相关论文: Inclusion-exclusion and Segre classes
We prove a completeness result for Multiplicative Exponential Linear Logic (MELL): we show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relational model is exactly axiomatized…
Let $\mathrm{Hilb}_nS$ be the Hilbert scheme of $n$ points on a smooth projective surface $S$. To a class $\alpha\in K^0(S)$ correspond a tautological vector bundle $\alpha^{[n]}$ on $\mathrm{Hilb}_nS$ and line bundle $L_{(n)}\otimes…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
By excluding some sets, which don't include any eigenvalue of a tensor, from some existing eigenvalue inclusion sets, two new sets are given to locate all eigenvalues of a tensor. And it is shown that these two sets are contained in the…
This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second…
Index theory has had profound impact on many branches of mathematics. In this note we discuss the context for a new kind of index theorem. We begin, however, with some operator theoretic results. In [11] Berger and Shaw established that…
The complete group classification of a generalization of the Black-Scholes-Merton model is carried out by making use of the underlying equivalence and additional equivalence transformations. For each non linear case obtained through this…
We study the linear algebra of finite subsets $S$ of a Segre variety $X$. In particular we classify the pairs $(S,X)$ with $S$ linear dependent and $\#(S)\le 5$. We consider an additional condition for linear dependent sets (no two of their…
We implement a divide-and-concur iterative projection approach to context-free grammar inference. Unlike most state-of-the-art models of natural language processing, our method requires a relatively small number of discrete parameters,…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…
A fairly general continuation theorem of Leray-Schauder type for the class of so-called admissible multimaps is set forth. This result is then used to establish a universal rule for solving operator inclusions of Hammerstein type in…
We develop a new method to study intersection theory of the main component of the Hilbert scheme of points on complex manifolds. The main result is an iterated residue formula for tautological integrals. We formulate a Chern-Segre-type…
Confident prediction is highly relevant in machine learning; for example, in applications such as medical diagnoses, wrong prediction can be fatal. For classification, there already exist procedures that allow to not classify data when the…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group, similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup contains exactly the equivalence classes coming from the intended application to Clifford…
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $\leq_c$. This gives rise to a rich degree-structure. In this…
We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a nonsingular variety M `interpolates' between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and…
We prove a simple formula for MacPherson's Chern class of hypersurfaces in nonsingular varieties. The result highlights the relation between MacPherson's class and other definitions of homology Chern classes of singular varieties, such as…