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You are given a 2D integer array intervals where intervals[i] = [starti, endi] represents all the integers from starti to endi inclusively. A containing set is an array nums where each interval from intervals has at least two integers in nums. For example, if intervals = [[1,3], [3,7], [8,9]], then [1,2,4,7,8,9] and [2,3,4,8,9] are containing sets. Return the minimum possible size of a containing set.

Full list of shortcuts is available via the app and the Adobe website. These are the shortcuts I use most often.

You are given an array of integers nums. You are also given an integer original which is the first number that needs to be searched for in nums. You then do the following steps: If original is found in nums, multiply it by two (i.e., set original = 2 * original). Otherwise, stop the process. Repeat this process with the new number as long as you keep finding the number. Return the final value of original.

# DDSSM-DSSS Physical Guided SceneGen ## Overview DDSSM-DSSS-Physical-Guided-SceneGen is a research-oriented implementation inspired by the paper *“A film and television dynamic scene generation and special effects synthesis system integrating diffusion model and physical guidance mechanism” by Wenxiao Du and Xupeng Yao*. The system targets the challenges of generating visually compelling, physically consistent, and narratively coherent dynamic scenes for film and television production. :contentReference[oaicite:2]{index=2} Two major components define the framework: - **Diffusion-Driven Scene Synthesis Model (DDSSM)** A multimodal, diffusion-based latent scene generator that iteratively refines noisy latent states into visually detailed and semantically coherent scenes. - **Dynamic Scene Synthesis Strategy (DSSS)** A physics-informed refinement mechanism enforcing realism by embedding motion laws, collision dynamics, and structural constraints throughout generation. Together, these components provide a unified pipeline for synthesizing dynamic scenes that balance creativity with physical correctness. --- ## Core Concepts ### Diffusion-Driven Scene Synthesis Model (DDSSM) DDSSM uses a forward–reverse diffusion process to transform latent representations into high-quality scenes. The forward process gradually injects Gaussian noise into a latent vector, while the reverse process uses a neural network to denoise the representation step by step. Key characteristics include: - A **multimodal encoder** integrating visual, textual, and audio cues (see Figure 2, page 6) to build a unified latent scene space. :contentReference[oaicite:3]{index=3} - A **variational diffusion objective** minimizing reconstruction divergence across the reverse diffusion steps. - A **latent Markov chain** that refines representations by incorporating spatial–temporal structure (Figure 1, page 5). :contentReference[oaicite:4]{index=4} - A **feature refinement mechanism** addressing ambiguities across modalities. This architecture enables the model to generate complex, temporally coherent visual behaviors, such as motion trajectories or special effects dynamics. --- ### Physically-Guided Synthesis Strategy (DSSS) The DSSS module enforces physical plausibility during scene generation. It integrates: - **Gravity constraints** Ensuring objects exhibit proper downward acceleration. - **Momentum and collision laws** Guiding object trajectories and post-collision behavior. - **Structural stability constraints** Maintaining consistent spatial configurations. - **A feedback loop mechanism** Iteratively evaluating and correcting physical errors using: *F(x) = α·C(x) + β·P(x)* (page 7). :contentReference[oaicite:5]{index=5} The feedback loop continuously refines scenes to ensure consistency between visual frames and the physical world. --- ## Multimodal Encoder Design The multimodal encoder (Figure 2, page 6) integrates heterogeneous sources such as: - image streams - audio cues - textual prompts - structural annotations Using multiple Transformer layers, cross-modal attention, and feature stacking, the encoder produces stable and expressive latent codes for downstream diffusion. The model also supports extended multimodal physiological encoders (Figure 4, page 14), which can be incorporated for certain advanced applications. :contentReference[oaicite:6]{index=6} --- ## Model Architecture Summary The full system contains three primary pipelines: ### 1. Multimodal Encoding - Extracts spatial, temporal, and semantic cues. - Aligns modalities through attention integration. - Produces initial latent vector z₀ for diffusion. ### 2. Diffusion-Guided Scene Synthesis - Forward noise injection. - Reverse denoising with physical modifications. - Constraint-based latent refinement. ### 3. Physics-Guided Dynamic Refinement - Ensures consistent movement (e.g., falling, collisions). - Enforces real-world constraints. - Guarantees frame-to-frame temporal coherence. --- ## Applications This project is suited for: - Film & TV special effects generation - Virtual cinematography - Digital scene prototyping - Realistic motion & dynamics simulation - Physically consistent video generation --- ## Limitations While powerful, the system faces constraints: - High computational cost from diffusion processes. - Physiological and motion constraints may reduce creative freedom. (Page 10) :contentReference[oaicite:7]{index=7} - Requires careful tuning of physics–aesthetics balance. --- ## Future Directions Based on the paper’s discussion: - accelerating diffusion steps for real-time use - adaptive physical realism (user-adjustable physical strictness) - richer multimodal integration (speech, depth, optical flow) - hybrid differentiable physics engines --- ## Citation If you find this repository useful, please cite the original authors: > Wenxiao Du and Xupeng Yao. > *A film and television dynamic scene generation and special effects synthesis system integrating diffusion model and physical guidance mechanism.* > Faculty of Art and Design, Qilu University of Technology. --- ## License This implementation is intended for research, education, and prototyping only.

# DissemiGraph & SEM-GUIDE: Deep Learning for Fourth Classroom Content Dissemination This repository provides a reference implementation of **DissemiGraph** and **SEM-GUIDE**, a dual-module framework for recognizing and optimizing content dissemination patterns in the **Fourth Classroom** – informal, digitally mediated learning environments such as social platforms, online communities, and extra-curricular micro-learning spaces. :contentReference[oaicite:1]{index=1} The framework combines **graph neural networks**, **semantic-aware propagation**, and **strategic enhancement mechanisms** to both **model** and **actively guide** the spread of educational content in complex, decentralized ecosystems. --- ## 1. Background and Motivation The shift to digital and hybrid learning has extended education beyond traditional classrooms into what the authors describe as the **Fourth Classroom**: informal, interest-driven, and socially mediated learning spaces supported by digital platforms, social media, and micro-learning tools. Unlike conventional classroom environments, Fourth Classroom ecosystems are: - **Decentralized** – content is created, remixed, and shared by many actors. - **Dynamic** – topics, interests, and attention patterns change rapidly. - **Multimodal** – content may include text, images, video, and interaction traces. - **Weakly structured** – there is no fixed schedule or curated curriculum. :contentReference[oaicite:2]{index=2} Traditional dissemination models often assume static networks, homogeneous users, and simple diffusion rules. These assumptions fail to capture: - Temporal evolution of user interests and attention. - Semantic compatibility between content and learners. - The need for **active regulation** of dissemination to support pedagogy (not just virality). DissemiGraph and SEM-GUIDE are designed to fill this gap by offering: - A **semantics-aware graph model** of content spread. - A **strategic intervention mechanism** to improve educational impact while respecting user attention constraints. :contentReference[oaicite:3]{index=3} --- ## 2. Conceptual Overview The framework consists of two tightly coupled modules: 1. **DissemiGraph** – a deep graph model that predicts and analyzes content dissemination. 2. **SEM-GUIDE** – a strategic enhancement mechanism that actively steers dissemination toward pedagogical goals. :contentReference[oaicite:4]{index=4} ### 2.1 DissemiGraph DissemiGraph is designed to model **who** sees **what content**, **when**, and **with what semantic alignment**. Key ingredients: - **Content-Aware Initialization (CAI)** - Builds initial node embeddings for each learner from: - User profile and behavior history. - Content semantic embeddings from multimodal encoders (text, image, interaction). - Initial engagement estimates and temporal readiness features (activity rhythm, recency). :contentReference[oaicite:5]{index=5} - Produces rich, content-specific user states as the starting point of dissemination. - **Semantic-Guided Propagation (SGP)** - Message passing over the user interaction graph. - Neighbor influence is weighted by **semantic compatibility** between user profiles and content, using learnable projections and attention. - A gated recurrent update (e.g., GRU) maintains temporal continuity of user state while incorporating new messages. :contentReference[oaicite:6]{index=6} - **Temporal Dissemination Prediction (TDP)** - Uses recurrent states plus **temporal decay**, **semantic similarity**, and **learnable temporal smoothing** to estimate the probability that content will propagate between pairs of users at a given time. - Accounts for recency, interaction frequency, and noisy or sporadic engagements. :contentReference[oaicite:7]{index=7} Together, these components allow DissemiGraph to model both **micro-level user interactions** and **macro-level dissemination trajectories**. --- ### 2.2 SEM-GUIDE **SEM-GUIDE (Strategic Enhancement Mechanism for Guided Dissemination)** builds on DissemiGraph’s predictions to **actively optimize** how content spreads. It includes three conceptual submodules: :contentReference[oaicite:8]{index=8} 1. **Strategic Node Selection** - Selects users to intervene on (for boosting, highlighting, or promoting content) based on: - Semantic alignment between user and content. - Temporal engagement volatility and current attention capacity. - Network connectivity and influence potential. - Produces an intervention score that highlights the best candidates for activation. 2. **Guided Message Recalibration** - Adjusts propagation probabilities for strategically selected nodes. - Uses semantic alignment to peers, content domain filters, and temporal weights to recalibrate how strongly these nodes influence their neighbors. - Incorporates feedback loops to refine enhancement strength over time. 3. **Adaptive Feedback Mechanism** - Compares **predicted** versus **actual** engagement rewards and updates intervention scores accordingly. - Uses a learning-rate style parameter (possibly time-varying) to stabilize adaptation. - Minimizes cumulative error between expected and observed behavior so the system becomes better at targeting high-impact nodes over time. SEM-GUIDE turns the model from a **passive observer** of content flow into an **active controller** that can implement strategies like: - Prefer targeting semantically well-aligned learners. - Balance speed of spread and depth of engagement. - Respect cognitive and attention budget constraints. --- ## 3. Data and Evaluation Context The original paper evaluates the framework on several **Fourth Classroom and classroom-related datasets**, including: - A dataset of Fourth Classroom content dissemination patterns. - Datasets on educational content delivery, classroom interaction, and optimized content flow. :contentReference[oaicite:9]{index=9} Key aspects of the experimental setup: - Multimodal feature extraction from video, audio, textual transcripts, and engagement markers. - Training with state-of-the-art deep learning tooling, using metrics such as **Precision**, **Recall**, **F1 Score**, and **AUC**. - Comparisons against competitive baselines such as BERT-CRF, BiLSTM-CRF, ELECTRA, SpanBERT, FLERT, and T5-NER. :contentReference[oaicite:10]{index=10} The proposed method demonstrates: - Higher semantic coherence in predicted dissemination paths. - Improved dissemination efficiency and control. - Significant performance gains across datasets in F1 and AUC. :contentReference[oaicite:11]{index=11} --- ## 4. Intended Usage of This Repository This repository is designed to serve as: - A **research reference** for implementing graph-based, semantics-aware dissemination models in educational contexts. - A **sandbox** for experimenting with: - Different user graph structures. - Alternative content encoders (e.g., domain-specific language models). - Modified intervention strategies and reward functions. Typical use cases include: - Analyzing how learning resources spread in institutional or community learning platforms. - Designing intelligent **recommendation and boosting policies** for high-value educational content. - Studying trade-offs between exposure, engagement, and cognitive load in Fourth Classroom ecosystems. --- ## 5. High-Level API Sketch A typical pipeline using the provided implementation could look like: 1. Build a **user interaction graph** with edges representing interactions or relationships in your platform. 2. Compute content embeddings and user profiles using your favorite encoders. 3. Construct a `FourthClassroomBatch` containing: - Node features, content features, and temporal sequences. - Edge indices and any semantic or temporal metadata. 4. Call the main model to obtain: - Dissemination probabilities between users. - Strategically adjusted predictions under SEM-GUIDE. - Auxiliary diagnostics such as intervention scores or semantic alignment metrics. You can then plug these outputs into: - Simulation environments to test dissemination policies. - Real-time systems that trigger notifications, highlights, or recommendations. --- ## 6. Limitations and Future Directions While powerful, this framework has several limitations: - It assumes **reasonable quality semantic embeddings**; noisy or low-resource languages may require additional pretraining or adaptation. - It focuses on dissemination and engagement, not directly on **learning outcomes** such as knowledge gain or skill mastery. - Real-world deployment must consider **privacy, ethics, and fairness**, particularly when using fine-grained behavior signals or spiking-style architectures (as described in the SEM-GUIDE figures). :contentReference[oaicite:12]{index=12} Future extensions might include: - Integration with learning analytics to directly optimize for learning gains. - More explicit modeling of **fair exposure** and **equity of access** to high-quality content. - Better support for cross-lingual and cross-cultural Fourth Classroom scenarios.

# BACE-CICI Multimodal Assessment ## Overview BACE-CICI-Multimodal-Assessment is a research-style implementation inspired by the paper **“Multimodal Fusion for Analyzing English Learning Behaviors and Competence Assessment” by Long Shi**. The repository explores how multimodal behavioral data and curriculum optimization can be combined to model learner competence and generate adaptive instructional paths. :contentReference[oaicite:1]{index=1} The framework centers on two key components: - **Behaviorally Augmented Competence Embedding (BACE)** A multimodal encoder that fuses linguistic complexity, behavioral signals, and task descriptors into a unified competence embedding. - **Competence-Informed Curriculum Inference (CICI)** A curriculum strategy that selects tasks based on predicted competence gains, feasibility constraints, and topical coherence, effectively turning curriculum sequencing into a constrained optimization problem over competence trajectories. :contentReference[oaicite:2]{index=2} This repository is intended for experimentation and demonstration, rather than production use. --- ## Core Ideas ### Behaviorally Augmented Competence Embedding (BACE) BACE models the interaction between: - **Task descriptors** Including linguistic content, task difficulty and complexity features. - **Behavioral logs** Response correctness, response latency, revision counts and other behavioral markers. - **Latent competence** A low-dimensional representation of a learner’s current state, evolving over time as more tasks are completed. :contentReference[oaicite:3]{index=3} The model pipeline can be summarized as: 1. Encode the task text into a dense representation using a language encoder. 2. Map behavioral tuples into a behavioral embedding space. 3. Project task difficulty and structural descriptors into a complexity embedding. 4. Fuse all representations with a gated mechanism that allows behavior signals to dominate when textual information is ambiguous. 5. Use attention-based pooling over a learner’s history to obtain a global competence embedding. 6. Predict task-level success probabilities and competence trajectories, while regularizing for smooth progression over time. :contentReference[oaicite:4]{index=4} ### Competence-Informed Curriculum Inference (CICI) CICI treats curriculum design as an optimization problem over the latent competence space: - It computes **competence gaps** between the learner’s current state and each candidate task. - A feasibility mask ensures that only tasks within a reasonable difficulty band are considered. - The algorithm estimates the **expected learning gain** for each feasible task, balancing reinforcement against cognitive load. :contentReference[oaicite:5]{index=5} - A coherence constraint encourages smooth topic transitions between consecutive tasks. - Curriculum segments are selected to maximize cumulative reward while discouraging redundant or overly similar tasks. The result is an adaptive curriculum that aligns short-term difficulty with long-term competence development. --- ## High-Level Architecture Conceptually, the repository is organized into: - A **model module** that implements: - text encoding - behavioral encoding - complexity encoding - multimodal fusion - competence inference and prediction heads - A **training and curriculum module** that: - maintains learner histories - updates competence embeddings - invokes the CICI strategy to select the next tasks The implementation focuses on clarity and extensibility rather than maximum efficiency. --- ## Data Assumptions The framework assumes that each interaction example contains: - A **task** with: - raw text or a text identifier - scalar difficulty score - a vector of complexity features - A **learner behavior record** with: - a binary correctness label - response time - auxiliary behavioral features (for example revision counts or hesitation indicators) - A **learner identifier** so that multiple interactions can be grouped into a chronological session. Real-world multimodal deployments may additionally integrate audio, video, and gaze signals, but those are abstracted as generic behavioral features in this reference implementation. :contentReference[oaicite:6]{index=6} --- ## Intended Usage This project is intended for: - Researchers working on: - multimodal learning analytics - competence modeling - adaptive curriculum design - Engineers prototyping: - behavior-aware recommendation for learning platforms - learner modeling components inside intelligent tutoring systems - Educators and learning designers exploring: - how behavioral logs can be turned into interpretable competence trajectories - how data-driven curricula differ from static placement and sequencing The code is designed to be modified and extended to fit specific datasets and evaluation protocols. --- ## Limitations - The implementation is **simplified** relative to the full framework described in the paper and does not directly process raw audio or video streams. - The quality of competence estimation depends strongly on: - dataset size and coverage - reliability of behavioral annotations - diversity of tasks and difficulty levels - CICI assumes consistent engagement and does not explicitly model motivational or affective factors, which may be important in real educational environments. :contentReference[oaicite:7]{index=7} --- ## Future Work Potential extensions include: - Integration with real multimodal encoders for audio and video. - More advanced sequence models for long-term competence evolution. - Richer diversity and fairness constraints in curriculum optimization. - Dashboards to visualize learner trajectories and curriculum recommendations. - Interfaces to plug the model into real online learning platforms. --- ## Citation If this repository or its ideas are useful in your work, please consider citing the original paper: > Long Shi. *Multimodal Fusion for Analyzing English Learning Behaviors and Competence Assessment*. School of Foreign Languages, Pingdingshan University. --- ## License This project is provided for academic research and educational exploration only. Before using it in any real educational product, please review ethical, privacy, and fairness implications carefully.