Property A is a form of weak amenability for groups and metric spaces introduced as an approach to the famous Novikov higher signature conjecture, one of the most important unsolved problems in topology. We show that ...
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We present a simple linear programming (LP) based method to learn compact and interpretable sets of rules encoding the facts in a knowledge graph (KG) and use these rules to solve the KG completion problem. Our LP mod...
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In tabular multi-agent reinforcement learning with average-cost criterion, a team of agents sequentially interacts with the environment and observes local incentives. We focus on the case that the global reward is a s...
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We consider the constrained optimal control problem for the gradual-impulsive CTMDP model with the performance criteria being the expected total undiscounted costs (from the running cost and the cost from each time an...
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Non-point source (NPS) pollution is increasingly regarded as the main contributor to water quality degradation. Land-use structure can influence surface runoff and soil erosion, which can further affect the export of ...
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ISBN:
(纸本)9781665402682
Non-point source (NPS) pollution is increasingly regarded as the main contributor to water quality degradation. Land-use structure can influence surface runoff and soil erosion, which can further affect the export of NPS pollution. Thus, optimization of land-use structure is critical for water environmental protection. Taking the Xinfeng County in China as the study area, total nitrogen and phosphorus loads from different land-use types were first simulated in this research, based on the export coefficient model. Then, regional land-use structure was optimized through a linear programming model. Simultaneously, the characteristics of pollution output and the economic benefits of land-use after optimization were also analyzed. Results showed that the optimal areas of construction land and water would increase, while those of grassland and agricultural land would decrease. The optimal area of forestland would increase under the pollution reduction scenarios 1 and 2 (i.e., reducing the NPS pollution loads by 5% and 10%) and decrease under scenarios 3 and 4 (i.e., reducing the NPS pollution loads by 15% and 20%). In terms of the economic benefits of the land-use system, with the increase of NPS pollution reduction requirements, they would present a downward trend. These results can provide decision-makers with optimal land-use structures under multiple pollution reduction scenarios considering control of NPS pollution.
The article presents and evaluates a scalable algorithm for validating solutions to linear programming problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validat...
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High-throughput sequencing of mRNA (RNA-seq) provides a promise for transcriptome reconstruction by producing hundreds of millions of short reads. Current salient methods for genome-based transcriptome reconstruction ...
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ISBN:
(纸本)9781665429825
High-throughput sequencing of mRNA (RNA-seq) provides a promise for transcriptome reconstruction by producing hundreds of millions of short reads. Current salient methods for genome-based transcriptome reconstruction almost unanimously sank into details instead of considering it in a whole picture. We present TransCoord, which inclusively gathers all kinds of candidate transcripts into a two-phased linear programming model that aims both to minimize coverage deviation and reserve least transcripts under conserving the must. In this way, the outcome is a coordination of all candidates, instead of a union of all independently assembled parts. Test on 19 human and 5 Arabidopsis thaliana real RNA-seq datasets, TransCoord outperformed all 4 compared salient assemblers in sensitivity. TransCoord is available at https://***/lcc121/TransCoord
We consider a problem of estimating the probability that the optimal value of a stochastic linear program exceeds a large threshold. Inspired by the classical theory of linear programming, we partition the sample spac...
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ISBN:
(纸本)9781665433129
We consider a problem of estimating the probability that the optimal value of a stochastic linear program exceeds a large threshold. Inspired by the classical theory of linear programming, we partition the sample space of random components so that the optimal value can be generated without solving a linear program for each sample. This enables us to develop an efficient importance sampling scheme for computing the said probability when the random components are jointly normal. We prove its asymptotic efficiency under the regime where the threshold increases. Our numerical experiments reveal that the proposed method significantly outperforms the existing simulation techniques in the literature.
Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many dif...
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Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the same set of classes. One approach to solving this problem is to optimize the choice of representative against some measure that is meaningful in the context of the data. In this work, we provide a study of the effectiveness and computational cost of several `1-minimization optimization procedures for constructing homological cycle bases for persistent homology with rational coefficients in dimension one, including uniform-weighted and length-weighted edge-loss algorithms as well as uniform-weighted and area-weighted triangle-loss algorithms. We conduct these optimizations via standard linear programming methods, applying general-purpose solvers to optimize over column bases of simplicial boundary matrices. Our key findings are: (i) optimization is effective in reducing the size of cycle representatives, though the extent of the reduction varies according to the dimension and distribution of the underlying data, (ii) the computational cost of optimizing a basis of cycle representatives exceeds the cost of computing such a basis, in most data sets we consider, (iii) the choice of linear solvers matters a lot to the computation time of optimizing cycles, (iv) the computation time of solving an integer program is not significantly longer than the computation time of solving a linear program for most of the cycle representatives, using the Gurobi linear solver, (v) strikingly, whether requiring integer solutions or not, we almost always obtain a solution with the same cost and almost all solutions found have entries in {−1, 0, 1} and therefore, are also solutions to a restricted 0 optimization problem, and (vi) we obtain qualitatively different results for generators in Erdős-Rényi random clique complexes than in real-world and
Genes are transcribed into various RNA molecules, and a portion of them called messenger RNA (mRNA) is then translated into proteins in the process known as gene expression. Gene expression is a high-energy demanding ...
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Genes are transcribed into various RNA molecules, and a portion of them called messenger RNA (mRNA) is then translated into proteins in the process known as gene expression. Gene expression is a high-energy demanding process, and aberrant expression changes often manifest into pathophysiology. Therefore, gene expression is tightly regulated by several factors at different levels. MicroRNAs (miRNAs) are one of the powerful post-transcriptional regulators involved in key biological processes and diseases. They inhibit the translation of their mRNA targets or degrade them in a sequence-specific manner, and hence control the rate of protein synthesis. In recent years, in response to experimental limitations, several computational methods have been proposed to predict miRNA target genes based on sequence complementarity and structural features. However, these predictions yield a large number of false positives. Integration of gene and miRNA expression data drastically alleviates this problem. Here, I describe a mathematical linear modeling approach to identify miRNA targets at the genome scale using gene and miRNA expression data. Mathematical modeling is faster and more scalable to genome-level compared to conventional statistical modeling approaches. less
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