Related papers: La m\'ethode des fa\c{c}ons
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
We study sets of univariate hyperbolic polynomials that share the same first few coefficients and show that they have a natural combinatorial description akin to that of polytopes. We define a stratification of such sets in terms of root…
This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic…
We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification of a given real variety. We then show that the resulting…
This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on…
A novel method of asymptotic factorization of $n \times n$ matrix functions is proposed. Considered class of matrices is motivated by certain problems originated in the elasticity theory. An example is constructed to illustrate…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
This paper proposes an adaptive randomization procedure for two-stage randomized controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are few explicit examples of stratifications. The main goal of this paper is to construct…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…
The Stratified Foundations are a restriction of naive set theory where the comprehension scheme is restricted to stratifiable propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory.…
The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to…
The question about asymptotical behaviour of solutions for the system $\dot x=A_\nu x+f$ for big values of the parameter $\nu\in\frak A$ is considered. An approach to the reduction of a large class of problems to easily solvable problem…
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…
In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended…