Principles of coding, filtering, and information theory.

Includes bibliography.

Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Linguistics and Information Theory: Analytic advantages

The analytic advantages of central concepts from linguistics and information theory, and the analogies demonstrated between them, for understanding patterns of retrieval from full-text indexes to documents are developed. The interaction between the syntagm and the paradigm in computational operations on written language in indexing, searching, and retrieval is used to account for transformations of the signified or meaning between documents and their representation and between queries and documents retrieved. Characteristics of the message, and messages for selection for written language, are brought to explain the relative frequency of occurrence of words and multiple word sequences in documents. The examples given in the companion article are revisited and a fuller example introduced. The signified of the sequence stood for, the term classically used in the definitions of the sign, as something standing for something else, can itself change rapidly according to its syntagm. A greater than ordinary discourse understanding of patterns in retrieval is obtained.

Analogies between linguistics and information theory

An analogy is established between the syntagm and paradigm from Saussurean linguistics and the message and messages for selection from the information theory initiated by Claude Shannon. The analogy is pursued both as an end itself and for its analytic value in understanding patterns of retrieval from full text systems. The multivalency of individual words when isolated from their syntagm is contrasted with the relative stability of meaning of multi-word sequences, when searching ordinary written discourse. The syntagm is understood as the linear sequence of oral and written language. Saussureâ??s understanding of the word, as a unit which compels recognition by the mind, is endorsed, although not regarded as final. The lesser multivalency of multi-word sequences is understood as the greater determination of signification by the extended syntagm. The paradigm is primarily understood as the network of associations a word acquires when considered apart from the syntagm. The restriction of information theory to expression or signals, and its focus on the combinatorial aspects of the message, is sustained. The message in the model of communication in information theory can include sequences of written language. Shannonâ??s understanding of the written word, as a cohesive group of letters, with strong internal statistical influences, is added to the Saussurean conception. Sequences of more than one word are regarded as weakly correlated concatenations of cohesive units.

Science and information theory.

Mode of access: Internet.

Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.

Querying a building information model for construction-specific spatial information

The design and construction community has shown increasing interest in adopting building information models (BIMs). The richness of information provided by BIMs has the potential to streamline the design and construction processes by enabling enhanced communication, coordination, automation and analysis. However, there are many challenges in extracting construction-specific information out of BIMs. In most cases, construction practitioners have to manually identify the required information, which is inefficient and prone to error, particularly for complex, large-scale projects. This paper describes the process and methods we have formalized to partially automate the extraction and querying of construction-specific information from a BIM. We describe methods for analyzing a BIM to query for spatial information that is relevant for construction practitioners, and that is typically represented implicitly in a BIM. Our approach integrates ifcXML data and other spatial data to develop a richer model for construction users. We employ custom 2D topological XQuery predicates to answer a variety of spatial queries. The validation results demonstrate that this approach provides a richer representation of construction-specific information compared to existing BIM tools.

Mutually unbiased bases as submodules and subspaces

Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs.

A survey and analysis of the GNSS spoofing threat and countermeasures

Detection and prevention of global network satellite system (GNSS) “spoofing” attacks, or the broadcast of false global navigation satellite system services, has recently attracted much research interest. This survey aims to fill three gaps in the literature: first, to assess in detail the exact nature of threat scenarios posed by spoofing against the most commonly cited targets; second, to investigate the many practical impediments, often underplayed, to carrying out GNSS spoofing attacks in the field; and third, to survey and assess the effectiveness of a wide range of proposed defences against GNSS spoofing. Our conclusion lists promising areas of future research.

Multi-version documents : A digitisation solution for textual cultural artefacts

Textual cultural heritage artefacts present two serious problems for the encoder: how to record different or revised versions of the same work, and how to encode conflicting perspectives of the text using markup. Both are forms of textual variation, and can be accurately recorded using a multi-version document, based on a minimally redundant directed graph that cleanly separates variation from content.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

Cryptanalysis of the LAKE hash family

We analyse the security of the cryptographic hash function LAKE-256 proposed at FSE 2008 by Aumasson, Meier and Phan. By exploiting non-injectivity of some of the building primitives of LAKE, we show three different collision and near-collision attacks on the compression function. The first attack uses differences in the chaining values and the block counter and finds collisions with complexity 233. The second attack utilizes differences in the chaining values and salt and yields collisions with complexity 242. The final attack uses differences only in the chaining values to yield near-collisions with complexity 299. All our attacks are independent of the number of rounds in the compression function. We illustrate the first two attacks by showing examples of collisions and near-collisions.