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We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
We define a `tree of fusion systems' and give a sufficient condition for its completion to be saturated. We apply this result to enlarge an arbitrary fusion system by extending the automorphism groups of certain of its subgroups.
We introduce a formalism to couple integrity constraints over general-purpose knowledge bases with actions that can be executed to restore consistency. This formalism generalizes active integrity constraints over databases. In the more…
A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type…
In this paper, matching of correlated high-dimensional databases is investigated. A stochastic database model is considered where the correlation among the database entries is governed by an arbitrary joint distribution. Concentration of…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
The big graph database model provides strong modeling for complex applications and efficient querying. However, it is still a big challenge to find all exact matches of a query graph in a big graph database, which is known as the subgraph…
In this work we establish and investigate connections between causes for query answers in databases, database repairs wrt. denial constraints, and consistency-based diagnosis. The first two are relatively new research areas in databases,…
Many web databases can be seen as providing partial and overlapping information about entities in the world. To answer queries effectively, we need to integrate the information about the individual entities that are fragmented over multiple…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Recent work on database application development platforms has sought to include a declarative formulation of a conceptual data model in the application code, using annotations or attributes. Some recent work has used metadata to include the…
When data schemata are enriched with expressive constraints that aim at representing the domain of interest, in order to answer queries one needs to consider the logical theory consisting of both the data and the constraints. Query…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…
Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…