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Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
Motivated by problems of statistical language modeling, we consider probability measures on infinite sequences over two countable alphabets of a different cardinality, such as letters and words. We introduce an invertible mapping between…
We present a two-stage approach for learning dictionaries for object classification tasks based on the principle of information maximization. The proposed method seeks a dictionary that is compact, discriminative, and generative. In the…
In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern…
In this thesis we give an algebraic characterization of the syntax and semantics of simply-typed languages. More precisely, we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…
The present paper records more details of the relationship between primitive elements and palindromes in F_2, the free group of rank two. We characterise the conjugacy classes of primitive elements which contain palindromes as those which…
The order of orbit generation in one-dimensional Lorenz-like maps is presented within a two letter symbolics scheme. This order is derived from the natural order of a set of fractions associated to the binary sequences. Its relation to the…
Trapezoidal words are finite words having at most n+1 distinct factors of length n, for every n>=0. They encompass finite Sturmian words. We distinguish trapezoidal words into two disjoint subsets: open and closed trapezoidal words. A…
Unlabelled Necklaces are an equivalence class of cyclic words under both the rotation (cyclic shift) and the relabelling operations. The relabelling of a word is a bijective mapping from the alphabet to itself. The main result of the paper…
Word embeddings are widely used in Natural Language Processing, mainly due to their success in capturing semantic information from massive corpora. However, their creation process does not allow the different meanings of a word to be…
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
Unique word OFDM is a novel technique for constructing OFDM symbols, that has many advantages over cyclic prefix OFDM. In this paper we investigate two different approaches for the generation of an OFDM symbol containing a unique word in…
Bimonotone subdivisions in two dimensions are subdivisions all of whose sides are either vertical or have nonnegative slope. They correspond to statistical estimates of probability distributions of strongly positively dependent random…
Certain concepts, words, and images are intuitively more similar than others (dog vs. cat, dog vs. spoon), though quantifying such similarity is notoriously difficult. Indeed, this kind of computation is likely a critical part of learning…
In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of…
We propose a simple new combinatorial model to study spaces of acyclic Jacobi diagrams, in which they are identified with algebras of words modulo operations. This provides a starting point for a word-problem type combinatorial…
This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…
We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…