Related papers: Consistency conditions for dimer models
Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.
The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…
In this paper we study the holomorphic bundles over a noncommutative complex torus. We define a noncommutative abelian variety as a kind of deformation of abelian variety and we show that for a restricted deformation parameter, one can…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
The condition of parameter identifiability is essential for the consistency of all estimators and is often challenging to prove. As a consequence, this condition is often assumed for simplicity although this may not be straightforward to…
We present analytic results for a special dimer model on the {\em non-bipartite} and {\em non-planar} checkerboard lattice that does not allow for parallel dimers surrounding diagonal links. We {\em exactly} calculate the number of closed…
We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…
We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an…
Let d be a positive integer. There are several versions of d-gonality for tropical curves, stable d-gonality and divisorial d-gonality, which are both inspired by d-gonality for compact Riemann surfaces. However, that conditions are not…
We present stability conditions for the category of coherent systems on an integral curve. We define a three-parameter family of pre-stability conditions in its derived category using tilting, and we then investigate when these conditions…
We describe a four-level hierarchy mapping both all discrete estimation problems and all estimators on these problems, such that the hierarchy describes each estimator's consistency guarantees on each problem class. We show that no…
A non-autonomous discrete delayed system for a one-species chemostat based on an Ellermeyer model for the continuous case is studied. Conditions for the persistence or the extinction of the solutions are obtained respectively in terms of…
Recently, Dreyer and Duderstadt have proposed a modification of the Becker--Doering cluster equations which now have a nonconvex Lyapunov function. We start with existence and uniqueness results for the modified equations. Next we derive an…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
We construct stability conditions on crepant resolutions of certain quotients of product varieties, giving as a special case the first examples of stability conditions on strict Calabi-Yau varieties of arbitrary dimension. Along the way, we…
Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We show that models with occasionally binding constraints are not generically coherent. Coherency requires restrictions on the parameters…
We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.
In this paper we prove a common generalisation of results by \v{S}penko-Van den Bergh and Iyama-Wemyss that can be used to generate non-commutative crepant resolutions (NCCRs) of some affine toric Gorenstein varieties. We use and generalise…
A new homological symmetry condition is exhibited that extends and unifies several recently defined and widely used concepts. Applications include general constructions of tilting modules and derived equivalences, and characterisations of…