Related papers: Ranks for strongly dependent theories
We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…
A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. There has been given the connection between conditions of superstability…
Let X be a smooth projective curve of genus g bigger then 2. For any vector bundle E on X let M_k(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0<k<r, x positive and either x less…
We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of…
We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a…
We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…
Let $E$ be a rank 2, degree $d$ vector bundle over a genus $g$ curve $C$. The loci of stable pairs on $E$ in class $2[C]$ fixed by the scaling action are expressed as products of $\Quot$ schemes. Using virtual localization, the stable pairs…
Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting…
We will define the Alexander duality for strongly stable ideals. More precisely, for a strongly stable ideal $I \subset \Bbbk[x_1, \ldots, x_n]$ with ${\rm deg}(\mathsf{m}) \le d$ for all $\mathsf{m} \in G(I)$, its dual $I^* \subset…
We define two families of expansions of $(\mathbb{Z},+,0)$ by unary predicates, and prove that their theories are superstable of $U$-rank $\omega$. The first family consists of expansions $(\mathbb{Z},+,0,A)$, where $A$ is an infinite…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
Stanford typed dependencies are a widely desired representation of natural language sentences, but parsing is one of the major computational bottlenecks in text analysis systems. In light of the evolving definition of the Stanford…
We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for…
Let $H\leq K$ be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever $a^g \in K$ where $a \in H, g \in G,$ then $a^g \in H.$ In this paper, we investigate the structure of a group G under the…
We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…
The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D.…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…