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Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…
This paper presents a systematic investigation of the integrability conditions for nonautonomous quad-graph maps, using the Lax pair approach, the ultra-local singularity confinement criterion and direct construction of conservation laws.…
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotopy deformation, geometric constructions in computer aided…
The universality of renormalization group limit cycle behavior is illustrated with a simple discrete Hamiltonian model. A non-perturbative renormalization group equation for the model is soluble analytically at criticality and exhibits one…
We give a self-contained introduction to isolated points on curves and their counterpoint, parameterized points, that situates these concepts within the study of the arithmetic of curves. In particular, we show how natural geometric…
We propose a strategy to study the analytic structure of Feynman parameter integrals where singularities of the integrand consist of rational irreducible components. At the core of this strategy is the identification of a selected stratum…
Classical controllability and observability characterise reachability and reconstructibility of the full system state and admit equivalent geometric and eigenvalue-based Popov-Belevitch-Hautus (PBH) tests. Motivated by large-scale and…
When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
We study nonautonomous mappings of the plane by means of spaces of initial conditions. First we introduce the notion of a space of initial conditions for nonautonomous systems and we study the basic properties of general equations that have…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…
This article is an exposition of an elementary constructive proof of canonical resolution of singularities in characteristic zero, presented in detail in Invent. Math. 128 (1997), 207-302. We define a new local invariant and get an…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, a…
The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
We establish the global existence and precise estimates of a class of singularity-free cosmological solutions in nonlinear Einstein-scalar-Gauss-Bonnet (ESGB) gravity with quadratic coupling, in close agreement with previous numerical…