Adaptive Monte Carlo Search for Conjecture Refutation in Graph Theory

Graph theory is an interdisciplinary field of study that has various applications in mathematical modeling and computer science. Research in graph theory depends on the creation of not only theorems but also conjectures. Conjecture-refuting algorithms attempt to refute conjectures by searching for counterexamples to those conjectures, often by maximizing certain score functions on graphs. This study proposes a novel conjecture-refuting algorithm, referred to as the adaptive Monte Carlo search (AMCS) algorithm, obtained by modifying the Monte Carlo tree search algorithm. Evaluated based on its success in finding counterexamples to several graph theory conjectures, AMCS outperforms existing conjecture-refuting algorithms. The algorithm is further utilized to refute six open conjectures, two of which were chemical graph theory conjectures formulated by Liu et al. in 2021 and four of which were formulated by the AutoGraphiX computer system in 2006. Finally, four of the open conjectures are strongly refuted by generalizing the counterexamples obtained by AMCS to produce a family of counterexamples. It is expected that the algorithm can help researchers test graph-theoretic conjectures more effectively.Comment: 27 pages, 11 figures, 3 tables; Milo Roucairol pointed out that both of our papers used an incorrect formula for the harmonic of a graph. The revised Conjecture 4 was able to be refuted. This paper and the GitHub repository have been updated accordingl

An Asymmetric Contrastive Loss for Handling Imbalanced Datasets

Contrastive learning is a representation learning method performed by contrasting a sample to other similar samples so that they are brought closely together, forming clusters in the feature space. The learning process is typically conducted using a two-stage training architecture, and it utilizes the contrastive loss (CL) for its feature learning. Contrastive learning has been shown to be quite successful in handling imbalanced datasets, in which some classes are overrepresented while some others are underrepresented. However, previous studies have not specifically modified CL for imbalanced datasets. In this work, we introduce an asymmetric version of CL, referred to as ACL, in order to directly address the problem of class imbalance. In addition, we propose the asymmetric focal contrastive loss (AFCL) as a further generalization of both ACL and focal contrastive loss (FCL). Results on the FMNIST and ISIC 2018 imbalanced datasets show that AFCL is capable of outperforming CL and FCL in terms of both weighted and unweighted classification accuracies. In the appendix, we provide a full axiomatic treatment on entropy, along with complete proofs.Comment: 15 pages, 5 figure

Cluster Analysis on Dengue Incidence and Weather Data Using K-Medoids and Fuzzy C-Means Clustering Algorithms (Case Study: Spread of Dengue in the DKI Jakarta Province)

In Indonesia, Dengue incidence tends to increase every year but has been fluctuating in recent years. The potential for Dengue outbreaks in DKI Jakarta, the capital city, deserves serious attention. Weather factors are suspected of being associated with the incidence of Dengue in Indonesia. This research used weather and Dengue incidence data for five regions of DKI Jakarta, Indonesia, from December 30, 2008, to January 2, 2017. The study used a clustering approach on time-series and non-time-series data using K-Medoids and Fuzzy C-Means Clustering. The clustering results for the non-time-series data showed a positive correlation between the number of Dengue incidents and both average relative humidity and amount of rainfall. However, Dengue incidence and average temperature were negatively correlated. Moreover, the clustering implementation on the time-series data showed that rainfall patterns most closely resembled those of Dengue incidence. Therefore, rainfall can be used to estimate Dengue incidence. Both results suggest that the government could utilize weather data to predict possible spikes in DHF incidence, especially when entering the rainy season and alert the public to greater probability of a Dengue outbreak

Cluster Analysis on Dengue Incidence and Weather Data Using K-Medoids and Fuzzy C-Means Clustering Algorithms (Case Study: Spread of Dengue in the DKI Jakarta Province)

In Indonesia, Dengue incidence tends to increase every year but has been fluctuating in recent years. The potential for Dengue outbreaks in DKI Jakarta, the capital city, deserves serious attention. Weather factors are suspected of being associated with the incidence of Dengue in Indonesia. This research used weather and Dengue incidence data for five regions of DKI Jakarta, Indonesia, from December 30, 2008, to January 2, 2017. The study used a clustering approach on time-series and non-time-series data using K-Medoids and Fuzzy C-Means Clustering. The clustering results for the non-time-series data showed a positive correlation between the number of Dengue incidents and both average relative humidity and amount of rainfall. However, Dengue incidence and average temperature were negatively correlated. Moreover, the clustering implementation on the time-series data showed that rainfall patterns most closely resembled those of Dengue incidence. Therefore, rainfall can be used to estimate Dengue incidence. Both results suggest that the government could utilize weather data to predict possible spikes in DHF incidence, especially when entering the rainy season and alert the public to greater probability of a Dengue outbreak

Genotyping-by-sequencing of a melon (Cucumis melo L.) germplasm collection from a secondary center of diversity highlights patterns of genetic variation and genomic features of different gene pools

Background: Melon (Cucumis melo L.) is one of the most important horticultural species, which includes several taxonomic groups. With the advent of next-generation sequencing, single nucleotide polymorphism (SNP) markers are widely used in the study of genetic diversity and genomics. Results: We report the first successful application of genotyping-by-sequencing (GBS) technology in melon. We detected 25,422 SNPs by the analysis of 72 accessions collected in Apulia, a secondary centre of diversity in Southern Italy. Analyses of genetic structure, principal components, and hierarchical clustering support the identification of three distinct subpopulations. One of them includes accessions known with the folk name of 'carosello', referable to the chate taxonomic group. This is one of the oldest domesticated forms of C. melo, once widespread in Europe and now exposed to the risk of genetic erosion. The second subpopulation contains landraces of 'barattiere', a regional vegetable production that was never characterized at the DNA level and we show was erroneously considered another form of chate melon. The third subpopulation includes genotypes of winter melon (C. melo var. inodorus). Genetic analysis within each subpopulation revealed patterns of diversity associated with fruit phenotype and geographical origin. We used SNP data to describe, for each subpopulation, the average linkage disequilibrium (LD) decay, and to highlight genomic regions possibly resulting from directional selection and associated with phenotypic variation. Conclusions: We used GBS to characterize patterns of genetic diversity and genomic features within C. melo. We provide useful information to preserve endangered gene pools and to guide the use of germplasm in breeding. Finally, our findings lay a foundation for molecular breeding approaches and the identification of genes underlying phenotypic traits