Related papers: Lattice equations arising from discrete Painlev\'e…
Proper lattices for the discrete BKP and the discrete DKP equaitons are determined. Linear B\"acklund transformation equations for the discrete BKP and the DKP equations are constructed, which possesses the lattice symmetries and generate…
We study the set of square-free parts of volume polynomials associated with four planar lattice polytopes. This is motivated by the problem of describing possible pairwise intersection numbers of four curves in $(\mathbb{C}^*)^2$ with…
We give a rational form of a generic two-dimensional "quad" map, containing the so-called $Q_4$ case, but whose coefficients are free. Its integrability is proved using the calculation of algebraic entropy.
In this article I study pairing of two interacting particles in ideal 1D, 2D and Bethe lattices. I employ the method of recursion that has been formulated recently by Berciu et. al. to compute the pair functions in real space without…
It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
The paper shows that there is a deep structure on certain sets of bisimilar Probabilistic Automata (PA). The key prerequisite for these structures is a notion of compactness of PA. It is shown that compact bisimilar PA form lattices. These…
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear $2\times 2$ system by taking into consideration the hierarchy through a reduction procedure. The Lax pair of the…
We establish that the quadrirational Yang-Baxter maps, considered on their symmetry-complete lattice, give an un-normalized form of the Painleve systems associated with affine-E8 symmetry. This is a unified representation bringing KdV-type…
We compute the lattice operations for the (pairwise) stable set in many-to-many matching markets when only path-independence on agents' choice functions is imposed. To do this, we first show that the sets of firm-quasi-stable and…
It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral…
We review the separation of variables for the Kowalevski top and for its generalization to the algebra o(4). We notice that the corresponding separation equations allow an interpretation of the Kowalevski top as a B2 integrable lattice.…
My main results are simple formulas for the surface area of d-dimensional lattice polytopes using Ehrhart theory.
We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${\mathbb Z}^{N}$ as…
We study the phase diagram of five-dimensional SU(2) gauge theories on anisotropic lattices with periodic boundary conditions. We locate a line of first order bulk phase transitions and second order phase transitions related to breaking of…
We construct lattice action for three-dimensional ${\cal N}=4$ supersymmetric gauge theory with matter fields in the fundamental representation.
Frustration in classical spin models can lead to degenerate ground states without long range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration…
A consistent formulation of a fully supersymmetric theory on the lattice has been a long standing challenge. In recent years there has been a renewed interest on this problem with different approaches. At the basis of the formulation we…
One of the authors has recently introduced the concept of conjugate Hamiltonian systems: the solution of the equation $h=H(p,q,t),$ where $H$ is a given Hamiltonian containing $t$ explicitly, yields the function $t=T(p,q,h)$, which defines…