相关论文: Model theory and combinatorics of banned sequences

Using Langer's construction of Bridgeland stability conditions on normal surfaces, we prove Reider-type theorems generalizing the work done by Arcara-Bertram in the smooth case. Our results still hold in positive characteristic or when…

In a recent paper, Gonek, Graham, and Lee introduced a notion of the Lindel\"of hypothesis (LH) for general sequences which coincides with the usual Lindel\"of hypothesis for the Riemann zeta function in the case of the sequence of positive…

We introduce weak exceptional sequence of modules which can be viewed as another modification of the standard case, different than the works of Igusa-Todorov \cite{Igusa-Todorov} and Buan-Marsh \cite{Buan-Marsh}. For hereditary algebras it…

The converse of Schur's lemma (or CSL) condition on a module category has been the subject of considerable study in recent years. In this note we extend that work by developing basic properties of module categories in which the CSL…

Recently, Bringmann, Ono, and Rhoades employed harmonic weak Maass forms to prove results on Eulerian series as modular forms. By changing the setting to Appell--Lerch sums, we shorten the proof of one of their main theorems. In addition we…

Szemeredi's regularity lemma is one instance in a family of regularity lemmas, replacing the definition of density of a graph by a more general coefficient. Recently, Fan Chung proved another instance, a regularity lemma for clustering…

We use the language and tools available in model theory to redefine and clarify the rather involved notion of a {\em special subvariety} known from the theory of Shimura varieties (mixed and pure).

We propose a new definition of effective formulas for problems in enumerative combinatorics. We outline the proof of the fact that every linear recurrence sequence of integers has such a formula. It follows from a lower bound that can be…

Precedential constraint is one foundation of case-based reasoning in AI and Law. It generally assumes that the underlying set of precedents must be consistent. To relax this assumption, a generalized notion of the reason model has been…

Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…

A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the…

Following the approach of Rota and Taylor \cite{SIAM}, we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax allows us noteworthy computational simplifications and…

In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…

Choices in the semantics and the signature of a theory are integral in determining how the theory is used and how challenging it is to reason over it. Our interest in this paper lies in the SMT theory of sequences. Various versions of it…

We propose a generalization of Bailey's lemma, useful for proving $q$-series identities. As an application, generalizations of Euler's identity, the Rogers-Ramanujan identities, and the Andrews-Gordon identities are derived. This…

We prove new upper bounds for the sup-norm of Hecke Maa{\ss} newforms on $GL(2)$ over a number field. Our newforms are more general than those considered in a recent paper by Blomer, Harcos, Maga, and Mili\`cevi\`c: we do not require square…

This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result…

We introduce a categorical language in which it is possible to talk about DNA sequencing, alignment methods, CRISPR, homologous recombination, haplotypes, and genetic linkage. This language takes the form of a class of limit-sketches whose…

Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…

In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein…