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Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…
Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be…
This paper extends a polynomial-time parsing algorithm that resolves structural ambiguity in input to a speech-based user interface by calculating and comparing the denotations of rival constituents, given some model of the interfaced…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
Edge computing has evolved to be a promising avenue to enhance the system computing capability by offloading processing tasks from the cloud to edge devices. In this paper, we propose a multi-layer edge computing framework called EdgeFlow.…
Navigating and visualizing multilayered knowledge graphs remains a challenging, unresolved problem in information systems design. Building on our earlier study, which engaged end users in both the design and population of a domain-specific…
Community Question Answering (CQA) is a well-defined task that can be used in many scenarios, such as E-Commerce and online user community for special interests. In these communities, users can post articles, give comment, raise a question…
The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
We present a new calculus which is well-adapted to quadratic algebras. This calculus consists in Koszul (co)homology, together with Koszul cup and cap products. Some applications are given. Koszul duality for Koszul (co)homology is proved…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
This paper presents a joint typicality framework for encoding and decoding nested linear codes for multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In…
Runge-Kutta formulas are some of the workhorses of numerical solving of differential equations. However, they are extremely difficult to generate; the algebra involved can be very complicated indeed. It is now standard, following the work…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
Data heterogeneity hampers the effort to integrate and infer knowledge from vast heterogeneous data sources. An application case study is described, in which the objective was to semantically represent and integrate structured data from…
We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meaningful physical…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…