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You are given an integer array nums and two integers, x and k. You can perform the following operation any number of times (including zero): Increase or decrease any element of nums by 1. Return the minimum number of operations needed to have at least k non-overlapping subarrays of size exactly x in nums, where all elements within each subarray are equal.

Generate a report of published courses with there published singular fees and tuition fee text as well as whether they have been overridden.

# README # RepresentationGraphEquilibrium (RGE) **An ELSI-aware graph-learning framework for structured stakeholder and survey data** RepresentationGraphEquilibrium (RGE) is a graph-based multiclass prediction framework designed to model relationships among heterogeneous Ethical, Legal, and Social Implications (ELSI) attributes and contextual variables. The framework combines feature-block representation learning, predictor-derived graph aggregation, representation consistency regularization, and fixed-point equilibrium inference. This repository provides a research-oriented implementation of the core RGE architecture described in the paper: > **Prediction of Technology Acceptance, Ethical Cognition, Genomic Data-Sharing Decisions, and Responsible Innovation Capacity with RepresentationGraphEquilibrium: An ELSI-Aware Approach** > > > **Author:** Bin Zhan > > **Affiliation:** Zhejiang A&F University, Hangzhou, Zhejiang, China > The implementation is intended to support transparent experimentation and reproducible model development. Dataset-specific preparation, graph construction, training, validation, and evaluation should be carried out according to the protocol documented in the accompanying study. --- ## 1. Research Overview Genomics education and innovation involve multiple related but distinct dimensions. These include genomic knowledge, educational experience, ethical cognition, data-sharing intentions, data-governance concerns, and responsible innovation practices. Conventional predictive approaches often analyze these outcomes independently and may not explicitly represent the relationships among heterogeneous stakeholder records. RGE addresses this modeling problem by representing each respondent or organizational record as a node and constructing weighted graph relations from non-target predictor similarity. The graph is computationally derived from the observed feature space. It must not be interpreted as a directly observed social, communication, or organizational network. The model is evaluated on four three-class prediction tasks: | Task | Abbreviation | Prediction target | Role in the study | | --- | --- | --- | --- | | Familial Genomic Sharing Intention | FGSI | Stated willingness to share whole-genome sequencing results with close biological relatives | Genomics-specific task | | Genomic Technology Ethical Cognition | GTEC | Empirical moral-judgment profile toward genetic technologies | Genomics-specific task | | Genomic Data-Sharing ELSI | GDS-ELSI | Willingness to share genomic and health information with for-profit researchers | Genomics-specific task | | Responsible Innovation Capacity | RIC | Cross-sectional responsible-innovation capacity category | External responsible-innovation transfer task | The FGSI outcome is a familial genomic-sharing intention measure. It is not a direct measure of general technology adoption or technology acceptance. The RIC task is an external responsible-innovation setting and should not be presented as direct evidence of genomics-specific organizational behavior. ## 2. Core Architecture RGE consists of three interconnected components, supported by an ELSI-aware input encoder. ### 2.1 ELSI-Aware Input Encoder The input representation is organized into four feature blocks: - **Ethical (E):** available ethical attitudes, judgments, or related attributes. - **Legal and Governance (L):** available privacy, consent, access, security, or governance attributes. - **Social (S):** available social and stakeholder-related attributes. - **Contextual (C):** educational, demographic, organizational, or other contextual variables. Each available block is encoded independently. A learnable scalar gate is computed for each block, and the gated block representations are fused into an initial node representation. A source dataset is not required to contain all four blocks. Missing dimensions should remain unavailable rather than being invented or transferred from another dataset. The block gates describe the model’s relative use of available predictor groups. They are not normative measures of ethical importance. ### 2.2 Graph Structure Aggregator (GSA) The GSA propagates information through a sparse, weighted similarity graph. Pairwise similarities are calculated using non-target predictors, with block-wise distances normalized by the dimensionality of each feature block. For each available block, the similarity kernel is: [ s_{ij}^{(b)} = (-). ] The available block similarities are aggregated to obtain the record-level relation score. A top-(k) neighborhood rule is then applied. The study uses (k=8), and the union of directed neighborhood selections produces a symmetric graph. Self-connections are added before symmetric degree normalization. The resulting normalized adjacency matrix is used to aggregate neighboring latent representations. An edge represents similarity in observed predictor space. It does not establish that two respondents interacted, belonged to the same organization, or influenced one another. ### 2.3 Representation Consistency Enforcer (RCE) The RCE encourages local coherence among records connected by high-confidence graph relations. The consistency subset is selected using the 75th percentile of nonzero training-graph edge weights. The consistency loss is combined with supervised classification and a variance-preservation term. This combination reduces the risk of representation collapse while retaining task-discriminative information. [ *{con} =* {(i,j)*{con}} A*{ij}|h_i*-h_j*|_2^2. ] The variance regularizer penalizes latent dimensions whose standard deviation falls below the target dispersion (). ### 2.4 Equilibrium State Solver (ESS) The ESS repeatedly updates the node representations using a deterministic graph-conditioned transition operator: [ U^{(t)} = H^{(t)}W_s + H^{(t)}W_g + H^{(0)}W_x + b_e, ] [ H^{(t+1)} = (1-)H^{(t)}+ (U^{(t)}). ] The damping coefficient is (). The solver stops when the relative fixed-point residual falls below (10^{-4}), or when the maximum of 50 iterations is reached. The equilibrium iteration index is a computational solver step. It is not longitudinal time and does not represent temporal change in the underlying population. ### 2.5 Prediction and Optimization The converged node representations are passed to a three-class prediction head. The training objective combines class-weighted cross-entropy, representation consistency, and variance preservation: [ = *{cls} +*{con}*{con} +*{var}_{var}. ] The study specifies (*{con}=0.10), (*{var}=0.05), and (). The reported optimizer is AdamW, with an initial learning rate of (10^{-3}), weight decay of (5^{-4}), and a maximum of 300 training epochs. --- ## 3. Datasets and Prediction Tasks The study derives four task-specific analysis datasets from publicly documented survey resources. The source data are not distributed as part of this repository. Users must obtain the data from the original source and comply with the corresponding access and reuse conditions. | Dataset | Records | Retained raw predictors | Target classes | | --- | --- | --- | --- | | FGSI | 112 | 7 | Low, moderate, high | | GTEC | 250 | 25 | Restrictive, intermediate, permissive | | GDS-ELSI | 1,229 | 18 | No, unsure, yes | | RIC | 740 | 24 | Low, moderate, high | ### 3.1 FGSI The FGSI analysis uses a university-based survey of young adults aged 18–25. The target is constructed from the mean stated intention to share whole-genome sequencing results with parents and siblings. The original 0–10 response scale is grouped into low (≤4), moderate (>4 and <7), and high (≥7) categories. Seven non-target predictors are retained: age, gender, previous genetics education, highest completed educational level, STEMM-field status, prior WGS awareness, and genetics-knowledge score. The two sharing-intention variables are excluded from the predictor matrix. The source article and supplementary materials are identified in the paper as: - Barnard et al. (2019), *Young adults’ attitudes to sharing whole-genome sequencing information: a university-based survey*. - DOI: `10.1186/s12920-019-0499-2`. ### 3.2 GTEC The GTEC analysis uses the 2025 Greek validation of the Genetic Technologies Questionnaire (GTQ-GR). The target is derived from the mean moral-judgment score on the original six-point scale: - Restrictive: score < 3.0 - Intermediate: 3.0 to < 4.5 - Permissive: score ≥ 4.5 The analysis retains 25 non-target predictors. GTQ-GR outcome items are excluded from the predictor matrix. The paper identifies the Open Science Framework project **Genetic Technologies Questionnaire - Greek Validation**, project identifier `YUD83`, as the data source. ### 3.3 GDS-ELSI The GDS-ELSI analysis uses the Italian component of the *Your DNA, Your Say* survey. It examines willingness to share genomic and health information with for-profit researchers. Eighteen non-target predictor fields are retained after removing identifiers, the target item, and duplicated target information. The paper identifies the Open Science Framework resource with DOI `10.17605/OSF.IO/ZPFGM`. The repository includes the survey data, data dictionary, study-design documentation, and questionnaire. The source resource is released under CC BY 4.0 according to the paper. ### 3.4 RIC The RIC analysis uses anonymized RRING Global Survey data on responsible research and innovation and competitive advantage. The target is derived from a normalized composite of responsible-research-and-innovation practice items and grouped into low, moderate, and high categories. The paper identifies the Zenodo resource with DOI `10.5281/zenodo.4972762`. The RIC task is treated as an external responsible-innovation transfer setting, not as a genomics-specific dataset. --- ## 4. Experimental Protocol The paper evaluates each task using five repetitions of stratified five-fold cross-validation, producing 25 matched outer-test evaluations per task. The same outer partitions are used for all compared models. Preprocessing parameters and graph-construction quantities must be fitted using the training partition only. These include continuous-variable normalization, categorical encoding dictionaries, missing-value statistics, block-specific similarity bandwidths, and the representation-consistency threshold. Training, validation, and test graphs are constructed separately. No graph edge should cross partition boundaries. Target labels and variables used to construct target labels must be excluded from graph construction. The primary metric is Macro-F1. Complementary metrics include accuracy, balanced accuracy, macro-averaged one-vs-rest AUROC, and macro-averaged one-vs-rest AUPRC. The study also considers calibration, predictive uncertainty, subgroup behavior, feature-block sensitivity, relational explanations, and graph-construction robustness. ### 4.1 Baseline Models The reported comparison includes the following tabular and graph-learning methods: - XGBoost - FT-Transformer - TabPFN - Graph Convolutional Network (GCN) - Graph Attention Network (GAT) - GraphSAGE The baseline implementations should use the same outer-test partitions and a documented, validation-based model-selection procedure. ### 4.2 Reported Macro-F1 Improvements The paper reports the following improvements over the strongest non-RGE comparator: | Task | Strongest non-RGE comparator | RGE Macro-F1 gain | | --- | --- | --- | | FGSI | TabPFN | +3.19 percentage points | | GTEC | TabPFN | +2.61 percentage points | | RIC | GraphSAGE | +2.49 percentage points | | GDS-ELSI | GraphSAGE | +1.92 percentage points | These are results reported in the paper and should not be treated as results reproduced by this repository until the experiments have actually been run. --- ## 5. Repository Contents A suggested organization for a complete research implementation is: - `README.md` — project overview, method description, data provenance, and reproduction notes. - `model.py` — core PyTorch implementation of the RGE architecture. Only `README.md` and the core model module are provided in this initial repository package. The remaining components should be added when their dataset-specific and experimental implementations are prepared. --- ## 6. Implementation Notes The accompanying model module implements the neural architecture and its principal training losses. It expects preprocessed feature blocks and a graph adjacency matrix as inputs. It does not automatically infer which questionnaire items are ethical, legal/governance, social, contextual, or target-defining variables. The dataset-specific preprocessing and target-construction rules must be implemented from the source questionnaires and data dictionaries. In particular: 1. Remove identifiers and all target-defining variables from the predictor space. 2. Fit preprocessing transformations on the training partition only. 3. Preserve block availability information rather than fabricating unavailable ELSI dimensions. 4. Estimate block similarity bandwidths from the training partition. 5. Construct separate graphs for training, validation, and test partitions. 6. Store the random seed, repetition, fold, preprocessing state, and graph parameters for each experiment. 7. Select model checkpoints using validation performance rather than test performance. The graph-building procedure described in the paper uses pairwise predictor similarity and a top-eight neighborhood rule. For large datasets, a memory-efficient nearest-neighbor implementation is recommended instead of materializing a full pairwise similarity matrix. The fixed-point solver in `model.py` uses differentiable unrolled iterations. This is a direct and transparent implementation strategy, but it may consume substantial memory when gradients are retained through all solver steps. For larger experiments, checkpointing or an implicit differentiation implementation can be considered and should be documented as an implementation change. --- ## 7. Reproducibility and Responsible Use The model predicts empirically defined survey or stakeholder-level categories. It does not determine whether a particular genomic data-sharing decision is ethically correct, whether a person should disclose genomic information, or whether an organization is normatively responsible. Graph edges represent predictor-space similarity, not observed social ties or causal relationships. Learned feature gates and relational influence values describe model behavior conditional on the available variables and modeling procedure. They should not be interpreted as causal effects or normative rankings. Subgroup metrics should be reported with sample counts and uncertainty estimates. Small subgroup sizes can produce unstable estimates. Predictive performance alone is not a fairness certification. The original datasets contain previously collected human-participant information. Users should follow the original repositories’ access terms, licenses, ethical documentation, and data-protection requirements. Do not upload identifiable participant information or restricted source files to a public repository. --- ## 8. Citation If this implementation is used in academic work, cite the original paper: **Bin Zhan.** *Prediction of Technology Acceptance, Ethical Cognition, Genomic Data-Sharing Decisions, and Responsible Innovation Capacity with RepresentationGraphEquilibrium: An ELSI-Aware Approach.* Please replace this provisional citation with the final journal citation, DOI, and publication details when they are available. --- ## 9. License No software license is specified in the paper excerpt used to prepare this repository package. Add a license only after the repository owner has selected the intended terms and confirmed that all included code and materials can be distributed under those terms. The licenses of the source datasets remain separate from the license of this code repository. Dataset reuse must follow the original source conditions. --- ## 10. Disclaimer This repository is a research implementation of the RGE model architecture described in the cited study. The core model module is not, by itself, a complete reproduction pipeline. Exact reproduction requires the original task-specific data, preprocessing decisions, graph construction, baseline configurations, random-seed schedule, and evaluation procedure. The model is intended for research and methodological evaluation. It should not be used as an automated decision authority for clinical care, genomic disclosure, participant eligibility, institutional governance, or ethical adjudication.

You are given an integer array nums. In one move, you may increase the value of any single element nums[i] by 1. Return the minimum total number of moves required so that all elements in nums become equal.

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal. In one move, you can increment or decrement an element of the array by 1. Test cases are designed so that the answer will fit in a 32-bit integer.

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal. In one move, you can increment n - 1 elements of the array by 1.

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Given an m x n binary grid grid where: grid[i][j] == 0 represents an empty cell, and grid[i][j] == 1 represents a mirror. A robot starts at the top-left corner of the grid (0, 0) and wants to reach the bottom-right corner (m - 1, n - 1). It can move only right or down. If the robot attempts to move into a mirror cell, it is reflected before entering that cell: If it tries to move right into a mirror, it is turned down and moved into the cell directly below the mirror. If it tries to move down into a mirror, it is turned right and moved into the cell directly to the right of the mirror. If this reflection would cause the robot to move outside the grid boundaries, the path is considered invalid and should not be counted. Return the number of unique valid paths from (0, 0) to (m - 1, n - 1). Since the answer may be very large, return it modulo 109 + 7. Note: If a reflection moves the robot into a mirror cell, the robot is immediately reflected again based on the direction it used to enter that mirror: if it entered while moving right, it will be turned down; if it entered while moving down, it will be turned right. This process will continue until either the last cell is reached, the robot moves out of bounds or the robot moves to a non-mirror cell.

You are given an integer n representing the number of nodes in a directed weighted graph, numbered from 0 to n - 1. This is represented by a 2D integer array edges, where edges[i] = [ui, vi, wi] represents a directed edge from node ui to node vi with weight wi. You are also given a string labels of length n, where labels[i] is the character assigned to node i, and an integer k. Return the minimum total edge weight of a path from node 0 to node n - 1 such that the concatenation of the labels of the nodes along the path contains at most k consecutive identical characters. If no valid path exists, return -1.