photoexcited carrier dynamics in cadmium arsenide (Cd3As2), which is one of the most stable Dirac semimetals that have been confirmed experimentally. By using low energy probe photon of 0.3 eV, we probed the dynamics of the photoexcited carriers that are Dirac-Fermi-like approaching the Dirac point. We systematically studied the transient reflection on bulk and nanoplate samples that have different doping intensities by tuning the probe wavelength, pump power and lattice temperature, and find that the dynamical evolution of carrier distributions can be retrieved qualitatively by using a two-temperature model. This result is very similar to that of graphene, but the carrier cooling through the optical phonon couplings is slower and lasts over larger electron temperature range because the optical phonon energies in Cd3As2 are much lower than those in graphene

Low CO_2 levels of the entire Pleistocene epoch

Quantifying ancient atmospheric pCO_2 provides valuable insights into the interplay between greenhouse gases and global climate. Beyond the 800-ky history uncovered by ice cores, discrepancies in both the trend and magnitude of pCO_2 changes remain among different proxy-derived results. The traditional paleosol pCO_2 paleobarometer suffers from largely unconstrained soil-respired CO_2 concentration (S(z)). Using finely disseminated carbonates precipitated in paleosols from the Chinese Loess Plateau, here we identified that their S(z) can be quantitatively constrained by soil magnetic susceptibility. Based on this approach, we reconstructed pCO_2 during 2.6–0.9 Ma, which documents overall low pCO_2 levels (<300 ppm) comparable with ice core records, indicating that the Earth system has operated under late Pleistocene pCO_2 levels for an extended period. The pCO_2 levels do not show statistically significant differences across the mid-Pleistocene Transition (ca. 1.2–0.8 Ma), suggesting that CO_2 is probably not the driver of this important climate change event