Towards a sketch based model of self-interpreters
Towards a theory of practice in metaheuristics design: A machine learning perspective
A number of methodological papers published during the last years testify that a need for a thorough revision of the research methodology is felt by the operations research community – see, for example, [Barr et al., J. Heuristics1 (1995) 9–32; Eiben and Jelasity, Proceedings of the 2002 Congress on Evolutionary Computation (CEC'2002) 582–587; Hooker, J. Heuristics1 (1995) 33–42; Rardin and Uzsoy, J. Heuristics7 (2001) 261–304]. In particular, the performance evaluation of nondeterministic methods,...
Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets
In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...
Towards an integrated theory of formal and natural languages
Towards applying computational complexity to foundations of physics.
Towards automated proofs of observational properties.
Towards Automatic Modeling of Economic Texts.
Towards parametrizing word equations
Classically, in order to resolve an equation over a free monoid , we reduce it by a suitable family of substitutions to a family of equations , , each involving less variables than , and then combine solutions of into solutions of . The problem is to get in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to . We carry out such a parametrization in the case the prime equations in the graph...
Towards parametrizing word equations
Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family of substitutions to a family of equations uf ≈ vf, , each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the...
Towards Reverse Engineering of PDF Documents
We present a progress report on our ongoing project of reverse engineering scientific PDF documents. The aim is to obtain mathematical markup that can be used as source for regenerating a document that resembles the original as closely as possible. This source can then be a basis for further document processing. Our current tool uses specialised PDF extraction together with image analysis to produce near perfect input for parsing mathematical formula. Applying a linear grammar and specific drivers...
Towards Sub-cellular Modeling with Delaunay Triangulation
In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...
Towards the automated synthesis of a Gröbner bases algorithm.
We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with...
Trace languages defined by regular string languages
Traced premonoidal categories
Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in cartesian categories.
Traced Premonoidal Categories
Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in Cartesian categories.
Traces of term-automatic graphs
In formal language theory, many families of languages are defined using either grammars or finite acceptors. For instance, context-sensitive languages are the languages generated by growing grammars, or equivalently those accepted by Turing machines whose work tape's size is proportional to that of their input. A few years ago, a new characterisation of context-sensitive languages as the sets of traces, or path labels, of rational graphs (infinite graphs defined by sets of finite-state...
Tracing cluster transitions for different cluster types
Track layouts of graphs.
Tractability of multivariate problems for weighted spaces of functions
We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.
Trajectories of rotations