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Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…

A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that the differential equation is replaced by a partial…

In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second…

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint…

In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established…

We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using…

The Schwinger-Dyson equation for a scalar propagator is solved in Minkowski space with the help of an integral spectral representation, both for spacelike and timelike momenta. The equation is re-written into a form suitable for numerical…

The model reduction problem for semistable infinite-dimensional control systems is studied in this paper. In relation to these systems, we study an object we call the semistability Gramian, which serves as a generalization of the ordinary…

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such…

The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…

In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of trial function for the high dimensional partial differential…

Dodgson's method of computing determinants was recently revisited in a paper that appeared in the College Math Journal. The method is attractive, but fails if an interior entry of an intermediate matrix has the value zero. This paper…

We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies…

Dyson's model in infinite dimensions is a system of Brownian particles that interact via a logarithmic potential with an inverse temperature of $ \beta = 2$. The stochastic process can be represented by the solution to an…

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket…

Solvable Hamiltonians for the $\beta$ and $\gamma$ intrinsic shape coordinates are proposed. The eigenfunctions of the $\gamma$ Hamiltonian are spheroidal periodic functions, while the Hamiltonian for the $\beta$ degree of freedom involves…

Associated to analytic Hamiltonian vector fields in $\mathbb{C}^4$ having an equilibrium point satisfying a non semisimple $1:-1$ resonance, we construct two universal constants that are invariant with respect to local analytic symplectic…

A convergent numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized…

An important challenge in statistical analysis lies in controlling the bias of estimators due to the ever-increasing data size and model complexity. Approximate numerical methods and data features like censoring and misclassification often…

We consider the time-varying actuator placement in continuous time, where the goal is to maximize the trace of the controllability Grammian. A natural relaxation of the problem is to allow the binary $\{0,1\}$ variable indicating whether an…