Related papers: On Enforcing Satisfiable, Coherent, and Minimal Se…
This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of dyadic relation, reflexivity, irreflexivity, symmetry, asymmetry, transitivity, intransitivity,…
Presented are algorithms for enforcing function diagram commutativity and anti-commutativity database constraints, using the database software application constraint-driven design and development methodology, in the realm of the…
Existence constraints were defined in the Relational Data Model, but, unfortunately, are not provided by any Relational Database Management System, except for their NOT NULL particular case. Our (Elementary) Mathematical Data Model extended…
This research paper introduces two new constraint types and four subtypes of database constraints added to our (Elementary) Mathematical Data Model, which are the duals of the existence and non-existence ones. They are formally defined,…
This paper presents a pseudocode algorithm for translating (Elementary) Mathematical Data Model ((E)MDM) schemes into Entity-Relationship data models. We prove that this algorithm is linear, sound, complete, and semi-optimal. As an example,…
Homogeneous binary function products are often encountered in the sub-universes modeled by databases, from genealogical trees to sports, from education to healthcare, etc. Their properties must be discovered and enforced by the software…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
Map-to-map matching is a critical task for aligning spatial data across heterogeneous sources, yet it remains challenging due to the lack of ground truth correspondences, sparse node features, and scalability demands. In this paper, we…
MatBase is a prototype intelligent data and knowledge base management system based on the Relational, Entity-Relationship, and (Elementary) Mathematical Data Models. The latter distinguishes itself especially by its rich panoply of…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality…
Mapping complex metadata structures is crucial in a number of domains such as data integration, ontology alignment or model management. To speed up that process automatic matching systems were developed to compute mapping suggestions that…
With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly…
We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any…
Consider a quantum cat map $M$ associated to a matrix $A\in\mathop{\mathrm{Sp}}(2n,\mathbb Z)$, which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of $M$ on any nonempty open set in the position-frequency…
Robotic systems demand accurate and comprehensive 3D environment perception, requiring simultaneous capture of photo-realistic appearance (optical), precise layout shape (geometric), and open-vocabulary scene understanding (semantic).…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…