scholarly journals Persistent Homology and The Shape of Evolutionary Games

2021 ◽  
pp. 110903
Author(s):  
Jakob Stenseke
1983 ◽  
Vol 28 (6) ◽  
pp. 421-422
Author(s):  
John C. Fentress
Keyword(s):  

Author(s):  
Moo K. Chung ◽  
Victoria Villalta-Gil ◽  
Hyekyoung Lee ◽  
Paul J. Rathouz ◽  
Benjamin B. Lahey ◽  
...  

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tun-Wei Hsu ◽  
Jong-Ling Fuh ◽  
Da-Wei Wang ◽  
Li-Fen Chen ◽  
Chia-Jung Chang ◽  
...  

AbstractDementia is related to the cellular accumulation of β-amyloid plaques, tau aggregates, or α-synuclein aggregates, or to neurotransmitter deficiencies in the dopaminergic and cholinergic pathways. Cellular and neurochemical changes are both involved in dementia pathology. However, the role of dopaminergic and cholinergic networks in metabolic connectivity at different stages of dementia remains unclear. The altered network organisation of the human brain characteristic of many neuropsychiatric and neurodegenerative disorders can be detected using persistent homology network (PHN) analysis and algebraic topology. We used 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) imaging data to construct dopaminergic and cholinergic metabolism networks, and used PHN analysis to track the evolution of these networks in patients with different stages of dementia. The sums of the network distances revealed significant differences between the network connectivity evident in the Alzheimer’s disease and mild cognitive impairment cohorts. A larger distance between brain regions can indicate poorer efficiency in the integration of information. PHN analysis revealed the structural properties of and changes in the dopaminergic and cholinergic metabolism networks in patients with different stages of dementia at a range of thresholds. This method was thus able to identify dysregulation of dopaminergic and cholinergic networks in the pathology of dementia.


Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.


2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yanping Zhang ◽  
Jing Peng ◽  
Xiaohui Yuan ◽  
Lisi Zhang ◽  
Dongzi Zhu ◽  
...  

AbstractRecognizing plant cultivars reliably and efficiently can benefit plant breeders in terms of property rights protection and innovation of germplasm resources. Although leaf image-based methods have been widely adopted in plant species identification, they seldom have been applied in cultivar identification due to the high similarity of leaves among cultivars. Here, we propose an automatic leaf image-based cultivar identification pipeline called MFCIS (Multi-feature Combined Cultivar Identification System), which combines multiple leaf morphological features collected by persistent homology and a convolutional neural network (CNN). Persistent homology, a multiscale and robust method, was employed to extract the topological signatures of leaf shape, texture, and venation details. A CNN-based algorithm, the Xception network, was fine-tuned for extracting high-level leaf image features. For fruit species, we benchmarked the MFCIS pipeline on a sweet cherry (Prunus avium L.) leaf dataset with >5000 leaf images from 88 varieties or unreleased selections and achieved a mean accuracy of 83.52%. For annual crop species, we applied the MFCIS pipeline to a soybean (Glycine max L. Merr.) leaf dataset with 5000 leaf images of 100 cultivars or elite breeding lines collected at five growth periods. The identification models for each growth period were trained independently, and their results were combined using a score-level fusion strategy. The classification accuracy after score-level fusion was 91.4%, which is much higher than the accuracy when utilizing each growth period independently or mixing all growth periods. To facilitate the adoption of the proposed pipelines, we constructed a user-friendly web service, which is freely available at http://www.mfcis.online.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.


2021 ◽  
Vol 74 (7) ◽  
pp. 1353-1402
Author(s):  
Luigi Ambrosio ◽  
Massimo Fornasier ◽  
Marco Morandotti ◽  
Giuseppe Savaré

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