The prevalence of sarcasm in multimodal dialogues on the social platforms presents a crucial yet challenging task for understanding the true intent behind online content. Comprehensive sarcasm analysis requires two key aspects: Multimodal Sarcasm Detection (MSD) and Multimodal Sarcasm Explanation (MuSE). Intuitively, the act of detection is the result of the reasoning process that explains the sarcasm. Current research predominantly focuses on addressing either MSD or MuSE as a single task. Even though some recent work has attempted to integrate these tasks, their inherent causal dependency is often overlooked. To bridge this gap, we propose MuVaC, a variational causal inference framework that mimics human cognitive mechanisms for understanding sarcasm, enabling robust multimodal feature learning to jointly optimize MSD and MuSE. Specifically, we first model MSD and MuSE from the perspective of structural causal models, establishing variational causal pathways to define the objectives for joint optimization. Next, we design an alignment-then-fusion approach to integrate multimodal features, providing robust fusion representations for sarcasm detection and explanation generation. Finally, we enhance the reasoning trustworthiness by ensuring consistency between detection results and explanations. Experimental results demonstrate the superiority of MuVaC in public datasets, offering a new perspective for understanding multimodal sarcasm.
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With the increasing relevance of web mining and content analysis in uncovering mobility patterns from large-scale online data, traffic flow prediction plays a crucial role in proactive urban planning and enhancing the responsiveness of intelligent transportation systems. However, existing traffic flow prediction methods often fail to explicitly capture correlations in continuous multivariate sequences that are naturally suited for trend and periodic pattern extraction by vision models and rely on fixed spatial graphs that neglect the cognitive advantages of granular-ball structures, which limits their ability to model interactions and strengthen spatiotemporal dependencies. To address these challenges, this paper proposes a Cross-domain Mamba framework that integrates Multi-scale Imaging and Granular-ball Computing for traffic flow prediction (MIGC-CMamba). First, a multi-scale sequence imaging method is presented, which converts the original time series into image modality and leverages MambaVision to capture both local and global dependencies. Second, a multi-granularity spatial graph is constructed via granular-ball clustering, which balances global trend representation and local detail preservation. Third, a cross-domain enhancement mechanism adaptively integrates temporal and spatial domains, strengthening spatiotemporal dependencies. Lastly, extensive experiments demonstrate superior performance over state-of-the-art baselines, highlighting how vision-based imaging, cognition-inspired granular-ball modeling, and content-aware mining jointly advance the modeling of spatiotemporal dependencies in traffic flow prediction.
In the modern internet, with the proliferation of real-time applications such as online gaming and video conferencing, the timely detection of network jitter has become a critical task in network measurement. Network jitter is defined as the abrupt fluctuations in packet inter-arrival times within network flows, which severely degrade the Quality of Service for these applications. Traditional jitter detection methods primarily focus on macro-level end-to-end or hop-by-hop latency variations, neglecting the fine-grained jitter that occurs within specific flows. In this paper, we present JitterSketch, the first sketch-based algorithm specifically designed for detecting jittery flows. JitterSketch employs a novel three-stage structure to efficiently filter out infrequent and stable flows, thereby identifying and reporting the jittery flows that have the most significant impact on network quality. Extensive experiments demonstrate that JitterSketch achieves an improvement of up to 50 percentage points in both recall and precision rates compared to baseline solutions, while maintaining high processing throughput. Furthermore, we deployed JitterSketch in a QoS simulation system, where it yielded significant improvements in QoS.
Using Web Mining and Content Analysis to find and understand clues from the massive amount of unstructured text online is very important for predicting future events and providing early risk warnings in important fields like finance and public safety. While Large Language Models (LLMs) exhibit potential in processing and understanding text, current text-based event prediction faces two primary challenges: first, an insufficient utilization of potential information within the text, such as causal relationships and latent associations, and second, limited predictive reliability constrained by issues like the LLM's own ability and hallucinations. To address these challenges, we propose a novel event prediction framework, Bidirectional Reasoning with Self-Correction (BRSC). BRSC comprises two complementary reasoning dimensions: temporal deductive reasoning, which analyzes the trajectory of historical events along the timeline to enable accurate trend extrapolation, and synchronic associative reasoning, which deeply mines details and latent connections from documents within a specific time window to extended semantic information. In addition, we use a self-correction mechanism that identifies and rectifies potential hallucinations and errors during the reasoning process. Extensive experiments on international relations event prediction demonstrate that BRSC achieves significant improvements over several leading LLM-based methods.
Knowledge tracing (KT) aims to personalize online education on large-scale web-based platforms by modeling students' evolving knowledge states from their interaction sequences. However, most KT models rely on a single encoder architecture (e.g., self-attention or RNN), with fixed inductive biases that fails to capture the diversity of learning behaviors. Specifically, student learning unfolds across multiple timescales, and interaction sequences contain diverse frequency components ranging from short-term variations to long-term trends. Our data-driven analysis reveals that existing encoders exhibit characteristic frequency biases (e.g., self-attention tends to emphasize low-frequency patterns), highlighting the limitations of any single architecture. To address this problem, we propose FA-KT, a frequency-aware mixture of heterogeneous experts framework. FA-KT combines self-attention, Mamba, CNN, and LSTM experts, each with complementary frequency biases. A frequency-aware router analyzes each sequence's frequency characteristics and adaptively combines experts to create dynamic, personalized encoders for individual students. Across five benchmark datasets, FA-KT consistently outperforms 20 strong KT baselines in predicting future performance. Code is available at https://pykt.org/.
The rapid spread of online misinformation poses a serious threat to public trust and social stability, making automatic fake news detection increasingly critical. In this work, we propose a novel retrieval-augmented fake news detection framework, Triple-R (Rewriting, Retrieval, and iterative Refinement), which emphasizes optimizing the retrieval query. Unlike prior retrieval-augmented methods that adapt either the retriever or the verification module, often overlooking the gap between news text and the evidence needed for verification, our approach focuses on adapting the search query to retrieve the most relevant evidence. Specifically, we employ a small language model as a trainable query rewriter, optimized via reinforcement learning with feedback from a frozen LLM-based fake news detector, to transform the original news text into effective retrieval queries. To further enhance evidence relevance, we introduce an iterative query refinement mechanism, which progressively updates rewritten queries based on previously retrieved results. Finally, the original news text and the evidence retrieved through refined queries are integrated for verification. Experiments on two real-world datasets demonstrate consistent improvements, validating the effectiveness of our approach.
The rapid advancement of multimodal large language models has enabled agents to operate mobile devices by directly interacting with graphical user interfaces, opening new possibilities for mobile automation. However, real-world mobile tasks are often complex and allow for multiple valid solutions. This contradicts current mobile agent evaluation standards: offline static benchmarks can only validate a single predefined ''golden path'', while online dynamic testing is constrained by the complexity and non-reproducibility of real devices, making both approaches inadequate for comprehensively assessing agent capabilities. To bridge the gap between offline and online evaluation and enhance testing stability, this paper introduces a novel graph-structured benchmarking framework. By modeling the finite states observed during real-device interactions, it achieves static simulation of dynamic behaviors. Building on this, we develop ColorBench, a benchmark focused on complex long-horizon tasks. It supports evaluation of multiple valid solutions, subtask completion rate statistics, and atomic-level capability analysis. ColorBench contains 175 tasks (74 single-app, 101 cross-app) with an average length of over 13 steps. Each task includes at least two correct paths and several typical error paths, enabling quasi-dynamic interaction.
Temporal Point Processes (TPPs) have been widely used for modeling event sequences on the Web, such as user reviews, social media posts, and online transactions. However, traditional TPP models often struggle to effectively incorporate the rich textual descriptions that accompany these events, while Large Language Models (LLMs), despite their remarkable text processing capabilities, lack mechanisms for handling the temporal dynamics inherent in Web-based event sequences. To bridge this gap, we introduce Language-TPP, a unified framework that seamlessly integrates TPPs with LLMs for enhanced Web event sequence modeling. Our key innovation is a novel temporal encoding mechanism that converts continuous time intervals into specialized byte-tokens, enabling direct integration with standard language model architectures for TPP modeling without requiring TPP-specific modifications. This approach allows Language-TPP to achieve state-of-the-art performance across multiple TPP benchmarks, including event time prediction and type prediction, on real-world Web datasets spanning e-commerce reviews, social media and online Q&A platforms. More importantly, we demonstrate that our unified framework unlocks new capabilities for TPP research: incorporating temporal information improves the quality of generated event descriptions, as evidenced by enhanced ROUGE-L scores, and better aligned sentiment distributions. Through comprehensive experiments, including qualitative analysis of learned distributions and scalability evaluations on long sequences, we show that Language-TPP effectively captures both temporal dynamics and textual patterns in Web user behavior, with important implications for content generation, user behavior understanding, and Web platform applications. Code is available at https://github.com/qykong/Language-TPP.
Logs serve as a primary source of information for engineers to diagnose failures in large-scale online service systems. Log parsing, which extracts structured events from massive unstructured log data, is a critical first step for downstream tasks like anomaly detection and failure diagnosis. With advances in large language models (LLMs), leveraging their strong text understanding capabilities has proven effective for accurate log parsing. However, existing LLM-based log parsers all focus on the constant part of logs, ignoring the potential contribution of the variable part to log parsing. This constant-centric strategy brings four key problems. First, inefficient log grouping and sampling with only constant information. Second, a relatively large number of LLM invocations due to constant-based cache, leading to low log parsing accuracy and efficiency. Third, a relatively large number of consumed constant tokens in prompts leads to high LLM invocation costs. At last, these methods only retain placeholders in the results, losing the system visibility brought by variable information in logs. Facing these problems, we propose a variable-centric log parsing strategy named VarParser. Through variable contribution sampling, variable-centric parsing cache, and adaptive variable-aware in-context learning, our approach can efficiently capture the variable parts of logs and leverage their contributions to parsing. By introducing variable units, we preserve rich variable information, enhancing the integrity of log parsing results. Extensive evaluations on large-scale datasets demonstrate that VarParser achieves higher accuracy compared to existing methods, significantly improving parsing efficiency while reducing the LLM invocation costs.
Cross-domain recommendation (CDR) addresses the data sparsity and cold-start problems in the target domain by leveraging knowledge from data-rich source domains. However, existing CDR methods often rely on domain-specific features or identifiers that lack transferability across different domains, limiting their ability to capture inter-domain semantic patterns. To overcome this, we propose \model, a semantics-driven framework for cross-domain sequential recommendation that leverages large language models (LLMs) to construct a unified semantic space. \model creates multi-view item features by integrating LLM-generated domain-agnostic semantics with domain-specific content, aligned by contrastive regularization. \model systematically creates LLM-generated domain-specific and domain-agnostic semantics, and employs adaptive fusion to generate unified preference representations. Furthermore, it aligns cross-domain behavior sequences with an adaptive fusion mechanism to synthesize interaction sequences from source, target, and mixed domains. Extensive experiments on real-world datasets show that \model consistently outperforms state-of-the-art baselines, demonstrating its effectiveness in capturing coherent intra-domain patterns while facilitating knowledge transfer across domains. Our code is available online. https://github.com/huangshanqiang/SemaCDR.
Click-through rate (CTR) prediction plays a pivotal role in online advertising and recommender systems. Despite notable progress in modeling user preferences from historical behaviors, two key challenges persist. First, exsiting discriminative paradigms focus on matching candidates to user history, often overfitting to historically dominant features and failing to adapt to rapid interest shifts. Second, a critical information chasm emerges from the point-wise ranking paradigm. By scoring each candidate in isolation, CTR models discard the rich contextual signal implied by the recalled set as a whole, leading to a misalignment where long-term preferences often override the user's immediate, evolving intent. To address these issues, we propose GenCI, a generative user intent framework that leverages semantic interest cohorts to model dynamic user preferences for CTR prediction. The framework first employs a generative model, trained with a next-item prediction (NTP) objective, to proactively produce candidate interest cohorts. These cohorts serve as explicit, candidate-agnostic representations of a user's immediate intent. A hierarchical candidate-aware network then injects this rich contextual signal into the ranking stage, refining them with cross-attention to align with both user history and the target item. The entire model is trained end-to-end, creating a more aligned and effective CTR prediction pipeline. Extensive experiments on three widely used datasets demonstrate the effectiveness of our approach.
Learner-item cognitive modeling plays a central role in the web-based online intelligent education system by enabling cognitive diagnosis (CD), the upstream and crucial component of the system, across increasingly diverse online educational scenarios. Although ID embedding remains the mainstream approach in cognitive modeling due to its effectiveness and flexibility, recent advances in language models (LMs) have introduced new possibilities for incorporating rich semantic representations to enhance CD performance. However, current studies often focus on a specific task, such as zero-shot CD, limiting the broader application of LMs in this field. This highlights the need for a comprehensive analysis of how LMs enhance embeddings through semantic integration across mainstream CD tasks. This paper identifies two key challenges in fully leveraging LMs in existing work: Misalignment between the training objectives of LMs and CD models creates a distribution gap in feature spaces, hindering the potential of LMs for embedding enhancement; A unified framework is essential for integrating textual embeddings across varied CD tasks while preserving the strengths of existing cognitive modeling paradigms, such as ID embeddings, to ensure the robustness of embedding enhancement. To address these challenges, this paper introduces EduEmbed, a unified embedding enhancement framework that leverages fine-tuned LMs to enrich learner-item cognitive modeling across diverse CD tasks. EduEmbed operates in two stages. In the first stage called role-aware interactive fine-tuning, we fine-tune LMs based on role-specific representations and an interaction diagnoser to bridge the semantic gap of CD models. In the second stage called adapter-aware representation integration, we employ a textual adapter to extract task-relevant semantics and integrate them with existing modeling paradigms to improve generalization across diverse CD tasks. We evaluate the proposed framework on four CD tasks and computerized adaptive testing (CAT) task, achieving robust performance. Further analysis reveals the impact of semantic information across diverse tasks, offering key insights for future research on the application of LMs in CD for online intelligent education systems.
Online game advertising is a prominent class of Web-mediated interactive services, where understanding and predicting player Lifetime Value (LTV) is a core scientific challenge in Web-scale user modeling, personalization, and digital economy optimization. However, the LTV prediction task poses severe challenges to traditional methods, which include data sparsity and complex distribution characteristics (such as zero-inflation, long tail, multimodal distribution, and cross-game). Existing methods struggle to capture the realistic and complex LTV distributions and exhibit limitations in leveraging cross-game data. We propose the first cross-game dynamic mixture framework with weighted sub-distributions for LTV prediction, DynaMoLTV. DynaMoLTV primarily models complex distributions via a zero-inflated mixture of lognormal (ZIMLN) loss, incorporates a game expert for cross-game data adaptation, employs a hierarchical payment classifier to capture consumption pattern variations, and integrates coarse and fine-grained losses to balance high-value user identification with LTV prediction accuracy. We conduct comprehensive experiments. The results demonstrate that DynaMoLTV achieves the best performance compared to five state-of-the-art baselines across metrics, including paid user identification, high-value user recall and LTV prediction accuracy. Specifically on three gaming datasets, DynaMoLTV reduces RMSE by 0.76%–46.65%, improves AUC by 0.94%–7.11%, and improves Norm-GINI by 0.63%–11.77% compared to five state-of-the-art baselines. DynaMoLTV also significantly improves ranking capabilities, with Recall@50K increasing by 17.64%–577.78%. We validate DynaMoLTV's effectiveness through two online A/B tests: (1) In the scenario of churned user re-engagement, DynaMoLTV increases online LTV by 20.3%-142.6% and downloads by 22.6%-37.7%. (2) In the scenario of online game advertising, DynaMoLTV increases GMV by 1.89% and GMV(ROI) by 27.31%. Our method has been fully deployed in a Web-based online game advertising platform, which ensures that LTV predictions remain personalized for online gaming ad delivery, supporting smarter and more inclusive decision-making on the Web.
The prediction objectives of online advertisement ranking models are evolving from probabilistic metrics like conversion rate (CVR) to numerical business metrics like post-click gross merchandise volume (GMV). Unlike the well-studied delayed feedback problem in CVR prediction, delayed feedback modeling for GMV prediction remains unexplored and poses greater challenges, as GMV is a continuous target, and a single click can lead to multiple purchases that cumulatively form the label. To bridge the research gap, we establish TRACE, a GMV prediction benchmark containing complete transaction sequences rising from each user click, which supports delayed feedback modeling in an online streaming manner. Our analysis and exploratory experiments on TRACE reveal two key insights: (1) the rapid evolution of the GMV label distribution necessitates modeling delayed feedback under online streaming training; (2) the label distribution of repurchase samples substantially differs from that of single-purchase samples, highlighting the need for separate modeling. Motivated by these findings, we propose RepurchasE-Aware Dual-branch prEdictoR (READER), a novel GMV modeling paradigm that selectively activates expert parameters according to repurchase predictions produced by a router. Moreover, READER dynamically calibrates the regression target to mitigate under-estimation caused by incomplete labels. Experimental results show that READER yields superior performance on TRACE over baselines, achieving a 2.19% improvement in terms of accuracy. We believe that our study will open up a new avenue for studying online delayed feedback modeling for GMV prediction, and our TRACE benchmark with the gathered insights will facilitate future research and application in this promising direction. Our code and dataset are available at https://github.com/alimama-tech/OnlineGMV.
In industrial recommender systems, conversion rate (CVR) is often used for traffic allocation, but fails to fully reflect recommendation effectiveness as it does not account for refund rate (RFR). Thus, net conversion rate (NetCVR), the probability that a clicked item is purchased and not refunded, is proposed to better show true user satisfaction and business value. Unlike CVR, NetCVR prediction involves a more complex multi-stage cascaded delay feedback phenomenon. The two cascaded delays Click->Conversion and Conversion->Refund in NetCVR have opposite effects. Therefore, traditional CVR methods cannot be directly applied. At present, the lack of relevant open-source datasets and online continuous training schemes poses a challenge. To address these, we first introduce CAscadal Sequences of Conversion And Delayed rEfund (CASCADE), the first large-scale open dataset derived from Taobao app for online continuous NetCVR prediction. We further analyze CASCADE and derive three key insights: (1) NetCVR exhibits clear temporal patterns necessitating online continuous modeling; (2) Cascaded modeling CVR and RFR for NetCVR outperforms directly modeling NetCVR; and (3) delay time, which correlated with both CVR and RFR, is an important feature for NetCVR prediction. Based on these insights, we propose neT convErsion caScaded modeLing and debiAsing method (TESLA). This continuous method features a CVR-RFR cascaded architecture, stage-wise debiasing, and a delay-time-aware ranking loss for efficient NetCVR prediction. Experiments show that TESLA outperforms state-of-the-art methods on CASCADE, achieving an absolute improvement of 12.41% in RI-AUC and 14.94% in RI-PRAUC on NetCVR over the strongest baseline. We hope this work provides a new direction for online delayed feedback modeling in NetCVR prediction. Our code and dataset are available at https://github.com/alimama-tech/NetCVR.
Multi-modal recommendation has become essential with the rapid expansion of online platforms such as e-commerce and video-sharing applications. In this work, we focus on the Multi-Modal New Item Recommendation (MMNIR) problem, where items with multi-modal content but newly introduced items lack interaction history. The MMNIR problem is particularly challenging in two aspects: (1) a large number of new items are created rapidly over time without any interaction data, (2) not all existing interactions are equally useful, and it is non-trivial to identify informative behaviors from users with similar preferences. However, previous methods fail to identify users with similar preferences and to capture informative behaviors from historical data. Furthermore, conventional models primarily rely on simple co-occurring signals, leading to spurious neighbors and neglecting the informative behaviors of truly similar users with consistent preferences. To fill this gap, we propose Joint Similar User Exploration and Informative Behavior Guidance (SuperG) for solving the MMNIR problem. SuperG first proposes a similar user exploration module to identify users with similar preferences to the target user. Then it incorporates an informative behavior mining module to retrieve informative behaviors from both the target user and similar users' histories to support new item recommendation. Finally, SuperG proposes a behavior-guided hybrid recommendation module to incorporate the retrieved behavioral signals to guide the recommendation of new items. Our empirical study on three real datasets demonstrates that SuperG outperforms the state-of-the-art models under the MMNIR setting.
Watch time prediction (WTP) has emerged as a pivotal task in short video recommendation systems, designed to quantify user engagement through continuous interaction modeling. Predicting users' watch times on videos often encounters fundamental challenges, including wide value ranges and imbalanced data distributions, which can lead to significant estimation bias when directly applying regression techniques. Recent studies have attempted to address these issues by converting the continuous watch time estimation into an ordinal regression task. While these methods demonstrate partial effectiveness, they exhibit notable limitations: (1) The discretization process frequently relies on bucket partitioning, inherently reducing prediction flexibility and accuracy. (2) The interdependencies among different partition intervals remain underutilized, missing opportunities for effective error correction. Inspired by language modeling paradigms, we propose a novel Generative Regression (GR) framework that reformulates WTP as a sequence generation task. Our approach employs structural discretization to enable nearly lossless value reconstruction while maintaining prediction flexibility. Through carefully designed vocabulary construction and label encoding schemes, each watch time is bijectively mapped to a token sequence. To mitigate the training-inference discrepancy caused by teacher-forcing, we introduce a curriculum learning with embedding mixup strategy that gradually transitions from guided to free-generation modes. We test our models extensively on two public datasets, a large-scale offline industrial dataset, and an online A/B test on Kuaishou App with over 400 million daily active users (DAU) and GR consistently outperforms existing state-of-the-art approaches significantly. Our code is available at https://github.com/snailma0229/GR.git.
Large language models (LLMs) have recently demonstrated strong potential for sequential recommendation. However, current LLM-based approaches face critical limitations in modeling users' long-term and diverse interests. First, due to inference latency and feature fetching bandwidth constraints, existing methods typically truncate user behavior sequences to include only the most recent interactions, resulting in the loss of valuable long-range preference signals. Second, most current methods rely on next-item prediction with a single predicted embedding, overlooking the multifaceted nature of user interests and limiting recommendation diversity. To address these challenges, we propose HyMiRec, a hybrid multi-interest sequential recommendation framework, which leverages a lightweight recommender to extracts coarse interest embeddings from long user sequences and an LLM-based recommender to captures refined interest embeddings. To alleviate the overhead of fetching features, we introduce a residual codebook based on cosine similarity, enabling efficient compression and reuse of user history embeddings. To model the diverse preferences of users, we design a disentangled multi-interest learning module, which leverages multiple interest queries to learn disentangles multiple interest signals adaptively, allowing the model to capture different facets of user intent. Extensive experiments are conducted on both benchmark datasets and a collected industrial dataset, demonstrating our effectiveness over existing state-of-the-art methods. Furthermore, online A/B testing shows that HyMiRec brings consistent improvements in real-world recommendation systems.
Multimodal recommendation advocates integrating the multimodal features of items with historical user behaviors to enhance recommendation accuracy across various online media platforms. The majority of existing methods concentrate on leveraging cross-modal learning over multimodal features to augment node representations. However, these approaches are confronted with two key challenges: i) augmented representations offer limited information gain for interactive prediction in the collaborative view, and ii) semantic discrepancy between the collaborative view and modality-augmented features remains inadequately addressed. To overcome these obstacles, we present a new Multi-view Semantic Contrastive Alignment (MSCA) approach for multimodal recommendation, which models and aligns node representations from multiple views. Specifically, we introduce a multi-view semantic pattern encoder that learns basic embeddings from the collaborative view and independently captures augmented semantic patterns from the item-item structural view and intra-modal view. Furthermore, a semantic contrastive alignment task is designed to mitigate the semantic divergence between collaborative embeddings and augmented representations by maximizing the mutual consistency between them, thereby facilitating an effective integration of both. Comprehensive experiments on three benchmark datasets confirm that the proposed MSCA consistently excels over diverse state-of-the-art baselines.
We study off-policy learning (OPL) in contextual bandits, which plays a key role in a wide range of real-world applications such as recommendation systems and online advertising. Typical OPL in contextual bandits assumes an unconstrained environment where a policy can select the same item infinitely. However, in many practical applications, including coupon allocation and e-commerce, limited supply constrains items through budget limits on distributed coupons or inventory restrictions on products. In these settings, greedily selecting the item with the highest expected reward for the current user may lead to early depletion of that item, making it unavailable for future users who could potentially generate higher expected rewards. As a result, OPL methods that are optimal in unconstrained settings may become suboptimal in limited supply settings. To address the issue, we provide a theoretical analysis showing that conventional greedy OPL approaches may fail to maximize the policy performance, and demonstrate that policies with superior performance must exist in limited supply settings. Based on this insight, we introduce a novel method called Off-Policy learning with Limited Supply (OPLS). Rather than simply selecting the item with the highest expected reward, OPLS focuses on items with relatively higher expected rewards compared to the other users, enabling more efficient allocation of items with limited supply. Our empirical results on both synthetic and real-world datasets show that OPLS outperforms existing OPL methods in contextual bandit problems with limited supply.