scholarly journals Grove Arctic Curves from Periodic Cluster Modular Transformations

Author(s):  
Terrence George

Abstract Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a large class of probability measures on groves for which we can compute exact generating functions for edge probabilities. Using the machinery of asymptotics of multivariate generating functions, this lets us explicitly compute arctic curves, generalizing the arctic circle theorem of Petersen and Speyer. Our class of probability measures is sufficiently general that the limit shapes exhibit all solid and gaseous phases expected from the classification of ergodic Gibbs measures in the resistor network model.

Author(s):  
Yu.V. Razovsky ◽  
◽  
M.S. Ruban ◽  
E.Yu. Gorenkova ◽  
◽  
...  
Keyword(s):  

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Hoda Bidkhori

International audience In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2) We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases; (3) In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets. We also study Eulerian triangular posets. This paper answers questions posed by R. Ehrenborg and M. Readdy. This research is also motivated by the work of R. Stanley about recognizing the \emphboolean lattice by looking at smaller intervals. Nous étudions les ensembles partiellement ordonnés finis (EPO) qui sont soit binomiaux soit de type Sheffer (deux notions reliées aux séries génératrices et à la géométrie). Nos résultats sont les suivants: (1) nous déterminons la structure des EPO Euleriens et binomiaux; nous classifions ainsi les fonctions factorielles de tous ces EPO; (2) nous donnons une classification presque complète des fonctions factorielles des EPO Euleriens de type Sheffer; (3) dans la plupart de ces cas, nous déterminons complètement la structure des EPO Euleriens et Sheffer, ce qui est plus fort que classifier leurs fonctions factorielles. Nous étudions aussi les EPO Euleriens triangulaires. Cet article répond à des questions de R. Ehrenborg and M. Readdy. Il est aussi motivé par le travail de R. Stanley sur la reconnaissance du treillis booléen via l'étude des petits intervalles.


2021 ◽  
pp. 113-149
Author(s):  
E. D. Lapshina ◽  
I. V. Filippov ◽  
V. E. Fedosov ◽  
Yu. V. Skuchas ◽  
P. Lamkowski ◽  
...  

There are very few publications on the classification of mountain mire vegetation in Russia. Several associations in the Southern Siberia mountains (Lapshina, 1996; Lashchinsky, 2009) and the Khibiny Mountains (Koroleva, 2001) are described. Mire vegetation in the Southern Urals is relatively well studied and described in the traditions of the ecological-phytocenotic dominant classification (Ivchenko, 2013; Ivchenko, Znamenskiy, 2015) while the knowledge on that of the Northern and Sub-Polar Urals is extremely limited. There is no information about the mires in the Polar Urals. The paper presents the results of classification of the class Scheuchzerio–Caricetea fuscae of the Yanganape mountain massif (67.68°—67.75° N, 67.72°—68.00° E) and adjacent plains in the Eastern macroslope of the Polar Urals, within the southern tundra subzone. The study area is mountain massif of about 250 m a. s. l., composed of limestone outcrops, with a wavy flat (60–90 m a. s. l.) plain around (Fig. 1–2). The classification is based on 138 relevés made in July 27–August 8, 2017 (Fig. 3). Relevés of similar syntaxa, established in the north of the Western Europe and the East European tundras (Ruuhijärvi, 1960; Dierssen, 1982; Lavrinenko et al., 2016), were included in analysis. DCA and t-SNE (t-distributed stochastic neighbor embedding) methods were used for ordination of syntaxa in multidimensional space (Maaten, Hinton, 2008). The calculations were made using the machine learning package for Python-Scikit-learn. In total, 13 associations, 11 subassociations, 12 variants from 6 alliances and 3 orders of the class Scheuchzerio–Caricetea fuscae were identified on the relatively small (about 70 km2) area. Within the order Caricion davallianae, syntaxa of the alliance Caricion atrofuscae-saxatilis, comprising low sedge-hypnum communities on carbonate mineral and organomineral soils in the mountains of the Western Europe, were identified and described for the first time on the territory of Russia. Three new associations (Ditricho flexicauli—Caricetum redowskianae, Tomentypno nitentis–Equisetetum palustre, Tomentypno nitentis–Eriophoretum vaginati) were described on the the Yanganape mountain massif (Table 1), which significantly expands the area of the alliance to the East. Alliance’ communities have some similarities with syntaxa of zonal dwarf shrub-grass-moss tundra vegetation (Lavrinenko, Lavrinenko, 2018), but are generally well differed by the species composition and community structure (Table 5). The order Caricetalia fuscae in the Eastern macroslope of the Polar Urals is represented by 4 alliances. In addition to Drepanocladion exannulati and Sphagno-Caricion canescentis, listed in the “Classification of Vegetation of Europe” (Mucina et al., 2016), we include into order the alliance Caricion stantis — moderately rich sedge-moss fen vegetation of the Subarctic and tundra zones, and the alliance Stygio–Caricion limosae, containing extremely waterlogged meso-oligotrophic and slightly acidic to neutral low sedge fens. There are 4 associations within the alliance Caricion stantis, including new ass. Scorpidio cossonii–Caricetum rariflorae (Table 2). Taking into account statistically significant differences in the species composition of sedge-moss communities dominated by various moss species (Fig. 15, 5-6), ass. Scorpidio scorpioidis–Caricetum chordorrhizae was taken out from ass. Drepanoclado revolventis–Caricetum chordorrhizae Osvald 1925 ex Dierssen 1982 broadly understood in the Western Europe. Its nomenclature type is the only relevé of Carex chordorrhizae-Amblistegium scorpioides-Ass. (Osvald 1925: 37), which sufficient for the original diagnosis, because it contains list of species with abundance and both name-giving taxa (ICPN, 2b, 7). The communities of both associations were identified in the Eastern macroslope of the Polar Urals, where they are represented by new subassociations, which significantly expands the distribution area of these associations to the East. Recently validly described in the Eastern European tundras (Lavrinenko et al., 1916) ass. Scorpidio revolventis–Caricetum rariflorae is also known for the North of the Western Europe (Dierssen, 1982). Its difference from western syntaxa is the absence of many boreal species, which are not able to exist in the severe climate in the North of Western Siberia, as well as the great number of plant communities with the diagnostic species of the alliance Caricion atrofuscae-saxatilis due to rich mineral nutrition, associated with the carbonate soils and calcium-rich groundwaters in the study area. New associations are established in two allian­ces: Carici aquatilis–Warnstorfietum tundrae in Drepanocladion exannulati and Sphagno squarrosi–Caricetum chordorrhizae in Sphagno–Caricion canescentis (Table 3). The floristic features of the latter alliance, whose communities on the northern limit of their distribution have a certain similarity to the arctic sedge-moss mire vegetation of the alliance Caricion stantis, are discussed. Oligotrophic communities of the alliance Scheuch­zerion palustris, occuring in acidic habitats, are placed in the order Scheuchzerietalia palustris that is in agreement with new interpretation of this alliance in the paper by Mucina et al. (2016). Two associations (Carici rotundatae–Sphagnetum baltici, Sphagno compaci–Caricetum rotundatae) are assigned to this alliance. There are few relevés for both Scheuchzerion palustris and Stygio–Caricion limosae alliances in the study area that is why their classification is preliminary, and it will be considered in the near future for the whole North of the Western Siberia on a larger data set. The classification results are confirmed by DCA-ordination of selected syntaxa (Fig.15, Б). However, the differentiation of communities is more clearly demonstrated by the t-SNE method, which allows displaying multidimensional hyperspaces on the plane (Fig.15, А).


2016 ◽  
Vol 37 (6) ◽  
pp. 1966-1996
Author(s):  
KONSTANTIN SLUTSKY

The main result of the paper is classification of free multidimensional Borel flows up to Lebesgue orbit equivalence, by which we mean an orbit equivalence that preserves the Lebesgue measure on each orbit. Two non-smooth $\mathbb{R}^{d}$-flows are shown to be Lebesgue orbit equivalent if and only if they admit the same number of invariant ergodic probability measures.


2020 ◽  
Vol 24 (9) ◽  
pp. 51-57
Author(s):  
E.V. Abakumov ◽  
A.E. Lemyakina ◽  
V.O. Titov ◽  
A.E. Vashchuk ◽  
Yu.N. Guzov ◽  
...  

Тhe problems of valuation of ecosystem services in connection with the activation of economic activity of the Russian Federation in the Arctic zone are discussed. The types of negative impacts on the Arctic ecosystems and their assessment, investment risks existing in ecosystem services are considered. It is shown that the application of the methodology and apparatus of ecosystem services contributes to the adequate assessment and creation of a hierarchical classification of "usefulness" and "benefits" that society can get from the existence, use and nonuse of ecosystems. The concept of ecosystem services in relation to Arctic consists of three components: identification, monetization and ecological risk assessment. The example of the Arctic ecosystems shows that the susceptibility to assessment and the accuracy of the assessment can be quite different and is largely dependent on the type of service in the classification. The analysis of possible ecosystem services and their relationship with the quality of life of people in the Russian Arctic indicates significant investment risks.


2009 ◽  
Vol 30 (2) ◽  
pp. 379-398 ◽  
Author(s):  
KARIANE CALTA ◽  
KEVIN WORTMAN

AbstractWe study the action of the horocycle flow on the moduli space of abelian differentials in genus two. In particular, we exhibit a classification of a specific class of probability measures that are invariant and ergodic under the horocycle flow on the stratum ℋ(1,1).


2021 ◽  
Vol 67 (4) ◽  
pp. 394-405
Author(s):  
V. S. Porubaev ◽  
L. N. Dyment

The need for classifying surface atmospheric pressure fields over the Arctic seas arose as a method was being developed for predicting the characteristics of discontinuities (leads) in the sea ice cover. Wind, which is determined by the atmospheric pressure field, acts on the ice cover and causes it to drift. Leads are formed in the ice cover due to the irregularity of ice drift. Ice drift can be caused by several factors, such as skewed sea level, tidal waves and currents. However, the main cause of ice drift in the Arctic seas is wind. Each typical field of surface atmospheric pressure corresponds to a certain field of leads in the ice cover. This makes it possible to predict the characteristics of leads in the ice cover by selecting fields similar to predictive fields of atmospheric pressure based on archived data.The variety of atmospheric pressure fields makes it difficult to find an analogue to a given field by simply going through all the corresponding data available in the electronic archive. Classification of atmospheric pressure fields makes it possible to simplify the process of selecting an analogue.To develop the classification, we used daily surface pressure maps at 00 hours GMT for the cold seasons (from mid- October to the end of May) 2016–2021. The atmospheric pressure fields, which were similar in configuration, and hence the wind fields, belonged to the same type. In total, 27 types were identified, applicable both to the Laptev Sea and the East Siberian Sea. Within one type, a division into subtypes was made, depending on the speed of the geostrophic wind.The wind intensity was estimated by the number of isobars multiples of 5 mb on the surface atmospheric pressure map. All the surface pressure fields observed over the waters of the Laptev and East Siberian Seas over the past 5 years have been assigned to one of the types identified using cluster analysis. Each type of atmospheric pressure within the framework of the forecasting method being developed is supposed to correspond to a field of discontinuities in the ice cover.


Sign in / Sign up

Export Citation Format

Share Document