explicit model
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2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Stefano D’Alesio

AbstractWe introduce a derived representation scheme associated with a quiver, which may be thought of as a derived version of a Nakajima variety. We exhibit an explicit model for the derived representation scheme as a Koszul complex and by doing so we show that it has vanishing higher homology if and only if the moment map defining the corresponding Nakajima variety is flat. In this case we prove a comparison theorem relating isotypical components of the representation scheme to equivariant K-theoretic classes of tautological bundles on the Nakajima variety. As a corollary of this result we obtain some integral formulas present in the mathematical and physical literature since a few years, such as the formula for Nekrasov partition function for the moduli space of framed instantons on $$S^4$$ S 4 . On the technical side we extend the theory of relative derived representation schemes by introducing derived partial character schemes associated with reductive subgroups of the general linear group and constructing an equivariant version of the derived representation functor for algebras with a rational action of an algebraic torus.


2021 ◽  
Author(s):  
Klementyna A Gawecka ◽  
Fernando Pedraza ◽  
Jordi Bascompte

Habitat destruction is a growing threat to biodiversity and ecosystem services. The ecological consequences of habitat loss and fragmentation involve reductions in species abundance and even the extinction of species and interactions. However, we do not yet understand how habitat loss can alter the coevolutionary trajectories of the remaining species or how coevolution, in turn, affects their response to habitat loss. To investigate this, we develop a spatially explicit model which couples metacommunity and coevolutionary dynamics. We show that, by changing the size, composition and structure of local networks, habitat destruction increases the diversity of coevolutionary outcomes across the landscape. Furthermore, we show that while coevolution dampens the negative effects of habitat destruction in mutualistic networks, its effects on the persistence of antagonistic communities are less predictable.


Author(s):  
Jonah Busch ◽  
Oyut Amarjargal ◽  
Farzad Taheripour ◽  
Kemen G Austin ◽  
Rizki Nauli Siregar ◽  
...  

Abstract Demand-side restrictions on high-deforestation commodities are expanding as a climate policy, but their impact on reducing tropical deforestation and emissions has yet to be quantified. Here we model the effects of demand-side restrictions on high-deforestation palm oil in Europe on deforestation and emissions in Indonesia. We do so by integrating a model of global trade with a spatially explicit model of land-use change in Indonesia. We estimate a European ban on high-deforestation palm oil from 2000–2015 would have led to a 8.9% global price premium on low-deforestation palm oil, resulting in 21,374 ha/yr (1.60%) less deforestation and 21.1 million tCO2/yr (1.91%) less emissions from deforestation in Indonesia relative to what occurred. A hypothetical Indonesia-wide carbon price would have achieved equivalent emission reductions at $0.81/tCO2. Impacts of a ban are small because: 52% of Europe’s imports of high-deforestation palm oil would have shifted to non-participating countries; the price elasticity of supply of high-deforestation oil palm cropland is small (0.13); and conversion to oil palm was responsible for only 32% of deforestation in Indonesia. If demand-side restrictions succeed in substantially reducing deforestation, it is likely to be through non-price pathways.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Liqin Zhang ◽  
Xiaojing Tian

Abstract In order to improve the modelling efficiency in dynamic system prediction, this paper proposes a predictive model based on high-order normal differential equations to model high-order differential data to obtain an explicit model. The high-order constant differential equation model is reduced, and the numerical method is used to solve the predictive value. The results show that the method realises the synchronisation of model establishment and parameter optimisation, and greatly enhances the modelling efficiency.


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