Size Of Set Research Articles

Encrypted Search Method for Cloud Computing Data Under Attack Based on TF-IDF and Apriori Algorithm

ABSTRACT This paper designs the MKSE and SEMSS methods. Among them, MKSE uses an improved TF-IDF weight calculation method to extract keywords and applies virtual keywords to construct inverted indexes, making it difficult for malicious attackers to infer the index content easily. SEMSS uses the Apriori algorithm to mine the co-occurrence relationship between words and find the keyword set that meets the minimum support threshold to improve the recall rate of search results. Finally, the security of the scheme is verified from the aspects of semantic security, effici this paper designsency, data integrity, etc. The results showed that the data encryption time of MKSE and TRSE methods increased gradually with the increase in document collection storage. The index build time was increased as the document set grew. The accuracy of the improved TF-IDF method was 63.8%. The running time of Apriori decreased with the increase of minimum support. When the minimum support was 12.0%, the Apriori algorithm ran for 211 seconds. The MKSE method was more efficient than the TRSE method in searching documents by query keywords. When the document set size was 3000, the SEMSS method had a full search rate of 81.09%. This research realizes the semantic security of outsourced data, which can efficiently and comprehensively carry out cryptographic retrieval based on keyword sorting.

A Method for the Rapid Identification of Rice Seed Blast Using Deep Learning and Hyperspectral Imagery

Rice seeds’ infection with rice blast will directly lead to rice yield reduction or even crop failure in the next year. Therefore, it is very important accurately identify infected rice seeds. In this study, deep learning and hyperspectral imaging techniques were used for that purpose. First, hyperspectral image data were collected. Then, the UeAMNet (unsupervised extraction attention-based mixed CNN) model—designed in this study—was used to analyze these data and the results compared with the 2DCNN, 3DCNN, A2DCNN, A3DCNN, Ue2DCNN, Ue3DCNN, UeA2DCNN, UeA3DCNN, MNet, AMNet and UeMNet models using different training set (Tr) sizes. The results showed that the new UeAMNet model was superior to the comparison models when using different Tr sizes, and the accuracy could reach 100%. Notably, when Tr was only 0.05, the accuracy of this model still reached 96.85%. This showed that the proposed method could successfully identify infected rice seeds. Therefore, this study provides an approach for rice germplasm management and also for the development of crop disease identification methods in other parts of the world.

A multi-party quantum private set intersection based on greatest common divisor

Private set intersection (PSI) is a cryptographic primitive that allows two or more parties to learn the intersection of their input sets and nothing else. In this paper, we introduce a new secure multi-party quantum computation for the greatest common divisor (GCD) and a PSI protocol based on it. The protocol extends the recent least common multiple (LCM)-based quantum private set union protocol by Liu et al. Performance analysis verifies the correctness and demonstrates the entire security of the suggested protocols in the semi-honest model. Additionally, it has been demonstrated that the complexity is efficient in terms of the input set size.

Feature Selection for Physical Activity Prediction Using Ecological Momentary Assessments to Personalize Intervention Timing: Longitudinal Observational Study.

There has been a surge in the development of apps that aim to improve health, physical activity (PA), and well-being through behavior change. These apps often focus on creating a long-term and sustainable impact on the user. Just-in-time adaptive interventions (JITAIs) that are based on passive sensing of the user's current context (eg, via smartphones and wearables) have been devised to enhance the effectiveness of these apps and foster PA. JITAIs aim to provide personalized support and interventions such as encouraging messages in a context-aware manner. However, the limited range of passive sensing capabilities often make it challenging to determine the timing and context for delivering well-accepted and effective interventions. Ecological momentary assessment (EMA) can provide personal context by directly capturing user assessments (eg, moods and emotions). Thus, EMA might be a useful complement to passive sensing in determining when JITAIs are triggered. However, extensive EMA schedules need to be scrutinized, as they can increase user burden. The aim of the study was to use machine learning to balance the feature set size of EMA questions with the prediction accuracy regarding of enacting PA. A total of 43 healthy participants (aged 19-67 years) completed 4 EMA surveys daily over 3 weeks. These surveys prospectively assessed various states, including both motivational and volitional variables related to PA preparation (eg, intrinsic motivation, self-efficacy, and perceived barriers) alongside stress and mood or emotions. PA enactment was assessed retrospectively via EMA and served as the outcome variable. The best-performing machine learning models predicted PA engagement with a mean area under the curve score of 0.87 (SD 0.02) in 5-fold cross-validation and 0.87 on the test set. Particularly strong predictors included self-efficacy, stress, planning, and perceived barriers, indicating that a small set of EMA predictors can yield accurate PA prediction for these participants. A small set of EMA-based features like self-efficacy, stress, planning, and perceived barriers can be enough to predict PA reasonably well and can thus be used to meaningfully tailor JITAIs such as sending well-timed and context-aware support messages.

Evaluation of genomic and phenomic prediction for application in apple breeding

BackgroundApple breeding schemes can be improved by using genomic prediction models to forecast the performance of breeding material. The predictive ability of these models depends on factors like trait genetic architecture, training set size, relatedness of the selected material to the training set, and the validation method used. Alternative genotyping methods such as RADseq and complementary data from near-infrared spectroscopy could help improve the cost-effectiveness of genomic prediction. However, the impact of these factors and alternative approaches on predictive ability beyond experimental populations still need to be investigated. In this study, we evaluated 137 prediction scenarios varying the described factors and alternative approaches, offering recommendations for implementing genomic selection in apple breeding.ResultsOur results show that extending the training set with germplasm related to the predicted breeding material can improve average predictive ability across eleven studied traits by up to 0.08. The study emphasizes the usefulness of leave-one-family-out cross-validation, reflecting the application of genomic prediction to a new family, although it reduced average predictive ability across traits by up to 0.24 compared to 10-fold cross-validation. Similar average predictive abilities across traits indicate that imputed RADseq data could be a suitable genotyping alternative to SNP array datasets. The best-performing scenario using near-infrared spectroscopy data for phenomic prediction showed a 0.35 decrease in average predictive ability across traits compared to conventional genomic prediction, suggesting that the tested phenomic prediction approach is impractical.ConclusionsExtending the training set using germplasm related with the target breeding material is crucial to improve the predictive ability of genomic prediction in apple. RADseq is a viable alternative to SNP array genotyping, while phenomic prediction is impractical. These findings offer valuable guidance for applying genomic selection in apple breeding, ultimately leading to the development of breeding material with improved quality.

Enhancing the accuracy of XPS calculations: Exploring hybrid basis set schemes for CVS-EOMIP-CCSD calculations.

Reliable computational methodologies and basis sets for modeling x-ray spectra are essential for extracting and interpreting electronic and structural information from experimental x-ray spectra. In particular, the trade-off between numerical accuracy and computational cost due to the size of the basis set is a major challenge, since molecular orbitals undergo extreme relaxation in the core-hole state. To gain clarity on the changes in electronic structure induced by the formation of a core-hole, the use of sufficiently flexible basis for expanding the orbitals, particularly for the core region, has been shown to be essential. This work focuses on the refinement of core-hole ionized state calculations using the equation-of-motion coupled cluster family of methods through an extensive analysis on the effectiveness of "hybrid" and mixed basis sets. In this investigation, we utilize the CVS-EOMIP-CCSD method in combination and construct hybrid basis sets piecewise from readily available Dunning's correlation consistent basis sets in order to calculate x-ray ionization energies (IEs) for a set of small gas phase molecules. Our results provide insights into the impact of basis sets on the CVS-EOMIP-CCSD calculations of K-edge IEs of first-row p-block elements. These insights enable us to understand more about the basis set dependence of the core IEs computed and allow us to establish a protocol for deriving reliable and cost-effective theoretical estimates for computing IEs of small molecules containing such elements.

Comparing innovative AI algorithms to assess echocardiographic videos for clinical modelling.

We conduct a comparative study that employs the use of multiple dynamic deep learning algorithms to develop predictive models with video-based echocardiographic images using sample size determination as a key variable to assess optimal performance metrics. Our study compares performance of 3D convolutional neural networks, video vision transformers, and hybrid convolutional neural networks and Long Short-Term Memory models within both supervised and semi-supervised domains using variable sample sizes. For supervised learning, the ResNet3D model achieved the lowest Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) across all training set sizes (200, 400, and 800-video datasets), with the best performance observed on the 800-video training set (MAE: 7.409, RMSE: 10.216). In the semi-supervised setting, both ResNet3D and ResNet+LSTM models benefited from the inclusion of unlabelled data, particularly at larger dataset sizes. Because semi-supervised models use both labelled and unlabelled data sets, our findings are significant in showing that performance of certain predictive models using mixtures of unlabelled and labelled data is comparable to those using only labelled data with similar sample sizes, thus obviating the need for large sample sizes of labelled data.

Constant-competitiveness for random assignment Matroid secretary without knowing the Matroid

Abstract The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an O(1)-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear one-by-one, revealing their weight at appearance, and the task is to select elements online with the goal to get an independent set of largest possible weight. O(1)-competitive MSP algorithms have so far only been obtained for restricted matroid classes and for MSP variations, including Random-Assignment MSP (RA-MSP), where an adversary fixes a number of weights equal to the ground set size of the matroid, which then get assigned randomly to the elements of the ground set. Unfortunately, these approaches heavily rely on knowing the full matroid upfront. This is an arguably undesirable requirement, and there are good reasons to believe that an approach towards resolving the MSP Conjecture should not rely on it. Thus, both Soto (SIAM Journal on Computing 42(1): 178-211, 2013.) and Oveis Gharan and Vondrák (Algorithmica 67(4): 472-497, 2013.) raised as an open question whether RA-MSP admits an O(1)-competitive algorithm even without knowing the matroid upfront. In this work, we answer this question affirmatively. Our result makes RA-MSP the first well-known MSP variant with an O(1)-competitive algorithm that does not need to know the underlying matroid upfront and without any restriction on the underlying matroid. Our approach is based on first approximately learning the rank-density curve of the matroid, which we then exploit algorithmically.

Fault-tolerant Verifiable Dynamic SSE with Forward and Backward Privacy

Dynamic Searchable Symmetric Encryption (DSSE) allows users to securely outsource their data to cloud servers while enabling efficient searches and updates. The verifiability property of a DSSE construction ensures that users do not accept incorrect search results from a malicious server while the fault-tolerance property guarantees the construction functions correctly even with faulty queries from the client (e.g., adding a keyword to a document multiple times, deleting a keyword from a document that was never added). There have been very few studies on fault-tolerant verifiable DSSE schemes that achieve forward privacy, and none of the existing constructions achieve backward privacy. In this paper, we aim to design an efficient fault-tolerant verifiable DSSE scheme that provides both forward and backward privacy. First, we propose a basic fault-tolerant verifiable DSSE scheme, dubbed FVS1 , which achieves forward privacy and stronger backward privacy with the update pattern (BPUP). However, the communication complexity for the search operation of this scheme is O ( u ) , where u is the total number of updates for the search keyword. To address this issue, we propose an efficient variant of the previous DSSE scheme, called FVS2 , which achieves the same functionality with an optimized communication complexity of O ( m + u ′ ) for search queries. Here m is the size of the result set and u ′ is the number of update operations made on the queried keyword after the previous search made on the keyword. This improvement comes at the cost of some additional information leakage, but it ensures the construction achieves backward privacy with the link pattern (BPLP).

Wannabe Bounded Treewidth Graphs Admit a Polynomial Kernel for Directed Feedback Vertex Set

In the Directed Feedback Vertex Set (DFVS) problem, given a digraph D and a positive integer k , the goal is to check if there exists a set of at most k vertices whose deletion from D results in a directed acyclic graph. The existence of a polynomial kernel for DFVS , parameterized by the solution size k , is a central open problem in Kernelization. In this paper, we give a polynomial kernel for DFVS parameterized by k plus the size of a treewidth- η modulator (of the underlying undirected graph), where η is any fixed positive integer. Since the status of the existence of a polynomial kernel for DFVS (parameterized by the solution size) is open for a very long time now, and it is known to not admit a polynomial kernel when the parameter is the size of a treewidth-2 modulator, solution size plus the size of the treewidth- η modulator makes for an interesting choice of parameter to study. In fact, the polynomial kernelization complexity of DFVS parameterized by the size of the undirected feedback vertex set (treewidth-1 modulator) in the underlying undirected graph, has already been studied in literature. Our choice of parameter strictly encompasses previous positive kernelization results on DFVS . Our result is based on a novel application of the tool of important separators embedded in state-of-the-art machinery such as protrusion decompositions.

Contributions of distractor dwelling, skipping, and revisiting to age differences in visual search.

Visual search becomes slower with aging, particularly when targets are difficult to discriminate from distractors. Multiple distractor rejection processes may contribute independently to slower search times: dwelling on, skipping of, and revisiting of distractors, measurable by eye-tracking. The present study investigated how age affects each of the distractor rejection processes, and how these contribute to the final search times in difficult (inefficient) visual search. In a sample of Dutch healthy adults (19-85years), we measured reaction times and eye-movements during a target present/absent visual search task, with varying target-distractor similarity and visual set size. We found that older age was associated with longer dwelling and more revisiting of distractors, while skipping was unaffected by age. This suggests that increased processing time and reduced visuo-spatial memory for visited distractor locations contribute to age-related decline in visual search. Furthermore, independently of age, dwelling and revisiting contributed stronger to search times than skipping of distractors. In conclusion, under conditions of poor guidance, dwelling and revisiting have a major contribution to search times and age-related slowing in difficult visual search, while skipping is largely negligible.

Semantically congruent auditory primes enhance visual search efficiency: Direct evidence by varying set size.

Task-irrelevant sounds that are semantically congruent with the target can facilitate performance in visual search tasks, resulting in faster search times. In three experiments, we tested the underlying processes of this effect. Participants were presented with auditory primes that were semantically congruent, neutral, or incongruent to the visual search target, and importantly, we varied the set size of the search displays. According to seminal accounts of semantic priming, priming effects can be explained by processes not related to search (i.e., facilitation of target encoding; McNamara, 2013), which would predict a priming effect that is independent of set size. Alternatively, we tested if auditory priming can serve as a source of guidance for visual attention toward the primed target (i.e., in terms of altering attention-directing priorities; Wolfe, 2021), as indexed by higher search efficiency with congruent priming. Experiment 1 found that auditory color word primes resulted in faster responses and, importantly, flatter search slopes for congruent compared to incongruent color targets, indicating a more efficient search. As with many naturalistic search behaviors, we used multiple-target search. Experiment 2 replicated the findings of Experiment 1 with a reduced target set. Experiment 3 extended these findings to complex audiovisual objects. Our results provide direct evidence that cross-modal priming can guide visual selective attention, as reflected by enhanced visual search efficiency. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Design and Development of Schema for Schemaless Databases

A schema database functions as a repository for interconnected data points, facilitating comprehension of data structures by organizing information into tables with rows and columns. These databases utilize established connections to arrange data, with attribute values linking related tuples. This integrated approach to data management and distributed processing enables schema databases to maintain models even when the working set size surpasses available RAM. However, challenges such as data quality, storage, scarcity of data science professionals, data validation, and sourcing from diverse origins persist. Notably, while schema databases excel at reviewing transactions, they often fall short in updating them effectively. To address these issues, a Chimp-based radial basis neural model (CbRBNM) is employed. Initially, the Schemaless database was considered and integrated into the Python system. Subsequently, compression functions were applied to both schema and schema-less databases to optimize relational data size by eliminating redundant files. Performance validation involved calculating compression parameters, with the proposed method achieving memory usage of 383.37[Formula: see text]Mb, a computation time of 0.455[Formula: see text]s, a training time of 167.5[Formula: see text]ms, and a compression rate of 5.60%. Extensive testing demonstrates that CbRBNM yields a favorable compression ratio and enables direct searching on compressed data, thereby enhancing query performance.

Maximizing glaucoma detection accuracy through high confidence AI predictions: A RIM One database study

Purpose: This study aimed to assess an artificial intelligence (AI) model's performance in glaucoma detection using the RIM One public database. Specifically, we examined the impact of considering only high‐confidence predictions from the AI model on overall diagnostic accuracy.Methods: The RIM One database provided 485 images, including 313 normal and 172 glaucomatous cases. Of these, 248 images were for training the EfficientNetV2B0 model, 63 for validation, and 174 for testing. Initially, the model's performance was evaluated on the entire test set, yielding an AUC of 96%. Subsequently, we investigated the model's performance when limiting predictions to those with a certainty probability over 95%, reducing the test set to 155 images.Results: The AI model achieved an AUC of 96% when considering all predictions. However, focusing solely on high‐confidence predictions ( > 95% certainty) increased the AUC to 100%. This adjustment reduced the test set size from 174 to 155 images. Statistical analysis using the De Long Test revealed a significant difference between the two AUC values, highlighting the efficacy of high‐confidence predictions.Conclusion: Our findings demonstrate that by considering only AI predictions with a certainty probability exceeding 95%, we can significantly enhance glaucoma detection's diagnostic accuracy. This approach resulted in a perfect AUC, indicating robust performance in identifying glaucomatous cases. The reduction in test set size suggests that 19 cases may require further evaluation through methods such as visual field testing or optical coherence tomography (OCT) to confirm or exclude the diagnosis of glaucoma. This selective approach not only improves the efficiency of glaucoma diagnosis but also streamlines clinical decision‐making by directing resources to cases with the highest predictive certainty.

Visuospatial attention at high altitude in two ethnically distinct groups of soldiers

Objectives: For strategic purposes, soldiers of different ethnicities are deployed in high-altitude (HA) areas from time to time. During their operations, hypoxia may influence visuospatial attention. Therefore, assessment of visuospatial attention is of paramount importance during HA tenure. Materials and Methods: Two distinct ethnic groups, composed of Indian and Kyrgyz lowland soldiers, were ascended to 3,200 m to assess visuospatial attention. Visual search experiments were conducted for a target in the presence of distractors while simultaneously recording the eye movements. The target present correct reaction time (RTP), target absent correct reaction time (RTA), slopes and intercept of reaction time X set size, fixation duration and saccade latency were measured at baseline, as well as on days 3, 7, 14 and 21 of the HA stay and day 3 of the return from HA. Results: At HA, most of the parameters were significantly changed. Kyrgyz soldiers had higher RTP (e.g. 2179.99 ± 992.21ms for Indian, and 2641.78 ± 142.28 ms for Kyrgyz, with 12 set size, on day 3 at HA) and RTA values, as well as a higher intercept of the visual search than Indian soldiers. Kyrgyz soldiers had higher fixation duration (e.g. 291.75 ± 7.40 ms for Indians, and 303.78 ± 18.93 ms for Kyrgyz, with 16 set size, on Day 3 at HA) and saccade latency (e.g. 326.21 ± 34.88 ms for Indian, and 356.67 ± 67.48 ms for Kyrgyz, with 12 set size, on day 3 at HA) values than Indian soldiers from day 3 onward. Conclusion: The task performance of Indian soldiers improved after day 3 at HA, whereas Kyrgyz soldiers struggled to adapt throughout their stay. The ethnogenetic diversity, life experience variables and demographic characteristics of Indian and Kyrgyz soldiers could all be contributing causes to differences in their visuospatial attention. The hypobaric and hypoxic environment further interacted with all these variations.

Adolescent and adult mice use both incremental reinforcement learning and short term memory when learning concurrent stimulus-action associations.

Computational modeling has revealed that human research participants use both rapid working memory (WM) and incremental reinforcement learning (RL) (RL+WM) to solve a simple instrumental learning task, relying on WM when the number of stimuli is small and supplementing with RL when the number of stimuli exceeds WM capacity. Inspired by this work, we examined which learning systems and strategies are used by adolescent and adult mice when they first acquire a conditional associative learning task. In a version of the human RL+WM task translated for rodents, mice were required to associate odor stimuli (from a set of 2 or 4 odors) with a left or right port to receive reward. Using logistic regression and computational models to analyze the first 200 trials per odor, we determined that mice used both incremental RL and stimulus-insensitive, one-back strategies to solve the task. While these one-back strategies may be a simple form of short-term or working memory, they did not approximate the boost to learning performance that has been observed in human participants using WM in a comparable task. Adolescent and adult mice also showed comparable performance, with no change in learning rate or softmax beta parameters with adolescent development and task experience. However, reliance on a one-back perseverative, win-stay strategy increased with development in males in both odor set sizes, but was not dependent on gonadal hormones. Our findings advance a simple conditional associative learning task and new models to enable the isolation and quantification of reinforcement learning alongside other strategies mice use while learning to associate stimuli with rewards within a single behavioral session. These data and methods can inform and aid comparative study of reinforcement learning across species.

Charge-transfer energy through the dipole moment.

The charge-transfer energy contribution is one of the most controversial components of the total interaction energy. Commonly, the energy associate to a charge-transfer process depends on population analysis. Therefore, the results further depend on how the population analysis is defined, and certainly, the results may be arbitrary. Moreover, another important feature of the current methods is the basis sets dependency. The results of methodologies that depend on orbital-based population analyses tend to have a strong dependency on the size of the basis set utilized. This basis set dependency is eliminated by using spatial partitioning population analyses. However, these methodologies still rely on the arbitrary choice of how to divide the space. In this work, we study the use of the molecular dipole moment as a reference to describe the charge transfer-free system, i.e., a system in which the charge-transfer process is avoided. We use the recently developed constrained dipole moment density functional theory methodology to constrain the dipole moment of several systems according to reference values. These dipole moment references do not present charge transfer nor polarization contributions. In this manner, we have calculated the charge-transfer energy contributions and the total interaction energies of 13 non-covalent complexes. In addition, we determined two long range charge-transfer excitations considering the dipole moment as a reference. The calculated charge-transfer energy contributions and excitation energies are in a very good agreement with the fragment-based Hirshfeld methodology. Nevertheless, the constrained dipole moments results do not depend on population analysis. Moreover, the method is robust with respect to the strength of the charge transfer and the basis set size.

Estimation of minimal data sets sizes for machine learning predictions in digital mental health interventions

Artificial intelligence promises to revolutionize mental health care, but small dataset sizes and lack of robust methods raise concerns about result generalizability. To provide insights on minimal necessary data set sizes, we explore domain-specific learning curves for digital intervention dropout predictions based on 3654 users from a single study (ISRCTN13716228, 26/02/2016). Prediction performance is analyzed based on dataset size (N = 100–3654), feature groups (F = 2–129), and algorithm choice (from Naive Bayes to Neural Networks). The results substantiate the concern that small datasets (N ≤ 300) overestimate predictive power. For uninformative feature groups, in-sample prediction performance was negatively correlated with dataset size. Sophisticated models overfitted in small datasets but maximized holdout test results in larger datasets. While N = 500 mitigated overfitting, performance did not converge until N = 750–1500. Consequently, we propose minimum dataset sizes of N = 500–1000. As such, this study offers an empirical reference for researchers designing or interpreting AI studies on Digital Mental Health Intervention data.

End-point carbon content correction in converter steelmaking based on the Kalman filter and CBR model

End-point carbon content at converter is one of significant indicators of end point control. While the bomb-dropping measurement technology can realise quick and effective measurement of end-point carbon content, it is difficult to achieve accurate end-point control due to its lower detection accuracy compared to other methods. Herein, a method was established for correcting the bomb-dropping measurement of end-point carbon content in converter steelmaking to improve its measurement accuracy, thus further achieve cost reduction and efficiency enhancement in converter production. Historical production data and Case-based Reasoning (CBR) model were adopted to establish the prediction model of end-point carbon content and Kalman filtering (KF) was used to fuse CBR model prediction and bomb-dropping measurement to get more accurate end-point carbon content of converter. Through data analysis and on-site tracking and sampling, the validity of correction was thus verified. Experiments showed that: the optimal ratio of the size of training set to test set of CBR prediction model was 95:5 and the optimal Weighting Number was 9; CBR model's average prediction error was 0.019%, bomb-dropping measurement's average error was 0.029% and the average error after KF fusion was 0.014%. The carbon content accuracy was improved by KF fusion by 51.7% compared with that of the original bomb-dropping measurement. Corrected end-point carbon content presented a more typical normal distribution. This method could reduce the measurement error in bomb-dropping.

On the inverse association between the number of QTL and the trait-specific genomic relationship of a candidate to the training set.

BackgroundAccuracy of genomic prediction depends on the heritability of the trait, the size of the training set, the relationship of the candidates to the training set, and the Min(NQTL,Me), where NQTL is the number of QTL and Me is the number of independently segregating chromosomal segments. Due to LD, the number Qe of independently segregating QTL (effective QTL) can be lower than Min(NQTL,Me). In this paper, we show that Qe is inversely associated with the trait-specific genomic relationship of a candidate to the training set. This provides an explanation for the inverse association between Qe and the accuracy of prediction.MethodsTo quantify the genomic relationship of a candidate to all members of the training set, we considered the k2 statistic that has been previously used for this purpose. It quantifies how well the marker covariate vector of a candidate can be represented as a linear combination of the rows of the marker covariate matrix of the training set. In this paper, we used Bayesian regression to make this statistic trait specific and argue that the trait-specific genomic relationship of a candidate to the training set is inversely associated with Qe. Simulation was used to demonstrate the dependence of the trait-specific k2 statistic on Qe, which is related to NQTL.ConclusionsThe posterior distributions of the trait-specific k2 statistic showed that the trait-specific genomic relationship between a candidate and the training set is inversely associated to Qe and NQTL. Further, we show that trait-specific genomic relationship between a candidate and the training set is directly related to the size of the training set.