Related papers: Slow Reflection
In this work we are concerned with the study of the strong order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces with additive noise. In particular the stochastic…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
We construct long sequences of braids that are descending with respect to the standard order of braids (``Dehornoy order''), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements…
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
We consider families of fast-slow skew product maps of the form \begin{align*} x_{n+1} = x_n+\epsilon a(x_n,y_n,\epsilon), \quad y_{n+1} = T_\epsilon y_n, \end{align*} where $T_\epsilon$ is a family of nonuniformly expanding maps, and prove…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are non-null in a…
Motivated by recent claims, we revisit how coherent perfect absorption (CPA) influences cavity and polaritonic linewidths. Using standard input output theory and measurements on single port bare microwave cavities and cavity magnon hybrids,…
While self-reflection can enhance language model reliability, its underlying mechanisms remain opaque, with existing analyses often yielding correlation-based insights that fail to generalize. To address this, we introduce…
In this paper we will study an important but rather technical result which is called The Reduction Property. The result tells us how much arithmetical conservation there is between two arithmetical theories. Both theories essentially speak…
We study the question of when a given countable ordinal $\alpha$ is $\Sigma^1_n$- or $\Pi^1_n$-reflecting in models which are neither $\mathsf{PD}$ models nor the constructible universe, focusing on generic extensions of $L$. We prove,…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
We prove that, for low-order (n < 5) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson's claim on SPR synthesis…
Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…
The weakly compact reflection principle $\text{Refl}_{\text{wc}}(\kappa)$ states that $\kappa$ is a weakly compact cardinal and every weakly compact subset of $\kappa$ has a weakly compact proper initial segment. The weakly compact…
Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with…
In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the…