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For users, recommendations can sometimes seem odd or counterintuitive. Visualizing recommendations can remove some of this mystery, showing how a recommendation is grouped with other choices. A drawing can also lead a user's eye to other…
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
The problem of mathematical modeling in geography is one of the most important strategies in order to establish the evolution and the prevision of geographical phenomena. Models must have a simplified structure, to reflect essential…
We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
We are living in the big data age: An ever increasing amount of data is being produced through data acquisition and computer simulations. While large scale analysis and simulations have received significant attention for cloud and…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
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…
In human spatial awareness, 3-D projective geometry structures information integration and action planning through perspective taking within an internal representation space. The way different perspectives are related and transform a world…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
In two previous papers, we exposed a combinatorial approach to the program of Geometry of Interaction, a program initiated by Jean-Yves Girard. The strength of our approach lies in the fact that we interpret proofs by simpler structures -…
Our world can be succinctly and compactly described as structured scenes of objects and relations. A typical room, for example, contains salient objects such as tables, chairs and books, and these objects typically relate to each other by…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…
Starting from the concept that knowledge comes as element of mediation between the convergent thinking, founded on experience, and the divergent thinking, placed in the perceptive, intuitive, creative dimension, in this paper we want to…
Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…