On understanding and interpretation in mathematics: An integrative overview

For decades, understanding has been considered as a basic theme of interest and a research object in Mathematics Education. In this theoretical overview paper we present a integrative framework for organizing the diversity of results that emerge from the different studies on mathematical understanding and its interpretation. The proposal is applied onto a representation of relevant literature that has arise in the area over the last two decades. With this overview we seek to provide an useful reference for: (a) advancing towards a better insight of understanding in mathematics, (b) establishing the specific limitations and open questions that demarcate the boundaries of understanding and interpretation in mathematics, and (c) orienting its future study using a shared base of consolidated knowledge

Improving Prolog programs: Refactoring for Prolog

Refactoring is an established technique from the object-oriented (OO) programming community to restructure code: it aims at improving software readability, maintainability and extensibility. Although refactoring is not tied to the OO-paradigm in particular, its ideas have not been applied to Logic Programming until now. This paper applies the ideas of refactoring to Prolog programs. A catalogue is presented listing refactorings classified according to scope. Some of the refactorings have been adapted from the OO-paradigm, while others have been specifically designed for Prolog. The discrepancy between intended and operational semantics in Prolog is also addressed by some of the refactorings. In addition, ViPReSS, a semi-automatic refactoring browser, is discussed and the experience with applying ViPReSS to a large Prolog legacy system is reported. The main conclusion is that refactoring is both a viable technique in Prolog and a rather desirable one.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Uncertainties in Forecasting: The Role of Strategic Modeling to Control Them

The growing concern about environmental depredations from transport activity at short-range and long-range horizon calls for policies aiming at reorientation of travel demand trends. However every transport policy is subject to risks, environmental or financial ones, and has often long-range effects. This explains the renewed interest in tools which allow detection of these risks and their consequences. There is however a methodological challenge in the elaboration of these simulation tools because we have to take into account many different uncertainties.This paper analyzes the uncertainties associated with transport forecasts using a strategic model recently developed for Lyon's conurbation. Different sources of error and uncertainly are tested and compared by means of the model. It is argued that a strategy of systematic exploration of uncertainly is the preferred way to cope with it and to detect long-term risks associated with transport policy.Travel modelling ; Strategic planning ; Urban area ; Uncertainty ; Forecasting

Adorno on Mimetic Rationality: Three Puzzles

In this paper, I examine Adorno’s controversial claim that human rationality is inherently mimetic. To do so, I break this claim down into three puzzles (the natural historical puzzle, the metaphysical puzzle, and the epistemic puzzle) and consider each in turn. The first puzzle originates in Adorno’s assertion that in the course of human history the mimetic moment of human thought “is melted together with the rational moment”. So whereas, on his narrative, mimesis has become an intrinsic component of human rationality, it appears that we are oblivious to this state of affair and unable to recognize the workings of mimesis in what we otherwise refer to as rationality. The second puzzle concerns the traditional metaphysical question regarding the possibility of knowledge. Adorno holds that the key to this question lies in the “mimetic moment of knowledge”, which he characterizes as the “moment of the elective affinity between the knower and the known.” The third puzzle concerns his views on how the mimetic moment of thought plays out in our epistemic practices. As he puts it, “consciousness knows of its other as much as it resembles that other,” which seems to entail that our very efforts to conceptualize objects somehow rely on imitative processes. I work out what I take to be the basics of Adorno’s understanding of mimesis and use them to make sense of each puzzle. I argue that Adorno’s insistence on the mimetic component of human rationality isn’t meant to promote more mimetic modes of comportment, but a reflexive awareness of the extent to which our rational activities already rely on imitative (or immersive) processes, even those we view as embodying the strongest claims to the contrary

Complex macrocycle exploration: parallel, heuristic, and constraint-based conformer generation using ForceGen.

ForceGen is a template-free, non-stochastic approach for 2D to 3D structure generation and conformational elaboration for small molecules, including both non-macrocycles and macrocycles. For conformational search of non-macrocycles, ForceGen is both faster and more accurate than the best of all tested methods on a very large, independently curated benchmark of 2859 PDB ligands. In this study, the primary results are on macrocycles, including results for 431 unique examples from four separate benchmarks. These include complex peptide and peptide-like cases that can form networks of internal hydrogen bonds. By making use of new physical movements ("flips" of near-linear sub-cycles and explicit formation of hydrogen bonds), ForceGen exhibited statistically significantly better performance for overall RMS deviation from experimental coordinates than all other approaches. The algorithmic approach offers natural parallelization across multiple computing-cores. On a modest multi-core workstation, for all but the most complex macrocycles, median wall-clock times were generally under a minute in fast search mode and under 2 min using thorough search. On the most complex cases (roughly cyclic decapeptides and larger) explicit exploration of likely hydrogen bonding networks yielded marked improvements, but with calculation times increasing to several minutes and in some cases to roughly an hour for fast search. In complex cases, utilization of NMR data to constrain conformational search produces accurate conformational ensembles representative of solution state macrocycle behavior. On macrocycles of typical complexity (up to 21 rotatable macrocyclic and exocyclic bonds), design-focused macrocycle optimization can be practically supported by computational chemistry at interactive time-scales, with conformational ensemble accuracy equaling what is seen with non-macrocyclic ligands. For more complex macrocycles, inclusion of sparse biophysical data is a helpful adjunct to computation

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute