Related papers: Enhanced specialization and microlocalization
This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular…
By preparing a sensor system around isolated exceptional points, one can obtain a great enhancement of the sensitivity benefiting from the non-Hermiticity. However, this comes at the cost of reduction of the flexibility of the system, which…
We study rotation of invariant vectors in tensor products of minuscule representations. We define a combinatorial notion of rotation of minuscule Littelmann paths. Using affine Grassmannians, we show that this rotation action is realized…
In this paper the local regularity of the Hilbert transform is considered, and local smoothness and real analyticity results are obtained.
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
Supervised distributional methods are applied successfully in lexical entailment, but recent work questioned whether these methods actually learn a relation between two words. Specifically, Levy et al. (2015) claimed that linear classifiers…
We investigate the close relation between certain weighted Sobolev spaces (Kondratiev spaces) and refined localization spaces from introduced by Triebel [39,40]. In particular, using a characterization for refined localization spaces from…
For a subanalytic Legendrian $\Lambda \subseteq S^{*}M$, we prove that when $\Lambda$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_\Lambda: \operatorname{Sh}_\Lambda(M) \rightarrow \operatorname{\mu…
We show that isolated surface singularities which are non-normal may have Milnor fibers which are non-diffeomorphic to those of their normalizations. Therefore, non-normal isolated singularities enrich the collection of Stein fillings of…
This work describes several first steps in extending Tate-Iwasawa's analytic method to define an L-function in higher dimensions. For generalizing this method the author advocates the usefulness of the classical Riemann-Hecke approach, his…
Fix a non-stacky component of the moduli of stable Higgs bundles, on which the Hitchin fibration is proper. We show that any smooth Hitchin fiber determines a microsheaf on the global nilpotent cone, that distinct fibers give rise to…
In this paper, we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics. The higher rho invariant is a secondary invariant and is closely related to positive scalar…
This work investigates how semantics influence localisation performance and robustness in a learned self-supervised, contrastive semantic localisation framework. After training a localisation network on both original and perturbed maps, we…
Self-supervised learning (SSL) models have recently demonstrated remarkable performance across various tasks, including image segmentation. This study delves into the emergent characteristics of the Self-Distillation with No Labels (DINO)…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon…
We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.
The Hilbert functions and the regularity of the graded components of local cohomology of a bigraded algebra are considered. Explicit bounds for these invariants are obtained for bigraded hypersurface rings.
Observations of enhanced Doppler frequency shift effect of the highly localized microwave backscattering in the upper hybrid resonance are reported. The experiment is performed at FT-2 tokamak, where a steerable focusing antenna set,…
We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a…