An Efficient HPR Algorithm for the Wasserstein Barycenter Problem with O(Dim(P)/ε)O({Dim(P)}/\varepsilon) Computational Complexity

In this paper, we propose and analyze an efficient Halpern-Peaceman-Rachford (HPR) algorithm for solving the Wasserstein barycenter problem (WBP) with fixed supports. While the Peaceman-Rachford (PR) splitting method itself may not be convergent for solving the WBP, the HPR algorithm can achieve an $O(1/\varepsilon)$ non-ergodic iteration complexity with respect to the Karush-Kuhn-Tucker (KKT) residual. More interestingly, we propose an efficient procedure with linear time computational complexity to solve the linear systems involved in the subproblems of the HPR algorithm. As a consequence, the HPR algorithm enjoys an $O({\rm Dim(P)}/\varepsilon)$ non-ergodic computational complexity in terms of flops for obtaining an $\varepsilon$-optimal solution measured by the KKT residual for the WBP, where ${\rm Dim(P)}$ is the dimension of the variable of the WBP. This is better than the best-known complexity bound for the WBP. Moreover, the extensive numerical results on both the synthetic and real data sets demonstrate the superior performance of the HPR algorithm for solving the large-scale WBP

ff-MICL: Understanding and Generalizing InfoNCE-based Contrastive Learning

In self-supervised contrastive learning, a widely-adopted objective function is InfoNCE, which uses the heuristic cosine similarity for the representation comparison, and is closely related to maximizing the Kullback-Leibler (KL)-based mutual information. In this paper, we aim at answering two intriguing questions: (1) Can we go beyond the KL-based objective? (2) Besides the popular cosine similarity, can we design a better similarity function? We provide answers to both questions by generalizing the KL-based mutual information to the $f$-Mutual Information in Contrastive Learning ($f$-MICL) using the $f$-divergences. To answer the first question, we provide a wide range of $f$-MICL objectives which share the nice properties of InfoNCE (e.g., alignment and uniformity), and meanwhile result in similar or even superior performance. For the second question, assuming that the joint feature distribution is proportional to the Gaussian kernel, we derive an $f$-Gaussian similarity with better interpretability and empirical performance. Finally, we identify close relationships between the $f$-MICL objective and several popular InfoNCE-based objectives. Using benchmark tasks from both vision and natural language, we empirically evaluate $f$-MICL with different $f$-divergences on various architectures (SimCLR, MoCo, and MoCo v3) and datasets. We observe that $f$-MICL generally outperforms the benchmarks and the best-performing $f$-divergence is task and dataset dependent.Comment: Accepted to TMLR in 202

Accelerating preconditioned ADMM via degenerate proximal point mappings

In this paper, we aim to accelerate a preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, for solving linearly constrained convex optimization problems. To achieve this, we first reformulate the pADMM into a form of proximal point method (PPM) with a positive semidefinite preconditioner which can be degenerate due to the lack of strong convexity of the proximal terms in the pADMM. Then we accelerate the pADMM by accelerating the reformulated degenerate PPM (dPPM). Specifically, we first propose an accelerated dPPM by integrating the Halpern iteration and the fast Krasnosel'ski\u{i}-Mann iteration into it, achieving asymptotic $o(1/k)$ and non-asymptotic $O(1/k)$ convergence rates. Subsequently, building upon the accelerated dPPM, we develop an accelerated pADMM algorithm that exhibits both asymptotic $o(1/k)$ and non-asymptotic $O(1/k)$ nonergodic convergence rates concerning the Karush-Kuhn-Tucker residual and the primal objective function value gap. Preliminary numerical experiments validate the theoretical findings, demonstrating that the accelerated pADMM outperforms the pADMM in solving convex quadratic programming problems

Study on Matching Ability Between Cement Particle Size and Permeability in the Process of Oil Reservoir Plugging

In order to satisfy the plugging demands of injecting the cement plugging agent into reservoirs with different radial depths, the technical studies of cement particle size optimization should be conducted. Through indoor experiment, the relationship between cement particle size and permeability was investigated by both macroscopic and microcosmic analysis. It is observed that the reservoirs which permeabilities are within 50~200mD are matching well with the cement agents which particle sizes are less than 5μm. And the permeabilities within 200~400mD are matching well with the cement agents which particle sizes are within 5~10μm, the permeabilities within 400~700mD are matching well with the cement agents which particle sizes are within 10~20μm, the permeabilities are above 700mD are matching well with the cement agents which particle sizes are more than 20μm. The plugging success rates of all the matching experiments are exceeding 90%. This research result is important to direct the plugging operation in the field.Key words: Plugging off and channeling prevention; Cement particle size; Permeability; Matching relationship; Experimental stud

The within-field and between-field dispersal of weedy rice by combine harvesters

International audienceAbstractWeedy rice (Oryza sativa L.) severely decreases the grain yield and profitability of rice is one of the most significant problems in the majority of rice fields worldwide. Few reports focus on the dispersal of weedy rice, especially how it rapidly spreads to large areas and long distances. Here, we quantify for the first time the within- and between-field dispersal of weedy rice associated with combine harvesting operations. We randomly sampled 31 combine harvesters to determine where and how much weedy rice seeds remained on the machines at three locations in Jiangsu Province, China. Based on the sampling results, the field area over which weedy rice seeds were retained on the combine harvester during harvesting was estimated to assess the within-field dispersibility of weedy rice seeds remaining in the harvesters. A tracking experiment was also carried out by tracing the distribution of weedy rice seeds along harvest trails, to estimate the dispersal of weedy rice seeds within the field being harvested. Weedy rice seeds remained in the harvest pocket, on the pedrail, and the metal plate of the combine harvester. On average, more than 5000 weedy rice seeds which were 22.80% of remaining grains could potentially be transported into adjacent fields by the combine after each rice field infested with weedy rice had been harvested. Of the statistical models compared, a double exponential model simulating the variation in seed retention predicted that weedy rice seeds remaining on the metal plate could be dispersed over 6473.91 m2 or 3236.96 m into the next field during the harvesting operation. Within the field, the number of fallen weedy rice seeds and their dispersal distance were positively correlated to weedy rice panicle density with the combine dispersing most of seeds away from their mother plant thus creating new weed patches. Therefore, fields that were severely infested with weedy rice should be harvested cautiously and separately and seed remaining in a harvester should be avoided to prevent intra- and inter-field, and even cross-regional dispersal of weedy rice

Reciprocity between abscisic acid and ethylene at the onset of berry ripening and after harvest

<p>Abstract</p> <p>Background</p> <p>The ripening of grape berry is generally regulated by abscisic acid (ABA), and has no relationship with ethylene function. However, functional interaction and synergism between ABA and ethylene during the beginning of grape berry ripening (véraison) has been found recently.</p> <p>Results</p> <p>The expressions of <it>VvNCED1 </it>encoding 9-<it>cis</it>-epoxycarotenoid dioxygenase (NCED) and <it>VvGT </it>encoding ABA glucosyltransferase were all increased rapidly at the stage of véraison and reached the highest level at 9th week after full bloom. However, <it>VvCYP1 </it>encoding ABA 8'-hydroxylase and <it>VvβG1 </it>encoding berry β-glucosidase are different, whose expression peak appeared at the 10th week after full bloom and in especial <it>VvβG1 </it>remained at a high level till harvest. The <it>VvACO1 </it>encoding 1-aminocyclopropane-1-carboxylic acid (ACC) oxidase, the <it>VvETR2 </it>(ethylene response 2) and <it>VvCTR1 </it>(constitutive triple response 1) had a transient expression peak at pre-véraison, while the <it>VvEIN4 </it>(ethylene insensitive 4) expression gradually increased from the véraison to one week before harvest stage. The above mentioned changes happened again in the berry after harvest. At one week before véraison, double block treatment with NiCl₂plus 1-methylcyclopropene (1-MCP) not only inhibited the release of ethylene and the expression of related genes but also suppressed the transcription of <it>VvNCED1 </it>and the synthesis of ABA which all might result in inhibiting the fruit ripening onset. Treatment with ABA could relieve the double block and restore fruit ripening course. However, after harvest, double block treatment with NiCl₂plus 1-MCP could not suppress the transcription of <it>VvNCED1 </it>and the accumulation of ABA, and also could not inhibit the start of fruit senescence.</p> <p>Conclusion</p> <p>The trace endogenous ethylene induces the transcription of <it>VvNCED1 </it>and then the generation of ABA followed. Both ethylene and ABA are likely to be important and their interplaying may be required to start the process of berry ripening. When the level of ABA reached the peak value, part of it will be stored in the form of ABA-GE. While after harvest, abiotic stresses principally (such as dehydration, harvest shock) could induce the transcription of <it>VvNCED1 </it>and the accumulation of ABA, thus starting the process of fruit senescence.</p

A pupil-positioning method based on the starburst model

Human eye detection has become an area of interest in the field of computer vision with an extensive range of applications in human-computer interaction, disease diagnosis, and psychological and physiological studies. Gaze-tracking systems are an important research topic in the human-computer interaction field. As one of the core modules of the head-mounted gaze-tracking system, pupil positioning affects the accuracy and stability of the system. By tracking eye movements to better locate the center of the pupil, this paper proposes a method for pupil positioning based on the starburst model. The method uses vertical and horizontal coordinate integral projections in the rectangular region of the human eye for accurate positioning and applies a linear interpolation method that is based on a circular model to the reflections in the human eye. In this paper, we propose a method for detecting the feature points of the pupil edge based on the starburst model, which clusters feature points and uses the RANdom SAmple Consensus (RANSAC) algorithm to perform ellipse fitting of the pupil edge to accurately locate the pupil center. Our experimental results show that the algorithm has higher precision, higher efficiency and more robustness than other algorithms and excellent accuracy even when the image of the pupil is incomplete.Science and Technology Support Plan Project of Hebei Province (grant numbers 17210803D and 19273703D Science and Technology Spark Project of the Hebei Seismological Bureau (grant number DZ20180402056) Education Department of Hebei Province (grant number QN2018095) Polytechnic College of Hebei University of Science and Technolog

Thermodynamic Behaviors of a Kind of Self-Decoupling Magnetorheological Damper

A theoretical model of temperature change on a kind of self-decoupling magnetorheological (SDMR) damper was established based on conservation of energy, and the constraint equation for structural design parameters of the SDMR damper was improved to satisfy heat dissipation requirements in this work. According to the theoretical model and improved constraint equation, the main structure parameters of SDMR damper were obtained and the damper was tested. The temperature performance test results indicate that the rising temperature makes the damping force decline, and the main affection factors of temperature variation are excitation methods and input current. The results also show that the improved constraint equation and design method introduced are correct and efficient in the engineering