اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Ring of Algebraic Functions on Persistence Bar Codes
148
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the ring of algebraic functions on the space of persistence barcodes, with applications to pattern recognition.
قيم البحث
اقرأ أيضاً
The Wasserstein distances are a family of $L^p$ distances, with $1 leq p leq infty$, for persistence diagrams. We define Wasserstein distances for persistence modules, the algebraic counterpart to persistence diagrams, and prove the following isometr
y theorem. The $p$-Wasserstein distance of a persistence module and its persistence diagram agree. Since our algebraic Wasserstein distances do not require computing a persistence diagram, they apply to persistence modules that are not interval decomposable and also to generalized persistence modules, such as multi-parameter persistence modules. We also prove structure theorems for maps from an interval module and maps to an interval module and show that for monomorphisms and epimorphisms of persistence modules there is an induced algebraic matching.
Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G=G_antG_aff, where G_ant is the maximal anti-affine subgroup of G, and G_aff the maximal normal connected affine subgroup of G.
In this paper we show that this decomposition extends to a decomposition M=G_antM_aff, where M_aff is the affine submonoid M_aff=bar{G_aff}. We then use this decomposition to calculate $mathcal{O}(M)$ in terms of $mathcal{O}(M_aff)$ and G_aff, G_antsubset G. In particular, we determine when M is an anti-affine monoid, that is when $mathcal{O}(M)=K$.
The set HLie(n) of the n-dimensional Hom-Lie algebras over an algebraically closed field of characteristic zero is provided with a structure of algebraic subvariety of the affine plane of dimension n^2(n-1)/2}. For n=3, these two sets coincide, for n
=4 it is an hypersurface in K^{24}. For n>4, we describe the scheme of polynomial equations which define HLie(n). We determine also what are the classes of Hom-Lie algebras which are P-algebras where P is a binary quadratic operads.
The deletion channel is known to be a notoriously diffcult channel to design error-correction codes for. In spite of this difficulty, there are some beautiful code constructions which give some intuition about the channel and about what good deletion
codes look like. In this tutorial we will take a look at some of them. This document is a transcript of my talk at the coding theory reading group on some interesting works on deletion channel. It is not intended to be an exhaustive survey of works on deletion channel, but more as a tutorial to some of the important and cute ideas in this area. For a comprehensive survey, we refer the reader to the cited sources and surveys. We also provide an implementation of VT codes that correct single insertion/deletion errors for general alphabets at https://github.com/shubhamchandak94/VT_codes/.
$mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $mathbb{Q}_0$ cannot be specified by the
usual axioms for meadows augmented by a finite set of axioms of the form $(1+ cdots +1+x^2)cdot (1+ cdots +1 +x^2)^{-1}=1$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
