Related papers: The Structure of Differential Invariants and Diffe…
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate…
A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains…
We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be…
We review a minimum set of notions from our previous paper on structural properties of SAT at arXiv:0802.1790 that will allow us to define and discuss the "complete internal independence" of a decision problem. This property is strictly…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
Cubic invariants for two-dimensional degenerate Hamiltonian systems are considered by using variables of separation of the associated St\"ackel problems with quadratic integrals of motion. For the superintegrable St\"ackel systems the cubic…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…
In this paper, we study the problem of image recognition with non-differentiable constraints. A lot of real-life recognition applications require a rich output structure with deterministic constraints that are discrete or modeled by a…
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
One of the main challenges in software verification is efficient and precise compositional analysis of programs with procedures and loops. Interpolation methods remain one of the most promising techniques for such verification, and are…
Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…
All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…
Recently a notion of self-duality for differential equations of maximal cuts was introduced, which states that there should be a basis in which the matrix for an {\epsilon}-factorised differential equation is persymmetric. It was observed…
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…