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The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. The framework we…
We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The…
We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen's theorem for correlated probability,…
In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach's fixed point theorems, a difficulty called Zero Problem is…
The general term of the Poincare normalizing series is explicitly constructed for non-resonant systems of ODE's in a large class of equations. In the resonant case, a non-local transformation is found, which exactly linearizes the ODE's and…
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution…
We analyse the long term behaviour of the measure-valued solutions of a class of linear renewal equations modelling physiologically structured populations. The renewal equations that we consider are characterised by a regularisation…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
In this study, we consider the nonlinear Sch\"odinger equation (NLS) with the zero-boundary condition on a two- or three-dimensional large finite cubic lattice. We prove that its solution converges to that of the NLS on the entire Euclidean…
We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider $\dot{x} = f(x,x)$ for a…
In this article, we develop a comprehensive ODE-theory for structured continuity equations in fibred probability spaces, which represent a class of heterogeneous PDEs arising as the meanfield limit nonexchangeable particle systems. After…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods…
The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems.…
We explore the computational content of Kronecker's lemma via the proof-theoretic perspective of proof mining and utilise the resulting finitary variant of this fundamental result to provide new rates for the Strong Law of Large Numbers for…
We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…
Convergence and stability results for the inverse Born series [Moskow and Schotland, Inverse Problems, 24:065005, 2008] are generalized to mappings between Banach spaces. We show that by restarting the inverse Born series one obtains a…