A Map-algebra-inspired Approach for Interacting With Wireless Sensor Networks, Cyber-physical Systems or Internet of Things

The typical approach for consuming data from wireless sensor networks (WSN) and Internet of Things (IoT) has been to send data back to central servers for processing and analysis. This thesis develops an alternative strategy for processing and acting on data directly in the environment referred to as Active embedded Map Algebra (AeMA). Active refers to the near real time production of data, and embedded refers to the architecture of distributed embedded sensor nodes. Network macroprogramming, a style of programming adopted for wireless sensor networks and IoT, addresses the challenges of coordinating the behavior of multiple connected devices through a high-level programming model. Several macroprogramming models have been proposed, but none to date has adopted a comprehensive spatial model. This thesis takes the unique approach of adapting the well-known Map Algebra model from Geographic Information Science to extend the functionality of WSN/IoT and the opportunities for user interaction with WSN/IoT. As an inherently spatial model, the Map Algebra-inspired metaphor supports the types of computation desired from a network of geographically dispersed WSN nodes. The AeMA data model aligns with the conceptual model of GIS layers and specific layer operations from Map Algebra. A declarative query and network tasking language, based on Map Algebra operations, provides the basis for operations and interactions. The model adds functionality to calculate and store time series and specific temporal summary-type composite objects as an extension to traditional Map Algebra. The AeMA encodes Map Algebra-inspired operations into an extensible Virtual Machine Runtime system, called MARS (Map Algebra Runtime System) that supports Map Algebra in an efficient and extensible way. Map algebra-like operations are performed in a distributed manner. Data do not leave the network but are analyzed and consumed in place. As a consequence, collected information is available in-situ to drive local actions. The conceptual model and tasking language are designed to direct nodes as active entities, able to perform some actions on their environment. This Map Algebra inspired network macroprogramming model has many potential applications for spatially deployed WSN/IoT networks. In particular the thesis notes its utility for precision agriculture applications

Integral Bases for the Universal Enveloping Algebras of Map Algebras

Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas in the universal enveloping algebras of the map algebras of sl_2 that allow us to write certain elements in Poincare-Birkhoff-Witt order.Comment: 20 page

Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

Map Calculus in GIS: a proposal and demonstration

This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin's (1990) Map Algebra, the term 'Map Calculus' is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church's (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme)

Consumption and circulation of prehistoric products in Europe: characterization of spatial evolutions by using map algebra

Modelling the evolution of the consumption of products in prehistory with map algebra methods brings good results. These methods are used to reconstitute the continuity of space from a distribution of points, without interpolation; to highlight the main metal consumption areas and to combine several parameters in order to understand the organization of space. The quantification of social and economic values of the archaeological discoveries distinguishes several different ways of metal consumption and different organizations of territories. Creating a protocol of analyses using various map algebra methods applied to several parameters can lead to propose models of spatial organization. Two case studies are presented from the results of a thesis dedicated to the metal consumption during the Bronze Age and some results of the research programme ArchaeDyn on the dynamics of consumption and circulation of raw materials and final products in the prehistoric Europe

Preference learning based decision map algebra: specification and implementation

Decision Map Algebra (DMA) is a generic and context independent algebra, especially devoted to spatial multicriteria modelling. The algebra defines a set of operations which formalises spatial multicriteria modelling and analysis. The main concept in DMA is decision map, which is a planar subdivision of the study area represented as a set of non-overlapping polygonal spatial units that are assigned, using a multicriteria classification model, into an ordered set of classes. Different methods can be used in the multicriteria classification step. In this paper, the multicriteria classification step relies on the Dominance-based Rough Set Approach (DRSA), which is a preference learning method that extends the classical rough set theory to multicriteria classification. The paper first introduces a preference learning based approach to decision map construction. Then it proposes a formal specification of DMA. Finally, it briefly presents an object oriented implementation of DMA