Sum Of Weights Research Articles

Online Euclidean Spanners

In this article, we study the online Euclidean spanners problem for points in \(\mathbb{R}^{d}\) . Given a set \(S\) of \(n\) points in \(\mathbb{R}^{d}\) , a \(t\) -spanner on \(S\) is a subgraph of the underlying complete graph \(G=(S,\binom{S}{2})\) , that preserves the pairwise Euclidean distances between points in \(S\) to within a factor of \(t\) , that is the stretch factor . Suppose we are given a sequence of \(n\) points \((s_{1},s_{2},\ldots,s_{n})\) in \(\mathbb{R}^{d}\) , where point \(s_{i}\) is presented in step \(i\) for \(i=1,\ldots,n\) . The objective of an online algorithm is to maintain a geometric \(t\) -spanner on \(S_{i}=\{s_{1},\ldots,s_{i}\}\) for each step \(i\) . The algorithm is allowed to add new edges to the spanner when a new point is presented but cannot remove any edge from the spanner. The performance of an online algorithm is measured by its competitive ratio, which is the supremum, over all sequences of points, of the ratio between the weight of the spanner constructed by the algorithm and the weight of an optimum spanner. Here, the weight of a spanner is the sum of all edge weights. First, we establish a lower bound of \(\Omega(\varepsilon^{-1}\log n/\log\varepsilon^{-1})\) for the competitive ratio of any online \((1+\varepsilon)\) -spanner algorithm, for a sequence of \(n\) points in 1-dimension. We show that this bound is tight, and there is an online algorithm that can maintain a \((1+\varepsilon)\) -spanner with competitive ratio \(O(\varepsilon^{-1}\log n/\log\varepsilon^{-1})\) . Next, we design online algorithms for sequences of points in \(\mathbb{R}^{d}\) , for any constant \(d\geq 2\) , under the \(L_{2}\) norm. We show that previously known incremental algorithms achieve a competitive ratio \(O(\varepsilon^{-(d+1)}\log n)\) . However, if the algorithm is allowed to use additional points (Steiner points), then it is possible to substantially improve the competitive ratio in terms of \(\varepsilon\) . We describe an online Steiner \((1+\varepsilon)\) -spanner algorithm with competitive ratio \(O(\varepsilon^{(1-d)/2}\log n)\) . As a counterpart, we show that the dependence on \(n\) cannot be eliminated in dimensions \(d\geq 2\) . In particular, we prove that any online spanner algorithm for a sequence of \(n\) points in \(\mathbb{R}^{d}\) under the \(L_{2}\) norm has competitive ratio \(\Omega(f(n))\) , where \(\lim_{n\rightarrow\infty}f(n)=\infty\) . Finally, we provide improved lower bounds under the \(L_{1}\) norm: \(\Omega(\varepsilon^{-2}/\log\varepsilon^{-1})\) in the plane and \(\Omega(\varepsilon^{-d})\) in \(\mathbb{R}^{d}\) for \(d\geq 3\) .

Mission Planning Method for Dense Area Target Observation Based on Clustering Agile Satellites

To address the mission planning challenge for agile satellites in dense point target observation, a clustering strategy based on an ant colony algorithm and a heuristic simulated genetic annealing optimization algorithm are proposed. First, the imaging observation process of agile satellites is analyzed, and an improved ant colony algorithm is employed to optimize the clustering of observation tasks, enabling the satellites to complete more observation tasks efficiently with a more stable attitude. Second, to solve for the optimal group target observation sequence and achieve higher total observation benefits, a task planning model based on multi-target observation benefits and attitude maneuver energy consumption is established, considering the visible time windows of targets and the time constraints between adjacent targets. To overcome the drawbacks of traditional simulated annealing and genetic algorithms, which are prone to local optimal solution and a slow convergence speed, a novel Simulated Genetic Annealing Algorithm is designed while optimizing the sum of target observation weights and yaw angles while also accounting for factors such as target visibility windows and satellite attitude transition times between targets. Ultimately, the feasibility and efficiency of the proposed algorithm are substantiated by comparing its performance against traditional heuristic optimization algorithms using a dataset comprising large-scale dense ground targets.

Fractional Vertex Cover Reliability of Graphs

Let G be a graph and let 0 ≤ p , q and p + q ≤ 1 . Suppose that each vertex of G gets a weight of 1 with probability p , 1 2 with probability q , and 0 with probability 1 − p − q , and vertex weight probabilities are independent. The \textit{fractional vertex cover reliability} of G , denoted by FRel ( G ; p , q ) , is the probability that the sum of weights at the end-vertices of every edge in G is at least 1 . In this article, we first provide various computational formulas for FRel ( G ; p , q ) considering general graphs, basic graphs, and graph operations. Secondly, we determine the graphs which maximize FRel ( G ; p , q ) for all values of p and q in the classes of trees, connected unicyclic and bicyclic graphs with fixed order, and determine the graphs which minimize it in the classes of trees and connected unicyclic graphs with fixed order. Our results on optimal graphs extend some known results in the literature about independent sets, and the tools we developed in this paper have the potential to solve the optimality problem in other classes of graphs as well.

High‐temperature ablation resistance prediction of ceramic coatings using machine learning

AbstractSurface ablation temperature and linear ablation rate are two crucial indicators for ceramic coatings under ultrahigh temperatures service, yet the results collection of such two indicators in the process is difficult due to the long‐period material preparation and the high‐cost test. In this work, four kinds of machine learning models are applied to predict the above two indicators. The Random Forest (RF) model exhibits a high accuracy of 87% in predicting surface ablation temperature, while a low accuracy of 60% in linear ablation rate. To optimize the model, the novel features are constructed based on the original features by the sum of the importance weights in the model. Thereafter, the importance of the newly constructed features increases significantly, and the accuracy of the optimized RF model is improved by 11%, exceeding 70% in accuracy. By validation with available data and experiments, the optimized model demonstrates precise predictions of the target variables.

Individual-based socioeconomic vulnerability and deprivation indices: a scoping review.

Several individual-based social deprivation and vulnerability indices have been developed to measure the negative impact of low socioeconomic status on health outcomes. However, their variables and measurable characteristics have not been unequivocally assessed. A comprehensive database literature scoping review was performed to identify all individual-based social deprivation and vulnerability indices. Area-based indices and those developed for pediatric populations were excluded. Data were extracted from all eligible studies and their methodology was assessed with quality criteria. A total of 14 indices were identified, of which 64% (9/14) measured social deprivation and 36% (5/14) measured socioeconomic vulnerability. Sum of weights was the most common scoring system, present in 43% (6/14) of all indices, with no exclusive domains to either vulnerability or deprivation indices. A total of 83 different variables were identified; a very frequent variable (29%; 5/14) related to an individual's social relationships was "seen any family or friends or neighbors." Only five deprivation indices reported a specific internal consistency measure, while no indices reported data on reproducibility. This is the first scoping review of individual-based deprivation and vulnerability indices, which may be used interchangeably when measuring the impact of SES on health outcomes.

Sensitivity of rainfed okra (Abelmoschus esculentus L. Moench) to mulch material and plant spacing in drought-prone tropical soils

Mulch regulates soil hydrothermal regime while suppressing weed growth, effects of which may depend on mulch material and/or similar to that of closed crop canopy. Combined use of organic or inorganic material as surface mulch and appropriate plant spacing may produce synergistic agronomic effects in water-stressed environments. This study evaluated the sensitivity of rainfed okra to mulch-spacing variants in droughty derived-savannah soils. With dry-grass mulch (DGM) and sawdust mulch (SDM) representing organic mulch material and black polythene (BPM) as inorganic/plastic, treatments were factorial combinations of surface-applied DGM, SDM and BPM with close (60 cm × 30 cm), intermediate (60 cm × 45 cm) and wide (60 cm × 60 cm) spacings. Crop growth/performance and fruit yield data were collected. Mulch material affected okra growth (with overall better results in BPM than SDM), but not flowering/fruiting and fruit yield. For plant spacing, sum of weights of pods and fruit yield were higher in close than intermediate and wide spacings, with fruit yields as 2.42, 1.21 and 0.76 t ha-1, respectively. Mulch-spacing interaction effects showed that BPM with close spacing gave the highest values for stem girth 8 weeks after sowing (SDM treatments gave the lowest), sum of weights of pods and fruit yield (2.93 t ha-1). Fruit yield, however, depended not on stem girth but on certain okra yield attributes. The BPM or, where not feasible, either of DGM and SDM, could be effectively combined with close spacing to improve okra productivity in droughty soils of the derived savannah.

Singular examples of the Matrix Bochner Problem

The Matrix Bochner Problem aims to classify which weight matrices have their sequence of orthogonal polynomials as eigenfunctions of a second-order differential operator. Casper and Yakimov, in [4], demonstrated that, under certain hypotheses, all solutions to the Matrix Bochner Problem are noncommutative bispectral Darboux transformations of a direct sum of classical scalar weights. This paper aims to provide the first proof that there are solutions to the Matrix Bochner Problem that do not arise through a noncommutative bispectral Darboux transformation of any direct sum of classical scalar weights. This initial example could contribute to a more comprehensive understanding of the general solution to the Matrix Bochner Problem.

Theoretical studies of the [formula omitted]-strong Roman domination problem

The concept of Roman domination has been a subject of intrigue for more than two decades, with the fundamental Roman domination problem standing out as one of the most significant challenges in this field. This article studies a practically motivated generalization of this problem, known as the k-strong Roman domination. In this problem variant, defenders within a network are tasked with safeguarding any k vertices simultaneously, under multiple attacks. The aim is to find a feasible mapping that assigns a (integer) weight to each vertex of the input graph with a minimum sum of weights across all vertices. A function is considered feasible if any non-defended vertex, i.e. one labeled by zero, is protected by at least one of its neighboring vertices labeled by at least two. Furthermore, each defender ensures the safety of a non-defended vertex by imparting a value of one to it while retaining a one for themselves. To the best of our knowledge, this paper represents the first theoretical study on this problem. The study presents results for general graphs, establishes connections between the problem at hand and other domination problems, and provides exact values and bounds for specific graph classes, including complete graphs, paths, cycles, complete bipartite graphs, grids, and a few selected classes of convex polytopes. Additionally, an attainable lower bound for general cubic graphs is provided.

A recipe for an effective selection of promising candidates for high-temperature superconductors among binary hydrides

Recent research on compressed binary hydrides have unveiled the potential for achieving superconductivity at near-room-temperature. Nevertheless, the available decision-making procedures standing behind the selection of constituent elements that may potentially exhibit high values of critical temperature (Tc) are far from optimal. In other words, a lot of experimental and numerical effort is wasted on exploring unpromising compounds. By conducting a deep study of a database containing over 580 binary hydride superconductors, we were able to observe some interesting relationships between Tc and selected physico-chemical properties of examined compounds. Among studied parameters, the ratio of the sum of the molecular weight of heavier atoms to the total mass of all hydrogen atoms in the chemical formula of hydride (MX/MH) was found to be the most valuable indicator that can help to screen for new promising superconductor candidates. This is because the highest Tc requires the lowest MX/MH ratio. Statistical analysis indicates a 28% chance of finding Tc > 200 K within 0 <MX/MH < 15. It is expected that these findings will not only allow for more efficient use of resources by improving future superconductor candidates selection but also they will accelerate ongoing experimental and numerical research that should bring new exciting discoveries in a much shorter time.

Sums of logarithmic weights involving r-full numbers

Sums of logarithmic weights involving r-full numbers

How likely is it to beat the target at different investment horizons: an approach using compositional data in strategic portfolios

Strategic portfolios are asset combinations designed to achieve investor objectives. A unique feature of these investments is that portfolios must be rebalanced periodically to maintain the initially established structure. This paper introduces a methodology to estimate the probability of not exceeding a specific profitability target with this type of portfolio to determine if this kind of build portfolio makes obtaining certain profitability targets easy. Portfolios with a specific distribution of fixed-income and equity securities were randomly replicated and their performance was studied over different time horizons. Daily data from 2004 to 2021 was used. Since the sum of all asset weights invariably equals the unit, the original data were transformed using the compositional data methodology. With these transformed data, the probabilities were estimated for each analyzed portfolio. The study also performed a sensitivity analysis of the estimated probabilities, modifying the weight of specific assets in the portfolio.

Research on the Consistency Evaluation of the Spindle Unit Stiffness Based on Comprehensive Weights

The spindle unit is the core component of a machine, and its stiffness is a key performance characteristic. The stiffness consistency is a key index to measure the stiffness of spindle units; however, there is a lack of unified evaluation methods for the spindle unit stiffness consistency. This paper proposes a comprehensive method for the evaluation of the spindle unit stiffness consistency based on fluctuations and comprehensive weights. First, the consistency of the spindle unit stiffness evaluation indices is expressed based on the fluctuations. Secondly, the subjective and objective weights of the spindle unit stiffness evaluation indices are given based on the AHP and CRITIC weight assignment methods. To obtain the comprehensive weights of the evaluation indices, the subjective and objective weights are synthesized based on the linear weighting method. Then, the consistency level of the spindle unit stiffness is obtained by the weighted summation of the comprehensive weights and fluctuations of the evaluation indices. Finally, the stiffness consistency of a group of spindle units is evaluated based on this method, and the evaluation result shows a 10.63% fluctuation, which indicates that its stiffness consistency level is class B, in line with the factory production requirements.

Embedding Enhancement Method for LightGCN in Recommendation Information Systems

In the modern digital age, users are exposed to a vast amount of content and information, and the importance of recommendation systems is increasing accordingly. Traditional recommendation systems mainly use matrix factorization and collaborative filtering methods, but problems with scalability due to an increase in the amount of data and slow learning and inference speeds occur due to an increase in the amount of computation. To overcome these problems, this study focused on optimizing LightGCN, the basic structure of the graph-convolution-network-based recommendation system. To improve this, techniques and structures were proposed. We propose an embedding enhancement method to strengthen the robustness of embedding and a non-combination structure to overcome LightGCN’s weight sum structure through this method. To verify the proposed method, we have demonstrated its effectiveness through experiments using the SELFRec library on various datasets, such as Yelp2018, MovieLens-1M, FilmTrust, and Douban-book. Mainly, significant performance improvements were observed in key indicators, such as Precision, Recall, NDCG, and Hit Ratio in Yelp2018 and Douban-book datasets. These results suggest that the proposed methods effectively improved the recommendation performance and learning efficiency of the LightGCN model, and the improvement of LightGCN, which is most widely used as a backbone network, makes an important contribution to the entire field of GCN-based recommendation systems. Therefore, in this study, we improved the learning method of the existing LightGCN and changed the weight sum structure to surpass the existing accuracy.

Does the accounting of the local symmetry fragments in quasi-SMILES improve the predictive potential of the QSAR models of toxicity toward tadpoles?

Models of toxicity to tadpoles have been developed as single parameters based on special descriptors which are sums of correlation weights, molecular features, and experimental conditions. This information is presented by quasi-SMILES. Fragments of local symmetry (FLS) are involved in the development of the model and the use of FLS correlation weights improves their predictive potential. In addition, the index of ideality correlation (IIC) and correlation intensity index (CII) are compared. These two potential predictive criteria were tested in models built through Monte Carlo optimization. The CII was more effective than IIC for the models considered here.

Detail-preserving image warping by enforcing smooth image sampling

Multi-phase dynamic contrast-enhanced magnetic resonance imaging image registration makes a substantial contribution to medical image analysis. However, existing methods (e.g., VoxelMorph, CycleMorph) often encounter the problem of image information misalignment in deformable registration tasks, posing challenges to the practical application. To address this issue, we propose a novel smooth image sampling method to align full organic information to realize detail-preserving image warping. In this paper, we clarify that the phenomenon about image information mismatch is attributed to imbalanced sampling. Then, a sampling frequency map constructed by sampling frequency estimators is utilized to instruct smooth sampling by reducing the spatial gradient and discrepancy between all-ones matrix and sampling frequency map. In addition, our estimator determines the sampling frequency of a grid voxel in the moving image by aggregating the sum of interpolation weights from warped non-grid sampling points in its vicinity and vectorially constructs sampling frequency map through projection and scatteration. We evaluate the effectiveness of our approach through experiments on two in-house datasets. The results showcase that our method preserves nearly complete details with ideal registration accuracy compared with several state-of-the-art registration methods. Additionally, our method exhibits a statistically significant difference in the regularity of the registration field compared to other methods, at a significance level of p < 0.05. Our code will be released at https://github.com/QingRui-Sha/SFM.

Optimal energy scheduling for residential consumers with demand management strategies

ABSTRACT The enhancement of energy networks and cost reduction can be achieved through the implementation of solutions like optimal energy scheduling for residential consumers. This paper proposes day-ahead electrical and thermal energy scheduling for residential sections in energy networks as a bi-criteria optimization approach. The bi-criteria optimization approach is modeled to minimize the operation cost and maximize the reliability of the energy system. Demand management strategies such as demand reduction and demand shifting are considered for residential consumers. The participation of residential consumers in demand management is presented considering electricity prices in the energy markets. The solving bi-criteria optimization approach is done via the weight sum method and LINMAP procedure-based-fuzzy approach. The proposed modeling is implemented in GAMS optimization software for verifying the demand management strategies in optimal energy scheduling in two case studies.

Portfolio management based on a reinforcement learning framework

AbstractPortfolio management is crucial for investors. We propose a dynamic portfolio management framework based on reinforcement learning using the proximal policy optimization algorithm. The two‐part framework includes a feature extraction network and a full connected network. First, the majority of the previous research on portfolio management based on reinforcement learning has been dedicated to discrete action spaces. We propose a potential solution to the problem of a continuous action space with a constraint (i.e., the sum of the portfolio weights is equal to 1). Second, we explore different feature extraction networks (i.e., convolutional neural network [CNN], long short‐term memory [LSTM] network, and convolutional LSTM network) combined with our system, and we conduct extensive experiments on the six kinds of assets, including 16 features. The empirical results show that the CNN performs best in the test set. Last, we discuss the effect of the trading frequency on our trading system and find that the monthly trading frequency has a higher Sharpe ratio in the test set than other trading frequencies.

Calabi-Yau four-, five-, sixfolds as Pwn hypersurfaces: Machine learning, approximation, and generation

Calabi-Yau fourfolds may be constructed as hypersurfaces in weighted projective spaces of complex dimension five defined via weight systems of six weights. In this work, neural networks were implemented to learn the Calabi-Yau Hodge numbers from the weight systems, where gradient saliency and symbolic regression then inspired a truncation of the Landau-Ginzburg model formula for the Hodge numbers of any dimensional Calabi-Yau constructed in this way. The approximation always provides a tight lower bound, is shown to be dramatically quicker to compute (with computation times reduced by up to 4 orders of magnitude), and gives remarkably accurate results for systems with large weights. Additionally, complementary datasets of weight systems satisfying the necessary but insufficient conditions for transversality were constructed, including considerations of the interior point, reflexivity, and intradivisibility properties, overall producing a classification of this weight system landscape, further confirmed with machine learning methods. Using the knowledge of this classification and the properties of the presented approximation, a novel dataset of transverse weight systems consisting of seven weights was generated for a sum of weights ≤200, producing a new database of Calabi-Yau fivefolds, with their respective topological properties computed. Furthermore, an equivalent database of candidate Calabi-Yau sixfolds was generated with approximated Hodge numbers. Published by the American Physical Society 2024

Optimal bipartite graph matching-based goal selection for policy-based hindsight learning

The sparse reward problem stands as a significant challenge in the field of reinforcement learning. Hindsight Experience Replay (HER) addresses this by goal relabeling, allowing the agent to learn from unsuccessful experiences. Some studies combine policy gradient methods with HER, resulting in policy-based hindsight learning algorithms. However, Policy-based hindsight learning involves the use of importance sampling, where the distribution of hindsight goals and the distribution of desired goals contribute to the computation of importance weights. When there is a significant difference between the two distributions, importance weights may become skewed, thereby impacting the evaluation of the policy and leading to suboptimal policies. To address this, we propose modeling the goal selection as an optimization problem for distribution matching. After we augment the original desired goals using Kernel Density Estimation (KDE), we further convert the optimization problem for distribution matching into a bipartite graph matching problem that minimizes the sum of weights. Our optimal bipartite graph matching-based hindsight goal selection method can select hindsight goals that are the most closely aligned with the original goals. Experimental results show that algorithms combined with the optimal bipartite graph matching-based hindsight goal selection outperform the original algorithms. Visualizations also demonstrate the superiority of our method in selecting hindsight goals.

Prediction of Overall Disease Burden in (y)pN1 Breast Cancer Using Knowledge-Based Machine Learning Model.

We aimed to construct an expert knowledge-based Bayesian network (BN) model for assessing the overall disease burden (ODB) in (y)pN1 breast cancer patients and compare ODB across arms of ongoing trials. Utilizing institutional data and expert surveys, we developed a BN model for (y)pN1 breast cancer. Expert-derived probabilities and disability weights for radiotherapy-related benefit (e.g., 7-year disease-free survival [DFS]) and toxicities were integrated into the model. ODB was defined as the sum of disability weights multiplied by probabilities. In silico predictions were conducted for Alliance A011202, PORT-N1, RAPCHEM, and RT-CHARM trials, comparing ODB, 7-year DFS, and side effects. In the Alliance A011202 trial, 7-year DFS was 80.1% in both arms. Axillary lymph node dissection led to higher clinical lymphedema and ODB compared to sentinel lymph node biopsy with full regional nodal irradiation (RNI). In the PORT-N1 trial, the control arm (whole-breast irradiation [WBI] with RNI or post-mastectomy radiotherapy [PMRT]) had an ODB of 0.254, while the experimental arm (WBI alone or no PMRT) had an ODB of 0.255. In the RAPCHEM trial, the radiotherapy field did not impact the 7-year DFS in ypN1 patients. However, there was a mild ODB increase with a larger irradiation field. In the RT-CHARM trial, we identified factors associated with the major complication rate, which ranged from 18.3% to 22.1%. The expert knowledge-based BN model predicted ongoing trial outcomes, validating reported results and assumptions. In addition, the model demonstrated the ODB in different arms, with an emphasis on quality of life.