Related papers: Distality Rank

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…

We describe new relations among conformal block divisors in $\operatorname{Pic}(\bar{\operatorname{M}}_{0,n})$. These relations appear from various rank-level dualities of conformal blocks on $\mathbb{P}^1$ with $n$ marked points. We also…

The back-and-forth relations $M\leq_\alpha N$ are central to computable structure theory and countable model theory. It is well-known that the relation $\{(M,N) : M \leq_\alpha N\}$ is (lightface) $\Pi^0_{2\alpha}$. We show that this is…

The Non-Linear Sigma Model (NLSM) is an example of a field theory on a target space exhibiting intricate geometry. One remarkable characteristic of the NLSM is asymptotic freedom, which triggers interest in perturbative calculations. In the…

Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…

Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…

Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…

We consider a monopolistic seller in a market that may be segmented. The surplus of each consumer in a segment depends on the price that the seller optimally charges, which depends on the set of consumers in the segment. We study which…

Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…

Let $k$ be a perfect field of positive characteristic and let $X$ be a smooth irreducible quasi-compact scheme over $k$. The Drinfeld-Kedlaya theorem states that for an irreducible $F$-isocrystal on $X$, the gap between consecutive generic…

Expansions of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N} ; < \rangle$ have been a fertile and active area of research ever since the publication of the seminal papers of B\"uchi and Elgot & Rabin on the…

Using an analogy with the rank theorem in differential geometry, it is shown that for a finite $n$-tuple $X$ in a tracial von Neumann algebra and any finite $m$-tuple $F$ of $*$-polynomials in $n$ noncommuting indeterminates,…

We consider the problem of ranking a set of objects based on their performance when the measurement of said performance is subject to noise. In this scenario, the performance is measured repeatedly, resulting in a range of measurements for…

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…

In the first part of the paper we study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and super-rosy theories. Then we try to develop analogous theory for arbitrary dependent theories.

This paper is a generalization of arXiv:0810.0808. We develop the de Rham homotopy theory of not necessarily nilpotent spaces, using closed dg-categories and equivariant dg-algebras. We see these two algebraic objects correspond in a…

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

In the literature, the notion of discrepancy is used in several contexts, even in the theory of graphs. Here, for a graph $G$, $\{-1, 1\}$ labels are assigned to the edges, and we consider a family $\mathcal{S}_G$ of (spanning) subgraphs of…

A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…

We call a singularity of a presymplectic form $\omega$ removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the…