Related papers: Generic mixing is rank-1
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
This paper investigates the structure of generic motives and their implications for the motivic cohomology of fields. Originating in Voevodsky's theory of motives and related to Beilinson's vision of a motivic $t$-structure, generic motives…
Generalizing the result of Agronsky and Ceder (1991), we prove that every Peano continuum admits a continuous transformation that is exact Devaney chaotic; that is, it has a dense set of periodic points, and every nonempty open set covers…
We present a class of minimal $U(1)_X$ models as a plausible solution to the $R_K$ anomaly that can also help reproduce the neutrino mixing pattern. The symmetries and the corresponding $X$-charges of the fields are determined in a…
We show that both small mixing in the quark sector and large mixing in the lepton sector can be obtained from a simple assumption of universality of Yukawa couplings and the right-handed neutrino Majorana mass matrix in leading order. We…
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The…
We introduce a novel concept of rank for subsets of finite metric spaces E^n_q (the set of all n-dimensional vectors over an alphabet of size q) equipped with the Hamming distance, where the rank R(A) of a subset A is defined as the number…
We introduce an ansatz of the PMNS matrix that consists of specific types of transformations. Bi-maximal mixing is taken for the neutrino masses, while a single-angle rotation in the 1-2 block is taken for the charged lepton masses.…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Motivated from the study of multiple ergodic average, the investigation of multiplicative shift spaces has drawn much of interest among researchers. This paper focuses on the relation of topologically mixing properties between…
Using a recent global analysis result after the precise measurement of $\theta_ {13}$, a possible Herimtian neutrino mixing ansatz is discussed, the mixing matrix is symmetric and also symmetric with respect with the second diagonal line in…
We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic…
In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle. On the contrary, saddle connections are fewer in translation surfaces with poles…
It has previously been hypothesized, and supported with some experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related…
We consider generalized interval exchange transformations (GIETs) of d intervals ($d\geq 2$) which are linearizable, i.e. differentiably conjugated to standard interval exchange maps (IETs) via a diffeomorphism h of [0, 1] and study the…
We use probabilistic, topological and combinatorial methods to establish the following deviation inequality: For any normed space $X=(\mathbb R^n ,\|\cdot\| )$ there exists an invertible linear map $T:\mathbb R^n \to \mathbb R^n$ with \[…
If T is an ergodic automorphism of a Lebesgue probability space (X,A,m), the set of coboundries B = db =T(b)+b with symmetric difference + form a subgroup of the set of cocycles A. Using tools from descriptive set theory, Greg Hjorth showed…
In the 1980s, category theorists introduced the Lawvere-Tierney $(\leq_{\mathrm{LT}})$ order in the Effective Topos, known to effectively embed the Turing degrees. Understanding its structure is a longstanding open problem in the area. In…
Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…
We prove that non-trivial homoclinic classes of $C^r$-generic flows are topologically mixing. This implies that given $\Lambda$ a non-trivial $C^1$-robustly transitive set of a vector field $X$, there is a $C^1$-perturbation $Y$ of $X$ such…